comment video_id video_name playlist_name comment_id annotator_openaichat_v0_setup annotator_openaichat_v8_confusion annotator_openaichat_v74_pedagogy
"Jerison rocks!" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7134.0 0.0 0.0 0.0
"46:27 Top 10 saddest anime betrayals" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1270.0 0.0 0.0 0.0
"moises cañas, mira como en el mit si responden las preguntas. Y teniendo muchas mas razones para ser creidos que en tu universidad." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13959.0 0.0 0.0 0.0
"i'm still a little confused, what is u naught supposed to represent? Are those just the linear combination of the eigenvectors?" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 13518.0 0.0 1.0 0.0
"Thank you Sir, It is a great help to teach these things." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 9235.0 0.0 0.0 0.0
"hes using the same trousers since lecture 1" PnPIqh7Frlw "Lec 24: Simply connected regions; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13146.0 0.0 0.0 0.0
"Pen di siri calculus de andar poori dunya basi hui ae" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8160.0 0.0 0.0 0.0
"So, can someone explain (or point in the right direction) how is the penalty actually helps our inverse problem? I understand what it will bump up very little sigmas of the og matrix, but why is that useful to us?" Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8807.0 0.0 1.0 0.0
"i used the varibles f(x) and g(x) instead of u and v" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13488.0 0.0 0.0 0.0
"How can I find the proof of Eckart-Young theorem mentioned in the video? Where is the link?" Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4808.0 0.0 1.0 0.0
"Many thanks Great!!!" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7594.0 0.0 0.0 0.0
"Actually I noticed the AREA VOLUME CONFUSION at the very first time and also understood the power of 1 :) So I deserve a Thank you from an MIT professor ...Hurrah!" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2232.0 0.0 0.0 0.0
"What a great lecturer! Everything is explaind so detailed, preciselly and clear. Now i understand why education in UK is US$12k and in US is US$60k. It is 5 times better then I achived in a 12 weak course in my Uni
Thank you!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11411.0 0.0 0.0 0.0
"Ok now we understand x axis when plotting against y axis is actually looking at an object from the top..
If we add the z axis we can understand that object little bit more" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 8047.0 0.0 0.0 0.0
"I wish I had the privilege to attend to one of his classes in person. You, professor, are a very enlightened person. All I can say is thank you for your devotion to quality education." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6202.0 0.0 0.0 0.0
"@hypnoticpoisons Use Euler’s formula with x =6t:

e^ix = cos x + i sin x

|e^ix| = |cos x + i sin x|
         = sqrt((cos x + i sin x)(cos x – i sin x))
         = sqrt(cos^2 x + sin^2 x)
         = sqrt(1)
         = 1" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 1879.0 0.0 0.0 0.0
"@bjrcboy whats funny is the boards they have are real slate and cost way more then white boards
and im with you white on back is easier on the eyes to read" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1791.0 1.0 0.0 0.0
"06:58 Anybody knows that why the dimension of symmetric matrix and upper triangular matrix are 6?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 295.0 0.0 1.0 0.0
"13:23 Those who want to audition." wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 415.0 0.0 0.0 0.0
"Really nice explanation" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 8527.0 0.0 0.0 0.0
"50.00 wrong solution?  " sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1334.0 0.0 1.0 0.0
"Watched this lecture over and over, and every word starts making sense. Great for background knowledge of ML. Love this man so much!" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 11288.0 0.0 0.0 0.0
"I've learn from him than my real teacher" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6419.0 0.0 0.0 0.0
"so there is really a mistake at 33:11... it has to be 3*2^(2/3)*V^(2/3)" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14347.0 0.0 1.0 0.0
"Thanks for the great video! One question: what does ""empirical"" mean here in ""empirical variance""? Thanks in advance!" a1ZCeFpeW0o "20. Principal Component Analysis (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 9712.0 0.0 1.0 0.0
"where can I exercise those home tasks he gives?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15221.0 0.0 0.0 0.0
"o, man...so many words, so many lines, useful for self confusion...relax, man, votka martini will do the job..." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 14097.0 0.0 0.0 0.0
"Amazing!! Really helped me in my studies" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2400.0 0.0 0.0 0.0
"An Indian edition of this book is available only in India
http://www.wellesleypublishers.com/buy.html" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 2416.0 0.0 0.0 0.0
"# in honor of Gilbert Strang; one of my favorite teachers of all time
# along side Richard Feynman

# returns the index of the value with largest absolute value
def largestAbs(arr, s):
    i = s
    curMax = abs(arr[s])
    for n in range(s, len(arr)):
        if abs(arr[n]) > curMax:
            curMax = abs(arr[n])
            i = n

    return i, curMax

# Guass - Jordan Elimination for finding the inverse of a matrix
def GJElim(M):
    # check if its square
    n = len(M[0])
    if len(M[:,0]) != n:
        return None

    # part of the Gauss - Jordan elimination algorithm
    I = np.identity(n)
    # we do this in order to bring the right hand side of the linear system along for the ride
    A = np.concatenate((M, I), axis=1)

    # we will loop through all the columns
    for j in range(n):
        '''
        find max value along with its index; if max value is 0 then no pivot available and thus there is
        not an inverse; if there is a pivot available, then go ahead and do a row exchange IF
        the max value is NOT already in the diagnol  aka --> when the row and col value are ==
        '''
        i, maxVal = largestAbs(A[:, j], j)
        if maxVal == 0:
            return None
        elif i != j:
            temp = np.array(A[i])
            A[i] = A[j]
            A[j] = temp

        # now multiply row j  --> M[j] * 1/M[j,j]
        # this makes the diagnol value have a 1, thus allowing us to easily eliminate the other values in col
        A[j] = A[j] * (1 / A[j,j])

        for r in range(n):
            # if r == j then this means we are on the diagnol; we only eliminate cols above and below
            if r != j:
                A[r] += A[j] * -A[r,j]

    return A" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 199.0 0.0 0.0 0.0
"Omg the orthogonality between nullspace and row space adds up so well with the v=[1,2,3] example prof. gave previous lecture. I've seen much less entertaining tv series than 18.06, this course should be on Netflix lol" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 8062.0 0.0 0.0 0.0
"What is the reason for wearing a baseball cap backwards?" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 11534.0 0.0 0.0 0.0
"This guy screwed up at 26:27 by by using d(e^w)/dw = e^w, which is the exact conclusion he needs to prove. He should've calculated derivative of ln(x) using definition of derivative. Then he can find derivative of e^x using inverse function derivative property. Can't believe this is MIT." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10560.0 0.0 1.0 0.0
"48:50 I had to look up why that is a right angle. It wasn't so obvious to me. But great lecture!" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1299.0 0.0 0.0 0.0
"I didn't get the 'mathemagic' transformation of \frac{\epsilon}{n} into \epsilon. I will be glad if someone provides an explanation or a reference to it." 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5266.0 0.0 1.0 0.0
"I paused the video when he wrote pi/2 and solved the integral many times getting pi/8 😢, thinking I was wrong" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5897.0 0.0 1.0 0.0
"Dang, this professor does every portion of the problem so quick that it would take me a little while to do each portion." aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3314.0 0.0 0.0 0.0
"Thank you" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9081.0 0.0 0.0 0.0
"ok ive watched this video till the 16 min, and i jus gotta stop there, why? Cuz uptill now i tried to follow wat hes saying, then he wrote that important formula, I got lost. Deep." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14127.0 0.0 0.0 0.0
"I have an exam in like.. 5 hours and am exhausted, yet, as soon as I heard the joke about Clinton and Monica, I spat out my morning coffee and laughed so hard my entire dorm woke up. Thank you so much for not only teaching me everything I need to know, but also making it fun and making it stick!" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 5518.0 0.0 0.0 0.0
"Wow The beauty of math: vector field" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12029.0 0.0 0.0 0.0
"Awesome explaination of the proofs!" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2756.0 0.0 0.0 1.0
"derivative of sum = sum of derivative" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12735.0 0.0 0.0 0.0
"Does anyone know which lecture he derive the general equation for a determinant? Would be a massive help thanks!" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 3446.0 0.0 1.0 0.0
"""You sure have to see it in R^3, because we're going to do it in R^10, and we may take a combination of 5 vectors in R^10, and what will we have...?


God knows..."" 

LOL!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 140.0 0.0 0.0 0.0
"The probability that 0 will happen is 1. It is absolutely likely to happen that you will get zero when we sum an infinite set of zeros." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 10234.0 0.0 0.0 0.0
"24:38 16*(first row) -9* (second row)= (third row)
Welcome back Doc Strang!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 740.0 0.0 0.0 0.0
"I want to be one of the students of  him" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6135.0 0.0 0.0 0.0
"Wouldn't the derivative of the magnitude of the position vector 14:57 tell you the speed with respect to the origin?

The magnitude of the position vector is the distance between the position and the origin.  The derivative tells you if the magnitude is getting larger or smaller, but that's the same as saying the distance to the origin is getting larger or smaller." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12013.0 0.0 1.0 0.0
"My main man Gilbert ""strong"" Strang is a BOSS!!! Thank you so much for the lecture!!!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7771.0 0.0 0.0 0.0
"What's the fullname of BPP?" Vp_AzDGQyrA "23. Probabilistic Computation, BPP" "MIT 18.404J Theory of Computation, Fall 2020" 11581.0 0.0 1.0 0.0
"This is a gold mind! [sic]" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10589.0 0.0 0.0 0.0
"Why cant all professors teach that good? Why did we need to suffer until this lecture?" bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 11801.0 0.0 0.0 0.0
"Excellent way of transfer of knowledge. Explaining difficult concept in the most easy and understandable way. 👍" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3682.0 0.0 0.0 1.0
cliffhanger! nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12658.0 0.0 0.0 0.0
"I tried to reach same conclusion using the fact that p is perpendicular to (b-p) i.e. p(t) * (b-p) = 0 and then substitute p=Ax but failed to get similar result as @28:31. There is an x(t) hanging around.
-> p(t) *(b-p) = 0
-> (Ax)(t) * (b-Ax)=0
-> x(t) * A(t) * (b-Ax)=0
-> x(t) *  [ A(t) * b - A(t) * A * x ] = 0

--?? can I justify that the second term must equate to zero?

any suggestions how to move forward? 

where "" ""(t) is  "" "" transpose." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6116.0 0.0 1.0 0.0
"23 is key time ." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 706.0 0.0 0.0 0.0
"I can feel professor Jerison progressively becoming more and more annoyed with that kid with all the questions." MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5188.0 0.0 0.0 0.0
"If anyone is struggling with this lecture, Wikipedia does a wonderful job of explaining the second derivative test intuitively: http://en.wikipedia.org/wiki/Second_partial_derivative_test#Geometric_interpretation_in_the_two-variable_case" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6497.0 0.0 0.0 1.0
"Simply genius Who said algebra  is difficult." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8668.0 0.0 0.0 0.0
"wonderful lecture" jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 15393.0 0.0 0.0 0.0
"This video quitely provides the proof of assumption of regression that features have to be uncorrelated/independent.  I have read that only  in theory but now I can see exactly why. Thank you prof strang" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 10958.0 0.0 0.0 1.0
"Never saw someone with so much logicality, understandability and clarity in teaching linear algebra, a true GENIUS of our times!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7818.0 0.0 0.0 0.0
"cool ,review" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12676.0 0.0 0.0 0.0
"Not very different from the profs we have... :)" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 7934.0 0.0 0.0 0.0
"Me too…it in our DNATGC" EBdgFFf54U0 "Lecture 14: Basic Hilbert Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 7646.0 0.0 0.0 0.0
"I have a question about the bias and variance of the estimator theta_hat = X_1 metioned at time : 11m00s.
- Why isn't the bias = (X_1 - theta)^2 ? Because bias = (E[X_1] -theta)^2 = (X_1 - theta)^2.
- Why is the variance  = 0? Because variance = E[(X_1 - E[X_1])^2] = E[(X_1 - X_1)^2] = 0." rLlZpnT02ZU "4. Parametric Inference (cont.) and Maximum Likelihood Estimation" "MIT 18.650 Statistics for Applications, Fall 2016" 5496.0 0.0 1.0 0.0
"Can someone Tell  me why @=T. ????" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3067.0 0.0 1.0 0.0
"Great lectures! It's been blessed to take prof Strang's class online." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 4306.0 0.0 0.0 0.0
"At 22:04, shouldn't it be 'E[XY]=theta0*E[X]+theta1E[X^2] -> E[XY]=(E[Y]-theta1*E[X])*E[X]+theta1E[X^2] -> E[XY]-E[X]E[Y]=theta1(E[X^2]-E[X]^2)'?" tBUHRpFZy0s "24. Classical Inference II" "6.041 Probabilistic Systems Analysis and Applied Probability" 2612.0 0.0 1.0 0.0
"if u think the lectures are very easy, then good! go download the problem sets then you will actually learn something. :)" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13544.0 0.0 0.0 1.0
"MIT is great!!!!!!
" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7530.0 0.0 0.0 0.0
"@sententia8 I thought for like 5 mins. on your sentence, and then eventually figured out that it was so non-mathematical! lolzz" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2006.0 0.0 0.0 0.0
"MIT 이래서... 최고의 인재들이 태어나는 군요." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7551.0 0.0 0.0 0.0
"@kaga13 yes ok, but I'm sorry. Didn't want to offend you, I just wondering.." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1915.0 0.0 0.0 0.0
"When he is looking up at the board above @17:17, and I'm scrolling the mouse to see it...... 2005 problem became 2017 problem.... doh! I troll myself. :(" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11616.0 1.0 0.0 0.0
"MITOPENCOURSEWARE:  US taxes and US citizen donations used to educate US economic competition world-wide.  Question:  WHY ?  Answer:  That is what the dominating public-private partnerships have decreed upon the American people:  (a) Our eaten flesh, and (b) Americans forcibly averaged into globalism.  To MIT:  Why have you gone along with such an agenda assuming you are still ""pro-America"" ?" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7556.0 0.0 0.0 0.0
"The most important concept and ---the camera man decided not to focus correctly!!" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 10195.0 1.0 0.0 0.0
"his passion to teach is one of the most beatiful things i have seen it ! wow .. he looks like feymann i mean his way of teach us" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13168.0 0.0 0.0 0.0
"""ZERRO""...funny accent.
" tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 142.0 0.0 0.0 0.0
"I disagree with the statement at 9:13 and 11:13. Should it not be combinations of columns of B or combinations of rows of A? Cj = A * Bj where Bj is the jth column of B. Similarly for rows, it's Ci.T = Ai.T * B where Ai.T is the ith row of A." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5285.0 0.0 1.0 0.0
"Spectacular teaching !!!! " VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 8865.0 0.0 0.0 0.0
"oh and by the way, that intro starts to piss me off after watching so many lectures !" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 14102.0 0.0 0.0 0.0
"Prof. Gilbert Strang was born on November 27, 1934. He wants to teach when he is 100. All the best!!!" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8297.0 0.0 0.0 0.0
"a lot of mistakes this guy makes." Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12286.0 0.0 0.0 0.0
"Having seen the lectures, I don't have much of a problem in the lectures, but then going onto MIT's site, I see the problemset, and I be like:


""HOW THE F*** DO PEOPLE DO THESE PROBLEMS???""" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4453.0 0.0 0.0 0.0
"Thank you so much OCW & Dr. Rodriguez for putting video lectures to these notes! Since last year's 18.102 notes were published to the website, they have been the most valuable and easily-approachable resource for me when learning functional analysis." uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 9354.0 0.0 0.0 0.0
"I am happy to see this person alive in 2019. May God gave him a long life" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5103.0 0.0 0.0 0.0
"THIS PROFEESOR OF MATHEMATICS IS NICE

I WANT TO GIVE HIM TIPS BEING A STUDENT

PLEASE SIR ALWAYS ATTEMPT THOSE QUESTIONS WHICH YOU SOLVE ON BLACK BOARD

OTHERWISE DON'T ATTEMPT

I LIKED YOUR WAY OF TEACHING BUT YOU WILL GET SOME TIME TO BE PROFESSOR WALTER LEWIN

HE WAS LEGEND

YOU SHOULD SEE HIS LECTURES TO TEACH STUDENTS AS AN EXAMPLE

I LOVE TO BE AN AUSTRONAUT TO WATCH YOUR PROGRAMMES" aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8996.0 1.0 0.0 0.0
"Where I stopped. 0:00 Dec 26" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11654.0 0.0 0.0 0.0
"what is  the professor's name ?" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15146.0 0.0 0.0 0.0
"Wonderful Explanation!" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 11983.0 0.0 0.0 0.0
"Actually as you seen in the lecture curl is defined as the cross product between the del operator and the vector field.The problem here is that the cross product is defined only in 3D(and 7D ),so I am also wondering how curl generalizes to higher dimension other than 7D" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2233.0 0.0 1.0 1.0
"I Really Like The Video Gradient; directional derivative; tangent plane From Your" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 4972.0 0.0 0.0 0.0
"a frenchman, giving an example based upon frog legs? how absurd." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12282.0 0.0 0.0 0.0
"So can a field only be an ordered field if it is {0} or has no upper bound - I don't mean does not have the least upper bound property, just no upper bound?" mlPLLXHZ8_U "Lecture 4: The Characterization of the Real Numbers" "MIT 18.100A Real Analysis, Fall 2020" 8745.0 0.0 1.0 0.0
"best explain i have seen yet !!!!" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 12539.0 0.0 0.0 0.0
"What the hell u have complied this shitty book" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 11561.0 0.0 0.0 0.0
"I always thought that the use of matrices (with the defined mathematical operations - especially the ability to find inverses -) should have facilitated the automation of solving systems of equations. Wouldn't that be a fun computer program to write? But (and correct me if I am wrong), this turns out to be a blunt instrument  involving far more calculations than necessary. So computers follow the ""simplex"" method. This does sort out the ""linear independence""  problem as you go along. And I concede that this method is actually more suitable for automation.   I look forward to seeing how Dr Strang handles this dilemma." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5046.0 0.0 0.0 0.0
"Professor just had a haircut" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8395.0 0.0 0.0 0.0
"'s' should be displacement, but that's a very minute correction" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 212.0 0.0 1.0 0.0
"In all this time. this is by far the best explanation of least squares I've ever seen. Honestly thank you very much for the video." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6624.0 0.0 0.0 0.0
"20:33 standard 4-step procedure of calculating probability." CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 659.0 0.0 0.0 0.0
"Like dislike. You plebs can not put a substance in this comment section" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7352.0 0.0 0.0 0.0
"@MITOCW can you up the course Real Analysis 18.100B?" cqdUuREzGuo "Lecture 8: Lebesgue Measurable Subsets and Measure" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 1670.0 0.0 0.0 0.0
GOAT nbENJ-Ce7Nc "Lecture 3: Cantor's Remarkable Theorem and the Rationals' Lack of the Least Upper Bound Property" "MIT 18.100A Real Analysis, Fall 2020" 3969.0 0.0 0.0 0.0
"Do you know better? :D" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3420.0 0.0 0.0 0.0
"He said ""toin coss"" twice at 25:10. :D" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 4599.0 0.0 0.0 0.0
"The closing statement is to die for 😁 thanks for the amazing lecture." 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10049.0 0.0 0.0 0.0
"It is not that Greek minds are behind. There are everywhere clever and stupid people.
BTW great lectures!" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6963.0 0.0 0.0 0.0
"Awesome lecture. Neat and consistent. The stability part is much better than what i have learned in linear system class." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 2762.0 0.0 0.0 0.0
"If he could interject comic relief every now and then he'd be phenomenal." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6501.0 0.0 0.0 0.0
"항상성과 매개변수가 같다면 오진법과 십진법에서 7로 잡아서 문제를 풀고 대비숫자를 기준으로 문제를 도출해서 문제를 풀면된다. 의사결정 지원 시스템에 문제를 기입하고 풀면 됩니다." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 15693.0 0.0 0.0 0.0
"thxxx a lot a lot " gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 14938.0 0.0 0.0 0.0
"is it my computer or is the sound level a bit low?" Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13638.0 0.0 0.0 0.0
"Fantastic lecture. Many thanks for this." X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 3733.0 0.0 0.0 0.0
"Jor jor se bolke logo ko scheme bata de" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 7141.0 0.0 0.0 0.0
"42:16 For some cuts of s1, it cannot be pumped I think (there is even/odd fashion there, but it's proof by contradiction, so one example should be enough). Let's say p is odd, then we cut <vxy> where x=""1"" and (v, y) has same number of ""0""s in that case it can be pumped, but what if p is even ? then x=""1"" and we are left with (p-1) which clearly cuts in unequal parts for v and y, so the number of zeros in one side (whichever) will be smaller than other side. As I mentioned earlier, since we are proving by contradiction, one example should be sufficient to show the contradiction. Any thoughts, why this wouldn't work ?

Edit: I got it wrong at first glance, the answer to my statement above is: You need to show there is NO way to cut the string such that it can be pumped." IycOPFmEQk8 "5. CF Pumping Lemma, Turing Machines" "MIT 18.404J Theory of Computation, Fall 2020" 1177.0 0.0 1.0 0.0
"I'm actually confused how easily amused the crowd was lol" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6303.0 0.0 0.0 0.0
"What B turns out to be" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 11382.0 0.0 0.0 0.0
"Genius teaching, every math student has to find a professor like him, in every domain of maths" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 3997.0 0.0 0.0 0.0
"i love statistics exam, after calculating, i dk what did i calculate, but i still calculated stuff😂" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 13428.0 0.0 0.0 0.0
"Can someone please explain the significance of the answer to his last question at 47:13 ?" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3088.0 0.0 1.0 0.0
"43:20 ㅋㅋㅋㅋㅋㅋㅋㅋㅋㅋ" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1204.0 0.0 0.0 0.0
"Not a fan of him proving the diffusion equation. I will use Chain Rule." wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 7913.0 0.0 0.0 0.0
"is that the best chalk?" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 13645.0 1.0 0.0 0.0
"Since I always hated it when sth is defined ""just so that it works"" or seemingly arbitrary..

The way I explain 0! = 1:
3! divided by 3 = 2!
2! divided by 2 = 1!
1! divided by 1 = 0! 

Same goes for x to the power of 0

Anyways the prof in this video explains things 100* better than my profs.. They just confuse me all the time and their slides look very complicated. Even these easy counting rules, that have been explained at high school pretty well..Luckily I found these videos on youtube" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 8675.0 0.0 0.0 0.0
"I am pretty sure that if I had been fortunate to attend his class, I would have gotten more interest in math and could be a better scientist." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5132.0 0.0 0.0 0.0
"Notes: 1. For Ax=b, we can draw a picture that projection vector p plus e is equal to b. To solve linear regression problems we can calculate the A'Ax=A'b firstly. Then p=Ax, e=b-p.
2. If A has independent columns then A'A is invertible." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 7941.0 0.0 0.0 1.0
"：）
" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15695.0 0.0 0.0 0.0
"This lecture was beautiful... The way everything connects and binds together is stunning... Invaluable knowledge! Thanks mr. Strang" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10831.0 0.0 0.0 0.0
"Professor Strang lays out the concept of vector spaces in almost tedious detail.  The result:  I finally confidently understand vector spaces at a very basic conceptual level and I'm already beginning to extrapolate for myself.  I imagine that this firm foundation will make the next few lectures that much easier and that much more rewarding.  Thank you Professor Strang and thank you MIT." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 8357.0 0.0 0.0 1.0
Yes!! Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12144.0 0.0 0.0 0.0
Amazing xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2348.0 0.0 0.0 0.0
"He is really good...thx for uploading this" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 4534.0 0.0 0.0 0.0
"Thanks!!!! Very helpful.
" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9839.0 0.0 0.0 0.0
"Im using this lecture series as a supplemental study aid for my multivariable calculus class right now and couldn't  help but talk myself through all the math on my midterm in a heavy french accent. All kidding aside, its incredible how even though this professor is teaching the brightest minds, he explains everything so clearly and logically that anyone could learn a ton from this course. MIT, i think its incredible that you guys post these lectures, your professors have an incredible way of communicating information and I think its extremely noble of you guys to make that accessible to anyone with access to a computer." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6579.0 0.0 0.0 1.0
"Math in the USA is really not difficult compared to what happens to African Nations." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7606.0 0.0 0.0 0.0
"Which book does this class use?" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11708.0 0.0 0.0 0.0
"So underestimated approaches have been revield through column space matters more then rows space.
So genius." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 8798.0 0.0 0.0 0.0
"x = x1, x2, x3, x4 are like potentials V1, V2, V3, V4 at each node

Ax = 0 gives potential differences (voltages) V2-V1 etc. 

I = V/R (Ohm's law) gives currents I1 to I5 (y1 to y5) at each node
(he uses C to denote R^(-1) matrix)

(A^T)y = 0, which is Kirchhoff's current law" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 15451.0 0.0 0.0 0.0
"At 1:11:30 why does he use the biased sample variance and not the unbiased one? Conceptually it doesn't matter?" 4HRhg4eUiMo "8. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 2603.0 0.0 1.0 0.0
"35:20 Being an orthogonal matrix does not mean that it is square." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 1007.0 0.0 1.0 0.0
"Hi, anybody knows if there is a way to get for free the book of the course? please email me primaveramanual@gmail.com" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4721.0 0.0 0.0 0.0
"Limitazos






A'limites




I" cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 7368.0 0.0 0.0 0.0
"9m30s or five! epic " yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 1447.0 0.0 0.0 0.0
"Can I complete and this while thoroughly understanding it within 14 days?(i mean all the 35 lectures in this course)
I have a two-week vacation and nothing to do.." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3004.0 0.0 0.0 0.0
"Feels like we can do math on our own when we intuite it better" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3751.0 0.0 0.0 0.0
"Its amazing how the previous recitation perfectly syncs with the lecture at 16:17" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 7082.0 0.0 0.0 0.0
"glad i found the MIT videos
from india" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12923.0 0.0 0.0 0.0
"seems that i have been in this classroom before, for some information theory course." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 14285.0 0.0 0.0 0.0
"22:52 so yağğğğğhhh y'know" TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 705.0 0.0 0.0 0.0
"Takes me back to my student days to experience that brilliance of the art of Mathematics! The way teaching was meant to be. The difference now being the ""enjoyable aspect"" of Professor Strang's obvious devotion to the subject. Brilliantly presented lectures on often abstruse aspects, with an inbuilt system of ""creativity and innovation"" for students. Surely remarkable." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 9012.0 0.0 0.0 0.0
"should have gone to MIT...(sigh)
" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14296.0 0.0 0.0 0.0
"I like the way of writing ""of"". It seems like sign of the zodiac" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 5687.0 0.0 0.0 0.0
"37:28 lol" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 1066.0 0.0 0.0 0.0
"Does he talk about the dropping the watermelon example in this video?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3453.0 0.0 0.0 0.0
"The person handling the cameras should be tracking the content pointed by the lecturer and not tracking the lecturer." z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10226.0 1.0 0.0 0.0
"Can it be applied in economics" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 3057.0 0.0 0.0 0.0
"This course is a mine of gold" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 10490.0 0.0 0.0 0.0
"co factors is how you normally find the determinant...." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 12660.0 0.0 0.0 0.0
"All of these are taught to students of India at high school level XII standard in Science stream, at much deeper level specially to students preparing for admissions in IITs." HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2305.0 0.0 0.0 0.0
"@gerax89gunner1 My 10th grade math teacher took 2 months to explain what this guy explained in like 40 mins :/" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1850.0 0.0 0.0 0.0
"diffrentiate sec in a sec!!!" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12746.0 0.0 1.0 0.0
"41:53 These are questions that should be asked in recitation, not in lecture." BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1165.0 0.0 0.0 0.0
"what is meant by a combination?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 15157.0 0.0 1.0 0.0
"Since San Francisco is relatively hilly, the elevation of a home may be a good way to distinguish the two cities." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8677.0 0.0 0.0 0.0
"These lectures are so old (but they are truly gold)
I guess some of the students back there have become professors themselves" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 10412.0 0.0 0.0 0.0
"1/x{f(1/μ)}/Y·{0}BINARY CODE OF PROBABILITY: http://www.youtube.com/playlist?list=PLVGVQ_r7lIfkbG2206E5boPDZW8erbdjW
Solve for h. When h'/μ of cartesian (x'y'z') with quantum binary being {0}" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 331.0 0.0 0.0 0.0
"This guy is awesome! When I did linear algebra, my prof taught us the simplest, most straightforward way to do things (bless his heart): this guy is teaching much more complicated ways, but the thinking is crystal clear." U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10525.0 0.0 0.0 1.0
"thanks for this great lecture, MIT and the OCW team!" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14587.0 0.0 0.0 0.0
"I'm confused at around 17:25, detA*I shouldn't be detA^n*I? cause it is the matrix of detA,so each row can be divided over detA, so that is detA^n*I!" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 6312.0 0.0 1.0 0.0
"That lecture has been recorded few years ago, but my teacher still sucks in that moment -_-" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 9903.0 0.0 0.0 0.0
"It's a bit depressing as to how badly the education system has failed you." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7018.0 0.0 0.0 0.0
"I wouldn't have built this mentality that I'll never be able to get even average at maths if we had teachers like this 🙏🙏🙏" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6270.0 0.0 0.0 0.0
"simply amazing!" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 14305.0 0.0 0.0 0.0
"Denis Auroux" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3344.0 0.0 0.0 0.0
"I dont get the bit @ 15:50 about small interval probabilities being a limiting case. Why are there any second order terms?" jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 5364.0 0.0 1.0 0.0
"This man has managed to teach me more in 2 lectures than my linear algebra professor has been able to teach me in 6. Seriously, these are saving my grade" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10852.0 0.0 0.0 0.0
"@HyperBorealOperator (First of all, I don´t speak english as a native language, so, sorry for my mistakes) I think that is kinda stupid to criticize these videos that are free, I mean, if Somebody were paying it would be ok to give ""not flattering"" comments...

There is a expression in my country ""A caballo regalado, no le mires el diente"" (Never look a gift horse in the mouth)

This is free men/woman...don´t worry, I know you are just making a observation and not criticizing" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1634.0 0.0 0.0 0.0
"If i ever do graduate, it’ll be 100% thanks to this guy." TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 6502.0 0.0 0.0 0.0
"Thanks sir" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9770.0 0.0 0.0 0.0
"https://m.youtube.com/watch?v=Y4xxj5tm2tA
Improve Your Life In Many Ways Today 🎉" cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 13262.0 0.0 0.0 0.0
"What a nice explaining! Before watching this lecture, I just memorized expectation and variance of binomial distribution. Now I definitely understood them. Thank you professor!" EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 11427.0 0.0 0.0 0.0
"I have extreme autism which makes me able to hold more information than 99.9% of the population, I did calculus at 7 years old. Normal people like you are mere insects to me, very simple and easy to manipulate. " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5524.0 0.0 0.0 0.0
"I am expecting something more serious other than this kind of ""informal "" proof" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5087.0 0.0 0.0 0.0
"where is lec 17" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15233.0 0.0 0.0 0.0
"So good to be back do decent quality after Lecture 4!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 8763.0 0.0 0.0 0.0
"53:38 H is positive definite when we are testing for a minimum. But for convex, if we only need d2f/dx2>=0, then I only need 2 diagonal entries if H be positive. No requirement for fxx and fyy." nvXRJIBOREc "Lecture 21: Minimizing a Function Step by Step" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1349.0 0.0 1.0 0.0
"how he got 1/delta X  at 20.16 and how he canceled while applying limit" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13229.0 0.0 1.0 0.0
"Excellent lecture, horrible recording. Hardly hear anything with max volume and why the camera has to shoot at the prof speaking rather than staying on the slides? It is very distracting and hard to follow." X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 3656.0 1.0 0.0 0.0
"Thank you very much for the clear  explanation of eigenvalue and singular value computation process. 
btw, I'm happy to be the first person who give a comment on this  brilliant lecture :D" d32WV1rKoVk "12. Computing Eigenvalues and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9440.0 0.0 0.0 0.0
"@31:00""The proper word, of course, is parallelepiped.  But for obvious reasons, uh..., I wrote box.""  rofl!" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 1535.0 0.0 0.0 0.0
"Why is it that for R^n n vectors give a basis if the n by n matrix with those columns is invertible?" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 11879.0 0.0 1.0 0.0
"how do we estimate the percentage of error in the observations while making the projection approximation?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 13222.0 0.0 1.0 0.0
"Well they want to be sure everyone knows the basics of it. Not everyone go to school in USA or Britain . For example, my school in Croatia did not even mention  matrices, mean, median and mode which are the basic things in US school system." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11360.0 0.0 0.0 0.0
"The Mister Rogers of Linear Algebra. (The soothing tone, the rhetorical questioning)" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9972.0 0.0 0.0 0.0
"what is the name of this teacher? He is A MA ZING ! jijijiji" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15167.0 0.0 0.0 0.0
"1:13:51 v1 ZULUL" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 587.0 0.0 0.0 0.0
❤️ yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 15609.0 0.0 0.0 0.0
"Teaching norms with their R2 pictures is just brilliant. So much insight, even emerging while teaching (sparsity of L1 optimum: it's on the axis!!). An absolute joy to watch & learn from" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9023.0 0.0 0.0 1.0
"Thank you MIT. #Grateful." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9162.0 0.0 0.0 0.0
"Saddle point means geodesic ? All about the second derivatives seems to be conversed to this story, covariant derivative, Christoffel symbol, and second fundamental form." 2K7CvGnebO0 "19. Saddle Points Continued, Maxmin Principle" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8590.0 0.0 0.0 0.0
"25:16 is a bit weird to me. If mu2 surpasses lambda1, both mu2 and mu1 would be larger than lambda1 then, the interlacing wouldn't hold anymore. Anyone understands what's going on?" AdTvkFsqcDc "16. Derivatives of Inverse and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 774.0 0.0 1.0 0.0
"in fact when you diferenciate 1/v in relation to v, you are using a quotient rule and cant use that to prove itself" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13586.0 0.0 1.0 0.0
"Really sir want to thank for your great job." 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 8530.0 0.0 0.0 0.0
"10:06 is not a function. Function is a relation in which there is a unique image of every element in the domain." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 341.0 0.0 1.0 0.0
"Finally got here," wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3772.0 0.0 0.0 0.0
"Understanding the meaning of legendary in these series of videos" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11120.0 0.0 0.0 0.0
"is this essentially calc 2 class?" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13661.0 0.0 0.0 0.0
"A legend of linear algebra" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 2132.0 0.0 0.0 0.0
"Matrix still exsist right here right now 2022 🤦‍♂️😂" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 7623.0 0.0 0.0 0.0
"Look at those chumps walking in late..." -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7414.0 0.0 0.0 0.0
"To be honest, it is not a clear lecture. Maybe MIT students are smart enough to learn totally" YAo1sd4kuOQ "2. Forbidding a subgraph I: Mantel's theorem and Turán's theorem" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 11028.0 0.0 0.0 0.0
"So how many families are there with more than just 2 repeated roots?  The example of 4 repeated roots showed 2 different Jordan decompositions, one with a size 3 and size 1 jordan block, and then another with two size 2 jordan blocks.  They are not similar.  What's the partition law for the number of families of similar matrices with d repeated roots?  Is there a connection with group theory?  How about multiple groups of repeated roots?   for 2x2 matrices, there's 2 cases: unique and single family of similar matrices, or single repeated eigenvalue and 2 families, the scaled identity, and the remaining family similar to the jordan form.  How many families for 3x3, 4x4, etc matrices?  curious..." TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 8769.0 0.0 1.0 0.0
"I knew Strang would use square brackets. Parentheses for matrices suck!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5632.0 0.0 0.0 0.0
"Do we also need to take absolute value of x at 48:22?" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3416.0 0.0 1.0 0.0
"Most of the space is wasted and the audio is not great either. It should zoom in his hand when he writes on the board.  The zoom should should be so that  the frame differencing is a maximum.  This way the focus is exclusively on the professor." KlAjiDivJoQ "Lecture 5: Zorn’s Lemma and the Hahn-Banach Theorem" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 7703.0 1.0 0.0 0.0
"I want to write on that chalkboard with that chalk." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6146.0 1.0 0.0 0.0
"Maybe it's just the subject but this guy explains so much better than Professor Jerison" CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7639.0 0.0 0.0 0.0
"Thank you so much." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9406.0 0.0 0.0 0.0
要是没有他和YOUTUBE。我永远都听不到MIT的线性代数课。为什么他们要这么好呢？免费共享出来呢？ 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 15657.0 0.0 0.0 0.0
"Good lectures but this guy is kind of a d*ck." rLlZpnT02ZU "4. Parametric Inference (cont.) and Maximum Likelihood Estimation" "MIT 18.650 Statistics for Applications, Fall 2016" 4142.0 0.0 0.0 0.0
"love the professor for clarity. I had no such a teacher in my college education" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13874.0 0.0 0.0 0.0
"Id like this guy to teach all subjects." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6455.0 0.0 0.0 0.0
"Fantastic Lecturer, very clear.." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 3726.0 0.0 0.0 0.0
"This guy is an amazing professor, I've learned Linear Algebra from him, despite being in college. Love from Brazil <3" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 10523.0 0.0 0.0 0.0
"Felt like climax of the movie" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 3752.0 0.0 0.0 0.0
"“I have a belly button”" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15589.0 0.0 0.0 0.0
"@Stephane4JC What goes to @Arstim goes to @poyanator and everyone who's watching this lecture.There's plenty of tougher courses on the nternet if this doesnt suit." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1730.0 0.0 0.0 0.0
"He has great presentation skills (Y)
" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4491.0 0.0 0.0 0.0
"That is the best writing chalk I have ever seen." eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9900.0 1.0 0.0 0.0
"How did transpose suddenly come into the picture?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 4843.0 0.0 1.0 0.0
"flux it continuity" phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12875.0 0.0 0.0 0.0
"36:09 😍😍 جميل" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1030.0 0.0 0.0 0.0
"@NothingPersonalTA Sorry third row would then be -5/2" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1691.0 0.0 1.0 0.0
怎么从空间变换角度理解满秩只有一解的意义？ 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 15628.0 0.0 1.0 0.0
"how to downlod soluton pdf" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13250.0 0.0 0.0 0.0
"Thanks very much MIT and Prof. Auroux, you are the best math professor I have ever seen...." YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9816.0 0.0 0.0 0.0
"Where is the 1 coming from is it a placeholder" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11689.0 0.0 1.0 0.0
"students get so excited by something minimal." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14405.0 0.0 0.0 0.0
"What graphing program were they using to plot the graphs and contour plots?" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 11495.0 0.0 0.0 0.0
"I got nothing but gratitude for these amazing instructors, they are so talented and enthusiasts!
For a second they made me want to come back to uni haha" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 5449.0 0.0 0.0 0.0
"Why center of mass of Cn+1 block= Cn+1
" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11802.0 0.0 1.0 0.0
"Whoa. I just finished his linear algebra course. Didn't realize it was such a while back. Thank you for all your work sir!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11761.0 0.0 0.0 0.0
"Can someone please explain why is AV1 =sigma1 U1" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3090.0 0.0 1.0 0.0
"18.06 was a very important stepping stone in my career." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 524.0 0.0 0.0 0.0
"physicist potentials are the opposite of mathematicians potentials looool." z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14184.0 0.0 0.0 0.0
"i watch all the lectures at 1.25x but not this guy. he is fast." Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13492.0 0.0 0.0 0.0
"If you can't get into MIT, go to a state university. The education is the same and cheaper and in today's crummy job market, you're lucky if you get a job even with an MIT degree." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6539.0 0.0 0.0 0.0
"sounds french. plus his last name is Auroux" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14387.0 0.0 0.0 0.0
"I think he got lost in this lesson, he should have use the propiertes of ln and make the equation lny=lna^x and then use the chain rule and implicit diferentiation and he would have finish right away" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6012.0 0.0 1.0 0.0
"The first video was recorded in Fall 2017. The rest of the lectures were recorded in Fall 2016, but video of Lecture 1 was not available. Only me notice this?" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 10113.0 0.0 0.0 0.0
"Somebody is coughing heavily . Please make a covid-19 test immediately 😂😂😂" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 8830.0 0.0 0.0 0.0
"The efforts Prof. Strang puts in at this age is in itself an inspiration for all of us.
Thank You!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10083.0 0.0 0.0 0.0
"I am really thankful to have this video, however, I do have one small criticism of the cinematography.  The camera zooms in and holds on old information for too long. I'm halfway through the video and this has happened several times. It's a small complaint, and really we are all lucky to be able to watch this for free, but this video is not as convenient to watch as other OCW vids due to this zoom and hold method of shooting the camera person utilized. " BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5136.0 1.0 0.0 0.0
"How advanced is this math? I know it's not real hard, but relative to other math classes at MIT, how hard is this one?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4800.0 0.0 0.0 0.0
"You're a great lecturer sir thanks for everything 🙏" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 12248.0 0.0 0.0 0.0
"Prof. Strang can get it. no homo" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8301.0 0.0 0.0 0.0
"Seriously, this guy is why reading the edited, vetted course book is superior to the lecture.  If you were truly a neophyte you'd be lost by so many of the skipped steps and failed contextual references. This lecture is targeted at grad students who want too feel nostalgic." uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 8632.0 0.0 0.0 1.0
"Who is responsible for the audio volume fluctuations?
GAH!
This video is almost unwatchable." tBUHRpFZy0s "24. Classical Inference II" "6.041 Probabilistic Systems Analysis and Applied Probability" 11740.0 0.0 0.0 0.0
"The curious room observationally curl because tabletop jointly visit despite a utter coast. longing, ill-informed oak" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 10067.0 0.0 0.0 0.0
"""make this lecture immortal""" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 165.0 0.0 0.0 0.0
"How did he replace x in x.P(x) by ""a"" for all x >= a?
Can somebody please explain?" 3eiio3Tw7UQ "19. Weak Law of Large Numbers" "6.041 Probabilistic Systems Analysis and Applied Probability" 4837.0 0.0 1.0 0.0
"I Really Like The Video From Your Second derivative test boundaries and infinity." 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4968.0 0.0 0.0 0.0
"I really don't know why would I pay thousands of dollars just to get a course that is not close to 1/100 of this just because it is "" for credit."" I have been watching his videos and using a textbook with a manual solution as a mean of self-learning. I learn more than what I got in class. Then I can spend my thousands of dollars to have a vacation or at least survive my life for years." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5909.0 0.0 0.0 0.0
"30:00, the way to remember it is that the work is a straightforward dot product of F with <dx, dy>, M goes with x and N goes with y and we add, and the flux is a dot product of F with the same vector rotated pi/2 so N goes with x and a minus sign with few choices left for M. Auroux missed a nice opportunity at the beginning to clarify the sign convention for flux by foreshadowing the result for closed curves with + being from the inside, out. I'm not faulting anyone, I couldn't give a lecture on this and keep possession of both my hands when erasing blackboards operated by hazardous machines. If he loses his hands, he'll never erase anything again. Be careful out there, Denis, we don't want to lose a great teacher." _CdoRiNSrqI "Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 882.0 0.0 0.0 1.0
"22:36 : positive semidefinite, not positive definite" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 701.0 0.0 1.0 0.0
"I like how he explained how a matrix multiplied by a matrix works. I never thought of it as: each row of the matrices say how many rows of the other matrix you want to make the final matrix." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5664.0 0.0 0.0 0.0
"13 :54 
angle along vertical axis should be  sin theta than why did he use cos theta? 
can someone explain ?" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 401.0 0.0 1.0 0.0
"Fundamental theorem of calculus virgin 2" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3954.0 0.0 0.0 0.0
"Great lecture ! " 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 4246.0 0.0 0.0 0.0
"Somethings are so beautiful when comprehended a certain way. 
Prof. Strang's lecture are as much about the art of transfering such beautiful comprehension one might have experienced as it is about Linear Algebra.
Many in youtube have the skill of making a difficult things easy to grasp. But what you also get from Prof. Strang is that sense of euphoria that comprehension of something beautiful invokes." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 8844.0 0.0 0.0 0.0
"Good teaching" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4156.0 0.0 0.0 0.0
"I wonder if he can tip without a calculator?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 6244.0 0.0 0.0 0.0
"this equation is failure KALKI!!!" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 14804.0 0.0 0.0 0.0
"where can i find the homework for this class?" TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15229.0 0.0 0.0 0.0
"good teacher except for his accent..." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12953.0 0.0 0.0 0.0
"Professor Strang you are amazing!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8374.0 0.0 0.0 0.0
"Presente! 🤚🤚🤚🤚" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 8244.0 0.0 0.0 0.0
"@michalchik it's the math dragon theorem" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1948.0 0.0 0.0 0.0
"what accent..?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15117.0 0.0 0.0 0.0
"22:38 That's the camera man" mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 702.0 1.0 0.0 0.0
"13:50 - it is a kind of reverse-engineering proof..." xaSL8yFgqig "Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 420.0 0.0 0.0 1.0
"What the hell , never seen easiest way to do this . thank you" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11558.0 0.0 0.0 0.0
"""Radiuses"" lol" XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 104.0 0.0 0.0 0.0
"Could someone please illustrate how the 7 has the most high probability for the problem at 31:00
Chose a number between 2 and 12
Win 100$ if you chose the sum of the 2 dice.

I didn't quite understand how its 7" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3239.0 0.0 1.0 0.0
"this guy is a legend" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14811.0 0.0 0.0 0.0
"Text book...........Please...!!!!!" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 9036.0 0.0 0.0 0.0
"Here I thought I was just really bad at math wtf this is not that bad and actually fun!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4673.0 0.0 0.0 0.0
"The guy is very slow and says a lot of ""umm""'s." CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10133.0 0.0 0.0 0.0
"time to start series 18.02 :)
" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14940.0 0.0 0.0 0.0
"28:20 polar coordinates" XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 835.0 0.0 1.0 0.0
thanku UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14616.0 0.0 0.0 0.0
"He is pretty good actually" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 4530.0 0.0 0.0 0.0
"@TryppingWins Yeah you're right, basically first year at Uni is a lot easier than A levels. Second year is a rude awakening, you work your ass off. Of course all the genius' posting here were discovering dark energy in their freshman year (or you would think that was the case the way they act so patronising and smug about this lecture.) It hasn't dawned on them that MIT have some experience in educating some of the brightest minds and recapping first principles might just have a valid purpose" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1745.0 0.0 0.0 0.0
"When I tell people I attended MIT :-)" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 11606.0 0.0 0.0 0.0
"you took a differential equations class in high school?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 15515.0 0.0 0.0 0.0
"Such great news! A course from professor Strang himself!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8951.0 0.0 0.0 0.0
"For the Expected number of fish ( ~ 19:00 ), shouldn't he include the possibility of catching N fish during the first two hours? Is the probability of 3 or more fish in 0 < t < 2 insignificant?" XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 3879.0 0.0 1.0 0.0
"Thank you very much, Professor, for such a beautiful explanation of the subject" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 9453.0 0.0 0.0 0.0
"@23:28 nice trick for figuring out how to get particular entries in matrix multiplication! (I wish I had realized this sooner.) At my school, vectors geometry and linear algebra are taught as separate courses. This professor is amazingly patient and illustrative. I wish I could have gone to his classes." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1515.0 0.0 0.0 1.0
"Thank, Pr... Very helpful!" Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9572.0 0.0 0.0 0.0
Whoa 4HRhg4eUiMo "8. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 11758.0 0.0 0.0 0.0
"""tHerIs nO pRerrEquIsItiS fIr dIz cUrsE""
- MIT" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 176.0 0.0 0.0 0.0
"Can sb explain what he is talking about at the end? (It is sth about permutations but I cannot understand coz of the sound)" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 3061.0 0.0 1.0 0.0
"A true legend in computational science and engineerng education." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2165.0 0.0 0.0 0.0
"When he says ""What is this good for?"" I want to say ""Absolutely NOTHING!""" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11623.0 0.0 0.0 0.0
"HELP! I think Strang might have got WRONG around 05:40. I think P U L is a SUBSPACE of P as P & L itself is a subspace of P.

Think like this: let p & l be a vector from P & L respectively. than u=p+l belongs to
P U L and u lies within P as p is within P and l is also within P.

Also c*p & c*l belongs to P & L respectively where c is scalar as P&L are subspace. so c*u=(c*p + c*l) belongs to P U L. 

Finally, zero vector lies in both P & L. so Zero vectors belongs to P U L.
So P U L is subspace.
" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 4402.0 0.0 1.0 0.0
"20:30 Where is the dx comes from? from d(u*v)/dx=u*dv/dx+v*du/dx get d(u*v)=u*dv+v*du, the integrate both side, ∫1d(u*v)=∫u*dv+∫v*du, finally we get u*v=∫u*dv+∫v*du" aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 657.0 0.0 1.0 1.0
"I miss Prof. David Jerison." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5871.0 0.0 0.0 0.0
"@MrDeathMental LOL" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1681.0 0.0 0.0 0.0
"so excited to see how easily it's proved. Great." wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 14329.0 0.0 0.0 0.0
"This was such a beautiful lecture!" z3SmljnD_nQ "15. Matrices A(t) Depending on t, Derivative = dA/dt" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10975.0 0.0 0.0 0.0
"Thank you prof Gil Strang." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9299.0 0.0 0.0 0.0
"Dont understand physic, he messed up everything; took 10 mins to explain simple problem; Listen Prof. Ramamurti Shankar from Yale university.
Subjectb choosen excellent but lecturer has troubles to talk fluently and clearly; he stops every other secs. I think Yale is much much better." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3487.0 0.0 0.0 0.0
"i thought the ""cular"" was a projection, NO! He wrote it on the wall lol" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 13485.0 1.0 0.0 0.0
43:24 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1205.0 0.0 0.0 0.0
"Hi, anybody knows if there is a way to get for free the book of the course? please email me primaveramanual@gmail.com" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4722.0 0.0 0.0 0.0
"25:45 - 26:33

Are a1 and a1 perpendicular to e OR
a1 and a2 perpendicular to the plane?" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 785.0 0.0 1.0 0.0
"Funny how previously the students have shuddered at the mere mention of Taylor series, or putting a 2x2 linear system in matrix form, but when partial differential equations are mentioned they don't bat an eyelid. Based on their previous responses, I would've expected to hear violent screams followed swiftly by a mass exodus from the classroom :)" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3959.0 0.0 0.0 0.0
"Isn't this just talking about bias variance tradeoff where we are minimizing frobenius norm + bias is zero since estimator is unbiased? Also the reason why variance is number is that we are minimizing variance of frobenius norm. 
What I understood is this" z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6899.0 0.0 1.0 0.0
"Duster ❤️" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3531.0 0.0 0.0 0.0
"thank you very much sir. you made my day . I've been struggling a lot to understand inverse and adjoint relationship and you nailed it ." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 14526.0 0.0 0.0 0.0
https://youtu.be/NynHmcuc8Yw QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13297.0 0.0 0.0 0.0
"uh, I misunderstood. After seeing the justification from Taylor expansion or quadratic approximation, I understand better why Prof. Auroux spent so much time on exploring the quadratic function earlier. This is a relatively harder topic, as reflected by those ""dislikes"". Thanks for the lecture. " 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14977.0 0.0 0.0 1.0
"Fantastic video. Love this guy." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3736.0 0.0 0.0 0.0
"Thanks Prof. Excellent" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9631.0 0.0 0.0 0.0
"Thank you Denis, you're a brilliant lecturer." z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9097.0 0.0 0.0 0.0
"this is lecture 1 in 2009 " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14865.0 0.0 0.0 0.0
"24:35....very odd." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 738.0 0.0 0.0 0.0
"Why did he chose specifically a square bottomed box??" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11807.0 1.0 0.0 0.0
"This guy is a genius ...... No doubt about that ..................... :)" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10515.0 0.0 0.0 0.0
"Where can i download the homework excersices?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11665.0 0.0 0.0 0.0
"is this how the conditional pmf at 16:39 is computed?

X<=2 && Y>=3

P{Y=3}=(2/20)+(4/20)=6/20   
P{Y=4}=(1/20)+(2/20)=3/20   
P{Y>=3}=P{Y=3}+P{Y=4}=6/20+3/20=9/20

P{X=1}=(1/20)+(2/20)=3/20
P{X=2}=(2/20)+(4/20)=6/20
P{X<=2}=P{X=1}+P{X=2}=3/20+6/20=9/20

P{X=1|Y>=3}
=P{X=1,Y>=3}/P{Y>=3}=P{X=1,Y=3}/P{Y>=3} + P{X=1,Y=4}/P{Y>=3}
=[(2/20)+(1/20)]/[(6/20)+(3/20)]
=(2/20)/(9/20) + (1/20)/(9/20)
=2/9 + 1/9 
=3/9

P{X=2|Y>=3}
=P{X=2,Y>=3}/P{Y>=3}=(P{X=2,Y=3}+P{X=2,Y=4})/P{Y>=3}
=[(4/20)+(2/20)]/[(6/20)+(3/20)]
=4/9 + 2/9 
=6/9

P{Y=3|X<=2}
=P{Y=3,X<=2}/P{X<=2}=(P{Y=3,X=1}+P{Y=3,X=2})/P{X<=2}
=[(2/20)+(4/20)]/[9/20]
= 2/9 +4/9 
=6/9

P{Y=4|X<=2}
=P{Y=4,X<=2}/P{X<=2}=(P{Y=4,X=1}+P{Y=4,X=2})/P{X<=2}
=[(1/20)+(2/20)]/[9/20]
=1/9 + 2/9 
=3/9" EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 13664.0 0.0 1.0 0.0
"I should be studying taxation, what I am doing here🙄🤔" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 5964.0 0.0 0.0 0.0
第一次知道三位直线参数方程是怎么来的 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15646.0 0.0 0.0 0.0
"Hope to meet him in MIT. I need to work Hard" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4787.0 0.0 0.0 0.0
"You cannot assume that 

""1 = .9999999999999999999999999""

because that is clearly false.

1 = .9999999999999.... infinitely repeating. 

""then why does: 1/3 = .333333333333333333333""

It doesn't. See above.

""3*(1/3) = .9999999999999999999999999999""

Wrong." zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12197.0 0.0 1.0 0.0
"https://crowdfund.mit.edu/project/2286

If you're watching this video then you know how beneficial MIT OCW is! Donate now! It literally took a minute and was so easy and I'm not someone who can be bothered donating to things normally..

But if like me you've ever had trouble learning something at school/uni or needed extra material or just been keen to learn then you may have benefited from all the great lectures + content MIT OCW provides! So give back a little even if it's just a few dollars and share and convince others to give too. :)

If we want humanity to progress then education is key and it's great to see one of the best universities in the world putting up it's resources to benefit everyone! 

Let's keep on learning and growing and making this world a better place as a result :)" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13257.0 0.0 0.0 0.0
"Can someone explain ""Take one of this one and none of that one"" at 40:56?  It looks like he's talking about a ""selector"" type version of using 0 and 1's .
Thanks." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3068.0 0.0 1.0 0.0
"Please fix the audio..." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 8203.0 0.0 0.0 0.0
"8:49 How we assign any number to the free columns (Variables that multiply those columns)??" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 1426.0 0.0 1.0 0.0
"he deserves better than this audience lol" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 13073.0 0.0 0.0 0.0
"I promise not to write another thing, but I can erase you know... lmao" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 5901.0 0.0 0.0 0.0
"I know it's great the job but to ""help"" with the open lessons it supposed one should give some economic support but what is the cost to start recording a video and then upload it? u just push record and that's all. Any way it's a great job but if u wanna really get value u have to ""impose"" your value so other case few people will consider that it has any value with its totally wrong" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5635.0 0.0 0.0 0.0
"i should jus tranfer to MIT...like right now..." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 13457.0 0.0 0.0 0.0
"Sir which book you have preferred for this" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8704.0 0.0 1.0 0.0
"So great to see prof Strang here on Youtube in 2020!! What fond memories.  I took Applied Math from prof. Strang back in 1995 or 1996 at M.I.T.  The math department (course 18) was filled with brilliant people who had no ability to communicate or teach, except prof. Strang and maybe one or two others.  Not only was he a brilliant teacher, but it was so liberating to realize that really hard math became easy when taught well, and that  perhaps I was not an idiot when I was having a hard time understanding when taught poorly." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8764.0 0.0 0.0 1.0
"I indexed this video on MyVindex for quick video referencing between the geometric, analytical interpretations and examples.  - http://www.myvindex.co/app.html#/home/iSKiXlzQ  .  Email me if you're interested in MyVindex at jmoseman01@gmail.com" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5595.0 0.0 0.0 0.0
"This comment section sure has a lot of egos. Math brainiacs feeling the need to show off their mad skillz: humility might do you some good. It's fantastic that this stuff is incredibly easy for you - it isn't for everyone, and proclaiming your genius to the world serves no one, it only comes off as arrogant.

If this is below your level - great, go to some higher level videos. In the meantime, show some respect for MIT and appreciation for their work in making good education open to everyone, and some consideration for your fellow students who may have more trouble with this stuff." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10485.0 0.0 0.0 0.0
"What's up with the dirty blackboard?" yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 11589.0 1.0 0.0 0.0
"I wish u were my professo Mr Strang, 
but hey, I have u as my Professor here online:
thank you very much for ur elegant  explanation.
Wish u good healt and long live Mr Strang" ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6234.0 0.0 0.0 0.0
"2019.12.19 thank you Gilbert Strang！" rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 624.0 0.0 0.0 0.0
"Fantastic lecture... i am so lucky to watch and learn.... i am an ordinary mother of two little girls and recently finding myself experiencing full of joy learning linear algebra. It is all happened to me beacuse of wonderful lecturer and mit. thank you for sharing with us. I am going to continue to learn. Many thanks from korea." ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3734.0 0.0 0.0 0.0
"Prof Strang the G.O.A.T!!!" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 8275.0 0.0 0.0 0.0
"25:49 no sure why a Cauchy sequence is also convergent." 0_w-R_g5lRA "Lecture 10: The Completeness of the Real Numbers and Basic Properties of Infinite Series" "MIT 18.100A Real Analysis, Fall 2020" 789.0 0.0 1.0 0.0
"""Some of them know more than me,"" wow...if only all professors were like this, once failed a unit cause I used knowledge the lec didn't teach💔" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 109.0 0.0 0.0 0.0
"David is amazing - well done MIT" BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3319.0 0.0 0.0 0.0
Good! VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 4162.0 0.0 0.0 0.0
"thank you so much because I was lost and my midterm is tomorrow. I very much needed this" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 14513.0 0.0 0.0 0.0
"If the latter, that's the bossest prof I've ever seen." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 6521.0 0.0 0.0 0.0
"One easy way to understand matrix multiplication using Machine Learning Classification strategy: 1. Rows of C are combinations of rows of B: just treat it as classification with one example but mutiple classifiers; 2. Columns of C are combinations of columns of A: just treat it as classification with multiple examples but only one classifier; 3. sumOf(Columns of A * Rows of B): jut treat it as classification with multiple examples and mutiple classifiers but should be added up with all features in data examples." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8078.0 0.0 0.0 1.0
"I love the 21st Century" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5773.0 0.0 0.0 0.0
"soooo helpful! Great lectures!" rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 14368.0 0.0 0.0 0.0
"# in Honor of Gilbert Strang and Richard Feynman
import numpy as np

# returns the index of the value with largest absolute value past starting
# from point s in the arr, which is the where we start in the column in 
# below algos case
def largestAbs(arr, s):
    i = s
    curMax = abs(arr[s])
    for n in range(s, len(arr)):
        if abs(arr[n]) > curMax:
            curMax = abs(arr[n])
            i = n

    return i, curMax

# Guass - Jordan Elimination for finding the inverse of a matrix
# note that this assumes that M is a Numpy array
def GJElim(M):
    # check if its square
    n = len(M[0])
    if len(M[:,0]) != n:
        return None

    # part of the Gauss - Jordan elimination algorithm
    I = np.identity(n)
    # we do this in order to bring the right hand side of the linear system along 
    # for the ride
    A = np.concatenate((M, I), axis=1)

    # we will loop through all the columns
    for j in range(n):
        '''
        find max value along with its index; if max value is 0 then no pivot available and 
        thus there is not an inverse; so we return None
         if there is a pivot available, then go ahead and do a row exchange 
         IF the max value is NOT already in the diagnol  aka --> when the row and col 
         value are ==
         '''
        i, maxVal = largestAbs(A[:, j], j)
        if maxVal == 0:
            return None
        elif i != j:
            temp = np.array(A[i])
            A[i] = A[j]
            A[j] = temp

        # now multiply row j  --> M[j] * 1/M[j,j]
        # this makes the diagnol value have a 1, thus allowing us to easily eliminate the 
        # other values in col
        A[j] = A[j] * (1 / A[j,j])

        for r in range(n):
            # if r == j then this means we are on the diagnol; we only eliminate cols above 
            #  and below
            if r != j:
                A[r] += A[j] * -A[r,j]

    return A




S = np.array([[1, 3],
              [2, 7]])
F = GJElim(S)
print(F)" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 198.0 0.0 0.0 0.0
"why we need approximation here, i see we can calculate exactly sin x and cosine x." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15377.0 0.0 1.0 0.0
"For a person who is not really good at math, I hope this will really help me to develop a big picture of what linear algebra is. Thanks Prof. Strang." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3845.0 0.0 0.0 0.0
"24:38 My fellow Imgurians, this is what you're looking for." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 741.0 0.0 0.0 0.0
"Whatever he said here just blows your mind." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11594.0 0.0 0.0 0.0
"I had to look up the word recalcitrant
" aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5473.0 0.0 0.0 0.0
"Congratulations for finding this recording! Thank you a lot!!!" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 3199.0 0.0 0.0 0.0
"Thank you! That's an amazing video." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9481.0 0.0 0.0 0.0
"amazing explanations" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 12345.0 0.0 0.0 0.0
"YouTube have to add some option so that we can like this video 100000000000000 times." twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12258.0 0.0 0.0 0.0
"Thank you for your leasons!" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 9293.0 0.0 0.0 0.0
"I sure will pay it back hundredfold. Thanks!!!" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5984.0 0.0 0.0 0.0
43:00 WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1192.0 0.0 0.0 0.0
"Thank you so much. I have finally understood this subject." 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 9409.0 0.0 0.0 0.0
"Anyone know where I can find some practice assignments? Or is there only the textbook? Thanks." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2506.0 0.0 0.0 0.0
"7:40 Nodes 1,2, and 3 form a loop? It seems strange since the direction of the edge connecting nodes 1 and 3. At least from my usual use of the word ""loop"" it doesn't seem like a loop since if you leave node 1 you can't get back to node 1. Comments anyone?" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1401.0 0.0 1.0 0.0
"I didnt know kermit used to be a math teacher." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5282.0 0.0 0.0 0.0
"I've watched Prof Strang before  my exams...." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6434.0 0.0 0.0 0.0
"In that Hat problem, why is P(X_i = 1) = 1/n?
Shouldn't it depend on the value of i. What I mean is for the first person it is 1/n but for the second it is 1/n-1 if the first one did not get his hat and 0 if the first one picked his hat." EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 6654.0 0.0 1.0 0.0
"why is this on the front page?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15348.0 0.0 0.0 0.0
"His linear algebra books are pure garbage. They are not at all recommended for those who want a deep insight into abstract algebra. All he does is provide a very computational approach towards learning linear algebra, which I think is very unfortunate." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4760.0 0.0 0.0 1.0
"👍👍👍 amazing, really a great work" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15705.0 0.0 0.0 0.0
"MIT blackboards tend to infinity" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7511.0 1.0 0.0 0.0
1:05 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 579.0 0.0 0.0 0.0
"I knew gauss jordan and i applied it several times but i never got the meaning of it.But man you finally explained the method.
Hats off to you man" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5633.0 0.0 0.0 1.0
"These videos are amazing for test review. My linear algebra teacher is awesome but these videos are nice to watch since hopefully I already know everything going on." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 10431.0 0.0 0.0 0.0
"Thank you so much, Professor Strang, and MIT." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9397.0 0.0 0.0 0.0
"I took linear algebra in fall 2014, is it weird that I'm rewatching this now for fun?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6108.0 0.0 0.0 0.0
"The derivative is not just the slope of a line. A function can be non-linear or may have 2 lines which are discontinuous... Refer to lecture 1." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10071.0 0.0 1.0 0.0
"I would be the annoying person with the laser pointer and the chewed paper peashooter." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6255.0 1.0 0.0 0.0
"Thank you" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9086.0 0.0 0.0 0.0
"Excellent lecture." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3657.0 0.0 0.0 0.0
"he skips so many stuffs." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 13114.0 0.0 0.0 0.0
"Better name's for dot is scalar, and for cross is vector product." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2886.0 0.0 0.0 0.0
"he gave both forms of the spelling at 0:50" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13078.0 0.0 0.0 0.0
"The binomial theorem can be applied to any real or complex exponent, so the limit power rule proof holds for any exponent" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10018.0 0.0 0.0 0.0
"If  l > d, would the probability of crossing greater than 1?" CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 6458.0 0.0 1.0 0.0
"If you enjoy Khan, you might also like a channel called PatrickJMT; although, you probably know him already." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6543.0 0.0 0.0 0.0
"I have so much respect for professor Gilbert Strang. He's at such an advanced age in these videos yet he can still give such great lectures. In fact it's 2018 and he still is giving lectures!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5557.0 0.0 0.0 0.0
cool Xn8wL2ItzZw "Lecture 9: Limsup, Liminf, and the Bolzano-Weierstrass Theorem" "MIT 18.100A Real Analysis, Fall 2020" 12675.0 0.0 0.0 0.0
"Sorry I'm having trouble keeping up, but for the Poisson example, where does that expression for mu(x) come from?


This is terrific by the way- thank you MIT for helping me stay even a little afloat in one of my classes." X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 8852.0 0.0 1.0 0.0
"Great lecture, thanks a lot ! Just a little question : at 41:00, isn't the saddle point supposed to be a minimum for x in its row and a maximum for y in its column ? Or maybe the opposite works too ? But if there were 2 saddle points in a matrix, then they would be equal... I'm a little confused." feb9j65Iz4w "24. Linear Programming and Two-Person Games" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4283.0 0.0 1.0 0.0
"haha i love this guy, " Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 13039.0 0.0 0.0 0.0
"Was a very good video." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11269.0 0.0 0.0 0.0
"I agree if we were talking about a community college, but I'm just guessing the caliber of student that gets accepted to MIT probably already knows a good amount about basic calculus such as this." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5025.0 0.0 0.0 0.0
"@MIT OpenCourseWare
Can you please tell me the difference between this course and the  on in this link: https://ocw.mit.edu/resources/res-6-012-introduction-to-probability-spring-2018/index.htm

They look similar to me in content. The one in the link looks more structured." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 1666.0 0.0 0.0 0.0
"Where is lecture 34? That's the 4th one missing :-o" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11684.0 0.0 0.0 0.0
"This professor is so wonderful! He presents each new bit of information in such a way that makes it seem intuitive to me and I just love listening to him lecture! " FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10908.0 0.0 0.0 0.0
"@KatherineRogers Actually, if a constant k=1/1m is used, then in the final formula for V you will end up with subtracting m^1 from m^2 which is apparently not correct." ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1650.0 0.0 1.0 0.0
"n! = n(n-1)(n-2) .... (n-(n-1))" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14009.0 0.0 0.0 0.0
"great explication" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12972.0 0.0 0.0 0.0
"Preparing for my MS/MTech at IIT Through this" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8240.0 0.0 0.0 0.0
"@joeglimmix by contrast his brain probably has 8 pack abbs " 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1906.0 0.0 0.0 0.0
"I'm curious. What was the last guy's doubt?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6317.0 0.0 0.0 0.0
"Sad to see the university level kids don't know how to compute  determinants.
in Pakistan, even the 6th grade kids know this ...!!haha" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8587.0 0.0 0.0 0.0
"maybe it's because they have to pay their professors so much? And they would probably use the money to fund more in internet education because money is allocated to specific parts within MIT." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13929.0 0.0 0.0 0.0
"I don't think it's arrogant to assume that if you're studying calculus, you should know that -3 is larger than -4." Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5335.0 0.0 0.0 0.0
"My heart skipped a beat at 12:02..." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 7760.0 0.0 0.0 0.0
"I cant understand why is the du/dt not in the equation (which is at 36:54) even with the explanation that provided on the comment lol" wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 5235.0 0.0 1.0 0.0
"Did he miss the explanation why u is eigenvector of A^t A after proving the u's are orthogonal?" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3374.0 0.0 1.0 0.0
"""Maybe I'll leave the author to prove that..."" 

He is the author of the textbook they are using though! Hah!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 85.0 0.0 0.0 0.0
"@lolololort 
1/2(1 + sqrt(5)) is also the golden ratio!  Math is amazing =]  I'm sure the professor knew the answer and didn't calculate it in his head on the spot." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 1932.0 0.0 0.0 0.0
"Good luck!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4143.0 0.0 0.0 0.0
"I'm sorry but in my opinion for any freshman at MIT, this stuff should have been covered in high school.   I mean, this is MIT after all.   Anyone agree with me?" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6378.0 0.0 0.0 0.0
"https://youtu.be/HgC1l_6ySkc where he corrects the error in this lecture." TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 13294.0 0.0 1.0 0.0
"@SaintTaurus, Calculus if fun! Duh! " YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1715.0 0.0 0.0 0.0
"it's great!" H_k1w3cfny8 "10. Continuous Bayes' Rule; Derived Distributions" "6.041 Probabilistic Systems Analysis and Applied Probability" 13696.0 0.0 0.0 0.0
"Nobel Prize for teaching linear algebra." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7906.0 0.0 0.0 0.0
"how about calling it an egg...
" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 13191.0 0.0 0.0 0.0
"Respect full thank you 🙏.
Love you so much sir..." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8559.0 0.0 0.0 0.0
"The proof at the end starts off with: f(x) x->a = f(a) - the definition of continuous. So f(x) x->a - f(a)=0. 

Then simplifies to f'(a)*0, this however only holds if a function is continuous. If a function was not continuous then it would simplify to f'(a)*some constant. As f(x) x->a - f(a)=c - is not continuous.

Which would make it not = 0. 

And in order to be differentiable x-a has to go to zero (by definition). That is how differentiable implies continuous.

I hope this helps." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10254.0 0.0 1.0 0.0
"I had up and downs throughout the course, but never less, this is the best course I had so far. 
Thank you Prof. Gilbert Strang for your teaching and thanks MIT for sharing these astonishing lectures for free!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5478.0 0.0 0.0 0.0
"May I say that the vectors in R span the same space as vectors in A after row operation because you can do a reverse ROW operation and construct the same vectors in A from R? It can't be true for column space because after row operations you most likely can't reverse and reconstruct the original column vectors from R through COLUMN combinations." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7633.0 0.0 1.0 0.0
"i have another idea for the proof of sin(x)/x=1 as x tends to 0
imagine the graph of sin(x)
as x tends to 0 the slope approaches 1 (f'(sin(x))=cos(x) and cos(0)=1). This would mean that x is the x value and sinx is the y. Since the slope approaches 1 then this means that the rise over the run (y/x)=1 or sinx/x=1" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13394.0 0.0 0.0 1.0
"I feel immensely happy every day when I watch  Dr. Casey Rodriguez's lecture" 0_w-R_g5lRA "Lecture 10: The Completeness of the Real Numbers and Basic Properties of Infinite Series" "MIT 18.100A Real Analysis, Fall 2020" 5391.0 0.0 0.0 0.0
MATHGASM! kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7496.0 0.0 0.0 0.0
"I love how you can actually see his brain thinking lol " 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 5755.0 0.0 0.0 0.0
"The bijection between subspace of row space and subspace of col space had been hinted quite nicely in previous lectures and in the textbook by Dr. Strang, e.g. he stressed the fact there lies an identity when we do row reduction. So nice that I figured this out when I walk through the previous materials. But still, he managed to show there's a new (to me) point of view to such bijection: pseudo-inverse works as *the* inverse function of the bijection mapping, and that the pseudo-inverse *also eliminates* some (resp. left) null space, just like what the original is doing. Such symmetry, such beauty." Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 10017.0 0.0 0.0 0.0
"Geometría 🤱🤱🤱🤱🤱🤱🤱🤱🤱🤱🤱🤱🤱🤱🤱🤳🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️🏋️" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4003.0 0.0 0.0 0.0
"Nice lecture sir.Love from India🇮🇳🇮🇳" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 7846.0 0.0 0.0 0.0
"Don't y'all love a good ol' rangle?" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3480.0 0.0 0.0 0.0
"ALSO, the limit was not properly taken as in the lecture video in the lecture notes. I guess the notes are meant to be supplementary and not the main material :/" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2180.0 0.0 1.0 0.0
"is that Zenon's Paradox?" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13644.0 0.0 0.0 0.0
"@20.50 .why even if w is positive if a is positive we have minima" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1510.0 0.0 1.0 0.0
"I took stats last year, it was tough! Luckily my school used Lumen which helped a lot! It had practice problems  so you can know what you do wrong, so u can go back and work on it before going on to your official home work. I was able to get an A but it was tough and had to put a lot of extra time aside dedicated just to my homework etc because i am very very bad at math. The lumen program  really helped a lot" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 6110.0 0.0 0.0 1.0
"Thank you professor Strang, thank you MIT OCW" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9319.0 0.0 0.0 0.0
"He's leading you to think, rather than proof after theorem." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 4639.0 0.0 0.0 1.0
"In the uploaded lecture slides of parametric hypothesis testing there is a typo. The equals sign of H1 on Slides 29/37 and 32/37 should have been not equals sign.The same slides that are in the video ( 1:17 and 8:09),  don't have the that error." a66tfLdr6oY "11. Parametric Hypothesis Testing (cont.) and Testing Goodness of Fit" "MIT 18.650 Statistics for Applications, Fall 2016" 6687.0 0.0 1.0 0.0
"Prof says @13.10 ,since Y and X are independent, we can write E[Z] = E[Y] E[1/X]

But we can this is true only if Y and 1/X are independent. Does independence of Y and X imply that Y and 1/X are independent too🤔?" l4NoMKEHQwM "11. Derived Distributions (ctd.); Covariance" "6.041 Probabilistic Systems Analysis and Applied Probability" 8282.0 0.0 1.0 0.0
"Lovely lecture." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 7487.0 0.0 0.0 0.0
"kenshin was a sick show!" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13749.0 0.0 0.0 0.0
"Thank you professor, Thank you MIT." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 9327.0 0.0 0.0 0.0
"These ones: ""I Really Like The Video Polar coordinates; area in polar coordinates From Your"" with the first line of the description." XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10423.0 0.0 0.0 0.0
"I am currently taking Heat transfer, His explanation broaden my knowledge. 'Multivariable Prof. wasn't of much of assistance'" seO7-TwXH_I "Lec 30: Line integrals in space, curl, exactness... | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5083.0 0.0 0.0 0.0
"Great lecture!!!Thank you Prof. Strang!" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4275.0 0.0 0.0 0.0
"Such a great lecturer, as well as in his classic Linear Algebra lecture series. Really nice to see him up and healthy, sharp and as a great step-by-step-explainer as ever." wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8929.0 0.0 0.0 1.0
"@ 17:04,  it should be d/dv (1/v). If v really is a function of x, as he wrote, then he is using the chain rule which he hasn't introduced yet..." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1469.0 0.0 1.0 1.0
"His lecture is so clear!" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4755.0 0.0 0.0 0.0
"excellent teaching! it makes complex things easier, break-down the points, better than other online class!." ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 12827.0 0.0 0.0 1.0
"The difference between EE and Math dept is EE starts counting at 0 and Math at 1....paraphrased at 18:10.  That made me laugh." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 10075.0 0.0 0.0 0.0
"Tnk u vry much sir" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11019.0 0.0 0.0 0.0
"This is so good, better than the matrix movie." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10718.0 0.0 0.0 0.0
"nice lecture" IfwfCe-JZaI "24. Structure of set addition IV: proof of Freiman's theorem" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 14042.0 0.0 0.0 0.0
"omg his French accent is so fucking weird" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14136.0 0.0 0.0 0.0
"This video is what is keeping me going in life, god bless calculus" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 10957.0 0.0 0.0 0.0
32:20 VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 927.0 0.0 0.0 0.0
"probability is the framework for dealing with uncertainty or situation in which randomness occur." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 14205.0 0.0 0.0 0.0
"That slight feed-back from his microphone is horrible" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9913.0 1.0 0.0 0.0
"It’s so refreshing to see Prof.Strang teaching again. Man what an exiting adventure." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7102.0 0.0 0.0 0.0
"Lecture starts at 2:50" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7296.0 0.0 0.0 0.0
"ayyeeee! I got this one!" TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 12504.0 0.0 0.0 0.0
wow z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15407.0 0.0 0.0 0.0
"We need an identity for the dude that passed by lol" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 11329.0 0.0 0.0 0.0
"Oh no, Trig functions. I hate trig!
" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8024.0 0.0 0.0 0.0
"I am doing a project on this topic it really helped me a lot..thank you" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5085.0 0.0 0.0 0.0
"Stuff invented by humans. Nothing real, nothing to be use." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8919.0 0.0 0.0 0.0
"I would say that the most efficient way for solving Ax=b would be solving A^t A x = A^t b (minimum square problem) using CG algorithm, due to my personal amazement with CG method. Pretty sure that it's not the case, but this method gives me chills. Hahaha" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 6269.0 0.0 0.0 0.0
"It may be award to be in a room with now students, but rest assured that we ARE LISTENING and learning!!!! Thank you!" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 6976.0 1.0 0.0 0.0
"I m sad that not to study this way in my high school when time was abundant ..I think course books n curriculum needs some rethinking for producing quality skilled high school graduates." zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5865.0 0.0 0.0 0.0
"12 years later, still the best lecture :))" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 385.0 0.0 0.0 0.0
"42:55...If...., we could postpone that evil day." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 1191.0 0.0 0.0 0.0
44:05 eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1228.0 0.0 0.0 0.0
"awesome :D" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12487.0 0.0 0.0 0.0
"He is a genius! I have read many different versions and understood only after this lecture. Highly recommended!! " 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 4498.0 0.0 0.0 0.0
"Can anyone explain how is he multiplying Identity matrix Id which is dxd with all-ones matrix which is nxn?????" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 3021.0 0.0 1.0 0.0
"Leonardo di caprio's father once told him ,"" if you want to see a great actor look at Robert de niro"" 
I tell you , if you want to see a great teacher look at professor Strang and remember his face" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 7328.0 0.0 0.0 0.0
"@GRNoam 

What do you think they do with the interactive white board? I respect your opinion but I find that the ""Smart Board"" makes the class more interesting so you don't get distracted and it has many features that can help you understand; I'd like to see someone watch a movie on a black board or display a graph, chart, diagram etc." MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1622.0 1.0 0.0 0.0
"Um Ótimo professor." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11118.0 0.0 0.0 0.0
"42:48 matix A^TA is not invertible, then what about the projection matrix P" QuZL5IKpO_U "24b. Quiz 2 Review" "MIT 18.06 Linear Algebra, Spring 2005" 1188.0 0.0 1.0 0.0
"speed 1.25 is perfect" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14388.0 0.0 0.0 0.0
"Thank u professor, what an excellent teacher u are..great, brilliantly conveyed every single notion of linear algebra in a lucent way, i feel fortunate to watch your lecture series which made me to love linear algebra and understand the concepts. I wish my teacher also should have watched your lectures once." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 9073.0 0.0 0.0 1.0
"Thank you from Colombia, it is pretty useful!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9294.0 0.0 0.0 0.0
"I actually started to watch this series as I drilled down to all the dependencies for the quantum phyics course (8.04) and build my learning path from it. This is fun! Do they indicate during the lecture when we're ready to do which problem set?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5020.0 0.0 0.0 0.0
"thank you for taking time to explain, if i remember correctly the lecturer explains this same point in the beginning of the next video. its as if he knew. " 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14495.0 0.0 0.0 0.0
"the derivative of 30x^3 + 12x^4 +15+ 1 is 90x^2+48^3=0 right???" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14683.0 0.0 1.0 0.0
"Very efficient" CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 11167.0 0.0 0.0 0.0
"No kidding I literally completed my STEM preperation from MIT OCW!!!" 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7875.0 0.0 0.0 0.0
"Fart 29:58" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 3746.0 0.0 0.0 0.0
"43:49 The ""actual humans"" statement is still on the tape 🤣" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1220.0 0.0 0.0 0.0
"“Everything is better when written put in linear algebra”, so true" rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15585.0 0.0 0.0 0.0
"the example of king's sibling is so profounding for me" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 14686.0 0.0 0.0 0.0
"I tried to ignore it, but what the heck is wrong with the camera-man?" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 6114.0 1.0 0.0 0.0
"A very noble gesture from MIT to make these videos freely available to public. Took me two weeks to watch all the 35 lectures. Really a great professor. Brought back memories of the maths classes by my BITS, Pilani (India) professors, some of who were world class those days (1985-89)." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2168.0 0.0 0.0 0.0
"Thank you so much, Professor Strang." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9398.0 0.0 0.0 0.0
"Linear algebra is wild" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7380.0 0.0 0.0 0.0
"34:44 It's funny that the column which dependent on others is called Free column" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 987.0 0.0 0.0 0.0
"I love his ackward humor xD" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5737.0 0.0 0.0 0.0
"what program is the lecturer using on laptop?" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15181.0 0.0 0.0 0.0
"For me, too many steps were skipped @20:20 . To understand this, it helps to know about elementary matrices. Basically, if you want to add k * row_i1 to row_i2, you can left multiply by m x m matrix I + M where M is all zeros except entry i2,i1 = k. To see why I + M has this effect, do the multiplication ""by hand"" (you can gloss over the effect of I by using the fact that matrix multiplication is distributive). Of course, the inverse of this is I + -M. This is where the 2 in his example comes from: the first (and only) step of elimination was to add -2 * the first row to the second row. So, we must add 2 * the first row to the second, which is the same as left multiplying by [[1, 0], [2, 1]]. Since this is the only elimination step, that ends up being the L matrix in this tiny example. In general, we would have to multiply a whole bunch of these inverse elementary matrices. Fortunately, that multiplication is very easy to do, because all of these elementary matrices are mostly zero, except on the diagonal." or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3866.0 0.0 0.0 1.0
"This is amazing........" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10620.0 0.0 0.0 0.0
"I Really Like The Video Lecture 07: Review. From Your" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4981.0 0.0 0.0 0.0
"how do we sketch a plane..
if i have ..
x+y=0
how to draw this on x,y,z plane?
what about 
x+2y=0
or 
2x+y=0?" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13226.0 0.0 1.0 0.0
"oh, in korea, we learn them when highschool, thank you, the class was very helpful to me🥰🥰🥰" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14117.0 0.0 0.0 0.0
"This is a complet detailes explanation so its really good" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10587.0 0.0 0.0 0.0
"1:02:00 Gaussian Inference w/Bayesian Methods" bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 573.0 0.0 0.0 0.0
"No part uno?" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 7888.0 0.0 0.0 0.0
👍👍 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 15701.0 0.0 0.0 0.0
"I’m very enjoy your course." L3-WFKCW-tY "33. Neural Nets and the Learning Function" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7119.0 0.0 0.0 0.0
"What's the justification for minimizing the square of the distance instead of the distance itself?" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11582.0 0.0 1.0 0.0
"This is amazing. Thank you Professor." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10618.0 0.0 0.0 0.0
"This guy is amazing. Thank you so much for this lectures!!!" sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10520.0 0.0 0.0 0.0
"APL , K and J are conspicuously absent from his list of languages for ML while they are very competitive with Julia . 
As is  http://CoSy.com which has the unmatched flexibility of being a vocabulary in an open to the chip Forth ," rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2183.0 0.0 0.0 0.0
"Great teacher !!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4336.0 0.0 0.0 0.0
"Splendidly explained. Thank you so much" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8873.0 0.0 0.0 0.0
"I love you" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5844.0 0.0 0.0 0.0
"Ah, ASMR lecture" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2279.0 0.0 0.0 0.0
"The questions the students are asking are cracking me up... just when I thought he couldn't break it down simpler..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10264.0 0.0 0.0 0.0
"But vector A can go on another direction. How would you know that?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2965.0 0.0 1.0 0.0
"cream cheese!" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 12695.0 0.0 0.0 0.0
"Lmfao he is good but his french accent make his lecture  weird" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7393.0 0.0 0.0 0.0
"Awesome video. Using it to get ahead for fall!  Thank you for providing this to the public. In the age of the internet, knowledge is as cheap as the wifi!" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 2776.0 0.0 0.0 0.0
"sorry guys, i have a silly question in the minute 9:10 in the second and third matrix in the third colum, why is -2 and 5? i did not undestand that part" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14374.0 0.0 1.0 0.0
"man wtf ?! i've seen this video over a billion times each weak it get posted again and again and again /!!!! why the fuck are they making copies of this stupid video 1 fucking video is enough!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13903.0 0.0 0.0 0.0
"Thank you so much Gil!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9345.0 0.0 0.0 0.0
"At 31:40, I thought he was saying ""sine"" instead of ""sign"". That confused me for a bit haha." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2641.0 0.0 0.0 0.0
"@ 38:30 it is technically India and not China! India is right on the other side of Boston" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1476.0 0.0 0.0 0.0
"Mean value theorem doesn't care. Mean value theorem doesn't give a shit. Mean value theorem is a honey badger." 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7650.0 0.0 0.0 0.0
"lol ""extreme autism"" " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13818.0 0.0 0.0 0.0
"Damn i thought professor lambeau from good will hunting would be in this" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3297.0 0.0 0.0 0.0
"Are you stoned?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2542.0 0.0 0.0 0.0
"I love the way he always explains everything from the beginning, he tells you the whole process." rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5790.0 0.0 0.0 1.0
"24:42 what in the!! XD. So random for no reason. This was so unexpected literally caught me so off guard and by surprise lol. Hilarious" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 753.0 0.0 0.0 0.0
"Star trek has led me very astray in this regard" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 8877.0 0.0 0.0 0.0
"This theorem should be called ""The Fundamental theorem of probability theory"" and the Central Limit Theorem, ""the Fundamental theorem of Statistics""" 3eiio3Tw7UQ "19. Weak Law of Large Numbers" "6.041 Probabilistic Systems Analysis and Applied Probability" 10943.0 0.0 0.0 0.0
"If I had tattoos, I would make a tattoo with Gilbert Strang's name on it:) Amazing guy, amazing lecture, amazing MIT" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6466.0 0.0 0.0 0.0
"How are some of these kids at MIT? STOP ASKING STUPID QUESTIONS. Yes, there are stupid questions." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4801.0 0.0 0.0 0.0
"From this lecture, I really understand Positive Definite Matrices and  Minima thanks  to Dr. Gilbert Strang. The examples really help me to fully comprehend this important subject." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 3938.0 0.0 0.0 1.0
"This is heaven for me <3
MIT <3" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10672.0 0.0 0.0 0.0
"@theRealCheeseCake money" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2039.0 0.0 0.0 0.0
"the question the student asks "" how do you get the formula?"" is a valid one. The formula comes from physics. In India particularly Tamilnadu students at their 16 or 17th age learn about this calculus, and some basic but very important physics concepts. And I heard most of our students including me and my friends too have more struggles to understands these concepts. so here is this is a course for engineering students or school students?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14738.0 0.0 0.0 0.0
"Here's something they didn't quite spell out to me in my Linear Algebra class:

Let E be the product of row operation matrices. Let F be its inverse, FE = I.
Obviously if Ax = b then EAx = Eb (because f(x) = f(y) for all f when x = y).
But also importantly and relevantly if EAx = Eb then Ax = b:
If EAx = Eb then Ax = IAx = (FE)Ax = F(EAx) = F(Eb) = (FE)b = Ib = b.
That is, divide by E (i.e. multiply by F) on both sides to recover Ax = b.

This is the justification for the algorithm: Compute E * [A b] where E is chosen such that solutions x can be read off easily. Solving E*[A b] means x solves EAx = Eb, but then Ax = b.

So the outputs of the algorithm are in fact solutions to Ax = b." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 4679.0 0.0 0.0 1.0
"13th or 14th" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 422.0 0.0 0.0 0.0
"i like his accent" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13414.0 0.0 0.0 0.0
"at 45:25 prof is talking about the other basis vectors for the column space
he says finally that since the dim of the column space is 2, he says any 2 vectors that are independent can form the column space
but is that possible? i mean the column space is a plane in 4 dimensional space right?
so if i pull out some two random independent vectors that are both out of the original column space, then their linear combinations will span an entirely new plane right?
math genius plz help this poor soul..." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 12456.0 0.0 1.0 0.0
yeeting 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 15478.0 0.0 0.0 0.0
"Golden hair ❤️" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4105.0 0.0 0.0 0.0
"10:30 shouldn't the rank of A^TA be m, so that the it's nullspace is only the nullvector? If A∈M(m x n, R) so A^TA∈M(m x m, R), right?. Hence the rank should be m. Can someone confirm this to me?" TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 348.0 0.0 1.0 0.0
"37:23 That is not the reduction formulae for the integral of x^n * e^x.... search the real one on Google. The G(n-1) function should be inside an integral." aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1064.0 0.0 1.0 0.0
"@44:00 by now Prof. Strang should know that nothing is ever taken out of the tape haha." NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1558.0 0.0 0.0 0.0
"yes, both stays the same!" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 15485.0 0.0 0.0 0.0
"Only just a couple of questions  asked, they must be sleeping in class. glad I have all week to punish my brain , I must be sick to injoy harming my brain trying to get this information down. Its not as all as easy for me as some , who can drink  a cold drink on a hot day in just a few minutes, getiing this easy information down , Were the slope of information is  computed as fast as it is pluged in plank time." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8120.0 0.0 0.0 0.0
"Like pelase
https://youtube.com/shorts/I5BauLvpTbU?feature=share" EBdgFFf54U0 "Lecture 14: Basic Hilbert Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 7360.0 0.0 0.0 0.0
"He's an ok teacher. He certainly doesn't hold your hand with this shit." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4632.0 0.0 0.0 0.0
"Denis Auroux. Thank you professor !!" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3349.0 0.0 0.0 0.0
"What is better is a power blackboard, motor driven, stacked 3 or 4 high, so you can run up several boards easily and they can be seen by a large lecture theatre (say a 400 seater)" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11516.0 1.0 0.0 0.0
"Just for the record he is an authority on Differentials and Multivariable proofs and was awarded a Distinguished Mathematical Professor Award only given to 30 MIT professors in the history of the Institution 😉👏" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7183.0 0.0 0.0 0.0
"Little notation mistake at around 16 min Null space of (A-I)^T" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 7391.0 0.0 1.0 0.0
"at 35:35 if we take derivative of the answer that is not going to be x^3(x^4+2). we need x^4 multiplied by (x^4+2)^6. Can anyone explain what is going on?" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12443.0 0.0 1.0 0.0
"this lecturer is the best lecturer i've ever had. never encounterd such clear explanations! very recommende :-)" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 14899.0 0.0 0.0 0.0
"The IIT part is true for sure.
" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 9967.0 0.0 0.0 0.0
"All living beings are blessed to have Gilbert Strang among them, whether they realize it or not." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 2298.0 0.0 0.0 0.0
"I really wish the sound was better..." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5938.0 1.0 0.0 0.0
"Thank you Prof. Strang! I've done many MOOCS in my life, but all of them were CS related. Decided to take this MOOC when I noticed that  I missed some theoretical Linear Algebra knowledge while working with Deep Learning and Machine Learning problems and, oh god, this was one of the best decisions I took in my entire 2020 year. Once again, thanks Prof. Strang and MIT!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9199.0 0.0 0.0 0.0
"nice!!!   
This way i never study determinant" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 14056.0 0.0 0.0 0.0
"Thank you MIT ! ,  thank you John Tsitsiklis !  , very good and interesting  lecture ." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 9125.0 0.0 0.0 0.0
"great lecture... awesome video... " VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 12988.0 0.0 0.0 0.0
"I also like LSD but math is just as cool." -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5036.0 0.0 0.0 0.0
"@Voltar143 If and only if americans will stop being lazy >.<" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1754.0 0.0 0.0 0.0
"Great explanation.." k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4227.0 0.0 0.0 0.0
"ty cameraman" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14965.0 1.0 0.0 0.0
"first derivative is with a plus!! I almost got mad" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12868.0 0.0 1.0 0.0
"@DGMedonja your'e a hero." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1608.0 0.0 0.0 0.0
"it all happened that i found this lecture where in fact that i got a case study with regards of Markov analysis. it really helps me a lot, and very comprehensive lectures." IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 13670.0 0.0 0.0 0.0
"This guy is amazing...When teachers taught this in my college everything went right off the top of my hat..." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10521.0 0.0 0.0 0.0
"I wish I had gotten into MIT." rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6198.0 0.0 0.0 0.0
Thanks nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9577.0 0.0 0.0 0.0
"is it math 101?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13637.0 0.0 0.0 0.0
"where is the Asian guy who  dividing subjects part by part" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 15241.0 0.0 0.0 0.0
"At 10:05 , why take the 0 as a multiplier? Doesn't the definition say that you are not supposed to take 0 as the multiplier for independence?" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 2583.0 0.0 1.0 0.0
"He is the iconic figure of what a good professor should be.  //salute" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4549.0 0.0 0.0 0.0
"8:47
Gilbert Strong" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 1425.0 0.0 0.0 0.0
"First wave of questions end at 20:06" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3823.0 0.0 0.0 0.0
"could someone please tell me which videos exactly have the signal processing part, because I studied a lot of that content already and I'm here for computer vision purposes" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12690.0 0.0 0.0 0.0
"If you think there are degrees of difficulty with CALC exams, then you really don't understand CALC." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6558.0 0.0 0.0 0.0
"I'm having a hard time finding the exact web page on ocw that has the assignments issued after every lecture, anyone know the link?" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6326.0 0.0 0.0 0.0
"a. E[#fish] = E[#fish|T<=2]P(T<=2)+E[#fish|T>2]P(T>2) = 0.6*2*P(T<=2)+1*P(T>2)=1.2*P(T<=2)+(1-P(T<=2)) = 1+0.2*P(T<=2)
b.E[#time] = E[#time|T<=2]P(T<=2) + E[#time|T>2]P(T>2) = 2*P(T<=2)+(2+1/0.6)P(T>2) = 2*P(T<=2)+2*P(T>2)+1/0.6*P(T>2) = 2+1/0.6*P(T>2)" XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 12298.0 0.0 1.0 0.0
"but we're not bulding any pyramids here in Egypt though :D lol
15:40" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12575.0 0.0 0.0 0.0
"Begin's poisson at 9:20" jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 2839.0 0.0 0.0 0.0
"Measuring even a curves outer perimeter will give it's minus integral..or plus?" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7653.0 0.0 1.0 0.0
"I can't understand why we introduce a new mechanism / model / ""hardware"" for enumerators - why do we need a ""printer"" mechanism when we can already write to the tape? We could just define some spans(s) of the tape as being the ""output strings"", no? That even happens to map directly to how most computer hardware lets the CPU communicate with peripherals - you simply write/read from a certain predefined address space in memory." TTArY7ojshU "6. TM Variants, Church-Turing Thesis" "MIT 18.404J Theory of Computation, Fall 2020" 5227.0 0.0 0.0 0.0
"Thanks to MIT ocw for another great course. Hoping to see more courses in fundamental mathematics in the future" 9_xG0AGRa-w "Lecture 2: Cantor's Theory of Cardinality (Size)" "MIT 18.100A Real Analysis, Fall 2020" 9804.0 0.0 0.0 0.0
"why don't re-recorded lecture 4...That will be really helpful...thanks anyway..." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 15315.0 0.0 0.0 0.0
nitesh j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 14061.0 0.0 0.0 0.0
"Winy have you published such a mess? Shame on you!" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 11954.0 0.0 0.0 0.0
"I don't know Julia, so I'm having a hard time following, but from what I can gather, all professor Edelman did in order to get ""forward diff"" was to define a ""tuple"" that holds both f(x) and f'(x). Then, he defined some operator overloads so that any iterative algorithm that calculates/approximates f(x) will also calculate f'(x). Is this right? If so, it doesn't seem that Julia would be the only language that you can do this in. All you need is polymorphism/overloading, which I think any modern language would support (e.g. C++, Python, which were both ""ruled out"")." rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5317.0 0.0 0.0 0.0
"I thought this was some measure theory stuff :))) but some how it goes into functional analysis" OHiu2F18dFA "Lecture 7: Sigma Algebras" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 6102.0 0.0 0.0 0.0
"The best explanation on the determinant of matrix ever! Thank you." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 9997.0 0.0 0.0 0.0
"I can barely hear the audio. Please remake this video next time." C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 5186.0 1.0 0.0 0.0
"I have a question....
Is there any theorem stating that A(T)*A is always a non negative defined symmetric matrix?
If not...let's say S is a skew matrix. We know for sure that it's not diagonalizable in R3....yet we might work to get the SVD form...is there any theorem stating that S(T)*S is always a non negative defined symmetric matrix?" HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 5510.0 0.0 1.0 0.0
"NOT SO GREAT" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 7804.0 0.0 0.0 0.0
"Add a public comment..." 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2241.0 0.0 0.0 0.0
"Like ainesten, what was 1?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 7350.0 0.0 1.0 0.0
"Indian kids be doing this in high school" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6710.0 0.0 0.0 0.0
"i believe strang is the best professor i've ever seen. you make things easy to understand

adjombi" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 13344.0 0.0 0.0 0.0
"How soul less and stupid do you have to be to devote your life to this bullshit.  The factoring problem,the algo, the intersection of p verse, measures of computational probablistic math...." 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 4893.0 0.0 0.0 0.0
"basically this video is all about linear approximations" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12509.0 0.0 0.0 0.0
"interesting video and very important for engineers.You should take advantage of this information. Congrats!!!" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13619.0 0.0 0.0 0.0
"i am peruvian, please MIT please, with subtitles in spanis, new videos. thanks." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13337.0 0.0 0.0 0.0
"page 35 of Deep Learning by YannLecunn brought me here
the best explanation linear combinations and this gave a completely new perspective on how to look at matrices" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 14166.0 0.0 0.0 0.0
"I know, right" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 5644.0 0.0 0.0 0.0
"Just wanted to say that blocking the rref matrix into [[I F], [0...]] form and solving for the nullspace matrix like that is one of the greatest things I've ever seen. It seems like it shouldn't work because F could have different shape than I, but it does. And it generalizes to when F doesn't exist, which helps you remember the ideas in the next lecture." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 7202.0 0.0 0.0 1.0
"Thankyou soooo much MIT........A huge respect for professor...
Gave the first exam( in home) and got 85😁😁😁😁😊...feeling very good and confident..." U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9874.0 0.0 0.0 0.0
"i literally waited years for this video. im going to binge watch this bitch" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 13423.0 0.0 0.0 0.0
"what is book he is referring as readings ?" CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 15151.0 0.0 0.0 0.0
"Can anyone explain what professor meant by pivot variables ?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 3029.0 0.0 1.0 0.0
"These lectures will live on forever." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 10422.0 0.0 0.0 0.0
"14:37 Lol. Not OK. Where is the proof?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 430.0 0.0 1.0 0.0
"Professor looks like james Stewart" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 8397.0 0.0 0.0 0.0
"I love that many universities and colleges do this sort of thing. Looking at different points of view on the same subject is very helpfull. This is extremely well explained, thank you." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 5771.0 0.0 0.0 0.0
"Thanks for posting this course, the instructor is great. If I may, there is only one request, in the future if the camera could move less frequently, the camera is following the instructor too closely, making me a bit dizzy." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 9693.0 1.0 0.0 0.0
"I am in awe of Dr. Strang. All of his material is golden, and he such an obvious passion for teaching. Amazing communicator and academic." cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5108.0 0.0 0.0 0.0
"18:52  It says I'm subtracting rows from lower rows when we are multiplicating the two matrix.
Was not able to get this.was able to simply multiply the matrix using combinations of columns and rows." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 549.0 0.0 1.0 0.0
"I've started and actually paid for many MOOCs in my life so far, but never finished any of them. This course is the first one I finished, probably in 3rd or 4th attempt. Thank you Professor Strang. Thank You MIT for sharing this wonderful material." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 6429.0 0.0 0.0 0.0
"I have a question regarding last proof. It is said that we can use expression x - x0 in denominator because x is always different than x0. And in continuation of proof that same expression is equate with zero. Is it because the value is so small that we can consider it to be zero? in that case, it seems almost as a matter of convenience when we consider it to be zero, and when not?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5501.0 0.0 1.0 0.0
"What an amazing man" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11452.0 0.0 0.0 0.0
"very good teaching" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 15012.0 0.0 0.0 0.0
"ma boi gilbert saving my butt once again" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 13893.0 0.0 0.0 0.0
"5 minutes of 18:06 is enough to take care of 18.03 😂😂😂😂😂" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 1331.0 0.0 0.0 0.0
"Seriously good lecture. Very thoughtful presentation." 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 8628.0 0.0 0.0 0.0
"i think he breaks with the usual convention for m * n Matrix being: m rows, n collums ... which confused me, but great lecture anyways ...

edit: I was wrong
9:12 ... misunderstood what he said there, ofc the columspace has m (rows many) components, because colums go m (rows-many) components down ... thanks Robert Smits" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 13470.0 0.0 1.0 0.0
"Awesome simplicity. Wish I had him in college" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2768.0 0.0 0.0 0.0
"Professor u saved me.Thanks for your lectures. Our college teacher is the worst in teaching linear algebra." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 8402.0 0.0 0.0 0.0
"You don't erase the board at MIT! You just raise it!  :P" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12202.0 1.0 0.0 0.0
"lol, the guy doing the subtitles is really funny (students inaudible response) !!! hahahahah. This lesson is pretty well thought out !! damn i wish i went to mit :(" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13841.0 0.0 0.0 0.0
"I just have to comment about this: I love how Prof Strang has this hierarchy of good matrices and not so good matrices and superior ways of decomposing them and so on. It's like every lecture he introduces another type of matrix and goes ""oh yeah and this type is a really good one. I mean, it's a special case of this other type of matrix, but this one is better than the rest, it's wonderful""" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 5608.0 0.0 0.0 1.0
"I find it almost impossible to follow. Am I the only one?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 5410.0 0.0 0.0 0.0
"At 47:20, why does he need to subtract row 3 from row 2 in order to calculate the cofactor of a21 ?" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 2683.0 0.0 1.0 0.0
"this man just related a rugby ball to the eigenvectors of a matrix. damn!" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 14906.0 0.0 0.0 1.0
" Thanks so much for video taping it and sharing it.  This is helping so many people!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 15536.0 0.0 0.0 0.0
"Is this a high school lecture?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6850.0 0.0 0.0 0.0
"very basic statistics learner here and I have some question. the p (hat) explained in 55:56, does the ˆ represent an estimated value?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 14997.0 0.0 1.0 0.0
"Thank you Professor Gilbert Strang. That's the most clear lecture (and easy to understand), I have ever listened to on the web. You are a great teacher and know your material, providing great insights where needed." or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9211.0 0.0 0.0 0.0
"How do you know what these 'punks' do or do not know?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 4857.0 0.0 0.0 0.0
"Various people, in commenting, are dissatisfied with the  presentation here.  First off, the professor is clearly in command of the subject matter.  This is MIT and the pace in tough. In this third lecture he is up to a weeks-ahead point  of a srandard calculus course.  And these students, if they put the standard 3 hours of study per hour of lecture, will master the lecture material.

One may search for a presentation that is superior, but if you find it, it will not be found at the third hour lecture.  Or one may put in the work to create a satisfactory ptrsentation, to see how you yourself would teach it." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11151.0 0.0 0.0 0.0
"1 - cos(thetha) goes to zero faster than thetha ..." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 314.0 0.0 1.0 0.0
"it was really funny when he saw his mistake :D:D" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 13686.0 0.0 0.0 0.0
"thank you" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 14465.0 0.0 0.0 0.0
"I love this guy!!!" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5806.0 0.0 0.0 0.0
"I’m confused about how he explained adding a x particular to nullspace will not give a subspace. I think it this way. Nullspace should always contain the origin, so in this case it is a plane going through the origin, since x particular is a vector not in that plane, adding them together will never give a zero, so it is not a subspace." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 7110.0 0.0 1.0 1.0
"It's clear that he likes physics. That's good." z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7034.0 0.0 0.0 0.0
"what other lectures does this amazing lecturer have?" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15178.0 0.0 0.0 0.0
"this teacher is to be appreciated . no matter the question , he still answers every single one with equale seriousness . my teachers never did this , they even tell me that my question is stupid sometimes" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14917.0 0.0 0.0 0.0
"As much as i like the geometric profs they are extremely hand wavey." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2572.0 0.0 0.0 0.0
"Where can I find the online homework? I can't find it in OCW." xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11660.0 0.0 0.0 0.0
"@Vihan S : Actually, vectors crop up everywhere in physics. Maxwell's equations for electromagnetism involve vectors, and where would we be today without an understanding of electricity? You wouldn't be watching this on your computer for a start.  " bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1752.0 0.0 0.0 0.0
"Likely they are too stupid to follow." BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7364.0 0.0 0.0 0.0
"@slimmerikje not in 6th grade but in 10th grade :p" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2019.0 0.0 0.0 0.0
"average value of a function f(x,y) in a region r  is what?" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12486.0 0.0 1.0 0.0
"Was anybody else screaming out ""LIKELIHOOD"" at 38:45??" bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 11270.0 0.0 0.0 0.0
"' don't feel rushed to cover everything...just stay with the class"" Wonderful piece of advice for us teachers." t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 206.0 0.0 0.0 0.0
"He's a bit slow explaining in my taste, but still I think he's a great professor " z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4624.0 0.0 0.0 0.0
"36:19 OOpsssssssssssss" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 1034.0 0.0 0.0 0.0
"My brain is degenerating as he explains the degenerate critical points tbh" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7737.0 0.0 0.0 0.0
"I'm just curious about null space.
So pretty much can I put any numbers into null space if column vectors can make the result 0?
For example, at 20:18,
instead of having 
-2     2
1      0
0     -2
0      1



Can I have two column vectors as null space
0         1
-1       -1/2
1         -2
0          2" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 6338.0 0.0 1.0 0.0
"such a great lecuture!" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 14413.0 0.0 0.0 0.0
"Completed 18.02.
Thank you MIT OCW and Prof. Denis Auroux!" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3180.0 0.0 0.0 0.0
"Que se supone que está explicando..????  está demostrando saltándose pasos de álgebra como si por eso fuera a ser mejor demostración... que quiere demostrar...  que sabe y que es chingón...  a los estudiantes hay que poner cada paso y exponer con claridad, nadie puede asimilar eso en una clase...  PÉSIMA EXPLICACIÓN" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8474.0 0.0 0.0 0.0
"so inspiring." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14335.0 0.0 0.0 0.0
Ty j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 11106.0 0.0 0.0 0.0
"At 23:39 why q2 goes to q1 if the input is zero, why not it has circle above it like q1." 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 2618.0 0.0 1.0 0.0
"If you are wondering he is using the slope-point formula in minute 30:38. 
I would also appreciate if someone can explain to me why he can use O(x²) in minute 47:30 to describe values with bigger exponents then 2 like x³,x⁴ and higher." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6537.0 0.0 1.0 0.0
迷一般的斐波那契数列通项公式，原来是这么来的！ 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 15666.0 0.0 0.0 0.0
"One of the best teachers! As a viewer of this course you feel the passion and love for math. He feels the math and can transfer his knowledge to other people. Well explained! Top!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8096.0 0.0 0.0 0.0
"Genius. Fantastic." tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4000.0 0.0 0.0 0.0
"doesnt the application of simpson's rule require n to be an even number?" zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12769.0 0.0 1.0 0.0
"This is the best professor evvvvvvvvver" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10744.0 0.0 0.0 0.0
"@hypnoticpoisons  does not matter since det A is equal to det A transpose" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 1875.0 0.0 1.0 0.0
"great. enlightening lecture" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 13020.0 0.0 0.0 0.0
"Absolutely well done and definitely keep it up!!! 👍👍👍👍👍" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 2213.0 0.0 0.0 0.0
"nice video!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14055.0 0.0 0.0 0.0
*8008* JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 231.0 0.0 0.0 0.0
"The average 0 to 1 value of skin covered by awesome tattoos under David Jerison's lecture shirts is probably 1" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9987.0 0.0 0.0 0.0
"@sahookah Because proving is math." phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1996.0 0.0 0.0 0.0
"26:05 ""What did it cost?""
~40:00 ""Everything""" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 793.0 0.0 0.0 0.0
"Hi, does anybody know the name of the book hes always referring to? :)" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 4727.0 0.0 0.0 0.0
"In the quiz 3 solutions on the course page, there's an error at the last bit of it. The equation should have been Av1 = sigma1u1, it got the v and the u misplaced. Don't know where to report it so I came here lol.." HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 6684.0 0.0 1.0 0.0
"""But, after class - TO MY SORROW - a student tells me, 'Wait a minute that [third vector] is not independent...'""
I love it.  What other professor brings this kind of passion to linear algebra?  This is what makes real in the flesh lectures worthwhile.  " nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 37.0 0.0 1.0 0.0
"43:41 I disagree.Since two solutionsa are Col [0,-1,1] & col [1,0,0] and a simple linear combination is col[1,-1,1] ,which is not a solution that means above two vector are just scattered vectors and dont even form a plane which skips origin.Am I right?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 1216.0 0.0 1.0 0.0
Thanks J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 9575.0 0.0 0.0 0.0
"Dr. Auroux is terrific at impromptu sketching. 19:14, look at the neatness of all six boards!" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3496.0 1.0 0.0 0.0
"hello to any fellow online multi students if y'all are passing by!! :D" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13135.0 0.0 0.0 0.0
"Doc tells you that some subjects are well-known. But,  the students' questions we can see that  subjects not so clear for them." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3427.0 0.0 0.0 0.0
"@32:00, Prof mentions ""if the eigenvalues are far apart, that's when we have problems"".  What does he mean by that?" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1537.0 0.0 1.0 0.0
"Just to check, so at about 27:38 the phi(k - j) = z? not y?" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 7199.0 0.0 1.0 0.0
"that was awesome." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14643.0 0.0 0.0 0.0
"For the condition to be a vector field, that seems like the formulation that the curl of the gradient of f=0 , meaning that its direction does not change and hence is a scalar." seO7-TwXH_I "Lec 30: Line integrals in space, curl, exactness... | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3884.0 0.0 1.0 0.0
"Hello MIT, I don't think this professor's style is my favorite, however I can't say thank you enough for your putting all these videos including recitations for free. Looking forward to your new updates." twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4655.0 0.0 0.0 0.0
"I always thought the N-1 was related to the fact that the variance of a single object is undefined (or at least nonsensical), so the N-1 ensures this is reflected in the maths? As well as something related to the unbiasedness of the estimator etc." Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5047.0 0.0 0.0 0.0
"Lec 1:  819k views,  last lecture:  57k views... Only the strongest survive" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7259.0 0.0 0.0 0.0
"Hi. Perhaps you could help me. If there are 6 greyhounds in a race, and they all have an equal chance of winning or coming second place, and if I put money on four out of the six greyhounds, what are the odds that one of my four selections will be successful (that is, how likely is it that either one of my four selections will come first or second)??? Hope you can help me! Cheers!" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 4732.0 0.0 1.0 0.0
"When a wise man points at the moon, the fool looks at his finger." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11611.0 0.0 0.0 0.0
"Nice explanation" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 7843.0 0.0 0.0 0.0
"I liked the lecture 7. It is like you finally get the result of e at the end of al those lengthy steps" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5703.0 0.0 0.0 0.0
"when i first run into linear algebra at university i was so stuck to understand even the basic topics of my courses. then after 2-3 years i discovered mr. Strang's lectures and i have to say i am so grateful for this professor because his teaching aproach made me understang the whole concept of linear algebra and i actually found it very interesting for the first time in my life. Plus i finally passed my courses after all these years xD god bless you mr. Strang :)" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 15206.0 0.0 0.0 1.0
"I tried to learn the concept from this video months ago and I swear he made me scared.

WHY DOES HE MAKE IT SOUND SO DIFFICULT???

This whole lecture is based on the point-slope equation which is really just the slope formula anyway. 

How do you get slope m?
(y_2 - y_1)/(x_2 - x_1) = m --> Slope

Then, get the x's over to the m

y - y_1 = m(x - x_1)  --> point-slope equation
Then, we solve for y,
y = m(x - x_0) + y_0 --> Linearization

He makes it seem as if the eq comes out of thin air.. :o" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6115.0 0.0 0.0 0.0
Wut? u4qQ1oIQcW8 "Lecture 25: Power Series and the Weierstrass Approximation Theorem" "MIT 18.100A Real Analysis, Fall 2020" 12099.0 0.0 0.0 0.0
"I just came for the first 5 min then I watched it till the end! So engrossing!" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 5596.0 0.0 0.0 0.0
"thanx alot for this great lectures, i´m from Portugal and I´m amazed with this oportunity that M.I.T. gave to every one around the world M.I.T.believes in a better world where everyone can get free high quality education. With this actitude of M.I.T., i´m starting to baleave myself that a better world is possible." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14622.0 0.0 0.0 0.0
"He is a god at linear algebra but from the statistics perspective, he failed." z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4499.0 0.0 0.0 0.0
"very good service given by MIT for other students who cant study at MIT
Thanks to MIT" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 15008.0 0.0 0.0 0.0
"The gold starts from 5:22" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 10123.0 0.0 0.0 0.0
"wtf :D Thats very easy in Germany you lern this in der 11th grade" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15442.0 0.0 0.0 0.0
"y not try diagonal method? its 200% more easy right?" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 15458.0 0.0 0.0 0.0
"Just finished!. 18.01. Will begin shortly 18.02 as well. Also finished 6.042J / 18.062J,  fnished supplementary Single & multi by Herbert  Gross. ( btw rest in peace )  had a break from 6.00 ( will continue and finish soon ) . Thank you for these amazing lectures MIT !" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7180.0 0.0 0.0 0.0
"@crazymofo741 
Sorry for my bad English, it is not my mother language, but I ""believe"" I can improve. I write in Portuguese and French very well thanks.
Any way thanks again for notating, next time I will put it first in the word corrector.
" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 1818.0 0.0 0.0 0.0
"This is a lecture of the best of the best quality. Thrilling" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 10597.0 0.0 0.0 0.0
"Well thanks prof." xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11358.0 0.0 0.0 0.0
"Sir, where is lecture 8? i cant find it?
" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8715.0 0.0 0.0 0.0
"الله يجزاكم خيراً." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15567.0 0.0 0.0 0.0
"Thank you Sir for these 2 series: Real Analysis and Functional Analysis. Can we be expectant of Complex Analysis?" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 9234.0 0.0 0.0 0.0
"@ 49:17 when he writes (-1) is actually correct. Why's it +1 when -e0 is -(1) seeing as e0 is 1? Great lecture though, seriously interesting. Makes me kind of want to do Mathematics in University, and I know this is just one lecture, but it doesn't seem to be as hard as I thought it would be. I guess it's just the fact that most people hate Math and find it super difficult, but I found this lecture enjoyable! Lol, sometimes can't believe I'm one to love Maths..." aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1480.0 0.0 1.0 0.0
"Can't remember last time i was so pleased learning maths, apart from a few 3b1b vids.
Thanks Sr." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3125.0 0.0 0.0 0.0
"Okay, if anyone is like me who is interested in Linear Algebra and not necessarily Differential Equations, but still wants to understand this lecture for the sake of completeness in this course, here is the list of all the Differential Equations theory you need for this lecture and where you can find content to learn it:

1. Separable differential equations - Khan Academy - this is for v(t)=exp(Lambda t) v(0)
2. 2nd order linear homogeneous equations - Khan Academy - you need this if you want to understand one calculation in the next item on this list (quick to learn anyways)
3. Systems of differential equations - MIT OCW 18.03, lectures 24 and 25 - basically does the first example in this lecture, but actually goes through the steps of explaining what is happening, highly recommended to watch both videos

As someone who is unlikely to apply a whole lot of differential equations in the future, I still found this lecture useful to reinforce the properties of Eigenstuff from the previous lecture, also the very last bit of the lecture is very cool" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 8053.0 0.0 0.0 0.0
"TRULY BRILLIANT PROFESSOR! YOU HAVE CONVINCED ME THAT YOU'RE A FUCKING GENIUS WHO KNOWS HOW TO DO LINEAR ALGEBRA.

NOW WHY DON'T YOU TRY TEACHING YOUR STUDENTS HOW TO DO LINEAR ALGEBRA.

AHAHAHA LOL" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 9000.0 0.0 0.0 0.0
"I have a math degree and I still enjoy these lectures. Auroux is a great lecturer." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5493.0 0.0 0.0 0.0
"I have a feeling that the lecturer does not know how to prove the law of cosines." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5491.0 0.0 0.0 0.0
"Because all this stuff is very easy. It is linear algebra 101" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 2831.0 0.0 0.0 0.0
"is it just me or do state colleges have a completely different syllabus?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13636.0 0.0 0.0 0.0
"The area underneath the line y = f(x) over a very small distance, d.x , being d.x f(x), making allowance for infinitesimal error as negligible, one discovers the change in the area under the line y=f(x), d.y , to be d.x[f(x + d.x) - f(x)], and declares the differential therefrom ... or something like that, this being in pursuit of a more visual and intuitively obvious statement of the root understanding of differentials." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9983.0 0.0 0.0 0.0
"@drsiegfriediseman You are right: in italian calculus courses there are better proofs, NOT better professors. Big difference here! :) We have a long math tradition but I think our teachers are now too proud and far from students. It isn't a coincidence that there aren't italian open courses on YouTube! Anyway, I'm very sorry for your bad experience, I hope you will have better experiences with italian colleagues." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1826.0 0.0 0.0 0.0
"Thankyou sir for very conceptual lecture thank you MIT open course feels like in the class awesome technical support" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 9873.0 0.0 0.0 0.0
"@ThePost1994 It's in the first 20 seconds of the video?" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1742.0 0.0 0.0 0.0
"if you are not familiar with laplace transform, especially coming from a signal and system background, you do get lost in here, it's not because of your poor understanding. But for EE, this is an essential and magic piece!" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 13550.0 0.0 0.0 0.0
"Interesting to see that even in his last lecture he keeps on solving questions, where most others tell some stories or engage time unproductively..." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 6732.0 0.0 0.0 0.0
"good  informative lecture ." 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 12940.0 0.0 0.0 0.0
"a smoooooth lecture indeed" 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 12290.0 0.0 0.0 0.0
"One of my heroes! Hats off Mr.Strang, you inspire a lot of people :)" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8083.0 0.0 0.0 0.0
"1:04:03 he's definitely say drug" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 577.0 0.0 0.0 0.0
"I've learnt Crammers rule , transposing , integration basics, differential basics ......  Am I doing ryt . I still don't know how this can be applied" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6421.0 0.0 0.0 0.0
"13:22
lec starting point" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 413.0 0.0 0.0 0.0
"To treenabalds,

It's because the second derivative of sinθ is -sinθ, it is EXCATLY zero when you plug θ=0.
That is, f''(0)=0.

And for cosθ, the first and third derivatives are EXCATLY zero when you plug θ=0. That is, f'(0) and f'''(0) are zero." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11048.0 0.0 1.0 0.0
"@38:45 why did we count the fix-up cost from just one of the D's. Shouldn't it be twice since we have D and -D in the matrix?" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 1546.0 0.0 1.0 0.0
"""Oh god, come out right here!"" ... ""Thank you, God!"" XD I was dying at those parts of the lecture. Not only does he teach skillfully, he's hilarious too." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 94.0 0.0 0.0 0.0
"P({x,y | 0<x,y<1,(x,y)!=(a,b)}) = 1 - p({x={a,b}) < 1 since p({x={a,b}) > 0 , supposed that p_1 = p({x={a,b}) than p_1 = a in reals such that for all b in reals a < b (which is possible since the real numbers are uncountable infinite) , I'm not quite sure that I expressed this right, but I think its a good resolution of the question asked in 11:10" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 8148.0 0.0 1.0 0.0
"Never using this in real life." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7823.0 0.0 0.0 0.0
"22:30 that's pretty crazy that the probably of a specific point is 0, but the area of the sample space is > 0." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 700.0 0.0 1.0 0.0
"Really useful. Thanks a lot" lWW54ts9Ubo "24. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 8536.0 0.0 0.0 0.0
"Es fácil, no se porque se complican tanto. Gracias por el material, gracias al MIT." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3576.0 0.0 0.0 0.0
"lovely 21:14" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 13887.0 0.0 0.0 0.0
"This man desirves an youtube award!!!!" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 10848.0 0.0 0.0 0.0
"16:45 Another very simple proof that there is no (finite) match: None of the dominoes is a possible ending point, because none of the pairs have matching suffixes." MGqoLm2aAgc "10. Computation History Method" "MIT 18.404J Theory of Computation, Fall 2020" 487.0 0.0 1.0 0.0
"Gauss thought of it because he was born earlier 😂 I died.

Then he said died earlier too. I died again." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3984.0 0.0 0.0 0.0
"The second basis for R^3 is not a basis, since -(1,1,2)+2*(2,2,5)=(3,3,8); i.e., the vectors are not linearly independent." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 10274.0 0.0 1.0 0.0
"no. I meant the points he makes with the chalk all the time for no reason :-)" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14076.0 1.0 0.0 0.0
"Why does this guy always makes points after every word?!" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11849.0 0.0 0.0 0.0
"This is so spectacularly good." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 10724.0 0.0 0.0 0.0
"I have just one question: How 1/2 (2Xo)(2Yo)= 2XoYo=2? If we do 1/2 *2 (XoYo) we are left with XoYo which i don't think is equal to 2 :X " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5533.0 0.0 1.0 0.0
"I REALLY tried to focus on this but I can’t math is just not my thing" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 4935.0 0.0 0.0 0.0
"This is a great lesson. I remember learning this a long time ago; it is all coming back." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10593.0 0.0 0.0 0.0
"So I guess you misunderstood the structure of the courses. They can't assume that you remember the stuff you did in high school so they sort of repeat it in the first units of the courses to build on that." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8729.0 0.0 0.0 1.0
"Multivariable calculus and linear algebra seem to go hand in hand." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7725.0 0.0 0.0 0.0
"@shuffledream I'm pretty sure he meant parallel, but no one bothered to correct him." phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2012.0 0.0 1.0 0.0
"pena que nao entendk ingles kk" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14171.0 0.0 0.0 0.0
"Absolutely well done and definitely keep it up!!! 👍👍👍👍👍👍" AeRwohPuUHQ "22. Gradient Descent: Downhill to a Minimum" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2221.0 0.0 0.0 0.0
"I am afraid that the teacher has mistakenly reversed the elements (2,2) and (2,3).  They are supposed to be -2 and 2 respectively, not 2 and -2. In fact it's 3 * (1, 2, 1) = (3, 6, 3), hence (3, 6, 3) - (3, 8, 1) = (0, -2, 2)." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5060.0 0.0 1.0 0.0
"Great explanation of the trapezoidal rule" jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4226.0 0.0 0.0 0.0
"@22:05 But how do we know B is invertable? I found a proof that does not assume B is invertable:

Suppose we have x such that ABx = lambda * x. Left multiply both sides by B: BABx = lambda * Bx. This shows that Bx is an eigen vector of BA, and its eigen value is lambda." k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1513.0 0.0 1.0 0.0
"I envy MIT students very much!" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5386.0 0.0 0.0 0.0
"I would be very happy if you people add subtitles! It does not have to be in my language. English is fine." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6256.0 0.0 0.0 0.0
"how did Gilbert age so much in the past 3-4 years? I'm worried for him..." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 13211.0 0.0 0.0 0.0
"Thank you professor" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9305.0 0.0 0.0 0.0
"Must say, the students in this course are not up to the mark. People in Asian, East European countries are far ahead compared to their American counterparts. Although, the professor is great and makes every effort to answer their rudimentary questions." eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7727.0 0.0 0.0 0.0
"upvote this!" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14982.0 0.0 0.0 0.0
"Thank you for these videos, they are helping a lot in my class :).
" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9275.0 0.0 0.0 0.0
"That is a FILTHY black board......seriously.....you need better cleaning materials." RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 9894.0 1.0 0.0 0.0
"Kept 1st lecture intro to one minute. Bless this man." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7211.0 0.0 0.0 0.0
"This. is. pure. gold." HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 10981.0 0.0 0.0 0.0
"Bayesian, yes bayesian.." 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 2811.0 0.0 0.0 0.0
"Is there anywhere I can get the problem sets that go along with these lectures?" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6841.0 0.0 1.0 0.0
"He made some nonintuitive things intuitive with just some simple example, love his videos" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4581.0 0.0 0.0 1.0
"Ok. You can touch the tangient point you find the fourt dimension.....:)
" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8050.0 0.0 0.0 0.0
"@anhhuyalex123 it's just the same problem done in a different way... he's setting dA/dx=0 to get the critical point.. just like he did, in the first method he used to solve the problem..." YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1782.0 0.0 0.0 1.0
"Professor Strang = ❤️❤️❤️❤️" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8343.0 0.0 0.0 0.0
"I am binge watching this series .....at the end of each one I tell myself that I will watch just one more episode :) !!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5068.0 0.0 0.0 0.0
"Anyone can help? I need a mathematical, not intuitive, proof... =(
" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2483.0 0.0 1.0 1.0
"Which course is better, this one or the Harvard one ?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 11716.0 0.0 0.0 0.0
"Behold, the god of teaching! Great lecture." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2840.0 0.0 0.0 0.0
"On 4:11, the nullspace vector isn't composed by 5 zeros?" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 8067.0 0.0 1.0 0.0
"Thanks from the bottom of my heart BTW for tese videos." hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9748.0 0.0 0.0 0.0
"For the first time I envy students in MIT. Because they have such genius lectures to attend." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3888.0 0.0 0.0 0.0
"15:00 How to get all possible combinations?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 444.0 0.0 1.0 0.0
Fantastic! QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3739.0 0.0 0.0 0.0
"form is pathetic" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12894.0 0.0 0.0 0.0
"@iDiViNeXx hi is from France" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1883.0 0.0 0.0 0.0
"@allenrobinson2012 Ah.  Well, jokes don't transfer well through text... Sorry about that." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1775.0 0.0 0.0 0.0
"Who disliked this video?
Just give me their names and I'll cut their heads off." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11730.0 0.0 0.0 0.0
"the best lecture i've ever seen..... he's really >>>WOW

In addation to that, he speaks batter than native speakers'." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14665.0 0.0 0.0 0.0
"do the students in mit have only one physics math and chem class a week how do they finish the portions
" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12757.0 0.0 0.0 0.0
"Hahaha, at 24:06, I thought the exact same thing, ""prof, what are you saying??""" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 4416.0 0.0 0.0 0.0
"Respected sir, may god bless you,. You will live for more than 100 years, you are a legend. Love from India ❤️" sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8566.0 0.0 0.0 0.0
外国的学生没中国的聪明。 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15620.0 0.0 0.0 0.0
"great lecture... awesome video... thank you for posting it.... " VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 12989.0 0.0 0.0 0.0
"thanks MIT, i'm from Colombia and i think these classes are very important for me, because i'm studying engineering in the National University of Colombia :)" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14558.0 0.0 0.0 0.0
"""lemme give an example, okay BRILLIANT example"" That ""brilliant"" always gets me " 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 164.0 0.0 0.0 0.0
"As a PhD guy, I can say if you master in this course, actually you master at LOTS of high-level subjects like econometrics, engineering, applied math, chemistry etc. Those ""graduate"" level courses sometimes just repeat the basic ideas from this course and make them hard to understand." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2563.0 0.0 0.0 1.0
"The way he parameterized the directional derivative was really confusing. " 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 10328.0 0.0 0.0 0.0
"13:05 that S looks perfect" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 405.0 0.0 0.0 0.0
"The Green's Theorem is only to work if the curve is closed..." tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9966.0 0.0 1.0 0.0
"I really have to think and imagine a lot in this lecture and I loved it" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5920.0 0.0 0.0 0.0
"42:27 we see Euler again, that guy never stops 😂✨" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1181.0 0.0 0.0 0.0
"Crystal clear explanation. Nice!" gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 3263.0 0.0 0.0 0.0
"I Really Like The Video First fundamental theorem of calculus From Your" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4947.0 0.0 0.0 0.0
"nice class" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 14030.0 0.0 0.0 0.0
"32:08 ""i had a 50/50 chance and life let me down"" LOL" HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 925.0 0.0 0.0 0.0
"37:23 he just gave an idea to DCEU for a superhero ... the invertible man." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1065.0 0.0 0.0 0.0
"I think the nearest distance between Clinton and Monica could be -16cm" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 6059.0 0.0 0.0 0.0
"I'm sure doing the proofs are part of their problem sets and recitation." -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6384.0 0.0 0.0 1.0
"thankyou sir!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14619.0 0.0 0.0 0.0
"@3.33 why must the subspace (the plane) go through the origin?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 1533.0 0.0 1.0 0.0
"I love how he continues to pretend that he just makes up all his examples ad hoc while in the end it always turns out that he prepped all of it in advance. ""Oh, what a great suprise that it worked out so well!!""" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 5749.0 0.0 0.0 0.0
"what was the point of the linear approximation for the GPS example? why not just plug the velocity into the original equation? is it because you save on computation time or something?" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15187.0 0.0 1.0 0.0
"Thank You Prof. David Jerison and Prof. Muller. 
Completed the whole Lecture series just now.
18/4/22" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9051.0 0.0 0.0 0.0
"@genomstic  Why the hell are you taking multivariable calculus in high school" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1848.0 0.0 0.0 0.0
"Oh, hi kermit" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8028.0 0.0 0.0 0.0
"Thanks Mit" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 9624.0 0.0 0.0 0.0
"I just started to think that matrices are magical things" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 5620.0 0.0 0.0 0.0
"@michalchik You're right !" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1946.0 0.0 0.0 0.0
"now i can feel the art of the linear algebra" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14090.0 0.0 0.0 0.0
"37:15 i guess that big time function cannot be found without using Zorn's lemma" asjAc90L8rE "12. Time Complexity" "MIT 18.404J Theory of Computation, Fall 2020" 1058.0 0.0 1.0 0.0
"Thank you MIT, Thank you so much" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9155.0 0.0 0.0 0.0
"where can I find a complete derivation of the formula z=z0 + a(x-x0) + b(y-y0) using parametric equations as he suggested at 8:38? I tried to do what he said but no luck!" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15222.0 0.0 1.0 0.0
"Professor Stang's lectures are best heard at 1.75 speed :)" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 8333.0 0.0 0.0 0.0
"You can find the value 2*y0, when the derivative of 1/x cut the Y exe, by making similar triangles. If the slope reflects a change from y0 to 0 when X changes from x0 to 2*x0 , so it should change from y0 to 2*y0 when X changes from x0 to 0. It's easiest to see in a graph.

The notation f' is from Lagrange, not Newton. I love MITOCW. Thanks!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12189.0 0.0 0.0 1.0
"Lectures are super useful.  Are there any answers to the assignments if I ma not enrolled to the MIT?" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7306.0 0.0 0.0 0.0
"21:00 Inverse Matrix" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 669.0 0.0 1.0 0.0
"Very nice." ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11220.0 0.0 0.0 0.0
"Dr. Strang is an MIT math legend forever." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 3506.0 0.0 0.0 0.0
"buen curso si señor" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12565.0 0.0 0.0 0.0
"Thanks prof." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 9756.0 0.0 0.0 0.0
"the applause was too short!




or maybe it's because I watched this at 1.5x--and dared to venture 2x for parts of this last lecture in my rush to finish the course :D" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 14659.0 0.0 0.0 0.0
"2:47 the straightest free-hand coordinate system I've ever seen!" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 872.0 0.0 0.0 0.0
"Thanks, teacher , and MIT, it help me a lot to understand Linear Algebra" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 9850.0 0.0 0.0 0.0
"i stop at 24:00 so i remember next time dont mind my comment" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 13462.0 0.0 0.0 0.0
"This is a great introduction to vector fields. When taught abstractly, it can be hard to visualise, so even the use of elementary examples makes a difference." xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10591.0 0.0 0.0 1.0
"I like the way he teaches.  Many years ago when I took Single Variable Calculus, a high school classmate and I used to sit in the back of class and make up short cuts to confuse the professor.  We both aced the class." YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5686.0 0.0 0.0 0.0
"Crystal clear! Thank you very much for sharing it" wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3265.0 0.0 0.0 0.0
"How do you know how ""smart"" they are?  Try to get a scholarship-that is the existing solution to wealth disparity, not a wish!  There are great professors everywhere, but I agree this one is particularly good.  Best of luck!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4856.0 0.0 0.0 0.0
"Lol. Me too
" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7407.0 0.0 0.0 0.0
"Take a bow Sir. You are a Gem of gems." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9006.0 0.0 0.0 0.0
"Is this entire course a combination of calc 1 and 2? Or just calc 1. I see the next course is multi-variable which is often known as calc 3." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6866.0 0.0 1.0 0.0
"Wow, all I was ever taught was the shortcut.." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12065.0 0.0 0.0 0.0
"I am happy that I could learn from MIT... Thank you sir" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5102.0 0.0 0.0 0.0
"31:30 the more meaningful ways of answering, continue with implicit differentiation
45:20 related rates" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 912.0 0.0 0.0 0.0
"Master class in presenting complex concepts -- state by state." IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 7601.0 0.0 0.0 0.0
"""Murderers...cheaters on quizzes"" - 17:41" 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 90.0 0.0 0.0 0.0
"Spherical cap of radius r and height h: pi*(h^2)*(3r-h)/3. Radius r is the radius of the sphere, not of the cap. Here r=1 and h=1-1/sqrt(2) which gives the answer. My HP-50g gives it as (8-5*sqrt(2))*pi/12 which is the same that was on the lecture. Personally I don't like roots in denominators in answers." RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8868.0 0.0 0.0 0.0
"I don't think I will ever get an admission from MIT :) but being able to listen to lectures from my dream school online for free is truly awesome! Thank you for these wonderful lectures." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5331.0 0.0 0.0 0.0
"Index for you guys
5:46 Introduction to the course
9:50 beginning of first class
25:50 third axiom
42:15 discrete uniform law example" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 6709.0 0.0 0.0 0.0
"Denis Auroux's focusing this lecture on physics is important but there's too much to say in too short of time.
That he mentioned the Maxwell Equations is important. His focus on classical mechanics is good. What he left out of his discussion of square matrices multiploed into the column vector was the concept of Eigen Value and Eigen Vector was that in 1925 Heisenberg for square matrices of infinite order created quantum mechanics" BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 3348.0 0.0 0.0 0.0
"I hope ona day I could be part of the MIT" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5588.0 0.0 0.0 0.0
"One of these days I'm going to invent an AI real time internet fed algorithm that detects gaps in the logical path of a learning process, both from a student and from a learning resource standpoints. Just... let me finish these videos first." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8102.0 0.0 0.0 0.0
"so...how to find the proper ""shift""?" d32WV1rKoVk "12. Computing Eigenvalues and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14355.0 0.0 1.0 0.0
"his drawings are awesome..." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13162.0 0.0 0.0 0.0
"BTW, the three error is called ""imprinting"". Because of the 3 in the numerator, it was imprinted in the solution which was now imprinted into the checking process. As a math tutor, this happens all the time in my lessons. There are about 3 ways to avoid or resolve imprinting. I usually cover this in my first private lesson of one on one." HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2807.0 0.0 0.0 0.0
a jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12275.0 0.0 0.0 0.0
"Thank you !!!!" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9092.0 0.0 0.0 0.0
"true what ""1966avc"" said, you helped us r helped me a lot. Thanks for your contribution to education" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14960.0 0.0 0.0 0.0
"God he is good !! but if you are having trouble visualizing the 9D space (lol) check out the 3Blue1Brown series on Linear Algebra." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 4094.0 0.0 0.0 1.0
"Where does he prove that sin(x)/x= 1?
" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11677.0 0.0 1.0 0.0
"from lecture 1 until here. Thanks MIT" sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12901.0 0.0 0.0 0.0
"03:41 ah-ha! the so-called traffic light vector" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 290.0 0.0 0.0 0.0
"At the beggining of the lecture prof. Miller told an excellent joke. I suppose the joke was good  only for mathematicians to laugh at. From the resonse it seems that the students are far from being mathemticians , because nobody laughed :)" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2725.0 0.0 0.0 0.0
"10 people were 10 years old" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 332.0 0.0 0.0 0.0
"Excellent professor and lectures!! Thank you!" mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 3669.0 0.0 0.0 0.0
"very handsome man with a nice British accent. I hope he doesn't pulverize me on my linear algebra final." 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15013.0 0.0 0.0 0.0
"I dont undertand why the eigenvectors are [lamba_1  1] and [lamba_2 1] at 49:19...
since it is NOT true that ((1 - lamba) * (lamba)) + 1 is lamba^2 - lamba - 1 ... or it is? or what is happening? " 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 5372.0 0.0 1.0 0.0
"The GOAT" cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9964.0 0.0 0.0 0.0
https://www.youtube.com/watch?v=Ik7beS1YbnM VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 13272.0 0.0 0.0 0.0
"yeah mr.white, yeah science" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 15468.0 0.0 0.0 0.0
"대칭 행렬의 경우 피봇들의 부호와 고유값의 부호가 같다." UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 15675.0 0.0 0.0 0.0
"I don't even understand English so what am I doing here lol" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5299.0 0.0 0.0 0.0
"What a cute professor
" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 11401.0 0.0 0.0 0.0
"I have a question.
What was that ""Junk"" part?
How did he get there?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5507.0 0.0 0.0 0.0
"Best handwriting includes writing everything in capital letters! " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2860.0 0.0 0.0 0.0
GREECE 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3977.0 0.0 0.0 0.0
"high quality blackboard action going on" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13157.0 1.0 0.0 0.0
"@slimmerikje thanks" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2020.0 0.0 0.0 0.0
"Understood after long time why and hows of Least squares in Regression ML" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 11121.0 0.0 0.0 0.0
"2,3,8,9,10,11,12,13,15,16,25 - chapters needed for economists" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 613.0 0.0 0.0 0.0
"Wow, just wow." 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12071.0 0.0 0.0 0.0
"+Frantisek Dracek He's not assuming that r is constant. He uses the formula for an area element for a curve r(theta) in polar coordinates.

What he says is when you rewrite Kepler's second law using the formula for area in polar coordinates you get conservation of angular momentum." BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 252.0 0.0 0.0 0.0
"@Arcanist4life also, just because some people didnt have some chapters on the school books, doesnt make them stupid :P" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1592.0 0.0 0.0 0.0
"So the j term you always make the negative, correct?" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8792.0 0.0 1.0 0.0
"@MatteoPascal for completeness, how would you prove that sin x < x < tan x in a small interval containing 0?" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1671.0 0.0 1.0 0.0
"thank you MIT for such a good course" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14482.0 0.0 0.0 0.0
"Wait, in the needle problem, you're calculating the probability for the needle to crosse only one of the lines (the top one).  But in your paper clip experiment, you counted all those that intersected both lines.  isn't that a flaw?  How would you count for the needle intersecting the other line which would be (d-x) away from the center of the needle.  Do we do l/2sin(theta)>=(d-x)?" CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 11262.0 0.0 1.0 0.0
"At 25:00  Mr. Stang wrote (row 1) transpose x equals 0, but I don't really understand.
I was thinking about to remove the ""transpose"" thing, and I was sooo confused." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2622.0 0.0 1.0 0.0
"Thanks MIT" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9594.0 0.0 0.0 0.0
"Ola piolin" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8055.0 0.0 0.0 0.0
"I'm sorry, but I cannot find the accompanying website, MITOCW. Love going through the problem sets; some assignments also." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 6379.0 0.0 0.0 1.0
"Letting *F* be the velocity field? Oh come on, can't we just use *v* ?" wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 7342.0 0.0 1.0 0.0
"how could v = [v1 v2 v3 v4]' dimension equals to 3?? in 31:00" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 13210.0 0.0 1.0 0.0
"Am i supposed to do a problem set per lecture ?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 2345.0 0.0 1.0 0.0
"MIT cheap blackboard lol" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 7514.0 1.0 0.0 0.0
*CREAK* FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 232.0 0.0 0.0 0.0
"Dr. Strang, I owe you my livelihood. I would never have gotten the opportunities in life that I've had without your lectures and I'm excited to go through this playlist to keep improving. <3" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3513.0 0.0 0.0 0.0
"Much better thant our teacher....." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 7718.0 0.0 0.0 0.0
"This guy gets it. Intuition is a must. Its actually the first time I saw a teacher teaching a subject the exact way I would." CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 10508.0 0.0 0.0 0.0
"Very fantastic lecture 👍" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11171.0 0.0 0.0 0.0
"I love how at 23:28, he gives the students that cheeky grin right before doing his erasing trick" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5745.0 1.0 0.0 0.0
"Very Good Content !!!!!!!

🤙👌💪

👏👏👏👏👏👏" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11155.0 0.0 0.0 0.0
"Thank u Prof." MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9069.0 0.0 0.0 0.0
"any recommended books on understanding the mathematical basis for statistics as covered in this lecture?" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 12379.0 0.0 1.0 0.0
"I really love how he pronounces ""cookbook"". I swear I've even started reading my textbook using his accent in my head." l4NoMKEHQwM "11. Derived Distributions (ctd.); Covariance" "6.041 Probabilistic Systems Analysis and Applied Probability" 5929.0 0.0 0.0 0.0
"This is a work of art!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10606.0 0.0 0.0 0.0
"can anybody explain why he place the solid in z plane with 0 x and 0 y,
it is the plane where direction of force is directed." RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12599.0 0.0 1.0 0.0
"nice lec" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 14040.0 0.0 0.0 0.0
"I don't care for this professor. I find him to be too boring. I enjoy math, but this man makes me want to fall asleep." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5298.0 0.0 0.0 0.0
"God bless you, Professor Strang." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 4088.0 0.0 0.0 0.0
"What a big chalk!!!" hwDRfkPSXng "Lecture 32: ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11393.0 1.0 0.0 0.0
"Took 18.06 in 1992 and he taught it.  Great stuff, and an awesome professor." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11070.0 0.0 0.0 0.0
"Isn't CLT about the distribution of your estimated mean being normal (rather than calculating the mean from a very large sample)? i.e. calculate your mean 1000 times and those 1000 means will follow a normal distribution" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 6891.0 0.0 1.0 0.0
"Man....MIT student's are lucky to have such professors ..." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7592.0 0.0 0.0 0.0
"Finished in COVID 19 July Quarantine 2020.
Many thanks to  Prof. David Jerison, MIT and OCW" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3810.0 0.0 0.0 0.0
"At last. my dream. I'm studying at MIT! Thanks OCW!" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2715.0 0.0 0.0 0.0
"Here I am trying to learn English, with a french accent teacher who teach statistics. What is the possibility I am be successful?" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 4672.0 0.0 0.0 0.0
"the concept of total differential sounds a little abstract initially. I finally got a better understanding after the whole lecture, plus the aid of Wikipedia. 

""Calculation of the total derivative of f with respect to t  does not assume that the other arguments are constant while t varies ... """ 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14678.0 0.0 0.0 0.0
"How young are these students? I'm 17 and we've started integrating already." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4910.0 0.0 0.0 0.0
"laughter @ 32:46" jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13760.0 0.0 0.0 0.0
"Really apreciate this lectures (on any subject) and your effort. Thank you very much. Is there any lecture, in other subject, which makes reference to hyperbolic functions and inverse functions?" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8506.0 0.0 1.0 0.0
"能听Gilbert Strang教授的课是我的荣幸！" AdTvkFsqcDc "16. Derivatives of Inverse and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15654.0 0.0 0.0 0.0
"they tend to forget its MIT... these guys aren't dumb to teach students beginner calc... or you could think of it as a refresher... " 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14787.0 0.0 0.0 0.0
"this helps alot.. thanks..." CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14847.0 0.0 0.0 0.0
"Bruh our university has his book as a recommendation lol" TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 2952.0 0.0 0.0 0.0
"Really got the points!
First time in my life I have completed a lecture on math and also learned multiple new things!
All concepts got cleared.
Thank you Gilbert Strang for introducing me to LA.
Respect++;" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8514.0 0.0 0.0 0.0
"Things we are not supposed to know:
1- The Fight Club
2- Sex
3- Determinants (25:50)" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10446.0 0.0 0.0 0.0
"yes, finally i understand" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15486.0 0.0 0.0 0.0
"44:40 I am lost here.
Especially because EA = I ,  then E * I = E. The math I've been learning for years is confusing me.
Is the identity matrix like a 1? For example, 3 * 1 = 3. So 3 is the E and I is the 1?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1240.0 0.0 1.0 0.0
"I know physics and kepler's law， but I never think it like this. thank you very much！" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5637.0 0.0 0.0 0.0
"Is this really MIT?" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 6877.0 0.0 0.0 0.0
"Hi professor and online collegueas. I'm a control engineering student, so Linear Algebra is the essential of my field of study. Despite I've taken a linear algebra course before and even sophisticated discussions in control systems, I never truly understood until now why it is better to think using columns instead of using rows. But now it's totally clear in my mind, so thank you very much, professor Gilbert. I'm anxious for the next classes." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 4714.0 0.0 0.0 0.0
"39:03 typo in subtitle, “only r genuine independent equations...” should be right, not “are” in place of “r”. Thanks a lot!!" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1091.0 0.0 1.0 0.0
(-1)(1,1,2)+2(2,2,5)=(3,3,8). nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 214.0 0.0 0.0 0.0
"Anyone knows why {fn=x^n } is linearly independent ?" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 2508.0 0.0 1.0 0.0
"Wow...looks like he aged 30 years in the last 10..." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 12092.0 0.0 0.0 0.0
32:57 VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 946.0 0.0 0.0 0.0
"I really enjoyed these lessons. If you tell a European student that during an entire linear algebra course only once did the professor write the word PROOF on the blackboard, he will never believe you!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5914.0 0.0 0.0 1.0
"hahaha, dau lai vo do thoi, phai o do thoi :D:D:D:D thuong de xap dat roi, deo cho bon may loi dung :D do mat day." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 13051.0 1.0 0.0 0.0
"jmaginary is totally a word." Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13724.0 0.0 0.0 0.0
"@hypnoticpoisons I think x is limited to numbers between 0 and 1" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 1878.0 0.0 0.0 0.0
"I learn more about calculus from physics lessons than from this calculus class.   That's disturbing in the sense that understanding calculus is infinitely easier when applied to physical phenomena which invariably involve it.

Why..  really why.. is mathematics taught in such an amorphous way?
The curve of ""something"" doesn't really ground me in any way..  I hate that.

Calculus teachers of the world, please interpolate REAL WORLD understanding  into math.  You will encounter far less confusion." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5647.0 0.0 0.0 0.0
"he loved and  married to Linear Algebra or Linear Algebra is his first wife. Great person , god bless him" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13108.0 0.0 0.0 0.0
"ssssshhhh... Ok?" ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14391.0 0.0 0.0 0.0
i J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13320.0 0.0 0.0 0.0
"at 16:28 why did delta v go to 0 with delta x ?" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12415.0 0.0 1.0 0.0
"20:14 Should be 2n - 3" hDwkKrWqdZE "3. Forbidding a subgraph II: complete bipartite subgraph" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 646.0 0.0 1.0 0.0
"universe sent him to teach LA" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14980.0 0.0 0.0 0.0
"cool mit" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12678.0 0.0 0.0 0.0
"Thank you so much.👌" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 9419.0 0.0 0.0 0.0
"A power series function becomes a logarithmic function by the diagonalisation.." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2146.0 0.0 0.0 0.0
"Prof. Strang really rushed the topic of eigenvalue and eigenvector.
I understood every lecture in this series except this.
I think I will have to check Khan Academy." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 8309.0 0.0 0.0 0.0
"I like the way he makes ""measures"" seem easy to understand" X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 5685.0 0.0 0.0 0.0
"he is a legend
thanks MIT" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 13089.0 0.0 0.0 0.0
"After three or more years of studying linear algebra, I finally understood the fundamental meaning of SVD ... really took me a long long way to get here... Thank you Dr. Strang." TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 2259.0 0.0 0.0 0.0
"21:47 those blackboards are very nice actually.
I also watched the Stanford physics lectures (by professor Leonard Susskind), and they also have very nice blackboards (whiteboards actually).
I found that top universities always have excellent blackboards, because those good professors always prefer to do the demonstrations and calculations by themselves on the board.

My uni was very mediocre and so were the teachers. after a whole semester they seldom wrote anything on the board, all they do is repeating what's on the textbook and playing the powerpoint with most calculations and results already written on it, 
One exception was my Mathematical Physics professor, he was a brilliant guy and he always do the demonstrations on the board, and during classes we can often hear him complain about the size of the board and the poor quality of the chalk :)" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 685.0 1.0 0.0 0.0
"Is it me or Gilbert Strang's lecture delivery is ""similar"" to Frank Underwood's dialogue delivery ?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 6788.0 0.0 0.0 0.0
"How would 1/2 lead to Fractional Math? " kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4907.0 0.0 0.0 0.0
"How admirably clear." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 4799.0 0.0 0.0 0.0
"My final course in college. Loved statistics and can be used in real life after college.  Level of significance 3.14, mode. mean  sample population chi square.  love it This professor seems really good at teaching and keeping the class fun" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7753.0 0.0 0.0 0.0
"Professor Strang thank you for explaining and analyzing Definitions and Inequalities  from probability and statistics. The pictures and examples really help me to understand the quality of this lecture." nrDkb2MAwSA "20. Definitions and Inequalities" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8367.0 0.0 0.0 1.0
"The notes made no sense. This lecture made it seem so simple" _CdoRiNSrqI "Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10205.0 0.0 0.0 0.0
"Anyone know how to find the null space using sagemath please?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 2502.0 0.0 1.0 0.0
"the confusion arises from leibniz notation where d^2/dx^2 would represent the second derivative.  still pretty dumb question though aha" TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14679.0 0.0 1.0 0.0
"48:47 Random burp" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1297.0 0.0 0.0 0.0
"Playing this at 2" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8195.0 0.0 0.0 0.0
"Why students do not participate in the lecture?
MIT is probably the best technical university, but the way of teaching which lecturer shows isn't good. Maths requires talking about the problem and solving it together. The lecturer should ask student what to do in some examples.
It's the the best way to remember most from the lecture.
 
Greetings from  Materials Engineering faculty from Warsaw University of Technology 

" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11913.0 0.0 0.0 1.0
"very nice best taecher" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15028.0 0.0 0.0 0.0
"Anyone noticed that there were no students (at least in the front 6 rows) in this lecture?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 2510.0 1.0 0.0 0.0
"i guessed the 1 3 before he put it up! 
                       2 6" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13385.0 0.0 0.0 0.0
"you do have him
" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15502.0 0.0 0.0 0.0
"I am crying right now. I am an economics student and I have been waiting for MIT OCW to release lectures on Real Analysis for so long. My whole mathematical economics training has been due to MIT OCW from calculus, linear algebra, differential equations to statistics and ML. Thank you MIT." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 5080.0 0.0 0.0 0.0
"How did people learn linear algebra before Gilbert was born?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4840.0 0.0 0.0 0.0
"Thanks for everything ❤" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9683.0 0.0 0.0 0.0
"what happened to the sound this time? loool more echo this time
 IM absolutely loving studying this way its soooo better than reading GODDAMN books! 
he has great proficiency.
but dont forget to practice problems on the topics u go thru it helps retain the lecture ideas" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 15142.0 1.0 0.0 1.0
"sets of :size is equal ; when 2 or more  sets   equal a quality  in one or more of the  *number logic strategies to arrive at a sum of &that sum ,which can be any defined by  theory that hold the axioms of math * at a guess" 9_xG0AGRa-w "Lecture 2: Cantor's Theory of Cardinality (Size)" "MIT 18.100A Real Analysis, Fall 2020" 14288.0 0.0 0.0 0.0
"Timestamps and Summary for Lecture 3: Quotient Spaces, the Baire Category Theorem and the Uniform Boundedness Theorem

0:00 - Recap of Lecture 2
Last lecture: linear operators between normed vector spaces are continuous if and only if they are bounded. The space of bounded operators between two such NVS's itself forms an NVS, under the operator norm. When the target is a Banach space, this space of bounded operators also becomes Banach: this is a way to identify new Banach spaces from existing ones, by considering all bounded operators into them. 

0:59 - Subspaces
A subspace of a given vector space is internally closed under addition and scaling (linear combinations). Theorem: a subspace W of a Banach space V is itself Banach if and only if it is a closed subspace of V with respect to the metric induced by the norm. Closure amounts to showing that W contains all of its limit points (every convergent sequence in W has its limit in W). We can take any sequence in W; by hypothesis (completeness) it is Cauchy and converges in W. Conversely, if the subspace is closed, we can take a Cauchy sequence in W -- regarding it as a sequence in the ambient Banach space V, it converges to an element in W by closure. This shows every Cauchy sequence in W converges in W, so W is Banach. 

5:14 - Quotient Spaces
Another crucial way to form new spaces from old by passing to substructures involves the process of taking quotients. Given a subspace W of V, introduce (and verify) an equivalence relation on vectors in V by identifying two vectors together if their difference lies in W. This allows us to form the quotient set V/W under that equivalence relation; furthermore, it naturally inherits the operations from V and becomes a vector space in its own right. 

11:31 - From Seminorms to Norms
Recall that a seminorm satisfies homogeneity and the triangle inequality, but not necessarily definiteness -- consider the norm of the derivative of a function; it exhibits the former two properties but resolves to zero on constant functions. Theorem: a seminorm on a vector space descends to a norm on its quotient taken with the subspace of all vectors on which the seminorm is zero. Intuitively: the presence of vectors with seminorm zero represent an ""obstruction"" of the seminorm from becoming a norm. By collapsing the obstruction in the quotient, we obtain a true norm. 

23:11 - Baire Category Theorem
A cornerstone of general topology with vital applications in analysis. The version given here states that if a complete metric space can be expressed as the countable union of closed sets, then at least one of the closed sets contains an open ball (eq. has an interior point/nonempty interior). It can be reformulated to state that the countable intersection of open, dense sets in a complete metric space remains dense. (Note: a second result, not as relevant to functional analysis, states that the same holds true for locally compact regular spaces. This is especially important in the study of locally compact Hausdorff spaces. The version proven here requires some form of the Axiom of Choice; over ZF it turns out equivalent to a weaker form of Choice that is sufficient to build up most of real analysis). 

50:39 - The Uniform Boundedness Theorem
Our first major functional analysis result: it states that a sequence of pointwise-bounded operators on a Banach space is also bounded uniformly. More precisely, a sequence of linear operators from a Banach space to a normed vector space is bounded uniformly in the operator norm as soon as each individual operator is bounded. By showing that each of these operators have bounds that might vary with each point, this theorem claims that a bound can be chosen for all operators in the sequence that is independent of the point, and can be applied globally." 58B5dEJReQ8 "Lecture 3: Quotient Spaces, the Baire Category Theorem and the Uniform Boundedness Theorem" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 11015.0 0.0 0.0 0.0
"I'm amazed these students had not seen the law of cosines. It seems that they are not a big deal after all" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6305.0 0.0 0.0 0.0
"I Really Like The Video Matrices; inverse matrices From Your" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4988.0 0.0 0.0 0.0
"I don't understand 11:25 why A square can be written in the way on the blackboard. I think A^2 should be (S Lambda S^-1)^T   (S Lambda S^-1), the result differs from the one on the blackboard. Could someone explain this?" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 5337.0 0.0 1.0 0.0
"This man is a legend. Thanks for everything." k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10857.0 0.0 0.0 0.0
"@Phughy I know people your age who were doing calc 3 and diffy q's, someone's dick is always bigger." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1701.0 0.0 0.0 0.0
"this is a great lecture. the way he handled the law of cosines off the cuff was brilliant. " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14850.0 0.0 0.0 0.0
"best det class i ever had." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 12537.0 0.0 0.0 0.0
"Did anyone else have to playback speed at .25x??😂😂😂😂" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3368.0 0.0 0.0 0.0
Legend srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 7317.0 0.0 0.0 0.0
"31:53 - my first ""ahaaaaa"" moment...so excited to move forward with this course, just brilliant!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 916.0 0.0 0.0 0.0
"What an elegant way of lecturing. Thank you, sir." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 11455.0 0.0 0.0 0.0
"You could say that about a lot of math, the trick isn't usually in doing the algebra. It's understanding the relationships between numbers and equations. " kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12200.0 0.0 0.0 1.0
"@zikriya25 This was recorded using professional equipment (and with a lot of post-processing). Not the kind of camera you can just bring to lecture and film your professor with." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2082.0 1.0 0.0 0.0
"Thank goodness for browser extensions. Setting this video to Mono makes it much easier to listen to. :D" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 9067.0 0.0 0.0 0.0
"Love your lectures. Thank you Sir" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 7473.0 0.0 0.0 0.0
"All mathematicians told that trisecting angles are impossible! I am Taha M. Muhammad telling ""It is possible!"". All can look at my trisecting invention ""Taha's Geometry Theory"" Step 1 - step 2- step 3. May be you have no idea about steps. Shortly, all of professors even honorable Einstein wanted to think to divide an angle directly into 3, but my theory is you are at ground level then think up tp one step on stairs, then go to and relax at step 3. YouTube is showing you how I trisect angles(above 0 to 360) degrees. Thank you for Universalities and math professionals who ignored my Qs and e-mails about trisecting. I thing may age is 76, poor, no job, and not famous then told ""Who is this needs to trisect angles and Einstein did no do it!""" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 2299.0 0.0 0.0 0.0
"what textbook did they use?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15183.0 0.0 0.0 0.0
"Went over my head. 
I have to rewatch." 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 11377.0 0.0 0.0 0.0
"Diagonal is king" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3363.0 0.0 0.0 0.0
"I am overjoyed by this lecture!! A beautiful system of linear (in)dependencies." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5129.0 0.0 0.0 0.0
"can someone please explain the ending statements he made about the second property" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 12626.0 0.0 1.0 0.0
"I’m so surprise. This should be a AP high school class. MIT student should be taking Linear Algebra and ODE first year." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7116.0 0.0 0.0 0.0
"funny guy" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12912.0 0.0 0.0 0.0
"Thank you ( ^ _ ^ )" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9094.0 0.0 0.0 0.0
"This professor is a pure legend" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 10897.0 0.0 0.0 0.0
Brilliant! lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 2938.0 0.0 0.0 0.0
"The lectures on backpropagation is ok, need the textbook referenced." lZrIPRnoGQQ "27. Backpropagation: Find Partial Derivatives" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10173.0 0.0 0.0 0.0
"by definition a function cannot produce 2 y's for a given x. so, equation for unit circle is not a function but both y=sqroot(1-x^2) or y=-sqroot(1-x^2) are." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12580.0 0.0 1.0 0.0
"what is the average mark for MIT students (if you know specifically calc. courses great)?" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15162.0 0.0 0.0 0.0
"Could we have the SGD convergence proof by Prof. Sra.
I was expecting that to be covered in Lec - 27 but due to lack of time, it was covered in subsequent lectures which weren't posted online.
Thank You" p-bXJIa7QVI "Lecture 30: Completing a Rank-One Matrix, Circulants!" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3243.0 0.0 1.0 0.0
"That's how good these students are, because I happen to know that there is an audience." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9933.0 0.0 0.0 0.0
"Thanks for the lecture series! Lecturers having to look at notes is bizarre to me, is it a common thing at MIT / US Universities?" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 9714.0 0.0 0.0 0.0
"Thank You MIT really appreciate what you doing." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9050.0 0.0 0.0 0.0
"Lecture 1: Dot Product
Lecture 2: Determinants
Lecture 3: Matrices
Lecture 4: Square Systems
Lecture 5: Parametric Equations
Lecture 6: Kepler's Second Law
Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds)
Lecture 8: Partial Derivatives
Lecture 9: Max-Min and Least Squares
Lecture 10: Second Derivative Test
Lecture 11: Chain Rule
Lecture 12: Gradient
Lecture 13: Lagrange Multipliers
Lecture 14: Non-Independent Variables
Lecture 15: Partial Differential Equations
Lecture 16: Double Integrals
Lecture 17: Polar Coordinates
Lecture 18: Change of Variables
Lecture 19: Vector Fields
Lecture 20: Path Independence
Lecture 21: Gradient Fields
Lecture 22: Green's Theorem
Lecture 23: Flux
Lecture 24: Simply Connected Regions
Lecture 25: Triple Integrals
Lecture 26: Spherical Coordinates
Lecture 27: Vector Fields in 3D
Lecture 28: Divergence Theorem
Lecture 29: Divergence Theorem (cont.)
Lecture 30: Line Integrals
Lecture 31: Stokes' Theorem
Lecture 32: Stokes' Theorem (cont.)
Lecture 33: Maxwell's Equations
Lecture 34: Final Review
Lecture 35: Final Review (cont.)" WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7275.0 0.0 0.0 0.0
"Great for reviewing!! Thanks for posting these leactures!" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4228.0 0.0 0.0 0.0
"All mistakes are fixed soon. What's the problem?  His explanation is clear" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2301.0 0.0 0.0 0.0
"I can see why sinx/x =1 as x -->0 and  d sinx/dx = cosx  until now. Thanks." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5200.0 0.0 0.0 0.0
"Just finished this course, thank you, Prof Dennis Auroux and MIT Opencourseware😊" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7177.0 0.0 0.0 0.0
"Thanks Prof. David Jerison and off course MIT and American society for this amazing science dissemination!!! The American society formed by the founding fathers is an example of freedom for humanity... thank you.. I love you.." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9630.0 0.0 0.0 0.0
"after going to my regular lecture, i watch MIT's and think- why do i waste my time going to mine" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12308.0 0.0 0.0 0.0
"Why not Leipzig continuous and just bounded?" 78vN4sO7FVU "Lecture 2: Bounded Linear Operators" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 11899.0 0.0 1.0 0.0
FINALLY LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 3721.0 0.0 0.0 0.0
@0:56 Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1493.0 0.0 0.0 0.0
"43:20
""I see you guys are having fun""
I guess he was thinking something like ""we'll see who has fun at the exam""" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 1202.0 0.0 0.0 0.0
"40:41 why empty again?" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1133.0 0.0 1.0 0.0
"Most boring mti class" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7696.0 0.0 0.0 0.0
"Didn't know 18.06 existed for centuries lol. The exam from year zero." HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 3396.0 0.0 0.0 0.0
"professor Strang you are excellent. Thanks a lot to you and MIT for these lectures and to all the supporters of OCW." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 14218.0 0.0 0.0 0.0
"positive definite matrix judgement is very useful and the details are well explained" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 14202.0 0.0 0.0 0.0
"It makes me a little bit sad he has grown this old. I still want him to be teaching with that much energy and patience as we see him teach the class of 2005" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6975.0 0.0 0.0 0.0
"Ok ... 7 is a lucky number ... :D" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8039.0 0.0 0.0 0.0
"truly a great intro to statistics. by the way, the variance estimator of gaussian is a biased one, I think [1/(N-1)] ∑(xi - µ)^2 would be a better choice" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 14961.0 0.0 1.0 0.0
GREAT QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3974.0 0.0 0.0 0.0
"I loved subspaces more than spaces." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 5857.0 0.0 0.0 0.0
"Hi everyone! Is it enough to watch video lectures, or should I read his textbook too? I found only shorten version with several chapters out. Is it critical to read the textbook too?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 4709.0 0.0 1.0 0.0
"Great lecture!" IycOPFmEQk8 "5. CF Pumping Lemma, Turing Machines" "MIT 18.404J Theory of Computation, Fall 2020" 4261.0 0.0 0.0 0.0
"He is the best teacher i've ever had.  How can i get in touch with him?  Please!!! Thank you so much." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 4547.0 0.0 0.0 0.0
"This guy is a beautiful example of how much value is added to a simple lecture, when teh lecturer knows his subject deeply and apprecaite what it is going to be used for at higher levels. He is doing an excellent job conveying the basics while teaching the students how he thinks. This is going to drive the students that just want to know how to solve the problem nuts, and be a boon in the long run for the really bright and intuitively deep students. I have never seen matrices taught with such love. I say this as a teacher that teaches basic matrix math." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10513.0 0.0 0.0 1.0
"""baby example""" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 146.0 0.0 0.0 0.0
"40:51
No pun intended?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 1139.0 0.0 0.0 0.0
"This lecturer is absolutely amazing." gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 10837.0 0.0 0.0 0.0
"I love his course and book about Linear Algebra.Thanks very much" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5739.0 0.0 0.0 0.0
"@zobazoba69 Because this is single variable calculus, not algebra. 
" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2085.0 0.0 1.0 0.0
"@gavilanch I´m glad they were made to be found! MIT rocks, more should follow their example!" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 1846.0 0.0 0.0 0.0
"Love your name." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 7474.0 0.0 0.0 0.0
"The two dimensional sound channel matrix has only one independent vector. Bad one." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 10307.0 0.0 1.0 0.0
"great professor. thank you mit for this classes." UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13000.0 0.0 0.0 0.0
"@Danielzinho020
That's really helpful daniel.
Please enlighten us some more..." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1613.0 0.0 0.0 0.0
"Love this man, thanks MIT for looking out for us!" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7461.0 0.0 0.0 0.0
"Finally someone who can explain image/range/column space clearly!!!  " 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 3776.0 0.0 0.0 0.0
"Professor Strang this lecture explains  in great detail Clusters in Graphs and how Eigenvectors  determine Clusters. The role of Spectral Clustering and it's start with the Laplacian Matrix. Thanks to MIT for all these fantastic lectures." cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8372.0 0.0 0.0 1.0
"Would any one please explain what did the professor mean between 13:13 and 13:44?" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12004.0 0.0 1.0 0.0
"if this professor's class would be a column vector, it will definitely be linearly independent of all other linear algebra classes. He squeezes in new and interesting stuff that is not in the other vectors" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13543.0 0.0 0.0 0.0
"This is more of a revision of Linear Algebra and Multivariate Calculus, for the actual contenton PCA, go to lecture 20 here
https://www.youtube.com/watch?v=a1ZCeFpeW0o" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 10691.0 0.0 0.0 0.0
"Excuse me, why the camera didn't follow Strang?" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 3700.0 1.0 0.0 0.0
"40:00 review needed" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 1121.0 0.0 0.0 0.0
"thank u sir u are the best, but i didn't understand the last problem :(" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14460.0 0.0 0.0 0.0
"yes. wtf is going on? it's kinda creepy." XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15488.0 0.0 0.0 0.0
breathtaking 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 12554.0 0.0 0.0 0.0
"Shout out to MIT for using subs instead of canceling class" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8656.0 0.0 0.0 0.0
"Please watch and subscribe if like students teach Calculus on muffin https://www.youtube.com/watch?v=7BhVwnQsEoE&list=PLmxUsPaiXHyya11kxPHGacRB0JSs0bEMq" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8217.0 0.0 0.0 0.0
"28:00 quite mind blowing haha" BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 830.0 0.0 0.0 0.0
"I love you" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 5845.0 0.0 0.0 0.0
"Professor did not finished, but students has started stand-up. Bad students!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8392.0 0.0 0.0 0.0
"the puzzle is really good!" Tx7zzD4aeiA "20. Central Limit Theorem" "6.041 Probabilistic Systems Analysis and Applied Probability" 14735.0 0.0 0.0 0.0
"*They are enjoying it more then netflix*" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 241.0 0.0 0.0 0.0
"Great lecturer!" phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4300.0 0.0 0.0 0.0
"Most interesting linear algebra lecture ever!! It's very easy to understand even for us chemistry students" Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7698.0 0.0 0.0 0.0
"Nasıl bu kadar iyi öğretebiliyorsunuz bilmiyorum ama bir saniye bile dikkatim dağılmıyor. Bütün dönem boyunca birleştiremediğim parçaları 2 videoda anlayıp 'nasıl yaniiiiiiiii!' diye bağırdım. Thank you Sir you are the best :))" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7807.0 0.0 0.0 0.0
"After the first lecture's lopsided assault on my auditory sensory apparatus, this lecture is like an eargasm. RELIEF!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2256.0 0.0 0.0 0.0
"Thank you!" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9474.0 0.0 0.0 0.0
"How can I make it so the speed is 2x for the rest of the videos?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4809.0 0.0 0.0 0.0
"Give this man a medal !" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4049.0 0.0 0.0 0.0
"Why is it that if there are more unknowns than there are equations there exists a non-zero solution to Ax=0?" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 11880.0 0.0 1.0 0.0
"How do you get to chose a random number for x? like x=0. How is this possible? what am I missing?" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4855.0 0.0 1.0 0.0
"""And for my last trick I will pull the answer down from the board above""" Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 28.0 1.0 0.0 0.0
"2:58 The definition of the Cauchy sequence.
11:28 A Cauchy sequence is bounded." 0_w-R_g5lRA "Lecture 10: The Completeness of the Real Numbers and Basic Properties of Infinite Series" "MIT 18.100A Real Analysis, Fall 2020" 876.0 0.0 1.0 0.0
"this is where the money is at" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14888.0 0.0 0.0 0.0
"I just realized multivariable calculus is the prereq of this course. I understand most of the part but there was confusion sometimes. Now I need to take cal 3 so I can continue these awesome lectures from professor Strang." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5613.0 0.0 0.0 0.0
"I don't understand the point he was trying to drive with the final 5 minutes or so. I imagine it will become more clear in the next lecture." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5346.0 0.0 0.0 0.0
"I don't get it" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5305.0 0.0 0.0 0.0
"I am an IITian. We do have some professors who teach this well. Most are very boring. Thanks, MIT." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5063.0 0.0 0.0 0.0
"25:10 


student: - *cough sound* 
professor: - something you wanna say..?" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 766.0 0.0 0.0 0.0
"nvr mind... i figured why u asked" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14095.0 0.0 0.0 0.0
"Such video lecture series are tremendously helpful. Please keep on uploading more videos on graduate courses in mathematics." RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 8953.0 0.0 0.0 0.0
inn eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13610.0 0.0 0.0 0.0
"Anybody who understand why he did 45/365? Is 45 the day 45 or what is it?" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2480.0 0.0 1.0 0.0
"❤️  ❤️  ❤️" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 15610.0 0.0 0.0 0.0
"Awful course!" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 2793.0 0.0 0.0 0.0
"for those unaware, this video was originally uploaded in very bad quality (you willl see complaints about this in the next one) and MIT OCW claimed to have lost the original recording and thus were unable to upload in higher quality. Fortunately, the seem to have found the tapes. Thanks MIT OCW!" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 12891.0 0.0 0.0 0.0
14:44 QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 436.0 0.0 0.0 0.0
"Its too easy." 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7093.0 0.0 0.0 0.0
"I love reviews." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 5768.0 0.0 0.0 0.0
"For all of you who are lost in this conference, don't worry, if you are just starting your career and have not seen calculus or differential equations, this will be almost impossible to understand, I think this conference seeks to show the potential of linear algebra in other fields, and I don't think it is necessary to fully understand it if you are just starting out, don't get frustrated by not understanding it, the level is much higher than the previous ones.

By the way, if you develop an interest in dynamic systems (chaos theory), this is definitely a conference that you will remember in the future." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 3848.0 0.0 0.0 0.0
"Yeah, it really was that good of a lecture. Professor Strang's Immortal Lecture." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12128.0 0.0 0.0 0.0
"""Calculus sucks"" - Strang, 2005 😆" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 38.0 0.0 0.0 0.0
"(65+41+70+90+58+82+76+78+59+59+84+89+134+51+72)/15 <> 67.5" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 221.0 0.0 1.0 0.0
"41:42 answer should be 6/16, he forgets to color and count (2,1)." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 1160.0 0.0 1.0 0.0
"You are right there is no audience. They are so good, they shut up and just listen(it's a joke)." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 12177.0 0.0 0.0 0.0
"Thank you, MIT! And thank you for enabling comments! Free speech kicks ass!" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 9501.0 0.0 0.0 0.0
"@floppydrive42 howd yah do on linear algebra final? i have to learn 100% in a week think im good?
" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 1838.0 0.0 0.0 0.0
"Thank you Prof.Strang!! and obviously MIT too!!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9204.0 0.0 0.0 0.0
"MIT, biggest name in leading edge technological schools... And they don't even have a white board? :-)" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7553.0 1.0 0.0 0.0
"I am watching those right now.  And I completely agree with you.  He tries to cover the material rather than give students UNDERSTANDING :(  I am deeply disappointed by MIT.  I thought the level of teaching there will be superb but this Professor ( i am sure he knows math ) makes easy things obscure.  Unless you already know and understand material it is impossible to follow him." BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5156.0 0.0 0.0 1.0
"goood one" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12956.0 0.0 0.0 0.0
"If there's only one thing to take away from Strang's lectures/lessons, it is this (which he emphasizes in one of his textbooks):


Understand in depth the four most fundamental subspaces: the row space, the nullspace, the column space, and the left nullspace." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6526.0 0.0 0.0 1.0
"I really don't think tracing the teacher throughout the whole lecture was necessary..." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5910.0 1.0 0.0 0.0
"Watching 3b1b's series and then this one paints such a rich picture of the connections between the symbolic and geometric interpretations for these ideas. So fascinating to see the differences in their approach, yet so illuminating to piece together the equivalences and build a deeper conceptual understanding." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 11291.0 0.0 0.0 1.0
"Anyone here, who took this class live in the classroom @MIT in 2005?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 2499.0 1.0 0.0 0.0
"They probably have 3 or 4 lecture each week, depending on the amount of credits the course is worth. Something like Monday, Wednesday, and Friday, I bet." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10442.0 0.0 0.0 0.0
TY 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 9003.0 0.0 0.0 0.0
"@blackrobe2007 

IM not 100% sure but my prof usually did things like this. He just used values that fit the condition so he could proceed." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 1794.0 0.0 0.0 0.0
"that accent would kill me" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14624.0 0.0 0.0 0.0
"In these series, every topic is covered of this professor books written" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 6688.0 0.0 0.0 0.0
"Just done the single variable calculus 18.01. Congrats to myself! Really Wonderful classes and professors.😁😁" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7162.0 0.0 0.0 0.0
"This professor is so good.

Doubt this will be read, but thanks so much for these, MIT.  It's an awesome, awesome program." hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10907.0 0.0 0.0 0.0
"Thank you, MITOCW, for this awesome course" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9505.0 0.0 0.0 0.0
"my dude... you said 0 + x = 0 for the additive identity... it should be 0 + x = x 😂" mlPLLXHZ8_U "Lecture 4: The Characterization of the Real Numbers" "MIT 18.100A Real Analysis, Fall 2020" 13977.0 0.0 1.0 0.0
"This guy is great." 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 10534.0 0.0 0.0 0.0
"Yes, because ""writing special erasable marker"" expresses much stronger academic competence." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12146.0 0.0 0.0 0.0
"Another beautiful course with incredible supporting materials. Both Prof. Auroux and MIT did a great job on this one." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2458.0 0.0 0.0 0.0
"I admire this person a lot, it shows his passion and dedication. At his advanced age, I hope I have the same love at work as he does." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5022.0 0.0 0.0 0.0
Genius wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3993.0 0.0 0.0 0.0
"This lecture is definitely a positive effect on my grasp of the matrix, and this lecture plays a pivotal role in the whole series. Thank you prof. Strang. Nobody has explained those concepts so clearly and coherently -- a whole new world is ahead of me. This is a must-see. A genuine human heritage." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 10800.0 0.0 0.0 1.0
"aaaaaaaaaaaaaaaand i didn't understand anything :(" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 12299.0 0.0 0.0 0.0
"holy crap he's not even your teacher and you're kissing his ass

i can see you get your profs to pass you" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13183.0 0.0 0.0 0.0
"Top teacher.💯💯 Usually scholars don't teach that well.😅😅😅" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11074.0 0.0 0.0 0.0
"Simply wonderful teaching" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 8672.0 0.0 0.0 0.0
"Teachers like this are born once in 400 years." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 9018.0 0.0 0.0 0.0
"Awesome lectures... Try watching at 1.25x speed... I am sure you will be able to catch up :) and save some time..." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 2765.0 0.0 0.0 0.0
"This is the best series of Probability on internet" P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 10745.0 0.0 0.0 0.0
"Really great!!!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8517.0 0.0 0.0 0.0
"May god bless every seeker with a guru like him. Respect and good wishes from India..You are awesome sir..May you have a long life and good health.." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 7634.0 0.0 0.0 0.0
"Hey, the closed caption just disappear once the word is showed, It should continue to appear until the next word change. And audio and video is not sync either." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4701.0 0.0 0.0 0.0
"37.50 ??" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 1051.0 0.0 0.0 0.0
"At 43:54, if we exchange rows of A, what spaces will stay the same? I understand that row spaces won’t change since it’s row combinations but why would null space not be changed as well? Wouldn’t left bill space stay the same?" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 2674.0 0.0 1.0 0.0
"The first question from the problem set asks for the eigenvalues of A+ when A square. I know that A and A+ have the same number of zero eigenvalues but I'm stuck searching for a relationship for the non zero ones. Some hint?? I check numerically and I verified that they are not 1/λ_i as one might have conjecture." ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10110.0 0.0 1.0 0.0
"Mit you do not have to use digitized voice system to make your point !!!" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7681.0 0.0 0.0 0.0
"ugh, I hate trig substitutions" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14976.0 0.0 0.0 0.0
"@redrum41987 Right, b/c I'm sure most of this stuff is dopily obvious to him but he's trying to explain in step-by-step still. " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1985.0 0.0 0.0 1.0
"thanks for the video! Question: can someone explain the difference between big Sigma and S. One is covariance matrix, one is sample covariance matrix. they are not the same thing? Thanks!" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 14585.0 0.0 1.0 0.0
"i dont think this is what youtube was made for ._." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13371.0 0.0 0.0 0.0
"The best math teacher ever." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 10004.0 0.0 0.0 0.0
"Prove induction theorem by well-ordering property! Nice and clear." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 8455.0 0.0 1.0 1.0
"37:17 or the groundwater flow equation =) So cool that the same equation can be applied to so many different things" wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 1059.0 0.0 0.0 0.0
"ty ty meow <3" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 14967.0 0.0 0.0 0.0
"Can anyone pelase explain to me how to get the result Of min 20:00 (like very detailed :( i dont understand )" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3039.0 0.0 1.0 0.0
"Trigonometry for AS and A level https://youtu.be/-WzZRx4vVxI" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11085.0 0.0 0.0 0.0
"bahut badiya" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12507.0 0.0 0.0 0.0
"In the example x^2+y^2-z^2=4, why did the 4 disappear when he eventually wrote the equation of the plane? Shouldn't it be the constant 8+ the original 4?" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 6665.0 0.0 1.0 0.0
"lawls even on a lecture about implicit differentiation YouTube can't avoid moronic arguments, humanity <3" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13761.0 0.0 0.0 0.0
"I've been waiting for this ever since I looked at Sipser's page and saw that it was being reviewed for OCW!" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 6408.0 0.0 0.0 0.0
"America is such a great country they even put lectures by great proffesors on YouTube for free...in my country the professors pretend to be illiterate outside the colleges.,,,😅" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2412.0 0.0 0.0 0.0
"he's a great professor. very rarely you see such a talented teacher in math." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 13120.0 0.0 0.0 0.0
"You just cannot miss anything Prof.Strang wrote on the board" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 12217.0 1.0 0.0 0.0
"God bless Dr. Strang!
There are Innumerable people in the STEM fields who owe their careers to stalwarts like him. A human treasure of knowledge!!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4070.0 0.0 0.0 0.0
"Why the seats in the classroom are all empty" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11921.0 1.0 0.0 0.0
"Is anyone watching this in 2022?" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6764.0 0.0 0.0 0.0
"Thanks for the analogy at 21:00. First time i got this :) " HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9706.0 0.0 0.0 1.0
"Professor Strang you are the first person who makes me deeply understand linear regression from linear algebra's point of view." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 8375.0 0.0 0.0 0.0
"Why 6 dimensions for symmetric? We have 3 for main diagonal and that's all. Isnt it?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 11764.0 0.0 1.0 0.0
"Maybe a faster way to do that integral is by parts taking u= (cosx)^3 and dv=cosx, shouldn't be hard to get that 2/3 integral of cosine to the 4 is equal to 2 times integral of cosine square! in that interval then use double angle fomula. But that's not the point of the lecture." YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7636.0 0.0 0.0 0.0
"Me, a greek person watching the video, what the hell perpendicular means ? Thank god he said the word with the greek origin at first!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7648.0 0.0 0.0 0.0
"Εύχομαι κάθε δάσκαλος να είναι τόσο καλός όσο ο καθηγητής Γιάννης Τσιτσικλής!" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 15546.0 0.0 0.0 0.0
"What a great professor he is." cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11414.0 0.0 0.0 0.0
"Can someone explain why A=LU is better than EA=U?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 3075.0 0.0 1.0 0.0
"the formula for cos(x-y) is identical to the dot product of two vectors written in trigonometric form.  the formula for sin(x+y) is equal to a determinate with cosx, cosy in the first row and sinx, siny in the second row.
-
using the properties of even and odd functions, one can then get back and forth between sin(x-y) and cos(x+y);" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14693.0 0.0 0.0 1.0
"He is working magic here in his lectures. I am experiencing one of those ""math is beautiful"" moments with these concepts and ways of thinking about matrices." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 4554.0 0.0 0.0 0.0
"09:22 guy gets the joke late, awkward laugh" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 298.0 0.0 0.0 0.0
"in fact it is" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13585.0 0.0 0.0 0.0
"i would i've loved to go to this college. only if i lived in the USA. yikes" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13507.0 0.0 0.0 0.0
"I just have one question not addressed in this lecture...what actual color is the blackboard?" Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5607.0 1.0 0.0 0.0
"Jeez that's a lot of homework" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7131.0 0.0 0.0 0.0
"It's interesting that students of this clase all over the world have the same questions .... all of them about algebra" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7052.0 0.0 0.0 0.0
"11:41
""Rows of C are combinations of rows of B.""

But, this only works for square matrices, isn't it?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 378.0 0.0 0.0 0.0
"19:08   No you dope!!!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 555.0 0.0 0.0 0.0
"That smile at the end, he knew he'd done a good job" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9914.0 0.0 0.0 0.0
"phew, my left ear had a hard time catching up" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 14183.0 0.0 0.0 0.0
"Very useful for Montreal Polytechnic school where we use Gilbert Strang book, but we only missed his explanations, so I was referred here" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11228.0 0.0 0.0 0.0
"~22:10 ""now I have to get serious""

so, what was all that other stuff?" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 15534.0 0.0 0.0 0.0
"the whole lecture was incredible.
godlike.
gausslike.
stranglike..!!!!!!!!!!!!" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 14751.0 0.0 0.0 0.0
https://www.youtube.com/channel/UC4bDpTs5tRVdSQuPRn7Mv1g VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 13265.0 0.0 0.0 0.0
"had no idea what was going on till 30:00" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13033.0 0.0 0.0 0.0
"Thank  you! Excellent!" BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 9041.0 0.0 0.0 0.0
"Geart job Sir, Thanks" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3990.0 0.0 0.0 0.0
"I'm very appreciative to have this course. Thanks MIT and Professor Strang. I'm getting good at this with your help!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 6396.0 0.0 0.0 0.0
"Points on the wheel do not have the same speed. Point of contact with the ground has 0 speed, the center has speed v, while the topmost point has speed 2v. By the time the centers moves some distance, the top point would have moved a greater distance. However if we fixate on a point on the rim, it will have variable speeds and would have covered various lengths in different time periods. The total length covered by one such point is arc length and it is more the circumference." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8225.0 0.0 0.0 0.0
"MIT should invent a better quality borad cleaner. Its hard to read the writngs on the board when it is cleaened." bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7542.0 1.0 0.0 0.0
"17:39 Why is abb rejected? From q3 it can transition to q4 using empty string, and the last 'b' can just be ignored." oNsscmUwjMU "2. Nondeterminism, Closure Properties, Conversion of Regular Expressions to FA" "MIT 18.404J Theory of Computation, Fall 2020" 513.0 0.0 1.0 0.0
"mathematics and chalk boards go together like proportional rates." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13917.0 1.0 0.0 0.0
"Excellent instructor but  poor hand writing." TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 3646.0 1.0 0.0 0.0
"Five minutes in and my mind is blown" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 3829.0 0.0 0.0 0.0
"The lecture is sooooo satisfying" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10164.0 0.0 0.0 0.0
"I did not understand at 30:15 he says there is a shortcut where look at the relative odds of these two events. how would this 'shortcut' work?" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 5259.0 0.0 1.0 0.0
"wasn't better to solve cone problem as following:we set infinit small volume dv=f(h)dhwhere f(h)=(pi) R^2,then we divide by dt then we plug in the values without the need to differenciate,because for such problem it happened to be easy to differnciate the function but sometimes it is not" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15060.0 0.0 1.0 0.0
"i'm sure mit will be number one in the wold in future education" 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13519.0 0.0 0.0 0.0
"@0:00 ""And, lift-off.""  LOL" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 1492.0 0.0 0.0 0.0
"49:04 Recalled an old meme 😂🤩" zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1304.0 0.0 0.0 0.0
"what prerequisite please???" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15179.0 0.0 0.0 0.0
"Are you a wizard? I'm telling the Ministry of Magic!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2537.0 0.0 0.0 0.0
"lol, college is so much better with the internet." ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13837.0 0.0 0.0 0.0
"I like Prof. Jerison. 👍🏻" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5659.0 0.0 0.0 0.0
"That was amazing and awe-inspiring. :)" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 9919.0 0.0 0.0 0.0
"What would the corresponding eigenvectors for -i and I at 41:00. Ther null space for the matrix is zero so are they the zero vector for both" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 11570.0 0.0 1.0 0.0
"After seeing some of these lectures and checking a couple of exams, I think MIT is actually not that difficult. The thing is they do have access to these awesome lectures and they're taught how to think. I'm positively sure that Calculus II and 18.06 are much more difficult in two universities I'm acquainted with than in MIT. However, they're taught how to think at MIT and most good universities just try to explore the limits of difficulty, rather than giving insights into thinking." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 2253.0 0.0 0.0 1.0
"I got it" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5448.0 0.0 0.0 0.0
"I think I spotted an error. To get a t statistic, we should use square root of n, not square root of (n-1)" QXkOaifVfW4 "9. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 5998.0 0.0 1.0 0.0
"I love his explanations. My linear Algebra prof. will just give us definitions, state theorums, and prove them and if were lucky we'll get an example, but never a solid explanation." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5740.0 0.0 0.0 1.0
"Eagerly waiting for that =) Hope the business world will understand how important free education for all people is..." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3545.0 0.0 0.0 0.0
"Does anyone know what text the professor uses?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3444.0 0.0 0.0 0.0
"853,620 quit already. " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1412.0 0.0 0.0 0.0
"Outstanding lecture-June 12th 2019" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8143.0 0.0 0.0 0.0
"For those confused by this lecture, don't worry, you should be, it's no a failure of yours, it's a syllabus description mistake.

I'm happy I see these videos as a review for things I ALREADY LEARNED years ago, because obviously if I were first exposed to this lecture with the prerequisites the course mentions, it wouldn't have been possible to understand this lecture.

While the course specifies 18.02 as a prereq, and then immediately dismisses in its syllabus as not important, this lecture requires both 18.02 and 18.03, the latter is not mentioned at all in the syllabus.  Universities usually parallelize these kind of courses with the parallel requisites such as 18.03, but OCW does not hint that at their site or here.

While for me it was nice, I recognize that if you don't know diff. eqs this would not be possible for you to learn.  The good news is that you can skip 1 or two lectures and you'd be right back on track, as this is just a nice implementation demonstration, but does not block Lin. Alg. learning." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 3900.0 0.0 0.0 0.0
"why exactly is the null space of (A transpose )(A) = to the null space of A ?" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 15317.0 0.0 1.0 0.0
"In 3D.
Ha. .. Ha.. Ha.." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6603.0 0.0 0.0 0.0
"@15:16, I apologies.......................That's how a matchless, renowned and extraordinary person respect everyone, everywhere.
Love you Prof. Gilbert Strange:)" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 1500.0 0.0 0.0 0.0
"At 23:31 the captions make a mistake, I think the professor meant: ""in terms of expanding, factoring and so on"", not vectoring.." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2616.0 0.0 1.0 0.0
"what the hell is this cross multiplying stuff with the quotient rule proof can someone explain his way from 1st to 2nd line :(" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15185.0 0.0 1.0 0.0
"Since for pi/4 it is part of a sphere, shouldn't the top be curve like the icecream on the top of the cone?" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8679.0 0.0 1.0 0.0
"There is no video for Lecture 13 as that was the day for the Midterm Exam." asjAc90L8rE "12. Time Complexity" "MIT 18.404J Theory of Computation, Fall 2020" 10373.0 0.0 0.0 0.0
"Dr. Strang is precious, protect him at all costs." UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 3508.0 0.0 0.0 0.0
"A derivative is the slope of a line.  Like if the line is Y = 2X, the slope is 2, so Y=2 is the derivative of Y=2X.  A limit is basically what the graph looks like it is going to do as it gets closer and closer to the limiting value." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2109.0 0.0 0.0 1.0
"""Lemme just do it the old fashioned way...""
blows my mind...." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 77.0 0.0 0.0 0.0
"thanks MIT really appreciate it...and this Professor is awesome...
those three people who disliked they must be next Albert Einstein" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14557.0 0.0 0.0 0.0
"This video repeatedly halts at about 20:00
I was hoping to catch the review which was about to begin here and then goo back to textbook problems,
also i can't seem to catch lecture 8 in my browser;  that's anothe hitch." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10959.0 0.0 0.0 0.0
"@ 15:02 could someone explain why Dr. Tsitsiklis got rid of the delta in the conditional probability?" H_k1w3cfny8 "10. Continuous Bayes' Rule; Derived Distributions" "6.041 Probabilistic Systems Analysis and Applied Probability" 1468.0 0.0 1.0 0.0
Excellent! IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 3684.0 0.0 0.0 0.0
"Would be golden if  the explaination to that factorization came in." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 12005.0 0.0 1.0 0.0
"""Don't be put off by this massive piece of junk here.""" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 42.0 0.0 0.0 0.0
"how the dimension of M is 9 ??" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 13248.0 0.0 1.0 0.0
"Thanks sir." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 9781.0 0.0 0.0 0.0
"It’s nice you got it on a linear line." wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7099.0 0.0 0.0 0.0
"is this the first year of college?" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13665.0 0.0 0.0 0.0
"bulb example is amazing" XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 12567.0 0.0 0.0 0.0
"Bruh I'm almost done with thise whole course I gotta get some kinda recognition like an MIT Nft or something (no cash) just some thing that can prove I've pushed through the course even a Soul bound token😩" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2951.0 0.0 0.0 0.0
"In which video the topic of Nth derivative is discussed??? i cant find !!!!!!!" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6697.0 0.0 1.0 0.0
"You're really precious, greetings and hugs from brazil! It's incredible how you can make such a hard subject becomes a adorable and important thing to learn <3" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 12251.0 0.0 0.0 0.0
"Yep, I love series" ZjjpLMKs7Tc "Lecture 12: The Ratio, Root, and Alternating Series Tests" "MIT 18.100A Real Analysis, Fall 2020" 12133.0 0.0 0.0 0.0
"anyone noticing the guy blowing his/her nose in 2:30" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 12389.0 0.0 0.0 0.0
"This helped me out so much. I which I had found it earlier...I hope this helps anyone else trying to search for ""Graph Laplacian"" find this video...: 
Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian Graph Laplacian." cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10574.0 0.0 0.0 0.0
"When you clear black board sir awesome" WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11643.0 1.0 0.0 0.0
"I love him yelling at that kid who asks the stupidest questions." PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5733.0 0.0 0.0 0.0
"The board work is terribly awesome..They challenge many of the standard vector calculus textbooks" BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 10023.0 1.0 0.0 0.0
"I thought these MIT wizards were meant to be the cream of the cream, how have they not come across the cosine rule yet? I'm not even out of high school and we've done far more complex stuff!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6099.0 0.0 0.0 0.0
"It is amazing thanks MIT" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6933.0 0.0 0.0 0.0
"Nice professor, nice teaching and nice school." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7854.0 0.0 0.0 0.0
"So you cannot go to a class you are not registered in MIT ? This is the first time I hear this thing..." mc1y8m9-hOM "22. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 8802.0 0.0 0.0 0.0
"Zero X -- Zero interest 18:18" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 12273.0 0.0 0.0 0.0
"Doubt at Checkin 3.1 at 28:30 Shouldn't the answer be B as we showed in the last lecture how to convert NFAs to DFAs, just like that we have to show GNFAs to DFAs even if we assume the transitions to be a single symbol ?" KAySmSEGc9U "3. Regular Pumping Lemma, Conversion of FA to Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 3490.0 0.0 1.0 0.0
"19:28 since the fact that  Q transpose times Q equals identity matrix is true for all matrix with orthonomal columns, doesnt Q times Q transpose also equals I ? the P= I always holds true for matrix with orthonomal columns?" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 561.0 0.0 1.0 0.0
"love prof. Strang" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13870.0 0.0 0.0 0.0
"Rachei de rir: ""... anybody below four is in trouble....""" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 8490.0 0.0 0.0 0.0
"At 36:30, why is it that moving from F'(x)=G'(x) to F(x)=G(x)+C uses MVT?" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2652.0 0.0 1.0 0.0
"I think it's better to first watch the amazing TA Linan Chen video  then come back and watch this lecture" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 6030.0 0.0 0.0 0.0
"There is one fundamental thing wrong in this lecture.
It is not true that the integral of u'/u du = ln u + C. It has to be ln (abs(u)) + C. This means e.g. that the integral of sec x dx = ln (asb(sec x + tan x)) + C. The same error occurs in the final example about completing the square. The answer to that example also does not have the necessary absolute signs." CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10376.0 0.0 1.0 0.0
"does anyone know how to obtain the reading material for this class the book George F. Calculus with Analytic Geometry?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12765.0 0.0 0.0 0.0
"What a brilliant professor. This was so so helpful" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 11399.0 0.0 0.0 0.0
"I absolutely love this teacher. Gauss thought of it because he was born before. And he died early. Really enjoyed and laughed about it. Amazing." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5009.0 0.0 0.0 0.0
"i cant understand why b should be in the different combination  col. space in A.
could anyone helps me?" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 13350.0 0.0 1.0 0.0
"Every lecture, the number of views is going down. For everyone else doing all the problems, watching the lectures, etc. - you have my respect. I'll see you at the end!" XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 3598.0 0.0 0.0 0.0
"الله يحرق اللينير" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 15568.0 0.0 0.0 0.0
"I have never been this excited to watch a teacher's lecture. Thank you sir." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5538.0 0.0 0.0 0.0
"How many MIT courses are there with no videos, and Prof. Strang comes through with an incredibly relevant course with full course videos. Amazing." nrDkb2MAwSA "20. Definitions and Inequalities" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4880.0 0.0 0.0 0.0
"what an amazing course , just did not want it to end. been here since lecture 1." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 15121.0 0.0 0.0 0.0
"what does ""rangle"" even mean? it is clearly a shorthand for rectangle" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15134.0 0.0 0.0 0.0
"i so badly want to write on that board with that piece of chalk :P it looks so nice to write with" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13459.0 1.0 0.0 0.0
"I didn't get why it had to be a plane. at 36:30" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5271.0 0.0 1.0 0.0
"least square problem: to solve a system of equations that has more equations than unknowns, i.e. non square matrix.
we solve by At Ax = At b, but since we cant find At for non square matrix, we approximate using svd" ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13767.0 0.0 1.0 1.0
"He is such an inspiration" lZrIPRnoGQQ "27. Backpropagation: Find Partial Derivatives" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4544.0 0.0 0.0 0.0
"What did Schmidt do actually?" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 11479.0 0.0 1.0 0.0
Brilliant! 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 2937.0 0.0 0.0 0.0
"This lesson should be learned before 18.06" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10841.0 0.0 0.0 0.0
"God bless Gilbert Strang and may his good health carry on for many more years. He is gifting the world with his work." sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4071.0 0.0 0.0 0.0
"Lt. Barclay lectures linear algebra" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7490.0 0.0 0.0 0.0
"Wow he call’s Prof. Strang “Gil”... I wish I was on these kinda terms with Gilbert." 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12031.0 0.0 0.0 0.0
"This is when the GOD guides you to find a treasure is to find such an amazing explanation, Thanks a ton." gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 10772.0 0.0 0.0 0.0
"44:23 that moment :v" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 1234.0 0.0 0.0 0.0
beautiful. VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 12520.0 0.0 0.0 0.0
"Thank you Prof. Strang!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9198.0 0.0 0.0 0.0
"I m here because of learning the mechanics of Fast Fourier Transofr" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5862.0 0.0 0.0 0.0
"This lecture made me throw away my usual school textbooks and grab some on my own after searching around, which actually will push me through some rigorous explanations like these, instead of ""take natural log and you will have answer"" Which many does" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10818.0 0.0 0.0 1.0
"Even if God taught linear algebra, it wouldn't have been better than this." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 3585.0 0.0 0.0 0.0
"41:40 ""exercise"" is misspelled ""excercise.""" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1156.0 0.0 0.0 0.0
"Why are these stupid students not clapping at 24:13 ?" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 11785.0 0.0 0.0 0.0
"markers use much more petroleum in their production than chalk... maybe it's environmental." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13912.0 0.0 0.0 0.0
"Oy, my textbook uses a much more complicated formula for det(A), glad to know the product of pivots shortcut." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8145.0 0.0 0.0 0.0
"Which book sir ?" P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 11712.0 0.0 0.0 0.0
"I thought they murdered the other prof for not remembering the sin sum formula :D" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6100.0 0.0 0.0 0.0
"he could prove better after squeeze theorem." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13072.0 0.0 0.0 0.0
"Can someone tell me what's the level of this course? Is it good for pre calculus? I just finished high school and I don't wanna fail in college (I'm going to CS) will this work for me?" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 3101.0 0.0 0.0 0.0
"great thanks!!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13009.0 0.0 0.0 0.0
"Saw the last video? Skip to 11:40 👍" XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 8603.0 0.0 0.0 0.0
"I'm so happy I got to witness the very first time he drew the vector pi-e" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 6376.0 0.0 0.0 0.0
"even his handwriting is beautiful..." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 12802.0 0.0 0.0 0.0
"Smart people fascinate me" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8724.0 0.0 0.0 0.0
"Linear Algebra, Spring 2005
Instructor: Gilbert Strang。" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7376.0 0.0 0.0 0.0
"Am I the only one who felt hard to follow the course? 6:31 means basically, using properties of variance, we have X bar as X_bar, the n observations of x are i.i.d. Bernoulli, Bernoulli's variance = E[x^2] - E[x]^2 = 1^2*p - 0^2*(1-p) - (1^2*p - 0^2*(1-p))^2 = p - p^2 = p(1-p). Having this variance, we can derive the variance of X_bar, which is var(X_bar) = var([X1+...+Xn]/n), know properties of variance, we take n out, as var(X_bar) = 1/n^2 * var(X1+...+Xn), since i.i.d., these xi all have the same variance, therefore we have n*var(xi) divided by n^2, so the variance(X_bar) = var(Xi)/n, so to standardize it (in CTL), we divide it by the square root of var(Xi)/n, which is what he wrote on the board. So, it all roots back to Prof. Tsitsiklis' Probability course." C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 2338.0 0.0 0.0 0.0
"I didn't catch what is the column space.
Is the number of independent vectors the number of dimension?" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 5264.0 0.0 1.0 0.0
"A truly awesome unique teacher, thank you Prof. Strang for making linear algebra easy." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 2166.0 0.0 0.0 0.0
"where can I get notes for this lecture?" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15225.0 0.0 0.0 0.0
"Thank you MIT OCW and Prof. Auroux for these lectures. And especially for the elegant way to define the always tricky differential notation. You are the best. Best wishes from Chile." 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9128.0 0.0 0.0 1.0
"....This is calculus at M I T. I know what you mean, but are you surprised he'd skip over the obvious stuff. " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 265.0 0.0 0.0 0.0
haha kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13034.0 0.0 0.0 0.0
"This is what I like about these good schools - that the teachers are devoted to teaching. Most other teachers are lousy and dull, and they end up naturally being egocentric. I love you guys." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10769.0 0.0 0.0 0.0
"This was a real eye opener, can't thank MIT OCW enough!!" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 10964.0 0.0 0.0 0.0
"BIG THANK YOU , I WISH I CAN ATTEND AND BE AT YOUR LECTURES " JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 2804.0 0.0 0.0 0.0
"@bjret They had a test on lec 9, it says it in end of lec 8. " YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1793.0 0.0 1.0 0.0
"teacher are so conservative..good point, thought about that too" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14442.0 0.0 0.0 0.0
"What the hell is he talking about he is rambling his ass off" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 11559.0 0.0 0.0 0.0
"22:01 mind blowing" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 694.0 0.0 0.0 0.0
"Is it me or this is more addictive than GOT" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 6792.0 0.0 0.0 0.0
"I was a bit confused after the last lecture but now it's clear why reduced row echelon form and rank are so important thanks professor" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 6149.0 0.0 0.0 0.0
"learned this about 30 years ago at Technion Haifa. If I could only have such videos or Instructor then life would have been a breeze" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 13765.0 0.0 0.0 0.0
"What's a long word for a bowl?  lol" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 11572.0 0.0 0.0 0.0
"The tutor was excellent but the students were childish. " 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 10305.0 0.0 0.0 0.0
"lufia covers traveling" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13891.0 0.0 0.0 0.0
"I was thinking he was a fantastic teacher.

A lot of teachers take it way too slow." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6169.0 0.0 0.0 0.0
"8:35 26:12" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 1421.0 0.0 0.0 0.0
"But I'll say that on the notes……" AdTvkFsqcDc "16. Derivatives of Inverse and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2956.0 0.0 0.0 0.0
"How many lectures can you guys cover per week typically?" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4886.0 0.0 0.0 0.0
"To remind myself, I'm putting the list here:

Lecture 1: Dot Product
Lecture 2: Determinants
Lecture 3: Matrices
Lecture 4: Square Systems
Lecture 5: Parametric Equations
Lecture 6: Kepler's Second Law
Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds)
Lecture 8: Partial Derivatives
Lecture 9: Max-Min and Least Squares
Lecture 10: Second Derivative Test
Lecture 11: Chain Rule
Lecture 12: Gradient
Lecture 13: Lagrange Multipliers
Lecture 14: Non-Independent Variables
Lecture 15: Partial Differential Equations
Lecture 16: Double Integrals
Lecture 17: Polar Coordinates
Lecture 18: Change of Variables
Lecture 19: Vector Fields
Lecture 20: Path Independence
Lecture 21: Gradient Fields
Lecture 22: Green's Theorem
Lecture 23: Flux
Lecture 24: Simply Connected Regions
Lecture 25: Triple Integrals
Lecture 26: Spherical Coordinates
Lecture 27: Vector Fields in 3D
Lecture 28: Divergence Theorem
Lecture 29: Divergence Theorem (cont.)
Lecture 30: Line Integrals
Lecture 31: Stokes' Theorem
Lecture 32: Stokes' Theorem (cont.)
Lecture 33: Maxwell's Equations
Lecture 34: Final Review
Lecture 35: Final Review (cont.) 


credit: dadgum it" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11042.0 0.0 0.0 0.0
"on the book there is a part I did not get at all-namely starting""to display a circle on screen,replace y""=-y' with finite finite difference equation"" from end of 315 page till 317,
anyone who has understood that part?" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 14148.0 0.0 1.0 0.0
"theorem: Expected value is linear operator" l4NoMKEHQwM "11. Derived Distributions (ctd.); Covariance" "6.041 Probabilistic Systems Analysis and Applied Probability" 14757.0 0.0 0.0 0.0
"Summary of this class , Since so many on comments are confused ->
Target -> Solve Ax=b / Ax=kx / Au=kv When A is big matrix.
**1)Finding Eigenvalues of Big Matrix ->
QR process ==> A0 -> Q0R0 , A1(SImilar to A0) ->R0Q0 = Q1R1 , A2 -> R1Q1=Q2R2 And Go on ultill we have a Upper Triangular Matrix 
QR process on original matrix will be expensive .First take the matrix to Hessenberg Form and then do QR process.
Take the Matrix A to Hessenberg form H using Arnoldi Iteration.
If The Matrix A is S(symmetric) Then , the hessenberg form will be tridiagonal And even easier to compute .

**2) Finding SVD ->
a)Find Q1 And Q2 such that Q1*A*Q2 becomes bidiagonal (The SIngular values will remain same since its unitary invariant)
b)Use some QR kind of method to find SVD from the bidiagonal Matrix 

**3)Solving Ax=b (Not on lecture but on Notes) ->
a)Use GMRES and get a answer on Krylov space
b)Use Conjugate Gradient if The Matrix A is Positive Definate" d32WV1rKoVk "12. Computing Eigenvalues and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8954.0 0.0 0.0 0.0
"43:15 ""well this will be used in about 5 years from now and it will start the deep learning revolution"" lol" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1199.0 0.0 0.0 0.0
"@junior1984able why did you make the function into an equation??" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1911.0 0.0 1.0 0.0
"""If there was an inverse to this dopey matrix"" I'm going to start calling Matrices dopey lol" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 69.0 0.0 0.0 0.0
"1:02:16 you indeed made me feel bad for choosing (c). This by far the most humiliating check-in yet." 3PzuSPQPEU4 "8. Undecidability" "MIT 18.404J Theory of Computation, Fall 2020" 575.0 0.0 0.0 0.0
"all is fine till financial example...should have chosen some simple example....." hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12322.0 0.0 0.0 0.0
"Some of these topics might be common knowledge, but the way he explains them - Mind = Blown 🙏🏻" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 8823.0 0.0 0.0 0.0
"matrices are sexy" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13920.0 0.0 0.0 0.0
"@trangnguyen1092 it's not bringing over to the other side

x approaching Xo = change in x approaching zero" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2047.0 0.0 1.0 0.0
"@TheSawman86 That's the joke idiot. " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1743.0 0.0 0.0 0.0
"I don't see what's so good about Gilbert Strang. I'm only able to learn and understand part of the content with him and so much of it I can't keep track of it.

I forget what is an invertible matrix, he always seems to just say this is invertible by just looking at it, and I can't see it by just looking at it, so that makes that hard to follow.


I can't keep track of what has n, n - r, m - r, all that gets jumbled up in my mind.


He wants me to go through steps with him, and sometimes I don't even know where's going with it, so I can't, I have to wait to see what he does, probably because he hasn't shown the steps first along with why they work, so that it never synched in my brain to begin with.

Occasionally I am able to answer a question right when he asks, but half the time, I'm only half following, if even that.

I don't see why other people think his teaching style is so amazing, it's so scattered, and doesn't clearly show how & why things work before expecting me to follow along with examples.

Though I think I'm pretty good at doing elimination.

I definitely can't multiply matrixes so fast as he does, I need to pause the video, and actually write down my work on paper, he just skips steps and writes them down.

Like I don't get it, his style is just way off for me, do I just learn differently then most people?, like I don't get it." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 5330.0 0.0 0.0 0.0
"08:10 how do you express the plan formed by two lines in general? " UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 296.0 0.0 1.0 0.0
"Is he french ?" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6771.0 0.0 0.0 0.0
https://youtu.be/MJhgfgwCC34 twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13295.0 0.0 0.0 0.0
"I really like his lectures!" ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 5922.0 0.0 0.0 0.0
"For a minute I thought the lecture was being given by Jimmy Dore. He sure could make good use from some statistics lectures." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3842.0 0.0 0.0 0.0
"The instructor looks like the ""Tom Yorke"" of statistics to me!" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 10141.0 0.0 0.0 0.0
"Love professor Casey. Can we get lectures of linear algebra, matrix algebra, complex analysis also?" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 7449.0 0.0 0.0 0.0
"really like this teaching  method. give me new insight about  matrix" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14256.0 0.0 0.0 0.0
"They learn derivative? at MIT? Well I think I have to go to Harvard directly..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10440.0 0.0 0.0 0.0
"Legend... Thats one word match their capability :)" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7323.0 0.0 0.0 0.0
"What is the use of calculus in economics?? Just Asking." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11541.0 0.0 0.0 0.0
"Hi can I post your videos to my facebook page?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4708.0 0.0 0.0 0.0
"Use 1/2 angle identity to integrate at 20:20 - https://raw.githubusercontent.com/RandyMcMillan/MAC2313/master/MITCalc3Lectures/WolframAlpha--intergral_sqrt_2_2cos_t___from_t_0_to_2pi___Definite_integral__2015_11_10_1124.png" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11131.0 0.0 1.0 0.0
"Shouldn't the answer to the fish question at 15:46 be equal to p(0,2)*p(1,3) instead of p(0,2)*(1-p(0,3))
I say this because the fisherman should fish for no longer than 1 fish. In the case of 1-p(0,3), he's considering all the possibilities that he could fish 1,2,3,4,5,6,7..... any number of fishes during that interval? from hour 2....5" XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 8649.0 0.0 1.0 0.0
"Very energetic teacher, handwriting is very clear and explanation is very satisfactory" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11168.0 0.0 0.0 0.0
"28:00 getting particular entry" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 829.0 0.0 1.0 0.0
"@zyflair dude that wasnt unexpected, it was an extreme moment, the board could have cut his hand off !" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2089.0 1.0 0.0 0.0
"junk = 1 over infinity maybe" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13726.0 0.0 0.0 0.0
"PERSONAL NOTES
1. Say p = 60% from n samples. How many samples would it guarantee that p > 50%? We need a model for this. The goal for our model is that the density must be as narrow as possible (least possible volatility), and the value that we're looking for is as close as it is likely to be. Assumptions: random (good way to model lack of infos, otherwise non-math wouldd suffice), i.i.d," VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8149.0 0.0 1.0 0.0
"Amazing moment at 4.10 or thereabouts when most of the students obviously thought it wasn't simply connected. I thought MIT students were supposed to be smart!" sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2384.0 0.0 0.0 0.0
"When you help others you hurt youself? (with education, economy, etc..) Is that what your main concept is ?" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11646.0 0.0 0.0 0.0
"excellent! thank you... " FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12830.0 0.0 0.0 0.0
"An absolute legend. Thank you so much for such great lectures." TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 2433.0 0.0 0.0 0.0
"His Linear Algebra is gospel, his Statistics not so much.. lol. 
Edit: Still love Prof. Strang!" z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4738.0 0.0 0.0 0.0
"@Yuxuan Wang
Give me a shout when you reach here :)" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 1759.0 0.0 0.0 0.0
"thank a lot" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 14450.0 0.0 0.0 0.0
"This is the best Linear Algebra course in my experience. Words are incapable of expressing my gratitude to Prof. Strang, his TAs, and the OCW team. I am overwhelmed with joy after completing this course." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 10731.0 0.0 0.0 0.0
"I have a question regarding matrix multiplications. If I've got 3 matrices A, B and C where: AB=C
If B is invertible, is it true that A times B inverse = C?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5502.0 0.0 1.0 0.0
"this was probably the most confusing lecture up till now ... so many crazy notations :(" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14924.0 0.0 0.0 0.0
"Am I the only Chinese to watching this video?" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2334.0 0.0 0.0 0.0
"this guy is so bad at mathematics......." BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14831.0 0.0 0.0 0.0
AWESOME! OYcdw5vOgIc "23. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 2186.0 0.0 0.0 0.0
"There is a Confucius in Chinese history, who is know for the teacher of all teachers. This person is the teacher for nearly everyone who study linear algebra, even for my teachers at school." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 10360.0 0.0 0.0 0.0
"Looks like I were at MIT." TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 7421.0 0.0 0.0 0.0
"Thanks for this lecture!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 9732.0 0.0 0.0 0.0
"what did he use for write? in can´t stop thinking about that!" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 15131.0 1.0 0.0 0.0
"Excellent Lecture ! Thank u MIT !" TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 3629.0 0.0 0.0 0.0
"Ένα μεγάλο ευχαριστώ, από Έλληνες φοιτητές!" jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 15543.0 0.0 0.0 0.0
"@igordz because we are european?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1888.0 0.0 0.0 0.0
"this guy is a genius.. holy moly he has a quick mind" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 14810.0 0.0 0.0 0.0
"love his sense of humour" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 13864.0 0.0 0.0 0.0
"SOMEONE BE AN EPIC GAMER AND PUT TIMESTAMPS ON THESE VIDEOS FOR JOHN" EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 8583.0 0.0 0.0 0.0
"no i think that is differential equations you single varible then multi variable then ODE and then if you like PDE partial differential equations but some places it might be calculus 3 different unis have different ways of doing the courses and different order" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14069.0 0.0 0.0 0.0
"meanwhile in Brazil, public and private universities retain knowledge as if it belonged to them.... you are wrong, knowledge belongs to society.... this is the big difference between slavery and freedom.... long live the united states of America." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13937.0 0.0 0.0 0.0
"Is anyone else amazed at how he lets you see both the forest AND  the trees... Simply the most elegant exposition of mathematics I have ever seen..." UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 6760.0 0.0 0.0 0.0
"@checkspender 
Typing a response on Youtube is more like a conversation rather than writing a college dissertation, wouldn't you think? Yet, there are always people focusing on each and every details in an attempt to push out rethoric for some strange reason. Perhaps the need to ventilate, or express some frustration in their lives, who knows. So, gentlemen, please, let's keep our eyes on the ball, shall we?" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1812.0 0.0 0.0 0.0
"sorry....but really not sorry 38:32.  Thank you Gilbert Strang!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 14380.0 0.0 0.0 0.0
"You're such an inspiration professor." Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12252.0 0.0 0.0 0.0
"I want to thank MIT for putting this up and Sir Gilbert Strang for such an amazing lecture" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 6144.0 0.0 0.0 0.0
"prof. Gilbert strang : when i say we i don't mean i
siraj the scammer : objection mylord" Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14213.0 0.0 0.0 0.0
"I like puppies too" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5679.0 0.0 0.0 0.0
"Great, I can hear with both of my ears!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4373.0 0.0 0.0 0.0
"think of it like this  give Me an A is this class  or caculate how you got a size 12 steel toe boot stuck in your rectum" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14789.0 0.0 0.0 0.0
"This man single handedly saved my university algebra course, my teacher was just reading notes, he's actually expalining in a very clear manner." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 10878.0 0.0 0.0 0.0
"when the math genius improvises jokes haaha :d" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 15213.0 0.0 0.0 0.0
"The mistake professor Strang made turned into a great connection to the new topic. That's why he is a genius" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10189.0 0.0 0.0 0.0
"Python scipy + matplotlib:


import matplotlib.pyplot as plt
import scipy.misc
import math


def binomial(n,k,p):
    nk = scipy.misc.comb(n,k)
    return nk * math.pow(p,k) * math.pow((1-p),n-k)

def getProbabilityList(n, p, calcFun):
    vals = []
    for i in range(n+1):
        vals.append(calcFun(n,i,p))
    return vals

def PlotProbabiltyRange(n,p):
    x = range(n+1)
    y = probRange(n,p, prob)
    plot(x,y)



def main():
    n = 100
    p = 0.5
    for i in range(1,n+1,1):
        y = getProbabilityList(i,p, binomial)
        x = range(len(y))
        plt.plot(x, y)
        plt.show()" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 8467.0 0.0 0.0 0.0
"Ah that explains it. I don’t understand the math but now I finally understand why my socks are getting wet when it rains" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 2277.0 0.0 0.0 0.0
"I do make this statement, after understanding Polynominal Crystal Algebra IV with the X-Axis,Y-Axis,& Z-Axis Polynominal Cyrstals revolving around""TIME""= 4D Algebriac, & Calculus Limit Questionaires using Newtonian Physics,WHY Don't you run that""STUPID FREEMASON U.S.A.IDIOT Government ,Now that you Fully Understand the Mathematics of Our UNIVERSE,you certainly can adapt it to""SCIENCE SOCIALISM of ELECTRIFICATION-Photons of Physics Calculus-Algebriac I,II,III & Algebriac IV Polynominal Graphing!!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5288.0 0.0 0.0 0.0
"""--"" - did you just heared this sound? :)" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 17.0 0.0 0.0 0.0
"bloodsaw I get 1-5 plus revew last 2 test 1 quiz" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 12548.0 0.0 0.0 0.0
"This is Gr lecture though took me little time to prove the gradient descent lies in range of region of confusion with min and max been individual sample gradients" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10579.0 0.0 1.0 0.0
"Absolutely well done and definitely keep it up!!! 👍👍👍👍👍" k2inA31Gups "18. Bayesian Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 2215.0 0.0 0.0 0.0
"On 6:00 , if L is contained on the plane P, wouldn't P U L be a subspace, which will just be P??" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 8068.0 0.0 1.0 0.0
"very very clear" tBUHRpFZy0s "24. Classical Inference II" "6.041 Probabilistic Systems Analysis and Applied Probability" 15042.0 0.0 0.0 0.0
"You have made it this far, you're awesome, give yourself a high-five" XtNXQJkgkhI "22. Bayesian Statistical Inference II" "6.041 Probabilistic Systems Analysis and Applied Probability" 12210.0 0.0 0.0 0.0
"It's very kind of you" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 7078.0 0.0 0.0 0.0
"x one , x two , x free" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15453.0 0.0 0.0 0.0
"What's the name of this professor?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11583.0 0.0 0.0 0.0
"Well, I believe this link explains why sometimes a picture is worth a thousand words. Hope it helps!
https://math.stackexchange.com/questions/2294272/average-height-of-a-point-in-half-circle/2294287" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11363.0 0.0 0.0 0.0
"This seems like a hard test" BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10919.0 0.0 0.0 0.0
"In A=LU part, what do L and U stand for? (Like ""E"" for elimination )" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 6605.0 0.0 1.0 0.0
"It took me about 40 days to finish this course. Thank you so much Prof. Auroux!" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6991.0 0.0 0.0 0.0
"Thank you MIT!!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 9152.0 0.0 0.0 0.0
"good lecture
" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12947.0 0.0 0.0 0.0
"These lectures are so good that I am falling in love with studies, specifically Linear algebra for the first time. I always dreaded the topic in my college days, just wish there was someone who could have referred me to these lectures back then." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 10411.0 0.0 0.0 0.0
"46 minutes. woah. can i haz crash course?" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1264.0 0.0 0.0 0.0
"Can we find homeworks/labs online?" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3109.0 0.0 0.0 0.0
"1.25 speed helps" 9_xG0AGRa-w "Lecture 2: Cantor's Theory of Cardinality (Size)" "MIT 18.100A Real Analysis, Fall 2020" 324.0 0.0 0.0 0.0
"Some time can be saved by not speaking out the rules about honesty etc. and instead handing out a link to the web file where the rules are spelt out in full." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 8829.0 0.0 0.0 0.0
"He keeps mentioning multiplication rule of probability here , but where did he teach that?" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 4562.0 0.0 1.0 0.0
"I AM COMING TO YOU TO LEARN MATHEMATICS FROM BASICS." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 4921.0 0.0 0.0 0.0
"i feel like those writings are popping out of the black board." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13376.0 1.0 0.0 0.0
"i didn't learn anything about linear algebra at my own university. then I found these lectures from MIT.

this stuff is GOLD!!" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 13358.0 0.0 0.0 0.0
"first row       (2 and 1) multiply by 16 ( 32 and 16)
second row (3 and 1) multiply by -9  (-27 and  -9)
then add the two rows                         (   5 and   7)
(or subtract if you multiplied by 9)" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12870.0 0.0 0.0 1.0
"This is the best explanation of exponential family i have ever come across." X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 10733.0 0.0 0.0 0.0
"At 32:32 the expression is actually S*Lamdba^100*c, and not Lambda^100*S*c ." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 2646.0 0.0 1.0 0.0
"Terrific, terrific lecture, esp his way of using linear combination / ""column picture"" to solve equations. I have never heard of it, but it is so much easier!  Thank you Prof. Strang/MIT for posting these lectures!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 9031.0 0.0 0.0 1.0
"Охеренная лекция! Чувак рулит. Лучше, чем препы с мехмата объясняет!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 15555.0 0.0 0.0 0.0
"Well i like this blackboard thing.... and if i am ever going to teach i will keep this in mind... as a student or follower of the lesson...life is easier when things are written like this... it gives you the time to write down what's saying and also writing...the board goes up and stays there if u're slow..and he makes right at the time what he's explaining...it makes it understandable.A power point slide is always fast, done, and the person who's explaining, most of the time, just reads it." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11354.0 1.0 0.0 1.0
32:56 M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 944.0 0.0 0.0 0.0
"Both parts of the FTC are proved in the next video, lecture 20 dumbass!
" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2912.0 0.0 0.0 0.0
"Would help if he wrote larger on the board for readability." QeYUHA0UMVg "Lecture 21: The Riemann Integral of a Continuous Function" "MIT 18.100A Real Analysis, Fall 2020" 12010.0 1.0 0.0 0.0
"They have such nice chalk at MIT" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10439.0 1.0 0.0 0.0
"Where is lec 17" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11682.0 0.0 0.0 0.0
"i love these lectures!  they are fantastic. i love the book too. i think it's really well written. overall, i really enjoyed this course" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 13430.0 0.0 0.0 0.0
"what b turns out to be." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 15126.0 0.0 0.0 0.0
"very good explanations..
description doesn't enlist his name?
i am very thankful to MIT for putting these kind of videos in public domain." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15004.0 0.0 0.0 0.0
"Another person that begins every sentence with the word ""so..."".  I can listen this only for a short while." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2460.0 0.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8443.0 0.0 0.0 0.0
"Little bit disappointed, thought it would the  course that follows rudin's book(18.100C),but still appreciate your upload MIT!" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 7390.0 0.0 0.0 0.0
"One of the reasons I truly like this awesome teacher is he always erase three pieces of blackboards  in a row, so I get a chance to skip" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 8100.0 1.0 0.0 0.0
"@aqcpatrick, my bad. You're right, -10 is correct." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1784.0 0.0 1.0 0.0
"O.O''' I actually saw the whole thing... Nice handwriting, by the way... :)" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7969.0 0.0 0.0 0.0
"Awesome Lecture!! Brilliant" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2752.0 0.0 0.0 0.0
"love his chalk" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 13862.0 1.0 0.0 0.0
"Utterly enthralling course, and exceedingly well taught. Thank you very much Dr Strang!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 11143.0 0.0 0.0 0.0
"Let me tell you that this was the point where 2 legends Gilbert Strang and Andrew Ng met, kudos to those who got it" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7334.0 0.0 0.0 0.0
"Could that eraser be any more chalk-dusty?" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3241.0 1.0 0.0 0.0
"What's with the sound, guys??!?" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 11591.0 0.0 0.0 0.0
"Bless this man" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2900.0 0.0 0.0 0.0
"29:00
IDENTITY MATRIX" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 848.0 0.0 0.0 0.0
👏👏👏 VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 15719.0 0.0 0.0 0.0
"Professor Strang, thank you!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8387.0 0.0 0.0 0.0
24:00 QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 723.0 0.0 0.0 0.0
"The description said this lecture contains hyperbolic functions. I watched the whole thing in hope of facing Coshx and Sinhx, none were discussed! " eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10073.0 0.0 1.0 0.0
"Physicists insert a minus sign to get a nice looking energy conservation law: 

K + V = constant.

Without the minus sign, conservation of energy would look like this:

K - V = constant.

Here K is kinetic energy and V is the potential energy." z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8192.0 0.0 0.0 0.0
"Listen with your headphones at the beginning, it would give you a classroom experience." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 7385.0 1.0 0.0 0.0
"@14:40 the kid in the white votes twice! WHAT A JERK
" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1499.0 0.0 0.0 0.0
❤️❤️❤️❤️❤️❤️❤️🇧🇩🇧🇩🇧🇩 BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15614.0 0.0 0.0 0.0
"Thanks for this great video MIT and Professor Auroux." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9730.0 0.0 0.0 0.0
"He teaches vector in very easy way😀😍" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4614.0 0.0 0.0 0.0
"@27:52 why isn't it a 3-d subspace in R4? Shouldn't all the linear combinations of two independent vectors in R4 be a 3d plane?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 1525.0 0.0 1.0 0.0
"itülüler yeter diyordu davut hoca dinlemiyordu" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 13717.0 0.0 0.0 0.0
"I'm relieved to see i haven't been the only student to come late to class." 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6368.0 0.0 0.0 0.0
"Why are there no lecture videos available for many courses? (e.g. Algebraic Geometry)." EBdgFFf54U0 "Lecture 14: Basic Hilbert Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 11779.0 0.0 0.0 0.0
"30:10 But only 3 needles cross the line?!?" CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 883.0 0.0 1.0 0.0
"DR. Strang thank you for linking linear algebra to real world technology. Circuit design and machine design uses linear algebra.  The development of Google uses linear algebra." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3284.0 0.0 0.0 0.0
"15:37 ""OH DAMN ... circle the wrong thing""

great professor .... mistakes happened to all" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 456.0 0.0 1.0 0.0
<3 VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 1457.0 0.0 0.0 0.0
"Is it me or is the video messed up?" BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 6789.0 0.0 0.0 0.0
"Man! the camera guy has completely messed up such a beautiful lecture!" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7580.0 1.0 0.0 0.0
"""Please come on Monday"" : Jeez if I could time travel, I'd get there somehow. who wouldn't ?" TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 101.0 0.0 0.0 0.0
"love his humour!" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 13863.0 0.0 0.0 0.0
"What a wonderful human, and must be excellent teacher as well." t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11435.0 0.0 0.0 0.0
YES!!! Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12109.0 0.0 0.0 0.0
"This professor is a legend." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 10896.0 0.0 0.0 0.0
"i understood shit from this...im more confused " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13487.0 0.0 0.0 0.0
"Really ? French students learned before the high school ! Is that a lesson for MIT engeneer?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8500.0 0.0 0.0 0.0
"An alternative way of deriving the equation
 If we have Ax=b with no solution. lets say c is the best solution so that Ac=proj(b on C(A)). then Ac-b is orthogonal to Ac so that the dot product of Ac-b and Ac is zero. But that can be writing in matrix form as (Ac)^t(Ac-b)=0
c^tA^t(Ac-b)=0, c^t(A^tAc-A^tb)=0 since we don't want c to be zero c^t can't be zero. that means A^tAc-A^tb=0 or A^tAc=A^tb" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 2434.0 0.0 0.0 0.0
"42:34 can someone explain the probability question again pls?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 1183.0 0.0 1.0 0.0
"great vid..keep the good work up pls" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13012.0 0.0 0.0 0.0
"That man. Is a legend. My gratitude and respect to Prof. G. Strang." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9905.0 0.0 0.0 0.0
"The norm is a real valued function, the range of the bounded linear functionals is the field of complex numbers.  In your demonstration of boundedness, you are comparing the size of a real number to a complex number, which doesn't make sense.  You need the magnitude of the complex number in front of the norm." pWs93gASTJk "Lecture 6: The Double Dual and the Outer Measure of a Subset of Real Numbers" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 10203.0 0.0 1.0 0.0
"美帥酷 正負零 神國人" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 15649.0 0.0 0.0 0.0
"Really a great lecture. He explains things simply that they seem obvious. I had never learned it as clearly as this in my college." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 8502.0 0.0 0.0 0.0
"Thanks MIT" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9600.0 0.0 0.0 0.0
"Why would I care about improving my English, it's my 4th language and I speak it well enough for anybody to understand my completely without a problem. Also, I'm not claiming to be extremely smart, I'm saying MIT sucks, $100k per year for an education you could have gotten by self-studying? No thank you. Besides, a lot of universities are above MIT's level of undergrad math. The IITs for example. This is a joke for them, primary school material. " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11934.0 0.0 0.0 0.0
"Where do x(sub naught) and y(sub naught) go at 40:59? It may be a rudimentary question, but I've been out of math classes for a number of years now. I am able to follow along with all of this except that one piece, and it's bugging me. What did I forget?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11676.0 0.0 1.0 0.0
"thats the easiest part of calc

math should test your logic/problem solving skills, not your memorization skills" BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14654.0 0.0 0.0 0.0
"why doe proffs banter about stupid shit just get to the point and save time for questions
they all seem to be like that" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15309.0 0.0 0.0 0.0
"anyone else notice at 8:13 that he said ""tre"" y squared at first and then corrected himself? french people ftw. " 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12383.0 0.0 0.0 0.0
"He is so lovely and fun" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4537.0 0.0 0.0 0.0
CORONA dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 2983.0 0.0 0.0 0.0
"i was the little sister and I got a dart right between the eyes, up about a half inch.  probability is 1." R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13490.0 0.0 0.0 0.0
"what does support of P tetha means please?" JTbZP0yt9qc "6. Maximum Likelihood Estimation (cont.) and the Method of Moments" "MIT 18.650 Statistics for Applications, Fall 2016" 15136.0 0.0 1.0 0.0
"for the equation: (A- lanbda* I)* X = 0, why should (A- lambda*I) needs to be singular?" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 12888.0 0.0 1.0 0.0
"43:30 How can column space of Q be same as column space of A?? I know that their dimensions are same, but Q is composed with orthogonal vectos and A is not. I need some helps guys {{{(>_<)}}}" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 1211.0 0.0 1.0 0.0
"I always thought that systems with less equations than unknowns might either have 0 or indefinitely many solutions. Dr. Strang, however, says that a system with 3 equations and 4 unknowns should have a solution (7:47). Am I not getting something?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 5045.0 0.0 1.0 0.0
"Thanks MIT" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9594.0 0.0 0.0 0.0
"36:39 i think that the guy to the left is getting it xD" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1042.0 1.0 0.0 0.0
"yeah you can see it by his accent" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15472.0 0.0 0.0 0.0
"I can barely hesitate to say that these lectures are incomparable to the lectures I attend for Linear Algebra at university. It's uncanny how often when watching these videos I think, ""I get it now, I get it!"" Cudos to you Prof. Strang!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5187.0 0.0 0.0 0.0
"Jedna planéta od povedala napi sa vody aby si mohol lietať ďalej" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 7128.0 0.0 0.0 0.0
"Why is it such a common spoonerism that he says ""toin coss"" instead of coin toss @25:16? I have the exact same issue when giving a lesson!" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 11876.0 0.0 0.0 0.0
"Well by the law of large numbers, delta method and Slutsky, I can hence say I am an idiot!" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 11347.0 0.0 0.0 0.0
"Where is Lecture 26 ? This is the 3rd lecture gone missing :-)" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11680.0 0.0 0.0 0.0
"Why does the range of y change for different values of x in the xy plane" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11848.0 0.0 1.0 0.0
"MIT using  Blackboard and chalk?? gotta step it up" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7549.0 1.0 0.0 0.0
"partial fractions in my country is known before calculus." HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14168.0 0.0 0.0 0.0
"let me change it from I to YOU . lol" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13781.0 0.0 0.0 0.0
"facebook was built in 2004, this was recorded in 2005....i wonder if he knew this biggest application of graphs....." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 12838.0 0.0 0.0 0.0
"Se ti vysypal čaj, nebo co? :-)" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8606.0 0.0 0.0 0.0
"Came here to learn calculus.. got busy reading the comments.. Damn!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2992.0 0.0 0.0 0.0
"Wow, this man explained everything what I had to learn in a 4 months in 30 minutes XD I'm 15 years old though." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12076.0 0.0 0.0 0.0
"I learned this in seventh grade. Seriously." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5654.0 0.0 0.0 0.0
"The passion and curiosity to explore are still shining brightly in his eyes and haven't subsided even a bit. G. Strang is an inspiration and is one of those fewest mathematicians who is loved as much for a person that he is as he is loved and appreciated for the knowledge that he gifting the world. Love you, Professor. Live long and stay healthy. The Universe is with you." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10220.0 0.0 0.0 0.0
"Prof slaying that navy blue shirt." BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8284.0 0.0 0.0 0.0
"Thanks so much MIT, I majored in math in my first semester and changed into literature when I became a sophomore;) because I had so much trouble in understanding (qwq) Now in this class it suddenly comes to me maybe it’s not my problem but the teachers haha (I am self-studying programming now!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9783.0 0.0 0.0 0.0
"Thank you! Mr. Strang." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9479.0 0.0 0.0 0.0
"lol. I came here just for learning maxwell's equation 6 years ago. Physics sucks so badly compared to math. I do not need any ""physics"" explanation." BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 13842.0 0.0 0.0 0.0
"does the prove for intersection conserve convexity needs a premise that A and B needs to be convex?" nvXRJIBOREc "Lecture 21: Minimizing a Function Step by Step" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12768.0 0.0 1.0 0.0
"why the projection matrix that projects b onto N(A ^ T)  is I - P ? Can somebody please make me see that?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 15368.0 0.0 1.0 0.0
"In the previous example, when we were at state 2, we directly took 0.2 as the probability to reach state 4. But here at 44:08, why are we using the u2 value?" HIMxdWDLEK8 "18. Markov Chains III" "6.041 Probabilistic Systems Analysis and Applied Probability" 6680.0 0.0 1.0 0.0
"e in N(At) is perp. to C(A) just killed me. 30:30
How smooth can someone explain the ""big picture"" step by step over weeks." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12780.0 0.0 0.0 1.0
"42:45 If A and B have the same four subspaces, then they have the same reduced row echelon form." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 1187.0 0.0 1.0 0.0
"I LOVE how he realizes the concept of vector spaces is difficult for most people to understand!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4931.0 0.0 0.0 0.0
"I have found the solution of generalized S-M formula. I mean the solution of (A + u1*v1 + u2*v2 + u3*v3 + ... + uk*vk )^-1" XhSk_Lw2X_U "14. Low Rank Changes in A and Its Inverse" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5528.0 0.0 0.0 0.0
"Thnks professor..." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10984.0 0.0 0.0 0.0
"Best lecture that explains intuition behind eigen values and eigen vectors. It's not just about cramming the formula." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 2863.0 0.0 0.0 0.0
"Bookmark, random sampling of matrix 36:20" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2907.0 0.0 0.0 0.0
"When talking about continuous random variables don't use the word random because there is nothing random about the distribution of the outcomes of these particular variables due to the nature of the samples being analyzed. Unfortunately this seems to be a misleading concept throughout almost all the videos on the internet regarding this subject. Even discrete random variables shouldn't initially be considered random due to the uncertainty of their distribution outcome. Uncertainty and randomness do not have the same meaning. An uncertain discrete variable could prove to be more likely random in it's outcome according to a more likely random type distribution.   When analyzing continuous variable distributions you're are admitting the existence of a value range (similar to a discrete distribution), but contrary to a discrete distribution you are also admitting that, without any trials and without knowing the outcome, that you are going to have a certain type of distribution that follows a certain type of symmetrical curve. As the values tend to get further from the peak of the curve their frequency starts to decrease more or less proportionally. It's almost like a rule that you follow. Being that the uncertainty lies only in the variance of the distribution. Normally dealing with continuous distributions you are analyzing co-related values (correlation between a infinite value and it's frequency), who's relationship is given through a formula. The problem is that there are no predefined rules, formulas or predefined co-relations for uncertain outcomes. Notice that I used the word uncertain and not random." 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 11632.0 0.0 0.0 0.0
"some one said no that they had not seen the law of cosine. I mean...... how did they get into MIT?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14360.0 0.0 0.0 0.0
"why are the vectors/edges of the cube not columns but rows suddenly ?" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 15284.0 0.0 1.0 0.0
"I'm honored to have Dr Harrison Wells himself as my professor ... Genius mind..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6329.0 0.0 0.0 0.0
"Did not quite understand @37:55, why we have three elements [ - - - ] in matrix size = 2 ,  Kindly help if someone understood" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3383.0 0.0 1.0 0.0
"really appreciate him" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 14248.0 0.0 0.0 0.0
"Am I the only one to believe ""He"" is the reason  Ross talks the way he does?" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 2335.0 0.0 0.0 0.0
"oh god ! 7:03" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 14104.0 0.0 0.0 0.0
"Good save, buddy." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 4155.0 0.0 0.0 0.0
"27:17 bottom left corner  that girl cracked his neck" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 818.0 1.0 0.0 0.0
"haha yeah i thought the same thing after reading the first sentence. If he/she is able to hold such amount of information, surely he should have grasped that 'extreme autism' isnt a medical condition? Theirs no doubt in my mind he watches way to much (big bang theory)" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13045.0 0.0 0.0 0.0
"41:11 Or am I
           -Michael from vsauce" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1149.0 0.0 0.0 0.0
"One of my students suggested a short cut to calculate probability P(Z>2) without using 1-P(Z<2) rule. If we flip the inequality sign and the sign of the z value, we always get the same answer in one step. In this particular case, P(Z>2) is equal to P(Z<-2) and the answer we can directly read from the Standard Normal Distribution table (for the z=-2 value). " Tx7zzD4aeiA "20. Central Limit Theorem" "6.041 Probabilistic Systems Analysis and Applied Probability" 8085.0 0.0 0.0 0.0
"I guess this course was prepared for engineers, not mathematicians or scientists ;-)" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5456.0 0.0 0.0 0.0
"Anyone else most thrilled about the quality of their chalkboards?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2488.0 1.0 0.0 0.0
"Best lecture ever!!!! I learned a lot! thank you professor Rigollet! Thank you MIT!!" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 2861.0 0.0 0.0 0.0
"At 46:26, when he calculated the minors, the number at 2nd row 3rd column should be -2 instead of -1." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2682.0 0.0 1.0 0.0
"He might correct it later, but as I am watching it:
I'm afraid Prof. Strang made a tiny error (pun not intended) at about 12:00. According to my understanding the right-hand side of the equation should be (1 2 2)^T not (1 2 3)^T. Can anyone confirm this?
Awesome lecture nevertheless." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 4586.0 0.0 1.0 0.0
"""accent this"" ""accent that"", I'm not even a native speaker, my english is very basic and I can understand this guy just fine... why are you americans complaining?" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 143.0 0.0 0.0 0.0
"Best explanation EVER." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 2856.0 0.0 0.0 0.0
"The fall from 2M views lecture one to 18k views lecture 17 (half way through) is crazy. Congratulations if you're still here. I've followed every lecture so far (notes and all) and I've gotta say, it is 100% worth my time. I might not have a degree from MIT, but I can say I've experienced how superb their education is firsthand. Thank you to Professor G. Strang and MIT OCW for making these lectures available online. You have made learning for me interesting again." 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 10101.0 0.0 0.0 0.0
"For the last part, why is it (right - left)? It is because the Method 2, setting the limit section on y-axis and evaluating the change of x-axis. That means (y+2)-(y^2) = dx.   

From the x-axis perspective, the x value from straight line (x=y+2) is definitely greater than the  x value from Arc BC (x=y^2). 

Or you can just simply draw a line e.g. y=1(horizontal line).  You will know the x value from straight line> x value from Arc BC" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3891.0 0.0 1.0 0.0
"this guys is crazy with that chalk" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14846.0 1.0 0.0 0.0
"this guy is such a joy to watch. his passion is contagious. love this guy" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14834.0 0.0 0.0 0.0
"""The students have to think with the teacher... you can't just zip through a proof"". This is such an essential part of teaching and learning and I am constantly amazed by how many professors have not realized this simple wisdom. Prof Strang is great." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 124.0 0.0 0.0 1.0
"Why aren't they giving a meaningful description of what a derivative is in plain English? E.g. The derivative of a function is the function that evaluates to the rate of change for a given input." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11791.0 0.0 1.0 0.0
"Well, the professor has a point when he say's ""you should have a question"". Nobody has any questions in these lectures, typically a sign that around 2/3 don't understand what's happening. I agree that the professor IS brilliant, but maybe a little too much so...you always feel clever when you watch clever people do their thing. Quality lectures though...." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11370.0 0.0 0.0 0.0
"very nice  ....Thanks" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 15027.0 0.0 0.0 0.0
"In high school and I already know this... Get on my level MIT!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6636.0 0.0 0.0 0.0
"Same comment as everyone else. This was a much better explanation than my professor gave. " srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 8598.0 0.0 0.0 0.0
"""the origin of the world is right here""" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 179.0 0.0 0.0 0.0
"Very helpful" CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11193.0 0.0 0.0 0.0
"@31:20 singular matrices take some non zero vector x to zero and there is no way A inverse can recover it, that's why A inverse does not exist. great explanation." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1536.0 0.0 1.0 0.0
"these lectures are great! thank you, MIT!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14780.0 0.0 0.0 0.0
https://en.m.wikipedia.org/wiki/Vandermonde_matrix 2K7CvGnebO0 "19. Saddle Points Continued, Maxmin Principle" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13260.0 0.0 0.0 0.0
"I strongly believe that the chart at mins 11 is not the best choice for illustration. I have been trying to fully understand it for 2 hours already." 4HRhg4eUiMo "8. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 5975.0 0.0 0.0 0.0
"Am I watched the previous lecture 🤔🤔" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 2342.0 0.0 0.0 0.0
"26:33 DENIEEEEDDD." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 803.0 0.0 0.0 0.0
"Dr Rodriguez is an absolute Top G. My man dropped the Real Analysis course (which I'm still devouring) a few months ago.

This was long awaited.

Thank Prof!" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 3493.0 0.0 0.0 0.0
"The instructor is a genius. Look at his CV." RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 10140.0 0.0 0.0 0.0
"these lectures are awesome, but as someone who didn't know anything about linear algebra, i DEFINITELY suggest watching these  videos by 3blue1brown instead or first, depending on amount of time avaliable: 

https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

One actually understands what ""matrix multiplication is a composition of linear transformations"" means and why that is really all one needs to know in order to truly understand matrix properties and operations (instead of just memorizing them)." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14776.0 0.0 0.0 1.0
"32:56 Thank you Prof. Strang." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 945.0 0.0 0.0 0.0
"Why is the expected value of sum = sum of expected values in case of the indicator function" EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 11886.0 0.0 1.0 0.0
"new vid, who dis? 👀" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 14020.0 0.0 0.0 0.0
"43:54 LMAO" 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1222.0 0.0 0.0 0.0
"find the form:1*2*3+3*4*5+5*6*7……+n(n+1)(n+2) like a 1*2+2*3…+n(n+1) can you prof ""n"" is not ""+"" or ""n"" is have a all number" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12861.0 0.0 1.0 0.0
"Snowing outside~" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8726.0 0.0 0.0 0.0
"@BYMYSYD  This is so wrong man....
you mean 
(X-Xo) --> 0????
it will make sense if you say what I just wrote...
you CAN NOT bring -Xo over the other side since  --> is not >
DUH." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1596.0 0.0 1.0 0.0
"thank you for providing this for free.
but pls don't write down all you said on blackboard, it's boring. 50minutes content, 40 of them are waiting to finish writing." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14493.0 1.0 0.0 0.0
"He's got such a lovely piece-by-piece, jigsaw-building lecturing style, as if he is rediscovering and rebuilding the knowledge in front of us" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4635.0 0.0 0.0 0.0
"excellent lecture" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12821.0 0.0 0.0 0.0
"Thank you." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9552.0 0.0 0.0 0.0
"Love from India" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7438.0 0.0 0.0 0.0
"never realized how immature MIT students were...." _CdoRiNSrqI "Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14018.0 0.0 0.0 0.0
"Alright, let's move into the space XD" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2321.0 0.0 0.0 0.0
"480p first time for me thx" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1287.0 0.0 0.0 0.0
"Oh, I didnt know Peter Crouch also interested in Linear Algebra!" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 8027.0 0.0 0.0 0.0
"This man’s awesome." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10881.0 0.0 0.0 0.0
"Chose a algorithm the Coonect with 01 2 code remember code number" cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3148.0 0.0 0.0 0.0
"to be clear: i understand the product rule and 'ax^a-1', but i'm confused about where the primes are coming from." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14943.0 0.0 1.0 0.0
"Professor, you have done extremely well. The sum of   the first n squares is worth mentioning, given these students will study real analysis, soon. You have set everything up for clear understanding.Cheers." hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8407.0 0.0 0.0 0.0
"Man, I miss calculus! So good to see these lectures!" WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7583.0 0.0 0.0 0.0
"The world need more professors like you sir." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 10340.0 0.0 0.0 0.0
"@gerax89gunner1 I agree, the differences between my high school teachers and these professors in terms of what you can learn in, say, an hour is pretty scary!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1849.0 0.0 0.0 0.0
"Thank you, so much from KSA, Riyadh." rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 9533.0 0.0 0.0 0.0
"Don't understand this , but love watching it all the same !" mlPLLXHZ8_U "Lecture 4: The Characterization of the Real Numbers" "MIT 18.100A Real Analysis, Fall 2020" 3477.0 0.0 0.0 0.0
"Lecture video timeline Links
Lecture 0:0
Elimination pivots and an example 3:9
Failure of Elimination method 10:34
Augmented matrix 14:50
Operations of matrices elimination 19:24
Row operations of Matrices Multiplication 20:22
Column operations of Matrices multiplication 21:43
Elementary Matrix 24:46
Include all elimination steps in one Matrix 33:29" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7302.0 0.0 0.0 0.0
"From the reverse reading formula of lim x-> c [f(x+c)-f(c)]/c to be df/dx at x=c, is actually the underlining principle for L'Hopital rule... If that statement makes sense to you. :D" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3933.0 0.0 0.0 0.0
"great, thank you" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13019.0 0.0 0.0 0.0
"MIT Lecture? Really??? Here in the UK we did all this - and more - at age 15 or 16. You Americans would be LOST at any decent UK University. As for trying Oxford or Cambridge - good luck, is all I can say...." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7504.0 0.0 0.0 0.0
"It appears that I may have to purchase the course text. I thought that I might get by without it.  Has anyone had success without the text? The lectures are pretty good." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 6908.0 0.0 0.0 0.0
"Wonderful! Thank you, Professor Gilbert Strang!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11994.0 0.0 0.0 0.0
"Professor Gilbert Strang ! 
I read your calculus book in highschool and it was awesome.
I didn't get into high end institutes in India, but it sure taught me a lot." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8325.0 0.0 0.0 0.0
"This guy always starts the topic mentioned in the video title towards the end and then teaches the majority of it in the next video, whose title is something else." XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10505.0 0.0 0.0 0.0
mvp TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 13968.0 0.0 0.0 0.0
"At 43.15 how does he know that the constants are a11 etc?? Can someone explain me? I know this works but I can't understand why does it works" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2670.0 0.0 1.0 0.0
"Haha why do all linear algebra professors make mistakes by producing random numbers. Their minds are too sophisticated for my comprehension. :P" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4413.0 0.0 0.0 0.0
"@Mrhellzya you dont have to be intrested, if you are capable of undertanding this then you would take the exams get the qualifications and the better job" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1687.0 0.0 0.0 0.0
"Seriously the best thing that I could have found on the Internet. Too bad my final is in 4 days. Naturally I will be staying on youtube for quite a few hours this week" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 8629.0 0.0 0.0 0.0
"Wow this is amazing, thanks MIT for the MITOPENCOURSEWARE ." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12041.0 0.0 0.0 0.0
"What an amazing lecture !!" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11448.0 0.0 0.0 0.0
"Thanks for such an excellent lecture. Please give proof of general l hospital rule." PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9704.0 0.0 1.0 1.0
superb UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14420.0 0.0 0.0 0.0
"Thanks for the course!" eEXSv0jChO4 "26. coNP is a subset of IP" "MIT 18.404J Theory of Computation, Fall 2020" 9709.0 0.0 0.0 0.0
"Passionate teacher who walks you through the sessions." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8156.0 0.0 0.0 0.0
"Hey! How come they have nkt seen Taylor approx. It was taught in 18.01." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4696.0 0.0 1.0 0.0
"i saw this in vectorial geo.. it is so cool!! i like it!!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13454.0 0.0 0.0 0.0
"@26:46:   mr + nr - r^2  =  mn - (m-r)(n-r)   makes sense as all (mn) parameters of A less a redundant bit due to the low rank." xaSL8yFgqig "Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1520.0 0.0 0.0 0.0
"Math is soooooo beautiful!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7608.0 0.0 0.0 0.0
"The verbal proof given at 46:22 seems to be fallible. Doesn't it argue for full mutual independence from pairwise independence?" gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 10311.0 0.0 1.0 0.0
"is a body of science" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 13625.0 0.0 0.0 0.0
perfection UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14178.0 0.0 0.0 0.0
"That formula for 3 X 3s looks very different than the one I learnt with cofactors all in row one and their corresponding ""minors"", the dot product that is and with the middle term negated." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 9887.0 0.0 1.0 0.0
"Glad to see you back" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4061.0 0.0 0.0 0.0
"so nice of Prof. Gilbert Strang" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 14342.0 0.0 0.0 0.0
"This is guy loves writing on the chalk board!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10671.0 1.0 0.0 0.0
"Why line is called a line?
Because it's ""line""ar 5:50;" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11898.0 0.0 0.0 0.0
"Now I can finally prove those spacial geometry formulas that I saw at school but couldn't prove because I didn't know calculus" ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7949.0 0.0 0.0 0.0
"43:00 where did he get 1/18(u^6) from?" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1196.0 0.0 1.0 0.0
"clearly MIT is toppest university in the 2012" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12656.0 0.0 0.0 0.0
"Thank you Prof. Strang, you're the best teacher!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9200.0 0.0 0.0 0.0
"24:44   system:  2a+3b=5  ,  1a+1b=7  solution:  a=16 , b=-9" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 754.0 0.0 1.0 0.0
"As of lecture #2, worst series in OCW I've found. Quality has skydropped since 18.01, what is it with European lecturers? Feeling the right way of teaching lies in proving complicate statements while defining nonintuitive math objects at uneasy peace rather than providing insightful examples, even tho this is just necessary ground knowledge and not the course core; and at the end of the day you can't even figure out how to solve problems from recitations. God I want Jerison back." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2573.0 0.0 0.0 0.0
"truly brilliant and impeccably clear" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 14962.0 0.0 0.0 0.0
"Thanks to him! I passed Linear Algebra.. I watched his videos for 4 days before final exam and I got 74 from final.. If I couldnt watch Dr.Strang's lectures, I would probably fail..." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 9810.0 0.0 0.0 1.0
"@sikory The author of the textbook." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2015.0 0.0 0.0 0.0
"Whole Class Is empty ...
Even though He Lectured in such a way that Class is full of students
Awesome" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11762.0 0.0 0.0 0.0
"28:00 Was it rotated to wrong direction? For example, if x = [0,1]^T, then AX = [1, 0]. So it is clockwise 90 degree rotation." k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 828.0 0.0 1.0 0.0
"How could I plug the UtU after sigma although they don't satisfy multiplication conditions concerning the size of matrices?" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4829.0 0.0 1.0 0.0
"I thought A^{T} A is positive semidefinite isn't it?" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6087.0 0.0 1.0 0.0
"does anyone know which book is he talking about?i mean in whole course he said its in the book??" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12767.0 0.0 0.0 0.0
"w 4 kolumnie bład rachunkowy?????" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15048.0 0.0 1.0 0.0
"It's such an amazing video. He made me know the real meaning of matrices, not just use it to compute" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7074.0 0.0 0.0 0.0
"The the French have a huge background in math, hence being some of the top guys in Finance. What's everyone whining about?" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10299.0 0.0 0.0 0.0
"Thank you Gilbert!" L3-WFKCW-tY "33. Neural Nets and the Learning Function" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9114.0 0.0 0.0 0.0
"Wish I had a chance to meet you!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11955.0 0.0 0.0 0.0
"I hope the mic is not very sensitive otherwise I'd be angry to see nobody replying to the professor's questions!" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 5593.0 1.0 0.0 0.0
"we only live so long....:-)'
" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 15077.0 0.0 0.0 0.0
"bro IIT's are nice.. I'm not gonna deny that but don't even bother comparing it to MIT. Any student in IIT is ready to give up their seat to get into MIT. If you ask an IIT student where do you want to study MIT vs IIT. What percent of students do you think will pick IIT if money is not an issue? You're paying for the quality of the educations and the opportunities. You are literally learning the from the BEST people possible. " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12558.0 0.0 0.0 0.0
"He is amusing.. Keeps the lecture interesting" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4508.0 0.0 0.0 0.0
"Thank You, Sir!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9060.0 0.0 0.0 0.0
"I love  it" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 5712.0 0.0 0.0 0.0
"Mmm that last problem: that 3x2 matrix multiplies with the zero matrix [0,0] does not result in another zero matrix?!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 7686.0 0.0 1.0 0.0
"he's so worried and messing it up while moving forward to next piece of the content" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13126.0 0.0 0.0 0.0
"""Don't all speak at once"", haha" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 41.0 0.0 0.0 0.0
"at 32:35 => Should not the first cost be 99*2 instead of 100^2 because there are 99 rows below first one. For pivoting each row below, you need to multiply the first row by some constant then subtract from the row you are pivoting. So, essentially are we not ending up having 2 operations per row for those 99 rows, hence, 99*2 instead of 100^2 ???" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 12439.0 0.0 1.0 0.0
"why i can't watch it?" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 15321.0 0.0 0.0 0.0
"Blackhole as singular has failed the singularity theory rather represent an unsteady conditions vaporises and disappeares into space cheating markov matrics of singularity.This really is a hats off to Einstein who predicted that Blackhole forming a singularity was not acceptable to him.Whether Hon.Rogen Penrose will explain this?
Sankaravelayudhan Nandakumar on behalf of Hubble Telescope Research Committee.9940463369 nandakumarcheiro.nandakumar@gmail.com
S.Nandakumar." lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 2899.0 0.0 0.0 0.0
"Good job! I recently uploaded a video in which I solve in detail an 
exercise with eigenvalues and eigenvectors:     
https://youtu.be/5KGBNkYIBTc" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 4130.0 0.0 0.0 1.0
"43:28
Strang sensei thinks student makes a mistake

Strang sensei : *Death*" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1210.0 0.0 0.0 0.0
"does anyone have solutions to the problem sets on ocw?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12763.0 0.0 0.0 0.0
"as long as your expectations are average about life, you will do fine with statistics." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 12406.0 0.0 0.0 0.0
"@Vegasred125 good i like the the spirit.I'am 27 and would like to learn math from the scratch!!.Are you on twitter by the way?" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1750.0 0.0 0.0 0.0
"I love and appreciate this. But I am going to use it to help me go to sleep. " 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5726.0 0.0 0.0 0.0
"Taught the subject with such simplicity :-) Thank You Professor Strang for helping me finish. Has given me the courage to explore the subject further." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9015.0 0.0 0.0 0.0
"Thank you Professor Strang! Thanks MIT OCW!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9223.0 0.0 0.0 0.0
"Great professor changed his shirt" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 4324.0 0.0 0.0 0.0
"4:28 God, isn' it false ? Shouldn't it be  x = 1 and y = 2 ? Y is okay but x = -1 doesn't seem correct" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 1320.0 0.0 1.0 0.0
"Anyone else want to hug him so much?" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 2492.0 0.0 0.0 0.0
"A ""random variable is a function in programming"".... mic drop!" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 2091.0 0.0 0.0 0.0
"I am 16 and I learn it at school in Australia." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5050.0 0.0 0.0 0.0
"What is the textbook used for this course?  It would be a help to supplement the lecture." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11539.0 0.0 0.0 0.0
"Truly amazing teaching skills. I want to see how well he would have explained it given more time." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11090.0 0.0 0.0 0.0
"Thank you. Prof. Strang." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9561.0 0.0 0.0 0.0
"His goal is to find the derivative of ln x which is w. At that case, derivative of ln x is unknown but can be found by using the fact that we know the derivative of e^x (which he found earlier). By taking exponential, he gets rid of the lnx whose derivative is not known and applies chain rule to find d ln x/ dx." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4751.0 0.0 0.0 0.0
"I Really Like The Video Projection Matrices and Least Squares From Your" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 4993.0 0.0 0.0 0.0
"16:20 This phrase was inspiring." IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 473.0 0.0 0.0 0.0
"Someone know what linear algebra book  use in MIT?" HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 8836.0 0.0 1.0 0.0
"Why can free variables take any value? I understood how to identify a free variable(column without pivot) but what does it mean for a variable to be free?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 11794.0 0.0 1.0 0.0
"Thanks thanks a lot" gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 9795.0 0.0 0.0 0.0
"thank a lot Vector spaces" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14454.0 0.0 0.0 0.0
"I just repeated watching this video twice and then got the idea of why L is better than E. Thanks Dr. Strang" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 5616.0 0.0 0.0 1.0
"i found a similar proof for the derivative of trigonometric functions. to prove sinx/x=1 we can imagine that as x----->0, the ratio of the opposite side to the hypotenuse approaches zero, but so does x. since they both because infintesimally small, but not exactly zero. their quotient should equal 1 right? " kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13380.0 0.0 0.0 0.0
"a big thanks tothis prof for his efforts to give us cours about linear algebra
" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 12279.0 0.0 0.0 0.0
"Mafia Mob moment at 11:36" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7560.0 0.0 0.0 0.0
Awesome. 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2787.0 0.0 0.0 0.0
"@stupidmonkey246 they've taken trig already. they know about vectors (thats when we learn them in florida). maybe not so much about cross and dot products. I wouldnt expect them to know any good algebra but at least component addition and the basics. i had a good trig teacher in high school and i was exposed to dot and cross products. " YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2029.0 0.0 0.0 0.0
"the bus arrival example is great after its further intuitive explanation, thanks." XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 14672.0 0.0 0.0 1.0
"Not as many comments. Did we lose some ppl somewhere???" TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 7918.0 0.0 0.0 0.0
"link to lecture notes https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/video-lectures/lecture-5-discrete-variables-probability-expectations/MIT6_041F10_L05.pdf" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 13807.0 0.0 0.0 0.0
"mathematical language is everywhere same so
people may have easy relationship" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13916.0 0.0 0.0 0.0
"Interesting fact: Almost everyone thinks this is easy never gets close chance into  MIT, so are their academic achievements." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6727.0 0.0 0.0 0.0
"I read something on SVD without even knowing about eigenvalues and eigenvectors, then watch a youtube video, explaining that V is actually the eigenvector decomposition of A^TA. Which is extremely insane when I got to see this video oh my godness. Now even haven't watched your SVD lecture, I can even tell the precise concept of it. Oh my godness Math is so perfect!!" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 5902.0 0.0 0.0 1.0
"This one was really good on probability" 2K7CvGnebO0 "19. Saddle Points Continued, Maxmin Principle" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10886.0 0.0 0.0 0.0
"Can anyone please tell me how always sigma1 > sigma2 > ... sigma_r ?" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3041.0 0.0 1.0 0.0
"30:57 ""Matlab will do it, but it will complain"" what a humour xd" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 900.0 0.0 0.0 0.0
"Ap gzb pada rahe hai" buEtwpGvQpI "18. Roth's theorem I: Fourier analytic proof over finite field" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 2514.0 0.0 0.0 0.0
"in 47:38 what's the point of limiting the boundaries of the integral to exclude zero regions? wouldn't integrating over those areas (over the entire x) just ""add"" zeroes, thus yielding the same result?" CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 13580.0 0.0 1.0 0.0
"people in the comments really tryna get into mit" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 14173.0 0.0 0.0 0.0
"""so anytime I'm multiplying cofactors by numbers I think I'm getting the determinant of something""" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 174.0 0.0 0.0 0.0
"I am lucky to have the teacher that explained us linear regression THAT VERY WAY! :D" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5116.0 0.0 0.0 0.0
"41:!2 NEWTON'S METHOD" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1142.0 0.0 0.0 0.0
"@iDiViNeXx Definitely Dutch, I'm thinking German. That's a fairly strong Germanian sounding accent." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1881.0 0.0 0.0 0.0
"at 42:48 he says he will tell us how to get from A to U and then says there's a better way - get from U to A but goes off on a tangent and runs out of time. Anyone know a summary of where he was going with that?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12453.0 0.0 1.0 0.0
"Really simplified! Thank you!" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 8529.0 0.0 0.0 0.0
"Don't forget another great thing about MIT. MIT does thing like share these lectures." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3473.0 0.0 0.0 0.0
"I <3 MIT ^_^" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 4920.0 0.0 0.0 0.0
"Why are free variables chosen for assuming 0 & 1 to solve the equation, why not pivot. If I do, I am getting a different null space & its valid null space.Can someone help to understand why only free variables are chosen why cant we continue with same process with pivot variables to be 0&1 and hence obtain more solutions" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 11776.0 0.0 1.0 0.0
"If X is in [0, d/2] we shouldn't be counting the paper clips outside two lines, right?" CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 6485.0 0.0 1.0 0.0
"Where would we be without Descartes??











                        Nowhere" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11699.0 0.0 0.0 0.0
"46:17 I think row 2 would then become 0 1 0 and not 3 1 0 as the professor wrote down on the board." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1268.0 1.0 1.0 0.0
"Intellectually stimulating and after just one drink you really hear the humor of this guy ... small example 44.10 ... ""I guess I am giving you infinitely many possibilities so I can't expect a unanimous answer"" ... LOL" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 6721.0 0.0 0.0 0.0
"So all these concepts are taught in my college course, but they don't really tell how different topics are related. Then come exams, where you are supposed to link everything together on your own. I think this is why Dr. Strang's lectures are special!" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 8739.0 0.0 0.0 0.0
"The best of the bests" ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10005.0 0.0 0.0 0.0
"The first lecture was not recorded. We are hoping to record it when the course is taught again in the Fall.  In the meantime, please check out the course site here http://ocw.mit.edu/18-650F16 where you will find the slides that were used in all of the lectures." C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 10109.0 0.0 0.0 1.0
"Thank you Dr. Gilbert Strang. I am a senior lecturer at Azerbaijan State Agrarian University. I teach the subject Linear Algebrain in English . You explain very clearly." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 9099.0 0.0 0.0 0.0
"God bless MIT! Thank you very much!" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4077.0 0.0 0.0 0.0
"Lectures are much more interesting if you ponder about them beforehand. Thinking on your free time gets you asking more questions during the lecture." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7305.0 0.0 0.0 0.0
"The pentagon cash isn't budgeted for stuff like this." -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10223.0 0.0 0.0 0.0
"@joaopp3
Yes, some lecturers become so used to their courses that they start to forget what it is that is considered difficult by new students, and stupidly assume that ""everyone"" ""just knows"" what all math symbols and proofs mean.
In my opinion, the best way to teach a new concept is to give a quick summary of what it is going to be about and then give a lot of examples, and encourage the students to help solving them.
That's exactly what professor Strang always does, and that's one of the reasons why he is so amazing.

I also think that it is very important that a lecturer shows a genuine fascination for the subject, and is always willing to help the students and respects that some of them may have a harder time than others with certain parts;
and it is also a huge plus if the lecturer has a sense of humour and presents the lecturers in a relaxed way.
And Strang seems to have all of these qualities as well." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 1903.0 0.0 0.0 1.0
"I love MIT. I will study there one day." HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5719.0 0.0 0.0 0.0
"Thanks for the proof of nds = <-f_x,f_y,1>dxdy" WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9722.0 0.0 0.0 0.0
"Gauss or Euler?" Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3983.0 0.0 0.0 0.0
"I'm the 1000 viewer, very well explained lecture i guess that i'm gonna see all of them.

Thanks MIT" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6390.0 0.0 0.0 0.0
"Gilbert Strang - a legend in the making..." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 4012.0 0.0 0.0 0.0
"I wish I could be there! D; " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6192.0 0.0 0.0 0.0
"Very nice thank you." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11213.0 0.0 0.0 0.0
"uspset now lol" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14987.0 0.0 0.0 0.0
"at [46:30], he first said that the derivative of  Rayleigh's quotient at the saddle points are zero, and it sounds like to me that he was recorrecting it by the eigenvectors, and how the values of the R(x) would be the eigenvalues. Can anybody shade some light? Thanks in advance." xaSL8yFgqig "Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12469.0 0.0 1.0 0.0
"mit has high quality of blackboard" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 13953.0 1.0 0.0 0.0
"this is how you read a lecture, thank you sir." gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 14862.0 0.0 0.0 0.0
"The captions are off just enough to be annoying. :P Great set of lectures, though!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10039.0 0.0 0.0 0.0
"@phtotti cum on.. 
you learn it, but im sure you don't understand the whole thing about it.. lolz
high school level of teaching and college is different.. FTW? ^_^" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1972.0 0.0 0.0 0.0
"I hope everybody who get something good from OCW could give back to it in some day anytime if you feel good, making it better and better as we can do and helping more and more people feel good like us, thanks." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5583.0 0.0 0.0 0.0
"10:56 - Could someone explain this? I didn't get the derivative." k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 355.0 0.0 1.0 0.0
"Extraordinary intellect and brilliant math professor" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3711.0 0.0 0.0 0.0
"Thank you so much." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9408.0 0.0 0.0 0.0
"I really respect Prof. Gilbert Strang!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5935.0 0.0 0.0 0.0
"Where are the labs? They are mentioned in the syllabus, but are not in the OCW material." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11655.0 0.0 0.0 0.0
"I've finished this course a while ago. still, going through Markov chains in probability was confusing till I came back and watched this, and again, Mr Strang came to the rescue.
I don't know how much I need to thank you for your online courses for it to be enough, as simply saying thank you doesn't do you justice. I just want to say that you, Mr Strang is one of a minority of people who indeed make this world a better place.
Thank you, from some corner of this Earth." lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 6415.0 0.0 0.0 0.0
"Totally confused once he got to three variables..." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11075.0 0.0 0.0 0.0
"It hurts so much seeing him getting old. He's the most beloved teacher I've ever had :'(." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6921.0 0.0 0.0 0.0
"Anyone have thoughts of whether to take notes on this or the MITx version on edX?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2498.0 0.0 0.0 0.0
"@turkeyburgerfries same problem with me" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2053.0 0.0 0.0 0.0
"All these lectures are GOLD. Thank you MIT for making them available for free." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 2310.0 0.0 0.0 0.0
"According to my stereo headphones, all the noise is coming from the left side of the room.." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 2227.0 1.0 0.0 0.0
"in which lecture is the rank nullity theorem discussed?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13604.0 0.0 1.0 0.0
"In india we learn this topic in class 11 maths" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6637.0 0.0 0.0 0.0
"Lecture 1: Dot Product
Lecture 2: Determinants
Lecture 3: Matrices
Lecture 4: Square Systems
Lecture 5: Parametric Equations
Lecture 6: Kepler's Second Law
Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds)
Lecture 8: Partial Derivatives
Lecture 9: Max-Min and Least Squares
Lecture 10: Second Derivative Test
Lecture 11: Chain Rule
Lecture 12: Gradient
Lecture 13: Lagrange Multipliers
Lecture 14: Non-Independent Variables
Lecture 15: Partial Differential Equations
Lecture 16: Double Integrals
Lecture 17: Polar Coordinates
Lecture 18: Change of Variables
Lecture 19: Vector Fields
Lecture 20: Path Independence
Lecture 21: Gradient Fields
Lecture 22: Green's Theorem
Lecture 23: Flux
Lecture 24: Simply Connected Regions
Lecture 25: Triple Integrals
Lecture 26: Spherical Coordinates
Lecture 27: Vector Fields in 3D
Lecture 28: Divergence Theorem
Lecture 29: Divergence Theorem (cont.)
Lecture 30: Line Integrals
Lecture 31: Stokes' Theorem
Lecture 32: Stokes' Theorem (cont.)
Lecture 33: Maxwell's Equations
Lecture 34: Final Review
Lecture 35: Final Review (cont.)" phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7277.0 0.0 0.0 0.0
"This professor gets more applause in class than any other Ive ever seen." YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10891.0 0.0 0.0 0.0
"@HappyBuddhazz99 I've learned this first hand; the only difference between going to let's say MIT, and a state university; is the name of where you got your degree. My cousin, who lectures at Stanford once every two weeks for a multi variable calculus class, has noticed that the class is using the same book as I am." 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1630.0 0.0 0.0 0.0
"How did he deduce that (A-B).(A-B) equals (|A|^2+|B|^2-2A.B) without expanding?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4833.0 0.0 1.0 0.0
"Thank you Dr. Strang and MIT. These videos are amazing and keeping me afloat in my class." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9101.0 0.0 0.0 0.0
"great lecture
" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12977.0 0.0 0.0 0.0
"here is the link to the whole playlist 
https://www.youtube.com/watch?v=PxCxlsl_YwY&list=PL4C4C8A7D06566F38" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13141.0 0.0 0.0 0.0
"Only the strongest survive but oscillates between +1 and -1 as inversion functions as diagonalised along x and y axis ." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8124.0 0.0 0.0 0.0
"Just finished the whole Single Variable Calculus course.
Thank you MIT OCW for making this possible.
Chile, 2019.


-One thing to rule them all
One thing to find them
One thing to bring them all
And in a matrix bind them-" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7175.0 0.0 0.0 0.0
"14:24 This clarifies the difference between Examples 2 and 3. Just shows how unintuitive some probability problems can be." R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 428.0 0.0 0.0 0.0
"This is phenomenal." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10704.0 0.0 0.0 0.0
"thanks a lot
" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14565.0 0.0 0.0 0.0
"So f""x is a weird Math's rollercoaster" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8753.0 0.0 0.0 0.0
"28:43 A small mistake here. These three vectors are not the basis.
(-v1 + 2v2 - v3=0)" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 842.0 0.0 1.0 0.0
"i'm sorry but what properties make the initial split (around 4:00) possible?

linearity says  that 

det 

a+a'  b+b'
c  d 

equals det

a  b
c  d 

plus det

a'  b'
c  d


or yet that you can factor a scalar out of a row in a way that

det

ta  tb
c   d

becomes

t * det

a  b
c  d





and I don't see how this makes it possible to split 

det
a  b
c  d

into det

a  0
c  d

plus det

0  b
c  d


am i missing something?" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 13517.0 0.0 1.0 0.0
"but why divide by n-1 to make it unbaised" 4UJc0S8APm4 "23. Classical Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 12577.0 0.0 1.0 0.0
"does anyone know what textbook they use for this course?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12766.0 0.0 0.0 0.0
"Of Anyone, Massachusetts ""Institute for Technology"" should be able to level the volume so we can hear it..  Breaking edge technology, but makes movies with 1990's PBS vibes..  WOW

Thanks for the videos though!" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 7993.0 0.0 0.0 0.0
"I Really Like The Video Integration by inverse substitution; completing the square From Your" CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4978.0 0.0 0.0 0.0
"Preparing for IIT/IISC M.S interviews. IIT Madras, Electrical Engineering department had recommended this lecture" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8239.0 0.0 0.0 0.0
"He says fxy = fyx , that's assuming both fxy and fyx are continuous" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4602.0 0.0 1.0 0.0
"Great!!!! (💝💝💝)^∞" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4372.0 0.0 0.0 0.0
"have been waiting for his functional analysis for a long time!!! 😃Thank you!" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 13063.0 0.0 0.0 0.0
"This is a 90-degree chapter, Strang meant business from the word go!" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10585.0 0.0 0.0 0.0
"@ 26:04 I have to admit, that took me a second to figure it out. 
Prof Strang didn't actually have anything wrong, he just couldn't see while in the middle of it why that was the case. He actually had it at 26:44 but let it slip through his hands.
For that you have to go back to when he was computing matrix ""V"".  The evec associated with eval of 18 was [1;-1] but it also can be written as [-1;1]

He chose the [1;-1] which had the effect once we made it to the final calculation of U * Diag^2 * V^t that it SWAPPED THE COLUMNS of A
His original A was [4,4;-3,3] and the calc'd one was [4,4;3,-3]
Had he chosen the 'other version' of the evec associated with Lambda = 18 when figuring out ""V"", he would have gotten back the same ""A"" he started with instead of the column-swapped version.
But what could go wrong? :-)" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 1473.0 0.0 1.0 0.0
"K.

Can I have my hat now, please?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7207.0 0.0 0.0 0.0
"I really love this course and the professor. Save my life!" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5930.0 0.0 0.0 0.0
"F prime is not Newtons notation for dervative. Newtons notation was a dot on top of the y variable." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3716.0 0.0 1.0 0.0
"Are there the seniors who took this course in their early under graduation courses .and  this has seemed very much helpful for them now ????" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 2533.0 0.0 0.0 0.0
"I watched Probability for Life Science, Lecture 1, Math 3C, UCLA, it's a very good class as well. Those of you who loves Prob and Stats, you should watch too" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 6182.0 0.0 0.0 0.0
"the cilynder oriantaion of C and C ' are opposite" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14675.0 0.0 1.0 0.0
"38:30 closed caption is wrong. It is ""discrete"" not ""discreet.""" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 1080.0 0.0 0.0 0.0
"he finally broke character and laughed on the blackboard cleaning trick." wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 13077.0 1.0 0.0 0.0
"i lost my mind when he taught about FFT. Anyway, Prof Gil. Strang is brilliant." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 13425.0 0.0 0.0 0.0
👍👍👍 VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 15704.0 0.0 0.0 0.0
30:13 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 884.0 0.0 0.0 0.0
"I Really Like The Video From Your Chain rule Higher derivatives" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4950.0 0.0 0.0 0.0
"i must say some guys ask really stupid questions. i felt like the professor having hard time not to say that." TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13442.0 0.0 0.0 0.0
"That's so unfair he says at 10:40 ish that they get all the formulas on the exam!! WTF we have to memorize ALL the stupid formulas" BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9937.0 0.0 0.0 0.0
"Dang - Prof Tsitsiklis is good! Reminds me of Gilbert Strang and Walter Lewin. Probably all MIT profs are good, eh?" XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 3312.0 0.0 0.0 0.0
"15:02 i couldn't find c for the projection matrix" QuZL5IKpO_U "24b. Quiz 2 Review" "MIT 18.06 Linear Algebra, Spring 2005" 446.0 0.0 1.0 0.0
"The brilliant series of lectures. However, this seems unclear one. I failed to understand the A derivation. What the system of equation does? Can you explain what Gilbert wanted to say? Wikipedia meantime does it trivially: A=[T(v1) T(v2) ..T (vn)]. " Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10025.0 0.0 1.0 0.0
"how can i get this lecture's  textbook??  pdf or something" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13200.0 0.0 0.0 0.0
look MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 13850.0 0.0 0.0 0.0
"@shakesbeer00 The parabola doesn't matter in terms of bounds because we know it becomes the unit circle in the xy plane. The double integral cares only about the xy plane, and so that's all you need to know in order to set up the integral." WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2010.0 0.0 0.0 0.0
"Excellent lecture. Thank you for sharing!" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3660.0 0.0 0.0 0.0
"I wish I was smart enough to understand what the fuck this guy is talking about." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 6211.0 0.0 0.0 0.0
"@gjeni7 It's in the beginning of the video. " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1852.0 0.0 0.0 0.0
"A text that will be suffiecient (if spelled correctly) for this course is CALCULUS
FOR ENGINEERS by DONALD TRIM
from university of manitoba. The course here in the hebrew university is too much hard, because they included logic, group theorem, induction and fields and computing methods first as a preview :(
good luck MIT anyway! :)" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2158.0 0.0 0.0 0.0
"Cool. He offers another direction here different from the book he wrote." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 3214.0 0.0 0.0 0.0
"@xkeikoxsanxdesu all the best mate, because its extremely hard to get into MIT even with A++ all round" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2066.0 0.0 0.0 0.0
"Genius of this Man is the way he is explaining such a difficult concept so easily..... Hatts Off. As per Indian Ethos I just want to touch your feet." rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3996.0 0.0 0.0 0.0
"You are lovely Dear Professor.
Thank you very much." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12174.0 0.0 0.0 0.0
"I have absolutely no idea what he's talking about (I just simply suck at math + I'm not that advanced) but the way he teaches it makes me curious about it and also wish I knew how to do math like that." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5514.0 0.0 0.0 0.0
"Not all heroes wear capes" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7916.0 0.0 0.0 0.0
"이게 계속 쓰지 말라던 로피탈이구나" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15687.0 0.0 1.0 0.0
Determinant srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 3359.0 0.0 0.0 0.0
"Just Completed the entire course. Multivariable Calculus was always on my mind since  my high school days. It was everywhere in electromagnetism, however somehow our teachers got away with 2D versions and some mischief, was just fine. Afterwards I went into Computer Science and never got chance to learn it. I always loved physics, however not knowing vector calculus was embarrassing, it was literally everywhere. Then I decided to do it this summer. Hats off to Professor Auroux, he teaches so smoothly never during the entire course I felt like once I feared it. It was so smooth (plus his board work! you will see what I mean when you take the course :)). I feel so much happy now, Thank you Professor Auroux and MIT for bringing us this wonderful course." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7148.0 0.0 0.0 0.0
"would be nice if he related d/dx ln u that he uses to the method taught in the book. Makes things confusing and synthetically hard." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15404.0 0.0 1.0 1.0
"16:55 There was a joke that we didn't get to hear :(" Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 492.0 0.0 0.0 0.0
"Amazing. Think about it, xparticular plus the nullspace gives final x in r4, is the same as y=a*x+b in r2! This really blows your mind. Great class" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 2406.0 0.0 0.0 0.0
"Excellent lecture from an excellent instructor" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3652.0 0.0 0.0 0.0
"perfect.   God bless you..." NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14177.0 0.0 0.0 0.0
"is there any textbook for this course?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 13652.0 0.0 0.0 0.0
"i just want to give him a hug for his love towards his teaching" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 13409.0 0.0 0.0 0.0
"@20:30 derived dist." H_k1w3cfny8 "10. Continuous Bayes' Rule; Derived Distributions" "6.041 Probabilistic Systems Analysis and Applied Probability" 1512.0 0.0 0.0 0.0
"at 49:55 why did he divided it by the length , if anyone could explain i will appreciate it" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12461.0 0.0 1.0 0.0
"I like the the way you are analyzing the questions" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5684.0 0.0 0.0 0.0
"""Maybe you don't need this class"" - oh yeah, I do." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 86.0 0.0 0.0 0.0
"Wow this old man is so smart. I would wish to see more lectures from him and learn much more of this stuff." wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12044.0 0.0 0.0 0.0
"Again very high quality of recording! Thanks. And surely great lection." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 2271.0 0.0 0.0 0.0
"Mark: I skip this lecture." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 7596.0 0.0 0.0 0.0
Brilliant hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2923.0 0.0 0.0 0.0
"This is extremely non-standard: the video starts with Professor Strang having already written his material on the blackboard.
We do not get to see the back of his head bobbing up and down as he spends half the video's time writing laboriously on the board. 
Who permitted this?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10661.0 1.0 0.0 0.0
"Sen nasıl  bir kralsın yaa." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 8626.0 0.0 0.0 0.0
"I am kind of confused about the y=Ce=CAx  in this lecture. How we can draw this conclusion from the process of resolving the equation instead of relying on the physical explanation?" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5112.0 0.0 1.0 0.0
"thanks for uploading" ImHAGH_OEow "Lecture 20: Taylor's Theorem and the Definition of Riemann Sums" "MIT 18.100A Real Analysis, Fall 2020" 14591.0 0.0 0.0 0.0
"41:52 -- LOL  (I'm officially a math-geek.  Then again, it's a calm, late-summertime Saturday Morning high in the Rocky Mountains and I'm watching this.  The conclusion was a bit forgone.)  Regrettably, way back in the day,  my fundamental default position was that all concepts were derivative and that prior to use their source must be known.  Here's how I wish a trusted mentor would have advised me regarding Linear Algebra in my third college semester: ""The core things of linear algebra have been completely made-up and have only subsequently been discovered to have very interesting properties and to be extremely powerful (but only under certain conditions.)  Linear is mostly a short-hand notation for some stuff with which you are already familiar -- systems of linear equations. (Demanding to know the legitimacy of this new symbology is nonsensical.  It's very much equivalent to demanding to know why the utterance 'dog' is used to express the concept of a canine.  Worse -- it's like trying to derive the significance of the 'og' part of that particulate word.)  The core things of linear algebra are merely tools -- or better yet: heavy machinery.  They allow mathematical professionals (of the type you seem to aspire to be)  to 'move around', or to think in broad terms, about vast quantities of calculations that you have become expert at doing manually.  As with any scientific concept, their perfection is provisional.  Rest assured though, that they have been studied extensively for many centuries.  What they're good for, how they can be worked with, and where they fail are are all reasonably well known (as an example from today: Associative works; Commutative does not.)  Many people find linear algebra very useful.   Now, before this get's out of hand, let me first say that you are absolutely not 'many people.'  Further, I fully understand that trust and acceptance and taking-the-easy-way-out and group-think all scare the livin'-be-jesus out of ya. So I'm not asking that trust me and study linear because I know that it's right (we've already established that I don't), nor that you go-along-to-get-along, nor that you buckle down and learn this because it's what everyone else is doing.  What I'm offering here, for your consideration, is that the baubles you'll pick up from mastering linear will likely give you a really nice view of the mathematical world -- and I'm pretty sure you'll like that.  Have fun!""" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1164.0 0.0 0.0 0.0
"Don't feel too akward professor, there are people actually listening on the other side, maybe even more eagerly than some of the students that get to be there in person." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 3472.0 0.0 0.0 0.0
"Although I have learnt Linear Algebra in last semester, Still feeling refreshed and amazed watching these lectures, Dr. Strang's teaching skill is sooo good!!!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2326.0 0.0 0.0 0.0
"People like this prof are a rare breed. Brilliant and yet able to articulate in a manner that everyone can understand. Thanks, MIT!" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 8170.0 0.0 0.0 0.0
"I love this professor's lectures on this topic. He has explained one of the most complex concepts in vector calc in a very simple way!thank you" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5833.0 0.0 0.0 1.0
"Why aren't there black cs professors?" 1VhnDdQsELo "14. P and NP, SAT, Poly-Time Reducibility" "MIT 18.404J Theory of Computation, Fall 2020" 11790.0 0.0 0.0 0.0
"Thanks for opencaourseware that we can learn from this legend of Linear Algebra...." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9690.0 0.0 0.0 0.0
"I Really Like The Video From Your Differential Equations and exp(At)" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 4952.0 0.0 0.0 0.0
"Single Variable Calculus?  Multi-Variable Calculus?  Can't we just say Calc 1, Calc 2, or Calc 3 instead of coming up with fancy names?" aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8684.0 0.0 0.0 0.0
"It is worth pointing out that A in the the notation N(A) (16:00) is a generic reference to matrix, not the Markov matrix used as a concrete example. Clarify this confusion, and we could better understand why the eigenvector of eigenvalue 1 is in the null space of ‘A’." lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 6973.0 0.0 1.0 0.0
"1:13:56 I am not sure why c has to be greater or equal to -1." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 588.0 0.0 1.0 0.0
"Pls Can Anybody answer me Where is Lecture 8 ??!!!!!!!!!!!" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8220.0 0.0 0.0 0.0
"Hereby you start a journey that many shall fail.


Warm wishes, traveler." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4682.0 0.0 0.0 0.0
"Is this the only lecture of the series in which he wears a different colored shirt (sky blue in rest all)😉?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 6884.0 0.0 0.0 0.0
"it is a fortune to have these videos. thank you" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13673.0 0.0 0.0 0.0
"He is probably the worst professor I ever saw to be completely honest." C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 4531.0 0.0 0.0 0.0
"I started off just wanting to pick up a few tips for 3D graphics.. dipping in .. and then this truly wonderful man drew me in. This is not mere teaching. It's sharing understanding, and the lectures are often the *exploration* of understanding. Thank you so much, prof. And thanks to  MIT, for sharing you with the world." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5970.0 0.0 0.0 1.0
"Thank's this is a good help for me, I have test of Differential calculus soon" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9571.0 0.0 0.0 0.0
"22:47 - ""Think of a solution, then figure out what b turns out to be."" I see what you did there, very clever." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 703.0 0.0 0.0 0.0
"last lecture . awesome lecture." aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13757.0 0.0 0.0 0.0
"""what b turns out to be...right! "" 😀" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 193.0 0.0 0.0 0.0
"I was kinda lost through this video, wondering why he was calculating dimensions of the four subspaces of this graph matrix, while also guessing why he chose the edge matrix A the way he did(As a CS student I'm used to seeing graph in a different way). Then literally at the final minute he explained how the transformation worked and I was overjoyed for having an epiphany. I love linear algebra now." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6157.0 0.0 0.0 0.0
"I can hear quite fine on this lecture but not lecture 1. Very strange." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5190.0 0.0 0.0 0.0
"For BPP, deep learning and for the general structure of neural networks the following comments may be useful. 

To begin with, note that instead of partial derivatives one can work with derivatives as the linear transformations they really are. 

It is also possible to look at the networks in a more structured manner. The basic ideas of BPP can then be applied in much more general cases. Several steps are involved. 

1.- More general processing units. 
Any continuously differentiable function of inputs and weights will do; these inputs and weights can belong, beyond Euclidean spaces, to any Hilbert space. Derivatives are linear transformations and the derivative of a neural processing unit is the direct sum of its partial derivatives with respect to the inputs and with respect to the weights; this is a linear transformation expressed as the sum of its restrictions to a pair of complementary subspaces. 

2.- More general layers (any number of units). 
Single unit layers can create a bottleneck that renders the whole network useless. Putting together several units in a unique layer is equivalent to taking their product (as functions, in the sense of set theory). The layers are functions of the of inputs and of the weights of the totality of the units. The derivative of a layer is then the product of the derivatives of the units; this is a product of linear transformations. 

3.- Networks with any number of layers. 
A network is the composition (as functions, and in the set theoretical sense) of its layers. By the chain rule the derivative of the network is the composition of the derivatives of the layers; this is a composition of linear transformations. 

4.- Quadratic error of a function. 
...
——-
Since this comment is becoming too long I will stop here. The point is that a very general viewpoint clarifies many aspects of BPP. 

If you are interested in the full story and have some familiarity with Hilbert spaces please google for papers dealing with backpropagation in Hilbert spaces. A related article with matrix formulas for backpropagation on semilinear networks is also available. 

For a glimpse into a completely new deep learning algorithm which is orders of magnitude more efficient, controllable and faster than BPP search in this platform for a video about deep learning without backpropagation; in its description there are links to a demo software. 

The new algorithm is based on the following very general and powerful result (google it): Polyhedrons and perceptrons are functionally equivalent. 

For the elementary conceptual basis of NNs see the article Neural Network Formalism. 

Daniel Crespin" L3-WFKCW-tY "33. Neural Nets and the Learning Function" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3837.0 0.0 0.0 0.0
"Did you figure out inverse cosine of 1/root10 before hand...or do you have a trick you used to figure it out immediately?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3392.0 0.0 1.0 0.0
"Fantastically succinct with a pinch, sprinkle if you will, of humor. This coupled with the high contrast between the chalk and chalkboard makes for a well-needed lecture. Very few professors can make me prefer lecture to just reading on my own, ADHD here. THANK YOU MIT!!" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3744.0 1.0 0.0 0.0
"My left ear feels grateful..." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7766.0 0.0 0.0 0.0
yes aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15481.0 0.0 0.0 0.0
"Whenever he wipes the board I get SOOO excited..." YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11652.0 1.0 0.0 0.0
"Any intuition for the rank to be n-1 ??" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2469.0 0.0 1.0 0.0
"For more intuition about the Green's Theorem, can it be thought of as- the potential energy stored in the rotational motion stored in the line integral of the closed curve is sum of the potential at the area inside curve, sort of like if you start twisting a rubber sheet, you get the work done on the closed curve when the rotation propagates radially outwards-building up from the work done on the closed curves of increasing radius?" tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3867.0 0.0 0.0 0.0
"@daemonpacman yeah... yours show better... but made by foreigns.. ;)" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1820.0 0.0 0.0 0.0
"""Mondie""" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 89.0 0.0 0.0 0.0
Perfect yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 8176.0 0.0 0.0 0.0
"https://www.youtube.com/channel/UCd9MR3W9EGwicP6fTJQN5Gw/videos     Here is a helpful playlist for you to revise linear algebra quickly. Do like, share and subscribe for more such content!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13267.0 0.0 0.0 0.0
"Just for clarity, for the 3SAT to CLIQUE conversion, the vertices of the graph are not the unique literals themselves, but rather for each clause in the formula there must be one vertex for each one of its literals. So formally, the vertices can be seen as ordered pairs (n,X), where n indicates a clause of the formula and X indicates one of its literals. Then the construction is that vertices (n,X) and (m,Y) are connected by an edge if and only if n≠m and the truth of X is consistent with the truth of Y." iZPzBHGDsWI "15. NP-Completeness" "MIT 18.404J Theory of Computation, Fall 2020" 7182.0 0.0 1.0 0.0
"Thank You, Professor Strang.
You are an awesome and an inspirational teacher.
I enjoyed this course very much." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9058.0 0.0 0.0 0.0
"he is so dam good at explaning! I love him!!!!!!!!!!!" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 13099.0 0.0 0.0 0.0
"Is that course for freshman year students?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6805.0 0.0 0.0 0.0
"The ""idea"" of orthogonal projection allowed me to understand the Christoffel symbols. I ""studied"" all the lectures on MIT 18.06 but I am still discovering the linear algebra anew. Thanks G.S. , thanks MIT." ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9954.0 0.0 0.0 1.0
"Thank you so much. I'm extremely grateful to be living in a time where this much knowledge is so accessible. I'll try my best to support this content :)" 3eiio3Tw7UQ "19. Weak Law of Large Numbers" "6.041 Probabilistic Systems Analysis and Applied Probability" 9411.0 0.0 0.0 0.0
"Legendary. No other words. And I’m only 5 lectures in! Can’t wait for more. Thank you to everyone involved in making MIT courses so available!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 7326.0 0.0 0.0 0.0
"I came here to fall asleep ended up learning a lot." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5181.0 0.0 0.0 0.0
"Long long time ago, almost failing in math classes, I came across Prof. Strang's linear algebra course. Now doing a PhD in machine learning focusing on stochastic optimization." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7412.0 0.0 0.0 0.0
"How do you prove the single row linearity of a determinant, I mean how is in matrix A + matrix B we sum ALL rows but in det(A) + det(B) we don't?" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 4858.0 0.0 1.0 0.0
"Strang is great, Youtube needs improvement... we need a speed between 1.5 & 1.75" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 8906.0 0.0 0.0 0.0
"Take a drink everytime he AUMM" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 9007.0 0.0 0.0 0.0
"1:13:20, when the professor is pointing to the slide, the camera should better point to the slide, too." 0Va2dOLqUfM "5. Maximum Likelihood Estimation (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 586.0 1.0 0.0 0.0
"Did he say ""i'll meet you tommorroww @2:00am""??
DAMN!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3377.0 0.0 0.0 0.0
"Thank you very much MIT!" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9432.0 0.0 0.0 0.0
"Brilliant./ Pura arivu external knowledge.Intelligence /Aha arivu ie internal knowledge." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2948.0 0.0 0.0 0.0
"Newton's method starts at 41:10 if anyone else is looking for that.

Good lecture :}" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7828.0 0.0 0.0 0.0
"There's one video on Khan academy multivariable calculus talking about this, didn't quite get it. Now after his explanation, I finally know what is that.XD" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 10389.0 0.0 0.0 0.0
"David Jerison is a condescending asshole. I looked up one of the midterms in the OCW for fun and it says at beginning or end after test “congratulate yourself by basking in your superiority as you wait for the others to catch up” or something along those lines. It is no wonder some MIT graduates have insufferable egos. Check the courseware yourself if you don’t believe me. His talk about calculus being under appreciated just reeks of a passive aggressive superiority inferiority complex." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3318.0 0.0 0.0 0.0
"At 02:10, in the denominator, why is the total circumference 2*pi ? Shouldnt it be 2*pi*a ?? I would suggest that since the radius is ""a"" and not 1? But appearently im wrong? Someone explain!" BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2579.0 0.0 1.0 0.0
"Today I have statrted this course. This is really awesome. I just want to know which book I should follow for this course?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11053.0 0.0 1.0 0.0
"Professor Strang thank you for explaining the Orhonormal Column's in Linear Algebra. These topics are important for a solid building blocks in advanced mathematics." Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8368.0 0.0 0.0 0.0
"There is a mistake at 38:53.  It should be E[alpha] = alpha." 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 10364.0 0.0 1.0 0.0
"How would you get that?" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4909.0 0.0 0.0 0.0
"I love this GrandPa - I really do - I hope someone closer to him let him know (I am in South Africa)" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5800.0 0.0 0.0 0.0
"@tbarker5252 So you are saying is that the graph with no loops he drew at about 38:00 is not a tree? He didn't give any definition, he said ""A tree is the name for a graph with no loops"" meaning that a graph with no loops is a tree, which is absolutely correct, no matter how you look at it! You certainly don't need any degrees to see that ;)" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2036.0 0.0 0.0 0.0
"My best professor !!!!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7736.0 0.0 0.0 0.0
"Wow,there are lots of math geniuses making comments.Just enjoy the lesson dumb fuckers." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12083.0 0.0 0.0 0.0
"I think I am getting the point of linear equations. Almost thirty Years after I should have gotten it." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5994.0 0.0 0.0 0.0
"Anyone else get annoyed at the students walking in late? ""You are blowing it, kid!""" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2486.0 0.0 0.0 0.0
"He is so slowly teaching, but is a wonderfull teacher." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 4539.0 0.0 0.0 0.0
Perfect j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 8175.0 0.0 0.0 0.0
"Very good. Thank you. But in the first example at min. 29:30 , why you go (-1) in the "" X ""direction ? I think it's (+1) , so the Vector will be < 1, 1, 0  >." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11191.0 0.0 1.0 0.0
"27:00 *""Gram had, like, one idea. I, I, ...I don't know WHAT Schmidt did""* 😂
Two seconds later: *""Meh, we don't need either of them actually.""* 😂😂😂

I read the comments in advance, then waited patiently for that roast 🦃🍗. Not disappointed 😂👽" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 812.0 0.0 0.0 0.0
"We learn this subject at high school in Russia" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11323.0 0.0 0.0 0.0
"my math class is using the textbook from Strang atm and these videos pretty much cover the concepts from it. I'm so glad I found this because I can't understand my math teacher at all because of his thick accent. I'm paying for an education but I'm getting it from here." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13990.0 0.0 0.0 0.0
"oh, these're beautiful, the arc length curves, we just were told to memorize the formulas, while learning them, in highschool, it's eato understand, thank you, Professor🌞" TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14119.0 0.0 0.0 0.0
"Guys I beg you that you help me out with this lecture.This is the 10th time i'am watching this.I understood only the first 4 steps." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4386.0 0.0 0.0 0.0
"Thanks @MIT opencourseware!
It would be great if you can put the lecture title for ease of student. 
thanks!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9584.0 0.0 0.0 0.0
legend rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13778.0 0.0 0.0 0.0
"How do we know that cos and sin are the only possible unique/independent solution to the differential equation @19:00" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 4854.0 0.0 1.0 0.0
"Lecture 8 is Exam 1, so no video was recorded." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7290.0 1.0 0.0 0.0
"this guy should have used wallis formula for cos^4 theta. this will be a LOT SIMPLER LOL" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14839.0 0.0 1.0 0.0
"This is calc 1... 
math is pretty universal the numbers aren't different on their campus. Granted less renown colleges have the majority of their freshmen starting higher than calc 1." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10654.0 0.0 0.0 0.0
"i confuse headache" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13352.0 0.0 0.0 0.0
"can you prof ""n"" is infinity" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12638.0 0.0 1.0 0.0
"When he lists all the topics, it's pretty impressive what has been covered in this unit of the course. I've had to watch videos 11 through 14 about 3 times to feel comfortable with them.Can't wait to see what's next..." ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11617.0 0.0 0.0 0.0
"😭😭.. Linear algebra was never understandable to me before, I always it only there to make my life difficult... This series saved me. So much love and respect Prof.Gilbert. Bless you. 💜" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 15738.0 0.0 0.0 0.0
"this guy is a complete mess..." WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 14809.0 0.0 0.0 0.0
"Can someone point out when the vector spaces start? Thanks!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 3097.0 0.0 1.0 0.0
"that is so great!!! My math teacher never teach me this way, she just told us to remember the formula and no need to understand what's behind." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14635.0 0.0 0.0 1.0
"7:11 the subtitle guy was not technical, lol. So everything is very cursive?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1394.0 0.0 0.0 0.0
"35:14 Ohh it looks like 12345 😍😍😍😍😍😍😍😍" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 1001.0 0.0 0.0 0.0
"@ 41:30 I think you mixed up notation authors. Lagrange's notation is the one that uses the prime symbol. Newton's notation is the dot notation. However, Newton *did* use prime symbols for integration notation; but the prime symbols were placed above the variable." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1477.0 0.0 1.0 0.0
"The facilities they provide and professors that they are hire are among the best in the world.  Those things are not cheap.

They need donations to provide the free education.  This, the free education, costs them money to produce and host.

Don't also forget that MIT went against the will of the rest of the top universities in being the first one to initially provide this free education.  They effectively coerced other top universities to do the same.  They are doing for the benefit of society." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10097.0 0.0 0.0 0.0
"18:26 Limits and Continuety" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 538.0 0.0 0.0 0.0
"Exam 4 has misprinted integrand in problem 3. You can find the correct one in the solutions." BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3620.0 0.0 1.0 0.0
"Are you accepted to MIT? If not, shut up. " eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2538.0 0.0 0.0 0.0
"We're so impressed about the fact that you all learned this in high school. Shut up about it." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11339.0 0.0 0.0 0.0
"@yalg22 @yalg22 1) is not the definition of the derivative since it is multiplied by (x-xzero)  
Also, independent limit taking is a neat trick.  It really makes no sense intuitively.  That is the whole problem with the proof.  Without independent limit taking you end up with 0/0 in the limit multiplied by some unknown delta f which also approaches zero in the limit under the assuption of continuity.  " ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2073.0 0.0 1.0 0.0
"This professor is a genius :)" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10895.0 0.0 0.0 0.0
"Thats A VERY VERY ESSENTIAL lecture for machine learning 
i used to do the transpose trick but didnt know where it come from, know i may die in peace" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9949.0 0.0 0.0 0.0
"This man is just a legend! Thanks Mr. Strang :)" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10868.0 0.0 0.0 0.0
"Man I love this video!" zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7570.0 0.0 0.0 0.0
"textbook suggested for this course?" QXkOaifVfW4 "9. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 14444.0 0.0 0.0 0.0
"Buy why is trace a sum of eige values and det product of it" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 2969.0 0.0 1.0 0.0
"You can't really call this a lecture on Max-min problems if he's doing graph sketching all the way up to 5 mins before the end of the lecture, and only then does he even mention maxima and minima." twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12196.0 0.0 1.0 0.0
"To have in America's schools and universities, good grades, you must not be smart. The biggest idiots get  good grades and a student space." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11038.0 0.0 0.0 0.0
fantastic cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 12843.0 0.0 0.0 0.0
"God bless you, just love each word comes out of his mouth. Very well explained. Spent a lot of time in books trying to understand the basic concept. The illustrations helped me to grasp the whole idea." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 4089.0 0.0 0.0 1.0
"This lecture is just amazing, what a beautiful thing, all coming together..." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 10804.0 0.0 0.0 0.0
"This is what I call a ""valuable"" math lecture. Time is spent to explain to students ""why"" things are true. While in institutions I've been to, time is spent to read slides for students and show them how to solve problems without even having a slightest idea about the procedure there making to solve a problem." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10768.0 0.0 0.0 1.0
"Isn't the dimension of N(C transpose) 14?
Because dimension of C^T is 20 and rank is 6." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 6896.0 0.0 1.0 0.0
"Math is such a beautiful thing..." XhSk_Lw2X_U "14. Low Rank Changes in A and Its Inverse" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7609.0 0.0 0.0 0.0
"its good....but too elementary.....we had learn it in High schools" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13710.0 0.0 0.0 0.0
"So far, this was the only difficult lecture. This lecture, I think, I'll need to work out a lot of what he's saying. It was ok in the beginning. It got tough until 30 min, then it gets back to being easy." 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8756.0 0.0 0.0 0.0
"00:00 - 14:20
equation of plane formed by 3 points in space

14:21 - 19:13
matrices 

19:14 - 29:02
matrix multiplication

29:03 - 37:29
identity matrix
transformations

37:30
matrix inverse" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 277.0 0.0 0.0 0.0
"Great thanks to these awesome lectures which give me insight for matrix..." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4347.0 0.0 0.0 0.0
"Those who are seeking a more rigorous point of view may refer to Appendix A.2 of the 18.01 (Fall 2006) course textbook: Simmons, George F. Calculus with Analytic Geometry." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10996.0 0.0 0.0 0.0
"Amazingly fabulous." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2409.0 0.0 0.0 0.0
"(1)Does it matter which matrix is taken the conjugate of when computing the standard norm?" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 215.0 0.0 1.0 0.0
"Professor Strang is my new favorite person." or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8351.0 0.0 0.0 0.0
"What if... It's over 9000? " 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11509.0 0.0 0.0 0.0
"Gilbert Strang is one of the BEST professors in the whole world! He has the power to really transmit knowledge and encourage students to learn more. He’s so charismatic and loves what he does. If a Nobel Prize of Mathematics existed it should be given to him for his great labour to the world of mathematics!!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4024.0 0.0 0.0 0.0
"Respect! Thank you Dr. Strang" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 8563.0 0.0 0.0 0.0
"sorry i'm confused at 32:22, it is 100 ^2, but i think it is 100, why it isn't 100? could anyone explain that to me? thx alot" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 14376.0 0.0 1.0 0.0
"23:37 Wow... Respect to MIT. In my school everyone would have burst out in laughter and it would have taken like 15 minutes to shut everyone up again." wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 716.0 0.0 0.0 0.0
"""We don't really know what it means to divide by differentials.""

I could have sworn Abraham Robinson was famous for something.. what was that again?" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 129.0 0.0 1.0 0.0
"Linear algebra, it's been almost 3 years but I think I've finally got you. *sob *wished I could go back in time" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7381.0 0.0 0.0 0.0
"wtf this math is trivial
" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 15448.0 0.0 0.0 0.0
"""Does that answer your question?"" Incredible respect. We had teachers which said that if you don't understand these you are an Idiot" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 40.0 0.0 0.0 0.0
"What book should i use for this course ." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11473.0 0.0 0.0 0.0
"I can only grasp the subject from figuring out what he draws, because his explanations just make me crazy. " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5195.0 0.0 0.0 1.0
"Thanks Dude" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9589.0 0.0 0.0 0.0
"Great lecture!" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4258.0 0.0 0.0 0.0
"There is so much clarity in his words and explanations and how he does applied to examples in to our reall life just brilliant {Se magnific } I wish he was my teacher !!!!! {+_+}" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10379.0 0.0 0.0 0.0
"great lecture again.." ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12979.0 0.0 0.0 0.0
"At 14:10 he makes a minor error, that really doesn't matter since its squared, but he says dy/dt of cos t = sin t when it should be -sin t." XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2590.0 0.0 1.0 0.0
"I'm really trying to see why matrix multiplication should work the way it does and I cannot find a good resource that talks about this specific topic. The fact that not even Gauss could see it is somewhat a consolation but I'd really love to get my hands on a nice explanation." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6367.0 0.0 1.0 0.0
"Is it just me, or do you also see a face on the board at 30:01?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6783.0 1.0 0.0 0.0
"omg.... I know this is stupid, but I have to say it. That movable board is awesome man!!! Go MIT!!!" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 14145.0 1.0 0.0 0.0
"If you mash right at a steady pace, you can hear my last brain cells spiriting away in agony as I try and fail to comprehend Linear Algebra." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 6554.0 0.0 0.0 0.0
"such a down to earth professor and speaks in such a friendly manner(Y)" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14411.0 0.0 0.0 0.0
"It's just a helpful way to think about it, as we can see when he talks about inverses." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7054.0 0.0 0.0 0.0
"Awesome erasing skills at 35:00" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2755.0 1.0 0.0 0.0
"Thanks! Took this course parallel to the linear algebra course at my university and this gave a much better understanding of the material. Amazing :) greetings from germany." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9835.0 0.0 0.0 0.0
"Really useful lecture!" feb9j65Iz4w "24. Linear Programming and Two-Person Games" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8534.0 0.0 0.0 0.0
"18:31 would ya just look at it?" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 544.0 0.0 0.0 0.0
"Is this statistics related to business field?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 6879.0 0.0 0.0 0.0
"From Yemen .. I LOVE YOU DR. GILBRT STRANG" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3927.0 0.0 0.0 0.0
"Thanks prof" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9755.0 0.0 0.0 0.0
"such great lecturing makes me wonder what part of MIT student success is due to innate ability and how much due to superior teaching" wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14416.0 0.0 0.0 0.0
"When he said this lecture is the Beginning of Real Linear Algebra,I got goose bumps" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11622.0 0.0 0.0 0.0
"26:29 I summarize all his interpretations of the question as ""Which columns in A are redundant to create C(A)?""" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 801.0 0.0 1.0 0.0
"This lecture is amazing..." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 10795.0 0.0 0.0 0.0
33:07 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 951.0 0.0 0.0 0.0
"I guess that's the problem with highschools, they gave us the formulas when I took calc in my university. Calc shouldn't be about memorizing 40+ formulas, but knowing when and how to use them or at least being able to derive some formulas on your own and understanding why they work." BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5454.0 0.0 0.0 1.0
"What can I say... I'm taking this lectures at night, before going to sleep, and I never thought I'd like to study calculus just for fun. I don't even like to study at all, but all these MIT lectures are so interesting! Also, Denis is cute :3" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11475.0 0.0 0.0 0.0
"the good thing about this is that he assumes you know nothing about vectors. My instructor at JHU went through the first few chapters because he assumed that we knew all the basics of vectors. MIT isn't a great school for no reason. I can tell already how much MIT respects its students." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14695.0 0.0 0.0 1.0
"That was a really clean demonstration of Least Squares. I would recommend that a look on Prof. Strang lecture https://www.youtube.com/watch?v=osh80YCg_GM to have the linear algebra perspective." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9917.0 0.0 0.0 0.0
"Fyi just a small clarification to Professor Strang first equation on eigenvalue decomposition. In general, the decomposition is : A = QLamQ_inv which in the case of a symmetric matrix, S = QLamQ_trans. In this case: Q_inv = Q_trans. Thankyou Wolfram Math World and python" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3964.0 0.0 1.0 0.0
"Kok kelasnya sepi? Hayoo pada titip absen yaa :))" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 7223.0 0.0 0.0 0.0
"Thank you so much. QtAQ" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9413.0 0.0 0.0 0.0
"I believe he is talking about ReLU and Batch norm? I'll find out!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5168.0 0.0 0.0 0.0
"Anyone have the intuition about why projection and least squares arrive at the same solution? My only piece of intuition is the notion of ""length"" is kind of ""squared""" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 2496.0 0.0 1.0 0.0
"this is too easy for a college student" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14886.0 0.0 0.0 0.0
"I'm doing a master's in Germany and we were supposed to go through all the lectures as an introduction to a course called Advanced Mathematics for Engineers. At the beginning I was quite reluctant to do that, but after the first lecture I couldn’t wait for the next one. Professor Strang is indeed a great teacher. Thank you MIT for sharing these splendid lectures!" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6320.0 0.0 0.0 0.0
"""If a matrix takes a vector to zero, there is no way its inverse can bring it back to life!"" - Gil Strang" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 68.0 0.0 0.0 0.0
"When I become teacher, I will clearly do geometric proofs! =D Love these ones, although the lack of precision. Look for better proofs at ""proof wiki"". There are a lot of good proof there. =)" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11602.0 0.0 0.0 1.0
"This lecture confused me from 20:00 onwards. Lots of leaps in this lecture" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 10786.0 0.0 0.0 0.0
"May I ask you guys a question, do Single Variable Calculus and Multivariable Calculus cover all the content of calculus and real analysis?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7630.0 0.0 1.0 0.0
"F'N lol. This is where my brain is at." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3718.0 0.0 0.0 0.0
"That whole first few seconds was me in Fall 2020 as an instructor. :(" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 9927.0 0.0 0.0 0.0
"sir you are awesome" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14312.0 0.0 0.0 0.0
"Thank you so much, MIT" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 9394.0 0.0 0.0 0.0
"I'm watching this with airpods and i was wondering why his voice pans in my right ear until i realised his recorder is on his right hip. Still, great lectures!" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 6399.0 1.0 0.0 0.0
"""The Sine"" ""The Cosine""

lol" CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 116.0 0.0 0.0 0.0
"Could have saved so many hours of useless cramming, mugging up and god knows what if I had found this earlier.." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3229.0 0.0 0.0 0.0
"I agree. Some people don't need to be an ass. " TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5030.0 0.0 0.0 0.0
"A great video! I have to notice that T(0)=0 ""proof"" is a bit funny :)" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2124.0 0.0 0.0 0.0
"He never erased ""ULA"" off the wall." UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 4589.0 1.0 0.0 0.0
"Paul is a lucky guy." wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 8157.0 0.0 0.0 0.0
"At all the school-kids out there: how many lessons do u need to unterstand it? Is this hour enough? Yes? Then go on in the same speed ... sure, you have made it in school. But this lesson is to be sure, that everyone has the same basics ... think about it ;-)" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2703.0 0.0 0.0 1.0
"At 4:40 it sounds like he says ""Wir werden to use the same method..."" kinda funny, haha." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2687.0 0.0 0.0 0.0
"hate this threom" sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13062.0 0.0 0.0 0.0
"20220527 簽" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 637.0 0.0 0.0 0.0
"clickety click. click click click. clickety." -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12657.0 0.0 0.0 0.0
"He's got the most cute french accent ^^

Great Lecture" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4636.0 0.0 0.0 0.0
"aight need to watch this again. matrix multiplication as elim and movement" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12316.0 0.0 0.0 0.0
"I was surprised to read that the real numbers are not countabal.  Uncountable, sure, but uncountabal?" PnDtMfyZSIE "Lecture 6: The Uncountability of the Real Numbers" "MIT 18.100A Real Analysis, Fall 2020" 6167.0 0.0 0.0 0.0
"I haven't seen matrices since college.  This is the absolute best explanation I've aver seen: clear; methodical; complete! I can't wait 'til Monday (Ooh! I don'e have to: there it is!)" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5572.0 0.0 0.0 1.0
"Absolutely well done and definitely keep it up!!! 👍👍👍👍👍" vMaKx9fmJHE "12. Testing Goodness of Fit (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 2220.0 0.0 0.0 0.0
"With all my endurance I listen to this saga until this lecture just to understand  Linear Regression" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 11966.0 0.0 0.0 0.0
"One like from India 🇮🇳" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8080.0 0.0 0.0 0.0
"Why am I binging these at 1:35 AM? I am not even in university yet..." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11770.0 0.0 0.0 0.0
"Hats off to professor Gilbert strang" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4441.0 0.0 0.0 0.0
"to the one who asked what the 32 and 11 stood for, for E21 means entry of the 2nd row, 1st column." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14950.0 0.0 0.0 0.0
"Thank you MIT" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 9122.0 0.0 0.0 0.0
"Thank you" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9086.0 0.0 0.0 0.0
Excellent! lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 3686.0 0.0 0.0 0.0
"How come 4x4 Matrix has 24 P's ?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 4819.0 0.0 1.0 0.0
"@DiireStraiits Lecture 8 :)" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1615.0 0.0 0.0 0.0
"Thank you very much dear professor Strang. You have been saving and will save so many students." k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9438.0 0.0 0.0 0.0
"U guys learn this in mit !! in india this is  taught to 15-16 yr old" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11111.0 0.0 0.0 0.0
"I wouldn't have seen it if I hadn't believed it: https://youtu.be/PIqwV3Kfc44" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 6271.0 0.0 0.0 0.0
"Just leaving my mark, I was a part of this circus" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7185.0 0.0 0.0 0.0
"What does Q.E.D mean?" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11486.0 0.0 1.0 0.0
"""The memory of where you started washes out.."". Restatement of mathematical equations like this makes these videos a gem. Thank you, MIT!" ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 120.0 0.0 0.0 0.0
"To think maths like him when old, requires passion and consistently." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11044.0 0.0 0.0 0.0
"Thanks to the professor  for this lessons! In our country there is no way to understand in such an easy way such kind of lesson
Thank U again, keep uploading" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9813.0 0.0 0.0 0.0
"38:24 Why does σ/(σ^2+δ^2) go to zero when σ goes to zero? I think it should be infinity because 1/σ (σ approaching zero) is 1/0 = infinity. Any one explains? Thanks!" Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1077.0 0.0 1.0 0.0
"I Really Like The Video Implicit differentiation inverses From Your" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4975.0 0.0 0.0 0.0
"wow this is crazy all theorem and proofs and no actual problems to practice i would be pissed " sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15422.0 0.0 0.0 1.0
"thank you mit, supposing i am going to donate , how can i do this from iran?" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14501.0 0.0 0.0 0.0
"42:01 
It think it is d/dx not d/dy.
🤔🤔🤔🥶 🇧🇩❤️" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1172.0 0.0 1.0 0.0
"I think there's a mistake at 9:36 . Instead y + dy should be x + dx, and it'll become (x + dx)^1/3 = y + dy" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6071.0 0.0 1.0 0.0
"Anyone know what the jingle at the beginning of the video is?" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2505.0 0.0 0.0 0.0
"i have a question ? kindly tell me  If statistics are not available for any experiment then how we  calculate the probability. Give examples please ....." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 13393.0 0.0 1.0 0.0
"In math everything is beautiful, it is the most elegant way to view the world.:D
" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6643.0 0.0 0.0 0.0
"Absolutely fantastic! Such a pleasure to learn about this interesting topic by a gifted teacher like Gilbert Strang." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2204.0 0.0 0.0 0.0
"lifesaver and im going to cross register every math class at mit. dont know why my professor assume im smarter than mit students" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 13790.0 0.0 0.0 0.0
"no el elemento (3,3) deberia ser -3? bueno.. de ahi en fuera entendi todo muy bien :)" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14066.0 0.0 1.0 0.0
"Thank you professor" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9304.0 0.0 0.0 0.0
"These lectures are actually fun! The book is also great. Thanks Gilbert." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 10404.0 0.0 0.0 0.0
"36:54 'I don't know why the author put these in here' . Funny part is he's the author of the book." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 1048.0 0.0 0.0 0.0
"I hope he breaks the curse" 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5585.0 0.0 0.0 0.0
"My teacher in our college just told us how to calculate Ax=b, but didn't explain the reason.
How exactly does the teacher in the video understand linear algebra is.
Conclusion that:1. Ax=b has solutions only when b is contained in column space of A. The solution may be multiple.
2. Consider all the x, which satisfy Ax=0, all the linear combination is called null space." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 7789.0 0.0 0.0 0.0
"couldn't have been better....great lecture.... :)" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12694.0 0.0 0.0 0.0
"Is the need for approximation really just to prove that the (slope y/x at theta -> 0) -> infinity? Don't we still can derive that when theta is 0 or multiple of pi using the parametric equations? Sorry for my bad English." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6813.0 0.0 1.0 0.0
"Thank You.... Excellent lecture!" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 9062.0 0.0 0.0 0.0
"@michalchik 
He talks about it in lec 2. He doesnt prove it, though." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1944.0 0.0 0.0 0.0
"35:39 the left theta mle - theta should have a transpose just like in the slides." QXkOaifVfW4 "9. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 1016.0 0.0 1.0 0.0
"@35:09 I don't believe I ever learned that the eigen vectors of a symmetric (or orthogonal) matrix are orthogonal. That seems... magical..." Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1542.0 0.0 0.0 0.0
"Long live!" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7411.0 0.0 0.0 0.0
"The last bit shows that there is no other way to calculate the area of a wedge like that than by dividing it to a triangle and a sector. This is IMHO one of the best showcases of sector being an unique area. It's the same thing about segment that it is a diffrence of a sector and a triangle." Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10152.0 0.0 0.0 1.0
"I watch on 2x and understood everything and now i am feeling like i need to watch again in 0.25x" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 6179.0 0.0 0.0 0.0
"00:00-10:00
Intro to vectors, unit vector, finding length of a vector

10:25-15:00
Vector addition and subtraction (algebraically and graphically)
Scalar multiplication

15:00-25:00
Dot product
a dot b = |a| |b| cos(theta)
a dot a = |a|^2

26:13-31:30
Computing lengths and angles using dot product
cos(theta) = a dot b / |a| |b| 

31:30
The sign of the dot product is the same as the sign of cos(theta)
If a dot b = 0 then cos(theta)=0, a and b are perpendicular
If a dot b < 0 then cos(theta)<0, theta > 90 degrees
If a dot b > 0 then cos(theta)>0, theta < 90 degrees

34:30
Equation of a plane using dot product" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 285.0 0.0 0.0 0.0
"I am really glad to see you again prof." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5135.0 0.0 0.0 0.0
"37:29 Here's where the genius says about his favourite subject." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 1067.0 0.0 0.0 0.0
"I am confident once I went through a Refresher up to this point that his explanation will be as clear as water😀 Because none of my advanced mathematics professors ever explained in such detail!! Awesome professor 👍🏾🙏" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5071.0 0.0 0.0 0.0
"At 31:20
does a dfa converted from nfa always contain 2^q states ?
I mean , Q' is equal to P(Q)  or Q' is a subset of P(Q) ?" oNsscmUwjMU "2. Nondeterminism, Closure Properties, Conversion of Regular Expressions to FA" "MIT 18.404J Theory of Computation, Fall 2020" 2639.0 0.0 1.0 0.0
"On 12:19 an Motorola batery is empty" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8064.0 1.0 0.0 0.0
"He is a virtuoso" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 4503.0 0.0 0.0 0.0
"The lecturer's name is David Jerison. It's on the title slate at the beginning of the video, and you can also find it at the MIT OpenCourseWare site." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10170.0 0.0 0.0 0.0
"You're the legend." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12254.0 0.0 0.0 0.0
"Shame that when I was in middle school, the math curriculum went up top algebra. I think students should at least finish Pre-Calculus by middle school. It saves time." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8635.0 0.0 0.0 0.0
"""you guys wanna know this because planes need it""..... um asteriod anyone?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 195.0 0.0 0.0 0.0
"What an absolutely incredible lecture!!!" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 11446.0 0.0 0.0 0.0
"Some student's questions are quite retarded... the lecturer is awesome!
" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8827.0 0.0 0.0 0.0
"The lecturer mumbling most of the times" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 10169.0 0.0 0.0 0.0
"This is way too much over my level, i need more practice." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10767.0 0.0 0.0 0.0
"Cramer Rule is good for solving 2 by2 and 3 by 3  linear equations.  Dr. Strang it seem me to that you are turn off by Cramer rule, however your lecture on the subject was another masterpiece. The volume of a box is also explained very well using determinants." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 3256.0 0.0 0.0 1.0
Superb!!! Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 8967.0 0.0 0.0 0.0
"Thank you professor Strang for all these lectures! I've remembered why I used to love math!" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 9315.0 0.0 0.0 0.0
https://youtu.be/nzB1FwcQels 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13304.0 0.0 0.0 0.0
"hat meet rabbit 🐇" rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13061.0 0.0 0.0 0.0
"started from 18.06 then to 18.085 and 18.086 cannot thank enough, professor Strang is a wonderful lecturer" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 14395.0 0.0 0.0 0.0
"I know Dr. Jerison won't be able to see this comment, but I just really want to say that, even though Dr. Jerison probably have vaguely guessed his impact from this Calculus course. But he would never know how MANY chinese students have their calculus SAVED by him. In fact this MIT OCW project has world impact, it will be a monument of the early Internet age" TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5634.0 0.0 0.0 0.0
"ayeee back here again!!! This is a great lecture! amazing details about the properties and proofs. I was just wondering how the hell det A = ad-bc. can't stop thinking about it. And here we areeee. Professor Strang proved it!!  Thank you Professor Strang and MIT OCW!! U are the best!" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 12503.0 0.0 1.0 1.0
"bro this guy looks like anthony fantano but math version" PuRJ9IgUW-M "Lecture 18: Weierstrass's Example of a Continuous and Nowhere Differentiable Function" "MIT 18.100A Real Analysis, Fall 2020" 12561.0 0.0 0.0 0.0
"First of all, thank you so much for this clear and lucid presentation of the material. At 7:30, when Dr. Rodriguez illustrates the example of the complement of an open ball in R^2, he states that the set is neither closed nor convex -- I believe he meant to say that it is only non-convex (it would be closed by definition, as the complement of an open set in the usual metric topology) which would demonstrate the necessity of convexity; the minimum norm occurs across the boundary of the disk. If it were both closed and convex as a counterexample, we couldn't conclude that either property was necessary for the length-minimization property to hold. To show that being closed is also needed, we could also (in addition to Dr. Rodriguez's second example) take an open ball not centered at the origin: a unique minimum-norm element (some point closest to zero) would occur on its boundary, which the ball does not contain because that is its set of limit points." KcI2_r51Eb8 "Lecture 17: Minimizers, Orthogonal Complements and the Riesz Representation Theorem" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 3817.0 0.0 1.0 0.0
"this is kind of strange Im a high school student and to be honest I don't feel like this is really complex, so is MIT really some exceptional college, or is it mostly reputation?? that was pretty simple." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14863.0 0.0 0.0 0.0
"Thank you so much Sir! Making a lecture without students at that time. Seeing your lectures is way easier than those college lectures that directly start with vector spaces second day." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9361.0 0.0 0.0 0.0
Awesome 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2750.0 0.0 0.0 0.0
"In 1:08:10, those lambda's should not be eigen values of Sigma ? (or covariance matrix ?)" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 6591.0 0.0 1.0 0.0
"At first, I though ""rangle"" was just a weird shorthand for rectangle" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2713.0 0.0 0.0 0.0
"Best linear algebra course ever! Best wishes for Prof. Strang's health during this horrible pandemic" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2865.0 0.0 0.0 0.0
"the idiot who filmed this particular video just focused on the professor - so when he walked away and was looking at the board, this person would focus the camera on the person - not the equation he was talking about.. not too bad, but the others were done much better.  - if you aren't quick writing things down, you have to pause often." 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14700.0 1.0 0.0 0.0
"If P(AUB) = P(A)+P(B) for independent events then why is the following solution wrong? Roll 4 4 sided dice. What are chances of getting at least on 4? P(AUBUCUD) = P(A)+P(B)+P(C)+P(D) = 1/4+1/4+1/4+1/4. I know this is wrong so save your breath in posting the correct solution which is 1-(3/4)^4. Why is the solution wrong? It's a good question and will raise an important point." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 6481.0 0.0 1.0 0.0
"30:15.....  I thought the answer would be 1/3 however you wrote down 2/3. I don't understand that?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 885.0 0.0 1.0 0.0
"It's so irritating that the subtitles are not synced with the audio :/" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7070.0 0.0 0.0 0.0
Quarentena 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8472.0 0.0 0.0 0.0
"I pity about the 19 freaks who disliked this video lmao. these are the actual dumbos." YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5899.0 0.0 0.0 0.0
"Measure the curve mabey itself ..it's inner area. Same eggs" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7652.0 0.0 0.0 0.0
"""Take a breath. Okay the tape won't but the lecturer will "" Hilarious :D" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 114.0 0.0 0.0 0.0
"He should learn how to teach from Gibert Strang" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 4606.0 0.0 0.0 0.0
"He makes everything look so clear." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4583.0 0.0 0.0 0.0
"I never learned LA in my undergraduate because I was scared of performing poorly. However, I need to know this stuff for a Neural Network class I am taking in my masters. I am so thankful that courses like these are open to public viewing, as I was able to complete the course lectures, learning this invaluable math. Now I feel more prepared and ready to tackle this next course." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5881.0 0.0 0.0 0.0
"i had this done in high school" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13387.0 0.0 0.0 0.0
"This is a fine lecture on elimination of matrices that I am finally learning for the the first time. DR. Strang, I love the way that you  explain matrix multiplication." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10588.0 0.0 0.0 0.0
"u forgot to multiplay c and d with 5 in 21:10" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 14971.0 0.0 1.0 0.0
"my goodness... he's such a badass lol" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13983.0 0.0 0.0 0.0
"It's a Spanish thing, the 'j' makes a sound like the 'h' in English. Like Jalapeño. Looks like he's from Mexico." U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7015.0 0.0 0.0 0.0
"MIT students...they even dont know determinant..wtf..
" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7547.0 0.0 0.0 0.0
"what is the mean ""sines of the eigenvalues""？ Thanks," UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 15166.0 0.0 1.0 0.0
"I am an engineering student at a two-year college that shall go unnamed. I can follow this man's MIT lecture far better than any other math professor I've had at junior college....Go figure." 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 5066.0 0.0 0.0 0.0
https://youtu.be/C0qrjkfg5wA J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13289.0 0.0 0.0 0.0
"really a fantastic professor, explain all this idea so clearly and naturally. I was confused about fourier series before, now I am pretty clear!" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 14247.0 0.0 0.0 0.0
"Just love the way he teaches ! Thank you " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7187.0 0.0 0.0 0.0
"anyone know if this course is for engineers only?" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12385.0 0.0 0.0 0.0
"9 vectors in 9  combination may fill up the information a sort of plane Rishy's apply for genetic control of humanbeings." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 1429.0 0.0 0.0 0.0
"I am so addicted to these lectures.. 
Thanks MIT and Prof Gilbert Strang. 
" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 5138.0 0.0 0.0 0.0
"@lubanks Gradients per second is not a real unit or measure." BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 1933.0 0.0 1.0 0.0
"I can assure that, he has that frenchy accent specially when saying zero" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5185.0 0.0 0.0 0.0
"Yes, we are all MITer." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12152.0 0.0 0.0 0.0
"the last part about the least squares interpretation gave me a sense of power" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14705.0 0.0 0.0 0.0
"Prof. Strang. Please dont wink at me. I'm too shy. : P

Kidding! I've grown used to it from your linear algebra series 😅

Thanks for your work and all the enthusiasm." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8314.0 0.0 0.0 0.0
"@MrHinderance Math is the universal language!!! :D" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1684.0 0.0 0.0 0.0
"personal notes :
when assigning probabilities to various parts of the sample space, we do not assign them to individual parts fo the sample space, rather to subsets of the sample space." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 14182.0 0.0 0.0 0.0
"Thank you prof. Strang for your work. Your original linear algebra book has a special place in my heart. I'm sure this course will be amazing too." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9303.0 0.0 0.0 0.0
"@michalchik yes but because you differenciate that and G(a) is always a constant then its derivative is G'(x)" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1950.0 0.0 1.0 0.0
"taylor series are awesome everyone flipped shit HAHAHA!! Stupid MIT kid" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14439.0 0.0 0.0 0.0
"Lôpital lu!!!!!!" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7492.0 0.0 0.0 0.0
merde. YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13939.0 0.0 0.0 0.0
"this lecture NEVER GETS OLD." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 14890.0 0.0 0.0 0.0
"24:44 thanks to prof. strang that he didn't get away by just taking an easy example and explained other cases where it didn't work.
.
.
.
32:20 the way professor strang visualise the 9 dimensions is so impressive" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 755.0 0.0 0.0 1.0
"19:20
Front row be like" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 559.0 1.0 0.0 0.0
"Tumhara thik nhi h lecture 👍" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11102.0 0.0 0.0 0.0
"Strang is very knowledgeable and a pleasure to listen to. I really got something out of his class (es)." HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 8911.0 0.0 0.0 0.0
"The material is easy, but It became so tedious and was not explained in any creative ways, voting it down." HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10181.0 0.0 0.0 0.0
"How do we get A2 from A1 ??" d32WV1rKoVk "12. Computing Eigenvalues and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4852.0 0.0 1.0 0.0
"at 07:28, you might want to make clear that w denotes one component involved involved in the second derivative. Then we care about its sign. " 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12409.0 0.0 1.0 0.0
"The final formula on the right side should be plus instead of minus." XhSk_Lw2X_U "14. Low Rank Changes in A and Its Inverse" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10104.0 0.0 1.0 0.0
"donation? MIT has money to blow. " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12771.0 0.0 0.0 0.0
"Think he has enough chalkboards lol" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10447.0 1.0 0.0 0.0
"9:45 - Strang: ""Columns of C are combinations of columns of A"", how? - Is it not the combination of columns of B?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1446.0 0.0 1.0 0.0
"huge respect, such a good lecture" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 13314.0 0.0 0.0 0.0
"25:12 awesome camera work" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 771.0 1.0 0.0 0.0
"Lecture itself is fine but you need to hire an actual human to operate the camera.  I assume you're using an owl or something similar and it is nauseating to have the camera swing around every second.  The lecturer doesn't need to be at the center. The notes on the board should be, and the camera should be kept steady on them.  A human student even if new woth a camera would know this and I highly encourage you to use one in the future." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 7293.0 1.0 0.0 0.0
"So does this mean that all (symmetric) rank k changes to a (symmetric) matrix form a partial order?" z3SmljnD_nQ "15. Matrices A(t) Depending on t, Derivative = dA/dt" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8750.0 0.0 1.0 0.0
"Totally nailed it 🔥🔥🔥" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11076.0 0.0 0.0 0.0
"Excellent class and excellent lecturer, i think that the guys didnt see the basis of linear algebra thats the reason that prof Auroux gave them an introduction of analitic geometry and elemental algebra, there are assignments that in Mexico are elemental at Facultad de Ingenieria UNAM: algebra(real numbers,  complex numbers, polynomials, ecuation systems and matrices), analytic geometry (polar curves, curves at space, vectorial algebra, surfaces), linear algebra (vectorial spaces, transformations, change of bases, function dependence; linear combinarions and theorems) obviously differential and integral calculus and finally in elemental maths vectorial calculus(multivariable calculus) that is linked to this, but prof Auroux resumed the basis in 2 hours thats awesome" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3637.0 0.0 0.0 0.0
"I thought the most important part of Applied math was problem solving and the most important part of pure math(creating new math) was proofs." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6098.0 0.0 0.0 0.0
"the fact that zero vector can be a subspace - what significance does this have in real-world problem solving ?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14689.0 0.0 0.0 0.0
"anyone knows where I can find this practice exam they're solving?" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12387.0 0.0 1.0 0.0
"33:40 Correction: Eigenvalue matrix be multiplied to S from the right. That has been made in the book. Probably, it slipped off Prof. Strang in the flow." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 966.0 0.0 1.0 0.0
"thank you!" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 14528.0 0.0 0.0 0.0
"35:00 matrix norm" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 995.0 0.0 1.0 0.0
"That one moment at 25:15 where he turns around and gives some unfortunate student  a genuinely chilling professorial stern look......priceless." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9909.0 0.0 0.0 0.0
"How come, my professors at Uni told me that sin(30º) was acceptable, but the professor here says that it must be radians, otherwise it would be wrong?" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4826.0 0.0 1.0 0.0
"4:20 If A is singular then $\lambda=0$ is an eigenvalue
15:00 An nxn matrix will have n eigenvalues and the tr(A) will be the sum of the eigenvalues
19:30 “A repeated lambda is the source of all trouble in 18.06”
25:00 Shows the polynomial contains the trace and the determinant, in the 2x2 case.
37:15  Example: Rotate vector by 90 degrees
38:47 The determinant is the product of the eigenvalues.
44:20 If we stick to symmetric matrices, or close to symmetric, then the eigenvalues will stay real.
46:50 With a triangular matrix, we can read the eigenvalues off of the diagonal" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 1317.0 0.0 0.0 0.0
"The solution for x involving w and z should be w+(v^T w)z/(1-v^T z). Strang has (vw^T)z in the numerator." XhSk_Lw2X_U "14. Low Rank Changes in A and Its Inverse" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10282.0 0.0 1.0 0.0
"Mathematically speaking, it does not tell you about distribution of Sn. Wow!! Thank you so much. Have done many revisions of this series." 3eiio3Tw7UQ "19. Weak Law of Large Numbers" "6.041 Probabilistic Systems Analysis and Applied Probability" 7613.0 0.0 1.0 0.0
"Thanks a lot to the person incharge of the camera..." 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 9666.0 1.0 0.0 0.0
"The key ideas all in one lecture! Bravo Dr. Gilbert Strang! Love your presentation!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10148.0 0.0 0.0 0.0
"Hello every MITers" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4657.0 0.0 0.0 0.0
"@goodman325 i totaly agree this is insane! My mathematics degree is much much more difficult than this!!!" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1854.0 0.0 0.0 0.0
Thanks　you! Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9859.0 0.0 0.0 0.0
"this is a bazillion times more straightforward and clear than the lectures i pay for at my university. :( I appreciate this being online" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 14849.0 0.0 0.0 0.0
"11:20 the matrix is not a rotation of any angle, it is actually a reflection.
(You can see that from the fact that det(Q)=-1)" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 371.0 0.0 1.0 0.0
"I was 9 years old when this video was recorded. lol" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 6147.0 0.0 0.0 0.0
"x and y axius = -391 degrees CELCIUS." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15452.0 0.0 0.0 0.0
GOAT yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 3970.0 0.0 0.0 0.0
"It would be easier if 5 penguins are used as a ""weak sample"" to work through the markov theory" 3eiio3Tw7UQ "19. Weak Law of Large Numbers" "6.041 Probabilistic Systems Analysis and Applied Probability" 7005.0 0.0 0.0 0.0
"this is fucking dope" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14860.0 0.0 0.0 0.0
"if they have the same the subspace they exist in the same dimension? is that it" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 13542.0 0.0 1.0 0.0
"49 min in and still hoping he'll get to PCA soon hahaha... great lecture though" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 1303.0 0.0 0.0 0.0
"Absolutely amazing!" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2200.0 0.0 0.0 0.0
"The prof did not have enough sleep the night before." HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10240.0 0.0 0.0 0.0
"Thanks Sir. You are very handsom" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9647.0 0.0 0.0 0.0
"Those blackboard dusters seriously need to be banged outside!!!" hDwkKrWqdZE "3. Forbidding a subgraph II: complete bipartite subgraph" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 10990.0 1.0 0.0 0.0
"""20:28 Cannot integrate $\sqrt{2-2\cos t}$ ???? ""  isn't that already in the text he is using ? I am sure every single textbook contains that   .... I assuming that nobody at MIT is actually watching this." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 21.0 0.0 1.0 0.0
"Man he's so swift with that chalk lol" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7573.0 1.0 0.0 0.0
"DR. Strang ,thank you for another classic lecture on orthogonal vectors and subspaces. Professor Strang, you are the grand POOBAH of linear algebra." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3276.0 0.0 0.0 0.0
"Everything goes over the head... Bad Professor... Cant even explain what is the rotation of a vector got to do with a matrix. He asks us to memorize the matrix !!!!!!! 
I am watching the course for a refresher. The lecture is missing some big chunks of information !!! 
For ex: Professor introduces Matrices with the help of a product of the matrices - Which according to me is like explaining velocity to define distance between two points !!!!
I would have explained it better given the same time !!!! 
Pray he does not do the same with tougher topics that are yet to come !!!!!" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3613.0 0.0 0.0 0.0
"""instantaneous rate of change"" newton is rolling in his grave lmao" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 160.0 0.0 0.0 0.0
"Right, this is starting to get hard now; first lecture that I've struggled with in this course.
I still think he is basically a good teacher, but he was just going a bit too fast; need to go back over this with a book." Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8573.0 0.0 0.0 0.0
"My favorite example of two bases for the same space: in the old days your showers had two knobs that let you adjust cold and warm water (per time). Modern showers let you adjust volume per time (~= warm + cold) and temperature (~= warm - cold). For every configuration of temperature and volume per time, there is some setting of cold and warm that achieves that configuration, but it might be tricky to find.

[Probably in practice this system is not linear. But it feels about right.]" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 7748.0 0.0 0.0 0.0
"W. Gilbert Strang, you are a gem of a teacher!  Thank you so very much!!" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 11238.0 0.0 0.0 0.0
"Is there a way for us to check the notes he is referring at 51:05 ?


Here is what i understood from this lecture:


1.We want to take a sample of a matrix multiplication. Recalling that a matrix multiplication is a sum of columns by rows, we choose the index randomly and get the corresponding rank 1 matrix.


2. We also want that this method converges to AB if we take the mean of different samples, which means that the expected value of this rank 1 sampling is AB. This will force us to rescale the sample by 1/pj.


3.Knowing this, we conclude that taking the rank1 sample of a matrix means taking (1/pj)*(aj*bj). Sampling isnt just about choosing a random index j, but rescaling the rank 1 matrix aj*bj.


4. We dont want pj to be arbitrary, we want it to be optimum in some way, the criteria he used was to choose the pj that minimizes the variance of the norm of the rank 1 sample. This variance is a number and not a matrix since its the variance of a norm.


5. Here comes the procedure he showed which is finding the formula of that variance and then apply langrange multiplier method.


However, i cant explain the presence of the ""s"" variable and the magical appereance of the Frobenius norm at 35:01


Although i can´t explain them, they should be there because otherwise, with that specific optimum pj, variance of norm turns to be zero, and i have the feeling that a zero variance is not a good conclusion. 


If someone has a good answer for this please let me know." z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6828.0 0.0 0.0 0.0
"The twist at the end was better than that of GOT's." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10306.0 0.0 0.0 0.0
"The quality of these are so high I forget they are in 480p" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10262.0 0.0 0.0 0.0
"This is a masterpiece by DR. Gilbert Strang of MIT. In control engineering, which is part of electrical engineering  linear algebra is a must. All students in this field of study, graduate and undergraduate must know linear algebra." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 10599.0 0.0 0.0 0.0
Thanks！ RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9860.0 0.0 0.0 0.0
"16:40 you can also use the special integration formula
1/a * arctan(u/a) at that point" aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 486.0 0.0 0.0 0.0
"Thank you for sharing us human these invaluable contents." QuZL5IKpO_U "24b. Quiz 2 Review" "MIT 18.06 Linear Algebra, Spring 2005" 9261.0 0.0 0.0 0.0
"This lecture becomes so laborious by giving abstract theory first instead of examples." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10785.0 0.0 0.0 1.0
"How is this an intro?" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 4875.0 0.0 0.0 0.0
"I Really Like The Video Determinants; cross product From Your" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4940.0 0.0 0.0 0.0
"I think the teacher should finish an idea first and then move on with the assumptions ... otherwise he just confuses" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6066.0 0.0 0.0 0.0
"35:00 why does it kill the basevector v2?  is it because it transforms it?" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 996.0 0.0 1.0 0.0
"MIT is for real. Not just for birds." twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7527.0 0.0 0.0 0.0
Best srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 2848.0 0.0 0.0 0.0
"It is a good idea to outline the contents of each tape in writing. The title, the chapter and the section that each tape contains. Like indexing each tape or giving an overall index for all of the tapes in a particular subject, say calculus. Thank you" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6924.0 0.0 0.0 0.0
"I'd watch these lectures for the fun of it. His Linear algebra lectures were amazing." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6284.0 0.0 0.0 0.0
"heh off to uni soon and good to brush up on A-level stuff =)" CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13128.0 0.0 0.0 0.0
"nice explanation..thanks" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 14034.0 0.0 0.0 0.0
"35:35 He seems to claim that positive definite matrices must be symmetric. But that' cant be true.. [2,0;2,2] is positive definite but not symmetric!" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 1014.0 0.0 1.0 0.0
"If anyone manages to see this, should I have done differential equations by now; or not? Also, before differential equations, should I do calculus 3/multivariate calculus; or differential equations first?
Thanks to anyone who responds and I hope you have had a lovely day so far!" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 6498.0 0.0 1.0 0.0
"i LOVE multivariable calculus!!" sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13322.0 0.0 0.0 0.0
"1:42 i wonder what life-story the two pink-heads on the bottom left are cooking up.." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 599.0 0.0 0.0 0.0
"Why du*dv = 5*dx*dy ? 'A' region is a rectangle but A' is a parallelogram and its area is not du*dv ..." UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11858.0 0.0 1.0 0.0
"at time 44:38, c f(x) > alpha implies f(x) > alpha/c only if c>0. If c<0 it becomes f(x) < alpha/c" ETmIxkbTm3I "Lecture 9: Lebesgue Measurable Functions" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 12479.0 0.0 1.0 0.0
"Im a bit confused when he talked that the gradient vector is perpendicular to the circle x^2 + y^2 = c ? did he mean that it's perpendicular to the tangent of the circle. And is that vector's direction parallel to the xy plane ?" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 6567.0 0.0 1.0 0.0
"I wonder what rally was going on..." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 6248.0 0.0 0.0 0.0
"32:25 there is an error. Is not (1+1/2 u) but (1-1/2 u)" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 930.0 0.0 1.0 0.0
"45:30 second approach to find SVD" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1255.0 0.0 1.0 0.0
"Thank you so much!!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9390.0 0.0 0.0 0.0
"I love these vids... but why do they cheer whenever he erases the board?" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5799.0 1.0 0.0 0.0
"Magnitude of cross product is the area..
But how do I find the magnitude of a vector that has three components
i,j,k?" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7563.0 0.0 1.0 0.0
"where is lecture 10" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 15237.0 0.0 0.0 0.0
"Beta distribution can be bimodal when both a and b are less than 1." bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 2884.0 0.0 1.0 0.0
"@GaolisVideoLog ..obviously you're still stuck up thinking like a modern day cavemen..you should atleast check out some of the very same teachings done by ""idiots in indian colleges by indian professors""..not that everyone follows the same way of teaching..but you know what I meant..( type in ITT madras""..)..Goodluck cavemen :)" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1623.0 0.0 0.0 0.0
"same here." BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14279.0 0.0 0.0 0.0
"all points of the nullspace are shifted by the vector x-particular" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 12324.0 0.0 0.0 0.0
"This lecture is the greatest one ever" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10813.0 0.0 0.0 0.0
"Oh how I wish my Linear Algebra professor had been this clear !!  Thank you! Thank you! Thank you!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 8009.0 0.0 0.0 0.0
"I have passed enough math and other subject exams.i quit class because other students and lecturers are crazy" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5550.0 0.0 0.0 0.0
"Instead of using the double angle formula and expanding the square he could've used complex exponentials to linearize cos theta to the fourth, right?" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6716.0 0.0 1.0 0.0
"Someone get that gent a chair and a overhead projector." C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 8834.0 1.0 0.0 0.0
"Can somebody please explain why they're called E21 and E32?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3065.0 0.0 1.0 0.0
"Can anyone tell me how the professor prove row rank = column rank? I am confused. I think the professor just gives a specific example, not a proof." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3045.0 0.0 1.0 1.0
"This is another fine lecture on inverses. This the first time that I have seen Left, Right and Pseudoinverses in a linear algebra class. I really learned these topics from DR. Strang. These topics are important in linear algebra, signal and systems theory and control engineering." Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 10636.0 0.0 0.0 1.0
"wow this is leaps and bounds better explained than my university teacher" oNsscmUwjMU "2. Nondeterminism, Closure Properties, Conversion of Regular Expressions to FA" "MIT 18.404J Theory of Computation, Fall 2020" 15423.0 0.0 0.0 0.0
"For all of you who made it to this point in this great course I recommend watching this short serie before taking the final reviews. Full of graphics with some good aha moments. https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 3849.0 0.0 0.0 0.0
"15:00 , You had lunch. you are strong. LOVE Prof." XhSk_Lw2X_U "14. Low Rank Changes in A and Its Inverse" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 443.0 0.0 0.0 0.0
"What's the difference between the two texts ,one shown by the sir and ""linear algebra and it's applications""?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11579.0 0.0 1.0 0.0
"For those who are confusing about the deviation process for (A+UV^T)^-1, please check this website of wikipedia:  https://en.wikipedia.org/wiki/Sherman%E2%80%93Morrison_formula" XhSk_Lw2X_U "14. Low Rank Changes in A and Its Inverse" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3911.0 0.0 1.0 0.0
"The first terms in part d and f of the examples should be weighted with the probability that scenario 1 occurs, right?" XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 10111.0 0.0 1.0 0.0
"Sir  speed cannot be zero so  how will you come to -20m/s" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8686.0 0.0 1.0 0.0
"Strang is love" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 8909.0 0.0 0.0 0.0
"Such a fantastic series. He breaks everything down so clearly. It also amazes me how fast they cover the material." _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8924.0 0.0 0.0 0.0
"I believe we live in a simulation now." 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 5174.0 0.0 0.0 0.0
"April 2018?" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2519.0 0.0 0.0 0.0
"The proofs that the limit of sin x/x and (1-cos x)/x tend to 1 and 0, respectively, as x approaches 0 could have been rigorously shown using the squeeze theorem. But, at this point, they haven't been introduced to the squeeze theorem yet." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10261.0 0.0 0.0 1.0
"@sacredsoma The lector doesn't explain it, but in that part he is working with one of the several definitions of the Poisson process, in which the process is defined as  a Lévy process. Deep knowledge of mathematical analysis, specifically measure theory, is required to understand these infitesimal properties of Lévy processes, that's why he doesn't say much about those second order terms." jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 1995.0 0.0 0.0 0.0
"vector spaces and subspaces are the most fundamentally important concepts of linear algebra to build a good foundation...no one is in class.." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14994.0 0.0 0.0 0.0
"He completely changed my view on linear algebra. The whole thing is just amazing!" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4467.0 0.0 0.0 0.0
"Fuck you, racist" TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3946.0 0.0 0.0 0.0
"Happy the videos are coming again. I want to go to MIT for graduate school" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4422.0 0.0 0.0 0.0
"What level is it? i am from switzerland and i need to repeat all the calculus for myself again, therefore i am looking for playlist just like that. :)" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11549.0 0.0 0.0 0.0
Thanksgiving! _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9858.0 0.0 0.0 0.0
"last one is awesome proof." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13759.0 0.0 0.0 0.0
"well i did .
before watching this video ." 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15090.0 0.0 0.0 0.0
"Inputting 100 cubic centimeters and 1 cubic meter yielded different answers because _the inputs were different._

One cubic meter equals one million cubic centimeters because we're calculating in the 3rd dimension. In the 2nd dimension, one square meter equals ten thousand square centimeters, and in the 1st dimension, one meter does equal one hundred centimeters.

When converting units in higher dimensions, you _square or cube the conversion factor._" ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6712.0 0.0 0.0 1.0
"Thanks sooo much!!" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 9794.0 0.0 0.0 0.0
"Prof. Strang is amazing because he weighs his words...doeesn’t fill the leecture with combinations of thhe same ideas inn different words." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 8305.0 0.0 0.0 0.0
56:00 Xn8wL2ItzZw "Lecture 9: Limsup, Liminf, and the Bolzano-Weierstrass Theorem" "MIT 18.100A Real Analysis, Fall 2020" 1351.0 0.0 0.0 0.0
"@fermixx he did it without the drawing... he drew the bounds.... and the way he figured the second bound drawing he did was just plug in the x y points into the substitution equations he made for u v..." UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1837.0 0.0 0.0 0.0
"Audio channels fixed!" TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 2737.0 0.0 0.0 0.0
"This course has something against the left ear." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 10488.0 0.0 0.0 0.0
"Thank you, professor. Also, [https://en.wikipedia.org/wiki/Otto_Hesse] -- This is how the Hessian came into the picture, as you I am certain already knew ;)" nvXRJIBOREc "Lecture 21: Minimizing a Function Step by Step" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9528.0 0.0 0.0 0.0
"Am I the only one who thinks that his writing on the board is very efficient and clear?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2340.0 1.0 0.0 0.0
"all the properties of determinants are like his little babies for Prof.Strang. He cants choose one over the other, they are all key properties :)." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 12326.0 0.0 0.0 0.0
"Respect Mr Auroux. Watched the entire series, camera man is the worst, chalk quality is amazing, very good explanation. Thanks MIT." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8555.0 1.0 0.0 0.0
"Too bad i hate the chalk sound on the board." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11058.0 1.0 0.0 0.0
"Excellent accent" 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 3634.0 0.0 0.0 0.0
"it seems the S-M-W formula he presented has a typo. It is plus, not a minus." XhSk_Lw2X_U "14. Low Rank Changes in A and Its Inverse" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13681.0 0.0 1.0 0.0
"@ShaneHayes123 I'm 17 and on my second year of uni, physics...what's your point? :O " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1720.0 0.0 0.0 0.0
"While deriving distribution of time until kth arrival, it appears we have assumed that there will never be two arrivals in succession..! Does the argument change any bit if this assumption doesn't hold..? More so are we really correct to assume this at the first place?" gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 11720.0 0.0 1.0 0.0
"How do we find x(t) , y(t), and z(t)
For a given three vectors?" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4851.0 0.0 1.0 0.0
"these are new things in math , im very excited to see this" feb9j65Iz4w "24. Linear Programming and Two-Person Games" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14770.0 0.0 0.0 0.0
"how does his theorem in 30:55 mean that the MLE just going to be an average?" JTbZP0yt9qc "6. Maximum Likelihood Estimation (cont.) and the Method of Moments" "MIT 18.650 Statistics for Applications, Fall 2016" 13228.0 0.0 1.0 0.0
"I like this trick (a^T*b / a^T*a) * a = a * (a^T*b / a^T*a) = (a * a^T) / (a^T * a) * b = P * b." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5693.0 0.0 0.0 0.0
"Having such a person makes me love maths" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4454.0 0.0 0.0 0.0
"If you have too little, the federal government gives you enough grants to make up for it =P" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6548.0 0.0 0.0 0.0
"Dear Professor Strang, you and your lectures are more than gold. I just googled what the rarest and most  precious metal is, and it turns out to be Palladium, so you and your lectures are pure Palladium!
Everything in the video is clearly explained, informative, clarifying and vastly illuminating. I'm excited about what is to come in next in the video lectures! 
Bravo and applause" xaSL8yFgqig "Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3330.0 0.0 0.0 0.0
"Thanks for this wonderful lecture." EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 9736.0 0.0 0.0 0.0
"wow MIT. nice im in harvard" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 15411.0 0.0 0.0 0.0
"Thank a ton Sir." 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 9063.0 0.0 0.0 0.0
"the rest wont be uploaded-." -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14740.0 0.0 0.0 0.0
"After all theses years, MIT finally decided to post pure math videos.
I haven't thought such a day would happen..." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 2247.0 0.0 0.0 0.0
"thanks a lot, professor" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 14573.0 0.0 0.0 0.0
"In windows 10 you can force mono sound:
Go to settings [win+i] > Accessibility > Sound; and here you have a toggle for combining both channels." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6698.0 0.0 0.0 0.0
"candy bars lol" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12643.0 0.0 0.0 0.0
"Thanks for sharing this" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 9701.0 0.0 0.0 0.0
"damn, you'd think that at MIT the professors would go at a much faster pace and talk as if assuming the students already know this shit, but this professor just oozes clarity at every step. My prof here at usc skips a lot and talks too fast lolz" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12715.0 0.0 0.0 0.0
"you nailed it!!!" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15512.0 0.0 0.0 0.0
"the way dis nigga talks is so nice" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14748.0 0.0 0.0 0.0
"i'm wondering that when he draw the picture of the complete solution , why doesn't the Null space pass the origin ?" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 13522.0 0.0 1.0 0.0
"Too helpful for me" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11064.0 0.0 0.0 0.0
"@non523  I'm sorry for your compact mind. You think that a black board is what defines a prestigious institution. You do not deserve to know this course at all.
" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1959.0 1.0 0.0 0.0
"The best linear Algebra teacher!!" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 10000.0 0.0 0.0 0.0
"Really irritating how the camera follows the lecturer's every movement rather than staying on the blackboard." mlPLLXHZ8_U "Lecture 4: The Characterization of the Real Numbers" "MIT 18.100A Real Analysis, Fall 2020" 8523.0 1.0 0.0 0.0
"😖😖 He's the best professor I know and yet my brain doesn't get it at once😂" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 15737.0 0.0 0.0 0.0
"Can anyone explain how projection matrices and fitting the lines automatically minimizes the least square error?" QuZL5IKpO_U "24b. Quiz 2 Review" "MIT 18.06 Linear Algebra, Spring 2005" 3022.0 0.0 1.0 0.0
"Watching this in 2020, legendary to date!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 11301.0 0.0 0.0 0.0
"43:26 Min why does the nullspace stay the same?" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 1209.0 0.0 1.0 0.0
"How I understood the beginning example about the mean: We defined our sample space to be Omega = { [a,0] , [0,b] }. We defined the distribution over this sample space to be uniform (hence the 1/2). Now each sample can be seen as a random variable which takes on one of the values in Omega. By definition, the expectation is the sum of the products of each outcome with its probability. However, if we define a random variable to be the sum of the samples then we get the expectation of the new random variable is sum of the expectations of each sample. Each sample has the same expectation thus we can reduce the sum to a multiplication by s. 

PS I don't have very advanced knowledge of probability theory (I'm taking a course right now). If I have made a mistake let me know." z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4794.0 0.0 0.0 0.0
既に学習済みの内容なら英語の授業でも全く問題ないです。英語の数理経済の論文を読んで授業に備えます。 PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15635.0 0.0 0.0 0.0
"I didn't get too convinced about his explanation of wich he called properties A and B. It seems to me than that doesn't work that coherently... first of all because he said it only works in radians, wich is an error because the trigonometric functions are the same no matter the unit, but most importantly it finishes up seeming that both functions result 0/0... wich i could accept as 1 by stretching my mind, but never as 0." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5270.0 0.0 1.0 0.0
"He adds -x/xo^2 to the left as he adds -1/xo to the right.
It looks like this:
-1/xo=-x/xo^2+1/xo
X/xo^2=2/xo" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4459.0 0.0 0.0 0.0
"Thanks to MIT for explaining that one. I can think of an explanation for the origin of that phrase. You see, the Summer gets ""tricked"" into thinking it's gonna last. But alas! The Winter inevitably comes and the few days of its warm reign are over. And just like this short-lived summer period, the Indians got tricked by their conquerors too. Thus the term, ""Indian Summer"".

And Thank You MIT for these wonderful videos. Keep up the great work!!
Great Profs teaching in a great way! " Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9802.0 0.0 0.0 0.0
"this is so beautifully explained!!!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14875.0 0.0 0.0 0.0
"what is the reason behind R being upper triangular?" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 15169.0 0.0 1.0 0.0
"One problem a bit confusing. Normally a square of a matrix is the transpose with the matrix, the example here is like BB." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 8105.0 0.0 1.0 0.0
👍👍👍👍👍👍👍👍👍👍 0Qws8BuK3RQ "34. Distance Matrices, Procrustes Problem" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15712.0 0.0 0.0 0.0
"Minute 40. Left nullspace. I am yelling in my room: ""Yes! Is there, I am looking at it!" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7671.0 0.0 0.0 0.0
"Since I got a full-time job, I don't understand math anymore.  I guess I'm better at calculating money than numbers lmao" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8676.0 0.0 0.0 0.0
"love the tranquil waterfall in these MIT classrooms" TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 13876.0 1.0 0.0 0.0
"my bookmark 37:00" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13970.0 0.0 0.0 0.0
"I don't like how this man erases the board. But I like his explanation." 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5327.0 1.0 0.0 0.0
"Sorry for my humble input, but this lecture on linear transformation should have been at the beginning of the course." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8853.0 0.0 0.0 0.0
"awesome camerawork" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12489.0 1.0 0.0 0.0
"So far this is simple " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8755.0 0.0 0.0 0.0
"i hate the way i get educated i could get alot smarter by just following these awesome lectures online i dont even have to ask anything" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 13388.0 0.0 0.0 0.0
"So much energy for a recorded video with an empty class. Thank you so much Professor Gilbert!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 8778.0 0.0 0.0 0.0
"At this point I'm watching this for entertainment.
These people are talented and teach in such a easy way!
I always thought that I was  dumb but no.
Actually I haven't watched this before!
Thanks MIT!" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2732.0 0.0 0.0 0.0
"This Mathematician's handwriting is exquisite" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10459.0 0.0 0.0 0.0
"To derive the formula at 26:07 (Poisson distribution) from 25:06 (Binomial distribution), you need to write combination as factorials, then use stirling approximation for factorials and the definition of e" jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 11031.0 0.0 1.0 1.0
"Prof Strang is an example that age is no bar for learning" sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8272.0 0.0 0.0 0.0
"what is this surrealist camera work what are those dirty blackboards what world is thiss whattttt" yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 15175.0 1.0 0.0 0.0
DOPE 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3273.0 0.0 0.0 0.0
"Excellent! " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3687.0 0.0 0.0 0.0
"This is so helpful. I adore professor Gilbert so much. It was a bit surprising to go straight into linear equations at first, but it worked out in the end." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10722.0 0.0 0.0 0.0
"Man the energy ...  even though his body aged, his mind, movements and mimics are the same ... I never attend to your class physically but probably I learned more efficiently than my 20 years education best wishes for you !" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7575.0 0.0 0.0 0.0
"OMFG I thought he was saying HOLE or HOE instead of ROW around 26:50 lol I was so confused.... x2 speed am I right?" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7977.0 0.0 0.0 0.0
"I've waited almost a whole year for these lectures!!! Thanks Gil, you really bring a topic to life." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6433.0 0.0 0.0 0.0
"I have nothing but Love for you sir." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5547.0 0.0 0.0 0.0
"i dont know if that is the right way to learn mathematic 
because the goal of mathematics lecture that the student can later proof mathematical problem ... but i dont see here any formal defintion or proofs!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13369.0 0.0 0.0 1.0
"Was anyone there?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11271.0 0.0 0.0 0.0
"Thank you for this amazing lecture.It was boring when our teacher explained it but now all my questions faded ^^" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9277.0 0.0 0.0 0.0
"Very impressive and helpful specially for the people who can't afford to study but still want to learn in life." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11199.0 0.0 0.0 0.0
"Thank you for making this SO INTUITIVE. You rock." phbw9r1iUDI "7. Parametric Hypothesis Testing" "MIT 18.650 Statistics for Applications, Fall 2016" 9254.0 0.0 0.0 0.0
"I just caught that:  ""Keep them in their Gauss-given order"" (instead of God-given...hahaha)" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5599.0 0.0 0.0 0.0
"Congratulations on your adoption of Roman numbers at the beginning of your course titles. And it only took you about twenty-five years flat to figure out that putting numbers at the front made it possible for computers to list programs in order. 
Marvellous work, MIT, technical leader of America!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3200.0 0.0 0.0 0.0
"I haven't seen this stuff since 1987. Never used it in Electrical Engineering in my life. This was the most haphazard sloppy math I ever had to take." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 5573.0 0.0 0.0 0.0
"That makes me remember the first semester linear algebra lecture. He certainly takes his time to explain, what the interpretation is and that is wonderful. We were not so lucky unfortunately." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 9904.0 0.0 0.0 1.0
""" I need you guys, OK?""  We need you too" lWW54ts9Ubo "24. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 197.0 0.0 0.0 0.0
"Thank you Prof. Auroux. Best wishes from Chile." z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9189.0 0.0 0.0 0.0
"that illustration and this intuitive way of looking at pseudo inverse is great! good job!" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 14632.0 0.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits
Lecture 3: Derivatives
Lecture 4: Chain Rule
Lecture 5: Implicit Differentiation
Lecture 6: Exponential and Log
Lecture 7: Exam 1 Review
Lecture 9: Linear and Quadratic Approximations
Lecture 10: Curve Sketching
Lecture 11: Max-min
Lecture 12: Related Rates
Lecture 13: Newton's Method
Lecture 14: Mean Value Theorem
Lecture 15: Antiderivative
Lecture 16: Differential Equations
Lecture 18: Definite Integrals
Lecture 19: First Fundamental Theorem
Lecture 20: Second Fundamental Theorem
Lecture 21: Applications to Logarithms
Lecture 22: Volumes
Lecture 23: Work, Probability
Lecture 24: Numerical Integration
Lecture 25: Exam 3 Review
Lecture 27: Trig Integrals
Lecture 28: Inverse Substitution
Lecture 29: Partial Fractions
Lecture 30: Integration by Parts
Lecture 31: Parametric Equations
Lecture 32: Polar Coordinates
Lecture 33: Exam 4 Review
Lecture 35: Indeterminate Forms
Lecture 36: Improper Integrals
Lecture 37: Infinite Series
Lecture 38: Taylor's Series
Lecture 39: Final Review" ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8449.0 0.0 0.0 0.0
"Awesome explanation of concept!" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2757.0 0.0 0.0 0.0
"29:53 :')" TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 862.0 0.0 0.0 0.0
"black boards looking for a good home." phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12544.0 1.0 0.0 0.0
"awesome lecture! Thanks! BTW, the classroom is soooo large in MIT, LOL" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12492.0 1.0 0.0 0.0
"Never learnt so much in a single lesson" X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 7817.0 0.0 0.0 0.0
"Finally thank you" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 3778.0 0.0 0.0 0.0
"Hello! Why is Professor stop reducing n to zero (30:22) if actually we can continue reducing to negative numbers, e.g. n=-1,-2,-3." aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4663.0 0.0 1.0 0.0
"at 43:20 isn’t the case smaller the alpha, the larger the constant c, the more evidence against h1 instead of h0? Cuz like in the coin example, if you push the threshold wider to like 3.5 something, you go from originally rejecting h0 to accepting h0." 4HRhg4eUiMo "8. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 12454.0 0.0 1.0 0.0
"oh wow i took calculus in high school and these are mit kids...
i swore that guy was asian" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 14114.0 0.0 0.0 0.0
"Really intelligent professor of rare kind." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8521.0 0.0 0.0 0.0
"So, the second component of u(k+1) is useless, right? The actual value is given by the first component." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 8810.0 0.0 1.0 0.0
"It is a very amazing feeling to complete the course today. It has been an awesome journey. 
Thank you, Professor Gilbert Strang and MIT OpenCourseWare team for these amazing video lectures." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 6929.0 0.0 0.0 0.0
"@treeandplant it's not @poyanator but @Arstim who seems to not have learnt anything from his ""co-called"" economics studies...his comment proves his whole education is shit lol" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2048.0 0.0 0.0 0.0
"A=SQ， where A must be square matrix?" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2175.0 0.0 1.0 0.0
"very satisfactory explanation!" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 15035.0 0.0 0.0 0.0
"May I be able to get access to the mentioned and used books on this course" lZrIPRnoGQQ "27. Backpropagation: Find Partial Derivatives" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7631.0 0.0 0.0 0.0
"Is this Mathematical Statistics?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 6847.0 0.0 0.0 0.0
"where is this instructor from?" sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15245.0 0.0 0.0 0.0
"It made me realize that I'm smarter than 1 MIT student - for a minute, anyway." TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6974.0 0.0 0.0 0.0
"This series is phenomenal. Every lecture a gem. Thank you Mr Strang!" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10924.0 0.0 0.0 0.0
"can anybody explain 26:30?" yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 12597.0 0.0 1.0 0.0
"Absolutely well done and definitely keep it up!!! 👍👍👍👍👍" mc1y8m9-hOM "22. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 2217.0 0.0 0.0 0.0
"He radiates knowledge. Love the content!" wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4592.0 0.0 0.0 0.0
"I thought we learn calculus in 11th grade" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6103.0 0.0 0.0 0.0
"I love how the left audio channel is reverb only." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 5754.0 1.0 0.0 0.0
"Good professor with good old blackboard and white chalk teaching method. This is way better than all the fancy powerpoints that many teachers use now a days." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 4151.0 1.0 0.0 1.0
"In addition to shouting out answers I knew, I would also applaud right when he said thanks." Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 6623.0 0.0 0.0 0.0
"Please upload videos on measure theory too🙏😊" 9_xG0AGRa-w "Lecture 2: Cantor's Theory of Cardinality (Size)" "MIT 18.100A Real Analysis, Fall 2020" 8216.0 0.0 0.0 0.0
"Nailed it! what an awesome lecture" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7805.0 0.0 0.0 0.0
"Nice attitude at 30:30" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7839.0 0.0 0.0 0.0
"dap, 
asa cred si eu , in cateva minute reuseste sa clarifice ce nu au reusit alti profesori in ore de predat. Oare cand o sa avem si noi asa profesori?
Apropos, eu sunt student la IT in Luxembourg si de cele mai multe ori ma simt ca intr-o scoala nu intr-o universitate uitata de lume....
Ma bucur ca datorita acestui gen de site, acest gen de profesori extraordinari sunt ""disponibili"" si noua celor care nu v-om ajunge sa participam la vreunul din cursulire lor." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12721.0 0.0 0.0 0.0
"the way he teaches counting is a real contribution to humanity" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 14750.0 0.0 0.0 0.0
"Event B is the whole shaded part, right? 
Not just the part under A3?" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 3594.0 0.0 1.0 0.0
"The courses of MIT seems really easy, in my university Tec de momterrey, we see more difficult and deeper lectures." YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10065.0 0.0 0.0 0.0
Thanks ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9578.0 0.0 0.0 0.0
"In Da Vinci's words simplicity is the ultimate sophistication. " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6609.0 0.0 0.0 0.0
"25:11 I didn't understand this concept . Can anyone explain this in the comments." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 768.0 0.0 1.0 0.0
"Hats on the xs, hats off to Professor Strang!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4444.0 0.0 0.0 0.0
"Excuse me, why doesn't the calculation of F_100 at ""46:08""  time the eigenvector X_1? Am i missing something?" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 3699.0 0.0 1.0 0.0
"The greatest math teacher in the world now teaches Data analysis, Signal Processing and Machine Learning! Thank you very much!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10129.0 0.0 0.0 0.0
"Sorry where can I find the textbook professor was using in the video? What's the name of the textbook? Thanks" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8860.0 0.0 0.0 0.0
"@CEZA14n dude be thankful  , we do not have a professor we have the exam finally lol" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1606.0 0.0 0.0 0.0
"why should anybody care about this?" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 15357.0 0.0 0.0 0.0
"Sir ki exercise to classroom me hi ho jaati hogi" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8697.0 1.0 0.0 0.0
"Look how fast this guy writes 😂" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7417.0 0.0 0.0 0.0
"can someone tell me why did he integrated T and Volume ? what formula used ?" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12633.0 0.0 1.0 0.0
"38:34 to 39:02 I think there is something wrong in the  Lecture Notes WEEK 3 Lecture 6: The Uncountability of the Real Numbers (PDF)." PnDtMfyZSIE "Lecture 6: The Uncountability of the Real Numbers" "MIT 18.100A Real Analysis, Fall 2020" 1081.0 0.0 1.0 0.0
"Those chalks are amazing. I fell in love with the pink ones!!!" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10994.0 1.0 0.0 0.0
"This guy taught me more than I learned when I studied Maths for four years." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 10561.0 0.0 0.0 0.0
"his picture with grad(f) pointing up is a bit misleading around 9:00 I think. grad(f) is a vector in the x-y plane, pointing in the direction you should move in the x-y plane to maximize increase in f." AeRwohPuUHQ "22. Gradient Descent: Downhill to a Minimum" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13169.0 0.0 1.0 0.0
"Shouldn't the empirical covariance matrix be divided by n-1 and not n?" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 8650.0 0.0 1.0 0.0
"OK. This stuff is highly confusing, to say the least. As much as one could rather easily understand what a mean of a random matrix is, it's not that simple with variance. Variance is defined for a random variable or a vector. For a simple r.v. that has its values in R^1, it's just the expectation of (X-E(X))^2, that is E[(X - EX)^2]. For a vector that has its values in R^n it's a COVARIANCE MATRIX. Now, what would be the variance of a matrix? I've never heard of such a construct and I've studied maths (specialization: probability and stats) for 5 years at a technical uni. Maybe (and it's a guess) he wants to do this: Take the random element (which is a random matrix with a probability measure picking up a certain matrix out of a set with a probability of p_i, i=1...n, where n is the number of columns in A and rows in B, since we want to sample from all the columns of A, not only some r cols) and subtract from it the ""mean element"" (the mean of the matrices as calculated), then take the norm of this subtraction (which is a norm of a matrix), square it and multiply by the probability of the element selected. Then sum up over all the elements (sum over the matrices/elements or columns of A, which is the same as there's 1-to-1 correspondence between the cols of A and the set of matrices we're selecting from). So, this would give us the mean square distance of a random element from the ""mean element."" The distance would be the 2-norm or the Frobenius norm of a matrix/element. But this would be the EXPECTATION of the random function X : M -> R+ (a random map from the set of matrices/elements to R+ where X(*) = || * - EM ||^2, this being the square of the 2-norm of the element/matrix and EM = ""the mean matrix"", that is AB). So we are calculating the mean of the X mapping but this ""variance "" (as he calls it) is not some kind of ""matrix variance"" (as such things do not exist) but the expectation of the mapping as above. I can't explain what he's trying to do in a better way. He wants to minimize the expected squared distance from the randomly selected matrix to the ""mean matrix."" and hence he looks for a probability distribution on the columns of A that achieves that. At the same time, I don't understand the notation he's trying to use :( Highly confusing, prof. Strang." z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7976.0 0.0 1.0 0.0
"23:56 category theory burn 😂" 58B5dEJReQ8 "Lecture 3: Quotient Spaces, the Baire Category Theorem and the Uniform Boundedness Theorem" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 719.0 0.0 0.0 0.0
"In China, we learned these when we are in high school.😂😂" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6608.0 0.0 0.0 0.0
"You truly are a gentl person, greetings from belgium flandres and many thanks!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 12243.0 0.0 0.0 0.0
"18:49 Now he won't run out of pronouns" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 547.0 0.0 0.0 0.0
"I'm not able to understand because i'm still an eight grader hahahahahahaha" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6351.0 0.0 0.0 0.0
"Remember to increase playback speed to 1.5x’s." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 8550.0 0.0 0.0 0.0
"My professor isn't bad, but he doesn't hold a candle to this professor.  Zero obfuscation." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7782.0 0.0 0.0 0.0
"16:05
Can we think of these ""basis"" vectors as unit vectors??" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 468.0 0.0 1.0 0.0
"Gilbert Strang is an absolute gem. <3" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 4020.0 0.0 0.0 0.0
"in the class, the students who were around the age of 25 years, now would be of around 40 years!!" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 13596.0 0.0 0.0 0.0
"Does anyone know the deeper reason for why mean=variance=1 in the hat problem at the end?" EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 3441.0 0.0 1.0 0.0
"People started packing their stuff before he even finished" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8171.0 0.0 0.0 0.0
"my teacher has a lot to learn yet ... lololol" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14004.0 0.0 0.0 0.0
"I do think that calculating the eigenvectors of the system is an easier way to deal with figuring out the space of the steady space and the rate at which convergence happens.  Definitely worth examining as a comprehension supplement. Basically, the space defined by the eigenvectors of eigenvalue 1 is the steady space, and the largest eigenvalue not equal to 1 is inversely proportional to the rate of convergence." HIMxdWDLEK8 "18. Markov Chains III" "6.041 Probabilistic Systems Analysis and Applied Probability" 5294.0 0.0 0.0 1.0
"these kids applaud at the strangest things" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 14774.0 0.0 0.0 0.0
No. MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 7903.0 0.0 0.0 0.0
"4:57 if i transpose these guys, that product, then again, ... : why did he jump suddenly to this theorem without any definition of transpose nor the logical derivation? Did I miss something?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 1329.0 0.0 1.0 1.0
"smart example." IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 14322.0 0.0 0.0 0.0
"It does not seem like we are going for a perpendicular projection of the data points on the line. Rather we are taking error (e) in vertical directions. Is that still correct?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 6913.0 0.0 1.0 0.0
"Review needed" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 8569.0 0.0 0.0 0.0
"@24:50 I was really dumb to think that my time has come and angel of death was just trying to show his presence." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 1517.0 0.0 0.0 0.0
"Thank you!" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9466.0 0.0 0.0 0.0
"@aakksshhaayy That question was designed to be a bit of a mindfuck. It makes you focus at answering with respect to the normal vector because that is what you have to take the inner product with and put labor. If you are not focused you don't pay attention to the last part, the actual question (and not because of stupidity as many people would rush to imply here)." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1765.0 0.0 0.0 0.0
"What are the Prerequisties for this course. I'm not able to grasp the concepts" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11466.0 0.0 0.0 0.0
"Can we just appreciate that he can write in such a good handwriting with such speed in a black boards like MAN THAT CHALK SOUND!!!!!!😩😩❤️❤️" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3115.0 1.0 0.0 0.0
"This is great. I never got to learn this stuff in college so it is great to actually learn this at home in my own time which is video after video after video... Accelerated learning is great." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10668.0 0.0 0.0 0.0
"Dude, get a better eraser. Seriously, it's hurting me." bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3527.0 1.0 0.0 0.0
"Excellent explanation about Random variables. Random variables are just dunctions or simply a routine which give us some numerical value." 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 3643.0 0.0 0.0 0.0
"Finally finished all the videos and problems... Thanks to Prof.Tsitsiklis, TAs and MIT for great lectures!" rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 3770.0 0.0 0.0 0.0
"It amazes me that MIT has so shit quality" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 6907.0 0.0 0.0 0.0
"Denis: ""In case you don't see it...""
Me: By Jove, you've read my empty blank mind." phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3353.0 0.0 0.0 0.0
"Hope I will go to UTK, Thank you professor Strang" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4786.0 0.0 0.0 0.0
"This is so good." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10719.0 0.0 0.0 0.0
"at the end he says something about imaginary numbers to rescue the value of that integral calculated naively ...which turns out to be negative... what did he mean?? anyone knows?" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12475.0 0.0 1.0 0.0
"The mathematics fills my heart with beauty." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 10182.0 0.0 0.0 0.0
"Crisp explanation !
" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 3261.0 0.0 0.0 0.0
"Wow, the best explanation I have heard on discrete random vectors and the hat problem!!!!!" EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 12074.0 0.0 0.0 0.0
"I had sex while this video was playing in the background. Math gets you laid." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 5467.0 0.0 0.0 0.0
"Thanks........
Praveen
" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 9855.0 0.0 0.0 0.0
"Einstein couldn't do it, but... Gilbert can!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 3557.0 0.0 0.0 0.0
"if only I had known about this open courseware thing when I took calculus the first time, or even the second! Thanks, MIT, for sharing knowledge. Kudos to this professor, for shedding light on this monster class." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13535.0 0.0 0.0 0.0
"20:55 Does that.......make sense? hehe" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 663.0 0.0 0.0 0.0
"Worth mentioning: if row-reduction of the matrix generates the most natural row space basis without much effort, we can also generate the most natural basis of the column space of said matrix by doing row-reduction on the transpose of the matrix. This is all so incredibly fascinating!" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12000.0 0.0 0.0 1.0
"Brilliant lecture! Thank you!" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2929.0 0.0 0.0 0.0
"Gilbert Strang is so cool, thank you!" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4026.0 0.0 0.0 0.0
"I am confused with the Binomial part, especially about how to get the nXˆn-1△x from formula Xˆn+ nXˆn-1△x+ Junk?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5076.0 0.0 1.0 0.0
"I can not understand the pay off matrix game. Pleasr explain." feb9j65Iz4w "24. Linear Programming and Two-Person Games" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5194.0 0.0 1.0 0.0
"These are not too difficult." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10396.0 0.0 0.0 0.0
"i wish i had a chance to study in his class 'live' :) ... really superb way of teaching... " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13496.0 0.0 0.0 0.0
"what would Matlab do?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15188.0 0.0 0.0 0.0
"Great insights here" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 4233.0 0.0 0.0 0.0
"Man, these proofs are sloppy as fuck." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7587.0 0.0 0.0 0.0
"I Really Like The Video From Your Matrix Spaces; Rank 1; Small World Graphs." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 4962.0 0.0 0.0 0.0
"Is anyone interested in working through the course together? PM me. https://www.instagram.com/guhanpurushothaman/" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 6762.0 0.0 0.0 0.0
"Can somebody please clarify what happened at 42:14? Why d/dy (tan y) * dy/dx = 1? I don't get where the dy/dx comes from :/" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3064.0 0.0 1.0 0.0
"Collect Mr Strang's lectures like a puzzle now (Because he's really good)" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3162.0 0.0 0.0 0.0
"@JourneyAnyWay I have a literature test in a few hours. It's 3:54am... Oh well..." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1646.0 0.0 0.0 0.0
"I'm a chemical engg. student from India ..i watch mit videos regularly .. it helps me a lot.. sir.. your teaching style is awesome .. thanking you all.. for sharing such videos ..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6294.0 0.0 0.0 0.0
"Thankyou Sir, what a beautiful journey it has been...!!...:)" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9867.0 0.0 0.0 0.0
"One of the many things I like about this professor:  ""Let me tell you BRIEFLY what's in store.""  Three minute intro, not twenty minutes of child psychotherapy at the start of the course.  15 minutes in and he's explained the derivative." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8098.0 0.0 0.0 0.0
"these MIT guys are so dumb. length of the vector should be root 14. It seems many have answered 6. " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14768.0 0.0 1.0 0.0
"18:31 M(2^k) should be there and not M(2)" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 542.0 0.0 1.0 0.0
"@LittleMeSmiley Lol yeah. I mean I love America with all my heart, but fuck man, the people get treated like shit. All they care about are their rich and super rich. That is why once I graduate, PEACE!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1661.0 0.0 0.0 0.0
"hi from argentina and thanx for share that with the world, even not in my language this video makes all clear to me." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13155.0 0.0 0.0 0.0
"He reminds me of The Professor from Money Heist...the intelligence,shy nature." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4596.0 0.0 0.0 0.0
"My teacher's should've taught me this 10 years ago. Imagine where would I be if I knew this way of thinking back then :/" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7791.0 0.0 0.0 0.0
"Gr8 1 !!!" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4175.0 0.0 0.0 0.0
뿡 PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15678.0 0.0 0.0 0.0
"Exceptionally well explained, thank you" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 3696.0 0.0 0.0 0.0
Thanks! vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 9828.0 0.0 0.0 0.0
"completed it!!!!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 12666.0 0.0 0.0 0.0
"rangle is a funny sounding word." UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14244.0 0.0 0.0 0.0
"Gilbert Strang is a treasure to the world. His books are top notch, and the MIT Open Courseware has made it possible for myself and so many others to learn at our own pace. Many thanks Dr. Strang!" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4019.0 0.0 0.0 1.0
"I learned this when I was 16-17 in school...dissapointing." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5655.0 0.0 0.0 0.0
"He is like a Linear cell!!!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4520.0 0.0 0.0 0.0
"I have a question, if I project the projection again that's the same point that is P^2=P. But if I keep doing such it should tell P^3=P^4=P^n=P, and this property holds for Identity matrix. Is my logic correct?" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5506.0 0.0 1.0 0.0
"huge respect SIR. Thanks a lot. 
from BANGLADESH" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13313.0 0.0 0.0 0.0
"Gil 3:30.
Eckart & Young in 1936 were both at The  University of Chicago. The paper was published in the (relatively new?) journal Psychometrica. Ekhart had already worked in the foundations of QM with some of the founders. And went on to work in Fermi's section on the Manhattan Project. If I recall correctly, Eckart married the widow of von Neumann. And ended up at UCSD. He was very renowned in applied physics including oceanographicy/ geophysics.

Mr Gale Young was a grad student at Chicago. He also had a successful career taking his Master's from Chicago to positions in acedemia & US nuclear power industry." Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4005.0 0.0 0.0 0.0
"He reminds me of Feynman but he is even more clearer." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4593.0 0.0 0.0 0.0
"Our indian teachers are best. 
Jai hind 
Our teaching style is best as it is both side interaction." V3Wg_jrMSQY "Lecture 19: Differentiation Rules, Rolle's Theorem, and the Mean Value Theorem" "MIT 18.100A Real Analysis, Fall 2020" 8137.0 0.0 0.0 0.0
"Around 33:00, for the right-hand side of 'B', how did we obtain A'b/A'A  * A? 
The previous lesson, we obtained 'p' as aa'/a'a * b. How did the aa' *b in the numerator get switched to A'b * A?" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 2553.0 0.0 1.0 0.0
"25:00 why transpose of Row's were taken to find combination of row space? Will we be able to multiply transpose of row 1 to X?" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 760.0 0.0 1.0 0.0
"Amazing material." 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 2382.0 0.0 0.0 0.0
"It is immortal at 2020" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6951.0 0.0 0.0 0.0
"The captions at 32:15 are slightly off: instead of ""manage"", it should say ""massage""." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 10040.0 0.0 0.0 0.0
"if S = 1 + x + x^2 + ... + x^n
then Sx = x + x^2 + x^3 + .... + x^(n+1)

so S - Sx = 1 - x^(n+1) no?

*edit* okay, after writing it down I suddenly get it, my example is right for partial sums, but this thing goes to infinity." wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13529.0 0.0 1.0 0.0
"to the memory 🖤" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14949.0 0.0 0.0 0.0
"Amazing professor!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2388.0 0.0 0.0 0.0
"Great professor. We used his book for Linear Algebra and he came and taught as a guest lecturer at my University one time, Drexel University. My professor on the otherhand was a total insufferable dick that made the subject waaay more difficult than it needed to be just because he thought it made him look smart. Douche-bag!" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 4328.0 0.0 0.0 0.0
"Correct me if I'm wrong but Strang was introducing abstract algebra at the end. Once you have all of these linear transformation transforming more linear transformations, you have an even greater transformation of space. Absolutely love this man" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3219.0 0.0 0.0 0.0
"The golden ratio arose from the Fibonacci sequence and has nothing to do with eigenvectors or eigenvalues.  The beauty of using the eigenvectors and eigenvalue of a matrix though is limiting the effect of the transformation to the change in magnitude only, which reduces dynamics systems such as population growth that is a function of several variables to be encoded in a matrix computation without worrying about the effect of direction or rotation typically associated with matrix transformation. Since eigenvectors and eigenvalues change the magnitude of the parameter vector only, the idea of employing the Eigen transformation concept is quite genius. The same technique could be used in any dynamic system that could be modeled as a matrix transformation but one that produces a change in magnitude only." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 10124.0 0.0 0.0 0.0
"Can someone explain how a bunch of vectors are independent when nullspace of A is a zero vector?  
If  N(A) =0 then Ax=0 which would mean the Vs were dependent?" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 3070.0 0.0 1.0 0.0
"Where did the a come from around 14:00?" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11675.0 0.0 1.0 0.0
https://www.youtube.com/watch?v=titoevCaQcQ FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13282.0 0.0 0.0 0.0
"You can tell SVD is Professor Strang's favorite topic. This is the only lecture in 9:4 HD and audio channels upgraded." TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 12195.0 1.0 0.0 0.0
"Hi, I'm from Machupicchu,cusco,PERU. I want to know if it is good for career System engineer, A thousands apologizes if my English is bad." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4719.0 0.0 0.0 0.0
Wow EBdgFFf54U0 "Lecture 14: Basic Hilbert Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 12018.0 0.0 0.0 0.0
"Thank you." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9553.0 0.0 0.0 0.0
"I love how he's so polite in his lecturing: ""Please can I show you this?"". Even in his books he's like ""I hope you will let me show you this""." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 5751.0 0.0 0.0 0.0
amazing!!! Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12357.0 0.0 0.0 0.0
"Linear-Algebra became trivial because of this guy." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7383.0 0.0 0.0 0.0
"What a gem of a teacher! A legend. I did not learn C of calculus in 5 years of my engineering studies way back in 1974-79. Then came the blessing in disguise and by the way I had to teach some calculus to my daughter in her graduate course in economics. And that is how I landed onto Professor Gilbert Strang's video and I fell in love with calculus which all these years was kind of a terror to me. What a beautiful and stylish way of teaching mathematics. I never have seen any teacher with such a vast knowledge and at the same time  comfortable teaching beginners. God bless Professor Strang with health a d happiness.

Regards
Anup Kumar Gupta
India" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11406.0 0.0 0.0 0.0
"Thanks Professor Strang. " RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9641.0 0.0 0.0 0.0
"Around 14:30 I'm not sure about what that means, could anyone help?" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2547.0 0.0 1.0 0.0
"It would be great if he could use less similar looking letters. Uvuvuvuvuvuvuvuvuvuvuvuvuvuvuvuvvuvuuvuvuvuvuvuvuvuvuvuvuvuuvuvuvuvuvuvuvuuvuvuvuvuvuvuvuuvuvuvuvuvuvuvuvuvuvuvuvuvuvuvvuvvuvuvu" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7008.0 0.0 0.0 0.0
"Is there a ""Gilbert Strang Fan Club?""  If not, there needs to be!  I effin love this dude." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 6818.0 0.0 0.0 0.0
"@44:15 initially the formula is op=<a*theta-a*sin(theta),a-a*cos(theta)>
but then let 
a=radius 
a=1
op=<theta-sin(theta),1-cos(theta)>

x(theta)=theta-sin(theta)
y(theta)=1-cos(theta)

so here he parametrise the equation differently than before..

before when it was linear system

we can just use  formula 
Q(t)=InitialQ+t*(EndQ-InitialQ)
so if we have 
InitialQ=<1,2,3>
EndQ=<3,1,2>

we get 
x(t)=1+2t
y(t)=2-t
z(t)=3-t

so for curvature and circle it is different than linear system to parametrize the equation" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1559.0 0.0 1.0 0.0
"This kind of calculus have aplications in linguistic???" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10780.0 0.0 0.0 0.0
"The Man who makes me understand Linear Algebra" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9970.0 0.0 0.0 0.0
"Auto-generated subtitles 😢" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2747.0 0.0 0.0 0.0
"11:35 black noodles" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 377.0 0.0 0.0 0.0
"Can anyone explain whats relation of Eckart Young theorem and PCA ?" Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3030.0 0.0 1.0 0.0
"Я обожаю этого парня" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15559.0 0.0 0.0 0.0
"It is awesome！" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6938.0 0.0 0.0 0.0
"I wonder how he writes 'e' aside 'l'😂" CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 6240.0 0.0 0.0 0.0
"this guy is the worst teacher ever" 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 14835.0 0.0 0.0 0.0
"Pure Brilliance!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 8459.0 0.0 0.0 0.0
"Started this course today. Hope to complete it soon. Loving the journey of learning." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8884.0 0.0 0.0 0.0
"Can someone what is the relevance of the last plot to Markov process, I see it as the number of person at the queue when time tends to infinity. But how can we relate that kind of definition to a markov process, where we just need the probability of any state ?" ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 3102.0 0.0 1.0 0.0
"if you proved d/dx [e^u] and d/dx [ln x], then trick x^n =e^ln(x^n) = e^(n *ln x). d/dx [e^(n * ln x)] =(n *ln x)'  *  e^(n *ln x) = (n *ln x)' * x^n = (1/x * n   +  0)*ln(x))*x^n = (n*x^n)/x  =n*x^(n-1)" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13555.0 0.0 1.0 1.0
"The way he asks Why? Wins my heart.Long Live Strang Sensei" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 10323.0 0.0 0.0 0.0
"In India it is a compulsory question for board exam and my teacher just said the conditions as formulas and then made us practise a lot of problems of this kind. That's it!" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6611.0 0.0 0.0 1.0
"Idiotic course. He didn't even mention why we add the nullspace to our solution vector pretending he had already done that. Awful course. Impossible to learn linear algebra purely from this course. To all of you that think you are stupid reading those comments of people that this lecture has given insight, don't because they for sure use external resources as well." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 6457.0 0.0 0.0 0.0
"Dr. Strang is one of the best🙏" z3SmljnD_nQ "15. Matrices A(t) Depending on t, Derivative = dA/dt" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3507.0 0.0 0.0 0.0
"32:39 
when you are talking about your ex" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 934.0 0.0 0.0 0.0
"What was the deal with the delivery at the beginning?" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11567.0 1.0 0.0 0.0
"same bug in the exmple as in pres 7, column 3 and 4 are combinations of 1 and 2, therefore, you have 2 independent 3d vectors, ie. they do not span the space. class in coma." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 14277.0 0.0 1.0 0.0
"Thank you so much MIT OCW!" RzSp9nIFnbo "Lecture 11: Absolute Convergence and the Comparison Test for Series" "MIT 18.100A Real Analysis, Fall 2020" 9349.0 0.0 0.0 0.0
"What a goddamn miracle, that electrically powered black board!" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11407.0 1.0 0.0 0.0
"Well, it makes us more intelligent people, for one. But also I hope it helps some people discover the beauty of math in how all these ideas fit together." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11367.0 0.0 0.0 0.0
"I think ill leave this and the next lecture for some other day, coz i dont have enough solid background with diffs to understand these 2 lectures. those who has completed course are this two lectures a must for understanding the rest of the course? thanks" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 6022.0 0.0 0.0 0.0
"Thank you!" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9469.0 0.0 0.0 0.0
"why  this vid doesn't uploaded last course ? I take a summer course cause of calculus 102    :(" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15275.0 0.0 0.0 0.0
"It is great that we could press the pause button to think, those ""fortunate"" students didn't have this luxury, hehehe...  Yeah, they could still do that after lecture, of course...  Internet is great and MIT is so generous to put all these lectures up for free viewing...  Thank you very much" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 6946.0 0.0 0.0 0.0
"Guys I beg you that you help me out with this lecture.This is the 10th time i'am watching this.I understood only the first 4 steps.Please..." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4387.0 0.0 0.0 0.0
"Amazing material. Thank you." CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 2383.0 0.0 0.0 0.0
"Ah college hasn’t changed! He started with an interesting example, then went into technical speak. He is now relying on equations he knows but the students don’t. He should be giving real common sense examples then using the equations. I am teaching AP stats and he just seems to jump into complicated equations. If this is a first year stats course I feel sorry for the students. It seems teaching at the university level hasn’t improved in almost 40 years." C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 2276.0 0.0 0.0 1.0
"like the way using pyramids!!" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13793.0 0.0 0.0 0.0
"@tugishtagush LOL aurox could fold you into 2 mathematically with his brain son" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2051.0 0.0 0.0 0.0
"Nice video. I have never seen rising chalkboards. It would be nice to have these when I teach hehe." MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7866.0 1.0 0.0 0.0
"6:07 upper somthing:-)" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 1375.0 0.0 0.0 0.0
"What a curiosity at this age!!!" sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11400.0 0.0 0.0 0.0
"Mr. Free Lecture! The most famous professor in the world!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7713.0 0.0 0.0 0.0
"Is this high school level in USA??  professor is really good! " kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6873.0 0.0 0.0 0.0
"-5...just saying" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 257.0 0.0 0.0 0.0
"The charm of this course is after all these lectures, you feel so empowered and confident that is willing to give any linear algebra problem a try." Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 10042.0 0.0 0.0 0.0
"i'm from morocco i like this teacher , he is perfect" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13515.0 0.0 0.0 0.0
"this course is really helpful! my calculus pro just can't explain this well, oh how i long for going to MIT!" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14799.0 0.0 0.0 0.0
"indeed, rocked my world! listening to his lecture is a kind of pleasure!" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 13605.0 0.0 0.0 0.0
"This is very informative!! It makes me eager to go to class again tomorrow!!" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10765.0 0.0 0.0 0.0
"In a lot of classes that come with college, I think a lot of undergrads can relate to the frustration in dealing with concepts that the professor ""thinks you should know already"", when in reality, you see the course description (and even maybe the title of the course), you find that THING (for lack of better words) is, in fact what you should already know :D ...(hopefully I convey my message clearly; it's the result of not-even-a-semester spent at an engineering university can do)" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6621.0 0.0 0.0 0.0
"@hunglikehuang you weren't paying close enough attention to the French Man.  Some girl actually asked that question...i think he should have done it out, but basically the answer to your question is:

lAl dot lBl   =    lAl lBl  cos (theta)         the second formula is multiplying the lengths of vectors A and B, the first is multiplying the 'components'" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1873.0 0.0 1.0 0.0
"Seems like he had an extra cup of coffee this morning" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 8620.0 0.0 0.0 0.0
"thanks Gilbert. I am watching the lectures and learning a lot." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 14552.0 0.0 0.0 0.0
"At 32:41 when professor Strang says L2 norm of a matrix is 'sigma1', what does he mean by sigma1?" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2647.0 0.0 1.0 0.0
"I am so awed at the depth of maths and the presenter" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 5139.0 0.0 0.0 0.0
"Thank you for publishing this!" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9257.0 0.0 0.0 0.0
"He moves pretty fast through calc. It's easy to say that if you don't have a little experience with it you'll be confused. " ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4587.0 0.0 0.0 0.0
"14:00 also in pysics you understand that in our world there is absolutely, pun intended, no repetition. but this is maths and he should stick to it" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 425.0 0.0 0.0 0.0
"""Randomness is a big rug in which we sweep everything, we don't understand."" Leap of faith.
51:12 - because Real-time observation feels better." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 105.0 0.0 0.0 0.0
amazing... P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 12359.0 0.0 0.0 0.0
"he looks like mark ruffalo in the avengers" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13106.0 0.0 0.0 0.0
"there is some thing wrong with the graph during first 20 min
" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14766.0 0.0 1.0 0.0
"9.8ms^2 in the earth's surface." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1430.0 0.0 1.0 0.0
Lovely 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 7484.0 0.0 0.0 0.0
"For example at 7 or 8 minutes see the video https://www.youtube.com/watch?v=aW63-nmKQcA" sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3864.0 0.0 0.0 0.0
"Great man, wonderful teacher." t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4315.0 0.0 0.0 0.0
"Prof. Gilbert Implies God's Gift" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 8295.0 0.0 0.0 0.0
Soothing. J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8850.0 0.0 0.0 0.0
"Phenomenal lecture. Merci beaucoup Professor Auroux!" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 8188.0 0.0 0.0 0.0
"@h0wud0in2 It is difficult because it deals with some ideas that though simple are very abstract. Some people have a hard time thinking this abstractly. There is also a lot of new notions that don't correspond to anything that is very familiar. Finally, some of the algebra procedures like decomposition for fractions, path integrals and trig substitutions involve manipulating sets of symbols that are more complex than most people know how to deal with. At it core though, the ideas are simple/ " jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1861.0 0.0 0.0 0.0
"A legend" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 2131.0 0.0 0.0 0.0
"Thank you Gilbert daddy" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9113.0 0.0 0.0 0.0
"This is some nice chalk" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10725.0 1.0 0.0 0.0
"It took me some time to understand the A screwed up thing, but as soon as I got the idea, it turned out to be a good explanation! I'm always impressed by his teaching style." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 6993.0 0.0 0.0 0.0
"i am waiting this course for long time☺️☺️☺️ i am very happy" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 13339.0 0.0 0.0 0.0
"@*****  You`re so right." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1490.0 0.0 0.0 0.0
"just finished the series. Took about 2 weeks studying part time + 2 weeks full time. 

Time to start studying 18.02 multivariable." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13731.0 0.0 0.0 0.0
"Wow this guy is good. Geez so much better than my Lin. Alg. Professor was." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12039.0 0.0 0.0 0.0
"Lavada dikh raha hai board par" QeYUHA0UMVg "Lecture 21: The Riemann Integral of a Continuous Function" "MIT 18.100A Real Analysis, Fall 2020" 7252.0 1.0 0.0 0.0
"Professor Strang, I think you inspired Grant Sanderson regarding Linear Algebra:
https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8379.0 0.0 0.0 0.0
🕊 j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 15729.0 0.0 0.0 0.0
"Thank you, Dr. Strang!
I enjoyed the journey :)" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9493.0 0.0 0.0 0.0
"after 5 minutes I realized I was a fucking donkey" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12306.0 0.0 0.0 0.0
"Another way to prove that the determinant of a matrix with a zero row is zero would be to add one of the other rows to that row. That would create a duplicate row, which he proved the determinant of was zero." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 2462.0 0.0 0.0 0.0
"your inf  is   a  minimum ,because it is attained" KcI2_r51Eb8 "Lecture 17: Minimizers, Orthogonal Complements and the Riesz Representation Theorem" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 15524.0 0.0 0.0 0.0
"the sound of hard chalk on thick slate is marvelous" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 14742.0 1.0 0.0 0.0
"You're great at explaining matrices. 

I'm not so great at understanding them yet ><" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12250.0 0.0 0.0 0.0
"Lol ya, that exam looks easier than my exams, and I'm in AP Calculus AB (high school)." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7400.0 0.0 0.0 0.0
"thanks professor" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14601.0 0.0 0.0 0.0
"Just the accent tortures me 😫" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7194.0 0.0 0.0 0.0
"35:05 ""y is not a function of x"" - can we say that z is a function of x and y?" zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 998.0 0.0 1.0 0.0
"I don't understand why he thinks x is fixed and ""delta"" x is moving in here: https://youtu.be/9v25gg2qJYE?list=PL590CCC2BC5AF3BC1&t=448
Can anybody explain me pls?" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5355.0 0.0 1.0 0.0
"1:48 41:42 Math Humor 101" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 600.0 0.0 0.0 0.0
"I finished the lectures and took notes myself, which took around 16 days. But I am sure I will keep referring back to here from time to time. The explanation is excellent and generates the engineering style of thinking, problem thinking automatically. Thx Dr.Strang" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5421.0 0.0 0.0 1.0
"beautiful just beautiful" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12517.0 0.0 0.0 0.0
"very underastandable lecture!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15037.0 0.0 0.0 0.0
"""Gauss thought of it before we did but only because he was born earlier"" lol" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 48.0 0.0 0.0 0.0
"If I were half as smart as this guy I would still be able to get into MIT" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 6477.0 0.0 0.0 0.0
"all those kids in the class are so fucking smart" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12328.0 0.0 0.0 0.0
"""This is a degenerate matrix""
Very based" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 127.0 0.0 0.0 0.0
"It irritates me that they don’t ever erase completely." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6922.0 1.0 0.0 0.0
"33：06 why it's 100^2?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 973.0 0.0 1.0 0.0
"i didn't get why he switched 2 and 3 when talking Gaussian-Jordan elimination? " FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13357.0 0.0 1.0 0.0
"As a mathematician I'm wondering why it's not mentioned at all, that the ""nullspace"" is also called ""kernel"", ker(A) = nullspace(A), where A is a matrix. The column space of a matrix A on the other hand is also called ""Image"" of A.

Good lecture style. Thanks." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 2564.0 0.0 0.0 0.0
"this lecture is more immortal than lec. 15" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 14892.0 0.0 0.0 0.0
"Noble and invaluable teaching" mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 7907.0 0.0 0.0 0.0
"@StatelessEuphoria probably his accent...so bad how they do that. this guy is ver very very smart." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1729.0 0.0 0.0 0.0
"You'd think there would be some smart asses that would want to correct him, maybe they're just too shy at MIT" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12245.0 0.0 0.0 0.0
"@AnimeBelover true dat" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1587.0 0.0 0.0 0.0
"what book is he using?" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15127.0 0.0 0.0 0.0
"An Indian edition of this book is available only in India
http://www.wellesleypublishers.com/buy.html" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 2430.0 0.0 0.0 0.0
"the natural log comes from the anti-derivative of 1/x" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14720.0 0.0 0.0 0.0
"You sir are an Inspiration:)" nrDkb2MAwSA "20. Definitions and Inequalities" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12239.0 0.0 0.0 0.0
"42:00 i... whatever that is. Lol" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 1169.0 0.0 0.0 0.0
"what a stunning way in which you have given this lecture series, sir.
You are the best teacher Gilbert Strang Sir. And very very thanks to MIT OCW to give this beautiful lecture series totally free, and to indroduce the world to this amazing professor." Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 15114.0 0.0 0.0 0.0
"@Sadist102  Above all these comments there is a link to the course materials.  Follow that link and select Readings.  There you will find the book's author and title." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1714.0 0.0 0.0 0.0
"poor video capturing" yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 14200.0 1.0 0.0 0.0
"Finally understood why a projection matrix must satisfy P = P^T. It's because its eigenvectors must be orthogonal." HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 3784.0 0.0 0.0 0.0
"This is called learning !" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10655.0 0.0 0.0 0.0
"This guy makes so many mistakes and is on top of that really hard to follow..." yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 10554.0 0.0 0.0 0.0
"Is there is a mistake here??
The base 'e' initially defined at 14:15 was never referred to as natural number, and it was only supposed be some base for which the derivative of e^x is e^x because its slope at x=0 is assumed to be 1. This was never proved. Later on (at 24:30) it was just stated as a fact that e, the natural number, is really that base and that its slope at x=0 is 1. I thought the idea here was to prove the derivative of a^x by proving derivative of e^x, where e = natural number. What am I missing?" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6842.0 0.0 1.0 0.0
"Sir ,in the last of lecture How those two column vector passes through the origin ????" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 8689.0 0.0 1.0 0.0
"That's all I remember from Calc 1,  the derivative of x^2 = 2x lol.  Of course, that was the ""shortcut,"" but we had to do it with all the dy/dx notation.  I remember that I loved doing quotient derivatives for fun.  What's wrong with me?  Linguistics major BTW." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9930.0 0.0 0.0 0.0
thx cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 14936.0 0.0 0.0 0.0
"Who's monica?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 11757.0 0.0 0.0 0.0
"the camera man ruined the course" XtNXQJkgkhI "22. Bayesian Statistical Inference II" "6.041 Probabilistic Systems Analysis and Applied Probability" 14673.0 1.0 0.0 0.0
"I updated my knowledge on bayesian statistics :)" bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 6123.0 0.0 0.0 0.0
"One day I must be a Lecturer at MIT" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8074.0 0.0 0.0 0.0
"Gilbert Strang on Linear Algebra for Data Science ..... *Grabs Popcorn* . Thanks for the videos !!!" p-bXJIa7QVI "Lecture 30: Completing a Rank-One Matrix, Circulants!" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4030.0 0.0 0.0 0.0
"17:57 did someone sneeze?" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 521.0 0.0 0.0 0.0
thanks ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14545.0 0.0 0.0 0.0
"I liked this vid the moment I clicked on it." or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5704.0 0.0 0.0 0.0
"Much higher quality stats work at CW POST - LIU POST etc" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 7721.0 0.0 0.0 0.0
"Good class.I studied that,at 17,in spain." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4123.0 0.0 0.0 0.0
"this guy sounds like dr. scratchensniff from anamaniacs" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14841.0 0.0 0.0 0.0
"vector spaces 20:12" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14993.0 0.0 0.0 0.0
"he is." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13104.0 0.0 0.0 0.0
"I like your intelligent advanced lectures.they are very challenging..strang is the smartest.thank you." L3-WFKCW-tY "33. Neural Nets and the Learning Function" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5700.0 0.0 0.0 0.0
"Did we prove det(AB) = detA*detB in the lecture?" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 3389.0 0.0 1.0 1.0
"Ah, yes....most of my classmates were 16 years old when we had it in school. For most of my friends it was reaaaallly easy to understand...not for me, I am really bad at mathematics :D So ahm...they have it in university? Isn´t that a little bit late?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2281.0 0.0 0.0 0.0
"No one ever taught me matrices like this... God why don't we have teachers like him more?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7884.0 0.0 0.0 0.0
"Not gonna lie. I got lost half way" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7924.0 0.0 0.0 0.0
"It's sad talking to an empty classroom; I could never bring myself to do it." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 7068.0 0.0 0.0 0.0
"his french accent is marvelous :-)" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13164.0 0.0 0.0 0.0
"Gilbert Strang, you are truly an outstanding teacher! I am currently doing my Master's thesis in Finite Element Analysis and started watching these video lectures just for fun, since I already had some Linear Algebra back on my bachelor's. Your little sidenote at the end of a lecture about multiplying a system by A.transpose actually helped me crack a problem I'm dealing with right now. My finite element system had more equations than unknowns (because I'm fixing some internal degrees of freedom, not the nodes themselves) and I just couldn't figure out how to solve such system. I completely forgot about this trick of multiplying by a transpose!! THANK YOU SO MUCH!! My final system now has ""good"" dimensions and the stiffness matrix has a full rank!!!" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4036.0 0.0 0.0 0.0
"So you're saying being an engineer is a sedentary job doing calculus and testing out materials?

Geez we are scientists then, not engineers." eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8803.0 0.0 0.0 0.0
"Knowing that the class is empty, 19:09 becomes incredibly hilarious." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 7220.0 0.0 0.0 0.0
"00:00 Lecture overview
02:40 Elimination Success
10:35 Elimination Failure
14:30 Back-substitution
18:55 Elimination matrices
33:00 Matrix multiplication
37:00 Permutation matrix 
42:52 Inverse matrix" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 281.0 0.0 0.0 0.0
"I do not understand why at a constrained min/man, in any direction along level g=c the rate of change of f (gradient of f) must be zero? What am i missing?" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5292.0 0.0 1.0 0.0
"awesome lecture!!!" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 12493.0 0.0 0.0 0.0
"woke up this morning with the weirdest dream, i missed the test and had to drop the class. what a nightmare, i am 49 years old, lol." YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15390.0 0.0 0.0 0.0
"really like the lecturer, god bless!" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 14254.0 0.0 0.0 0.0
"I took stats 35 years ago, and worked as a statistician for a decade before switching to medical translation. I am interested now in my retirement to see how much I remember." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 6109.0 0.0 0.0 0.0
"How much MIT must one do to be eligible for a Brass Rat?" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4888.0 0.0 0.0 0.0
"The limit rests on the logic presented by Dedekind" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10178.0 0.0 0.0 0.0
"Doc Strang in 1080P！！！" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3426.0 0.0 0.0 0.0
"is the teacher french?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13648.0 0.0 0.0 0.0
"33:12 This is what anarchy sounds like" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 954.0 0.0 0.0 0.0
"i watched these now for the second time, it's still awesome. oh strang, you are great lecturer!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13493.0 0.0 0.0 0.0
"@jshowa6 Maybe by your 'logic'...  on which you're comparing A student, with THE CONTENT OF A lecture?... you're comparing non-comparable things... an acceptable refutal would've been to compare lecture contents. You're judging ONE item of student... here is ONE item of american higher education... don't know were your student is from, the quality of his/her university... but this lecture is supposed to be from the TOP OF USA'S TECHNOLOGICAL UNIVERSITIES. That makes you wonder......" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1907.0 0.0 0.0 0.0
"Anyone understand the equation at 32:15? I think x_free should be above x_pivot?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 2511.0 0.0 1.0 0.0
"@nomchews I don't think you're qualified to be taking shots at an MIT professor. 
" aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1958.0 0.0 0.0 0.0
"Thank you so much, Professor Strang!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9396.0 0.0 0.0 0.0
"@roostaj i fucking hate proofs" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 1993.0 0.0 0.0 0.0
"i can't imagine these lectures are 12 years old." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 13348.0 0.0 0.0 0.0
اكس YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 15565.0 0.0 0.0 0.0
"I love this guy's style... Can't seem to find videos on their website..." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5808.0 0.0 0.0 0.0
"Yo solo queria triangulitos y.u" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12155.0 0.0 0.0 0.0
"Shizzle! He forgot his neck tie!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 8639.0 0.0 0.0 0.0
"I wish I have him as a teacher!" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6205.0 0.0 0.0 0.0
"At 36:38, when A times b, shouldn't the number of columns in A equals the number of elements in b?  Then when you look at A times A times b, does it indicate A is a square matrix?" MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2653.0 0.0 1.0 0.0
"15:5 ""Let me call that matrix A....s, A Screwed up"" Great professor :D" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 459.0 0.0 0.0 0.0
"There is a circular argument there in 24:45.
Law of cosines used to prove geometric expression of dot product.
Geometric expression of dot product used to prove law of cosines." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10362.0 0.0 1.0 0.0
"""evil equations"" ^__^" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 150.0 0.0 0.0 0.0
"MIT has better blackboards than 20 years before when 18.06 was filmed." 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7519.0 1.0 0.0 0.0
"column operations (mp on right), row operations (mp on left)" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12663.0 0.0 0.0 0.0
"Wow he's such a good professor👍👍👍" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 12032.0 0.0 0.0 0.0
Brilliant.. t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2947.0 0.0 0.0 0.0
"why is it the the deviation formula is squared? i know it must be equal to zero." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15335.0 0.0 1.0 0.0
"MIT is great great great!!!!!!!!!!!!!👍👍👍👍👍👍👍👍👍👍👍👍👍👍👍" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7529.0 0.0 0.0 0.0
"The Prof. gives the lecture as though there is a full class. Hilarious:D, but every good explaining." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9974.0 0.0 0.0 0.0
"Terrible video. What is an example of  a Hilbert space with real numbers in a actual application. This man is just copying lines from a text book but provides no concrete examples that would explain Hilbert. Sad. A waste of time." EBdgFFf54U0 "Lecture 14: Basic Hilbert Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 9029.0 0.0 1.0 1.0
ห้องเรียนเงียบจังครับ 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15583.0 1.0 0.0 0.0
"You are amazing mr Strang. Give me deeper understanding about machine learning" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12166.0 0.0 0.0 0.0
"Such an amazing professor, he turns math into a fascinating story! 
If most teachers at MIT are even 70% that good, that explains how students there get so smart haha" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8946.0 0.0 0.0 0.0
"@zionen01 exactly right m8, im the same" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2083.0 0.0 0.0 0.0
"Notice that the smart ones are using Latex or MatLAB" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7946.0 0.0 0.0 0.0
"04:30 prerequisites" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 293.0 0.0 0.0 0.0
"Really interesting explanation, “You should not say sth if you don’t have to say it”" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 8522.0 0.0 0.0 0.0
"I finally understand the Pumping Lemma for regular languages!! 😊 I didn’t quite get it by reading the proof in the ’Sipser’ book the first time; but after this really great lecture by the author himself it’s all clear. He gave just the right amount of intuition necessary. Thank you Prof, and thank you MIT for making these courses available to everyone who wants to learn." KAySmSEGc9U "3. Regular Pumping Lemma, Conversion of FA to Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 5408.0 0.0 0.0 1.0
https://www.youtube.com/watch?v=l3vzfKKY2wU&t=3s J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13280.0 0.0 0.0 0.0
"I like how he said at 19:48 that people at MIT are very round" XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5665.0 0.0 0.0 0.0
👍👍👍👍👍 phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15709.0 0.0 0.0 0.0
"Absolutely well done and definitely keep it up!!! 👍👍👍👍👍" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 2209.0 0.0 0.0 0.0
"Great lecture.  I took single variable calculus twenty plus years ago and I enjoyed learning it again.  I look forward to MIT uploading the rest of the lectures and then moving onto multivariable calculus!" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4288.0 0.0 0.0 0.0
"*Just curious:* is it a coincidence that the sum of the errors in the example is zero (-1/6 + 2/6 -1/6 = 0) ?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 234.0 0.0 1.0 0.0
"WOW HIGH QUALITY THANK GOD" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11245.0 0.0 0.0 0.0
"A transpose is nothing but the row space right? so Null space of A transpose should lie in row space but professor say A^T.(b-P)=0 ,where b-p =e and e is in column space , but it should be in row space.right?" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2162.0 0.0 1.0 0.0
"When will the phd application open again? Currently the application is closed already, and I missed it..." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 11641.0 0.0 0.0 0.0
"I don't understand this at all yet, but this is my introduction to Gaussian elimination so hopefully it will get better the more I study the material" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5348.0 0.0 0.0 1.0
"When you're 100% screwed for finals...." phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11648.0 0.0 0.0 0.0
"TF?!  Why the hell did no one explain the vector origins of determinants to me before???  God damn rote mathematics instruction.  All computation and no theory makes a sad mathematician." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8978.0 0.0 0.0 0.0
"@Jameswb98   Lastima por tí...   ¿hay que recordar?  se recuerda lo que se conoce y despues se olvida, a mi nunca se me informo de la capaciodad de la audiencia así que no tengo que recordar nada sobre ellos... los  ""metodos algebraicas"" como lo escribes, creo que sé a que te refieres y no son garntía de demostración si no se  profundiza en  la justificación de cada acción algebraica,  si no se hace esto se pueden cometer falacias muy bien disfrazadas" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1644.0 0.0 0.0 0.0
"omg same O_O " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14141.0 0.0 0.0 0.0
"Watched all; learnt alot..
Thanks Prof.Auroux and MIT💞" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11285.0 0.0 0.0 0.0
"@matanorland1 believe it or not but most of their income is not from tuition, but grants, endowment, and other funding. the costs of world class/cutting edge research is very high." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1938.0 0.0 0.0 0.0
"Around 20:00. Why are the errors ""e"" the vertical distance between the line and the ""b"" points? Why don't we look at the shortest distance between b and p which is when you use a distance between b and the line that is perpendicular to the line (not parallel with y axis)?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 2550.0 0.0 1.0 0.0
"Muy buena explicación, que buen curso." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7729.0 0.0 0.0 0.0
"-0.618       1
    1        -1.618
The Null Space of the given matrix should be the zero vector because the RREF will become:
1      0
0      1
Which means the Null Space(and hence the Eigenvector) is the zero vector for the first Eigenvalue?
Correct me if I'm wrong?" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 256.0 0.0 1.0 0.0
"Amazing, thk u MIT and Prof. Gilbert Strang." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2404.0 0.0 0.0 0.0
"In this you learn that MIT students are the most disrespectful students as well as the chain rule.
" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6690.0 0.0 0.0 0.0
"positive definite matrices start at 35:14" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 14201.0 0.0 1.0 0.0
"Thanks for sharing this video, it helped me a lot." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 9702.0 0.0 0.0 0.0
"What a great lecture this Professor gives... That's probably why MIT is so good, they actually hire teachers that can teach! Congratulations" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 11410.0 0.0 0.0 0.0
"We assume that the misconception of complex numbers can conduct to the misunderstanding of algebric algorithms.
In that specific case we're also going to cope through practices in workspaces. Building C." ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11314.0 0.0 0.0 1.0
"These lectures will live on for as long as linear algebra lives and so will Gil Strang. Now, that's some way to become immortal." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10421.0 0.0 0.0 0.0
"That reply is at ""chinrxn""" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9910.0 0.0 0.0 0.0
"How many lectures can you guys cover per week typically?" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4885.0 0.0 0.0 0.0
"Thank you very much" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9427.0 0.0 0.0 0.0
"It's hard to begin with, but if you put in the effort every couple of days by doing exercises and reading up on it, watching this, doing your homework, Khan Academy, whatever you need - you will eventually get the hang of it. I think that doing Law essays and Scientific Research is much harder in reality. Don't worry =)" jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7048.0 0.0 0.0 1.0
"I've watched all his videos of 18.06 to study for my linear algebra finals and watching this video as last made me cry so much. It's really been my honor to say that I (sort of) am one of his students. Thank you professor" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6435.0 0.0 0.0 1.0
"will read the notes to see what he left out on the proofs" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15382.0 0.0 0.0 1.0
"mistake near 28:00 ----->  dy/dt = -2t     the position function starts as y= -t^2 so derivative should be negative for the dy/dt" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13949.0 0.0 1.0 0.0
"Probably the hardest class I'll take and probably the easiest for them." sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8258.0 0.0 0.0 0.0
"Funny how the reason people like professors isn't even related to the subject they teach. Like this guy's chalkboard-erasing skills. Or the way Walter Lewin makes dotted lines." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3960.0 1.0 0.0 0.0
"(28:13) Regarding the analogy with the center of gravity of a light rod with weights at discrete positions, if you'd like to visualize the balancing, the position marks should be further apart, 2 a unit to the right from 1, and 4 further two units to the right." 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 219.0 0.0 0.0 0.0
"3D blackboard!!!!!" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 1119.0 1.0 0.0 0.0
"Can my linear algebra teacher please learn to teach from you" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 3058.0 0.0 0.0 0.0
"Nice to learn." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7860.0 0.0 0.0 0.0
"Let's go with integrals" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7336.0 0.0 0.0 0.0
"I'm not sure why everyone thinks he's such a great lecturer. Don't get me wrong, he clearly knows what he's doing and talking about, but here are my qualms with his teaching style:

1) He hesitates a lot. It makes it difficult (at least, it did for me) to follow his train of thought because he paused so often to consider and ""reconsider"" what he was going to say. I find it much easier to follow a lecturer when he or she has a straightforward, flowing style of presentation.

(See above for 2)" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6359.0 0.0 0.0 0.0
"Beautiful course" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 2816.0 0.0 0.0 0.0
"he seems so much smarter at 1.5 speed lol. Watching at 1.5 I feel slow lol but at regular pace it feels like im learning along side him" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 13112.0 0.0 0.0 0.0
"Thank you for making these vids available, MIT! I'm taking calc II at my university in the Spring after a semester away from calculus, so I really appreciate being able to refresh my memory by ""taking"" a calculus course to prep! This professor is a lot more into proofs than the professor I had, so I'm even seeing familiar things in a new light. Thanks again! " kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9253.0 0.0 0.0 1.0
"Anybody studying this course nowadays?
I need some help" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2479.0 0.0 0.0 0.0
"This topic is so boring and easy. This is more suitable for the level of engineers. I don't know why it's a part of my mathematics course." xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10946.0 0.0 0.0 0.0
"fyi, for the curious: the sum of i squared with i from 1 to n is equal to n cubed divided by 3 plus n squared divided by 2 plus n divided by six.
" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12913.0 0.0 0.0 0.0
"q dira esta en ingles nooooo" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14234.0 0.0 0.0 0.0
"dude it says his name at the beginning of each vid" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12777.0 0.0 0.0 0.0
"In 22:38 isnt the dF/dt a vector? Can anyone explain. Thank you" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6595.0 0.0 1.0 0.0
"스트랭 교수님 감사합니다ㅠㅠㅠ 딥러닝을 공부함에 있어 선형대수를 공부해두는게 많이 도움될꺼같아서 수강하기 시작했는데 이렇게 시간가는줄 모르고 재밌게 들을줄은 몰랐네요!  2005년 강의지만 아직도 이렇게 강의하시는분은 많지않은거같아요.  정말 전반적인 수학이 편하게 느껴지는거 같습니다 ㅠㅠ 한국에서도 이렇게 강의 다 찾아보는 학생이 있다는걸 알아주셨음 좋겠네요!!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 15681.0 0.0 0.0 0.0
"Asi empiezan, con cosas faciles despues te revientan el cerebro XD" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2577.0 0.0 0.0 0.0
"Thank you so much. The material were so clearly articulated" TSI3LR5WZmo "25. Interactive Proof Systems, IP" "MIT 18.404J Theory of Computation, Fall 2020" 9414.0 0.0 0.0 0.0
"The best
" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 9991.0 0.0 0.0 0.0
"46:31 Use the Cofactor Formula from the beginning." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 1273.0 0.0 0.0 0.0
"I encourage anyone finding difficulty understanding this lecture to first visit Khan academy to see the proofs for the laws of logarithms and also to view the videos there about the formulas discussed here. (especially the definition of e and d/dx (ln x))

When I was first taking calculus I found this topic really hard to grasp (especially because my basics in logarithms was too weak). So what I did is that I first understood the properties of logarithms (from khan academy) by watching the proofs and then looked through the videos related to the formulas discussed in these lectures. Now when I see this lecture I feel it is a great lecture on this topic." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5380.0 0.0 0.0 1.0
"@evildude109 I'm British and you're totally right, MIT is one of the most distinguished University's in the world. No matter where you're educated, the initial lectures have to cater for a spectrum of ability. There will be people doing this as a requirement for their major which has no connection to hard science. Social science subjects need a grounding in this. The critics either never made it to college or are too young to know how the system works. " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1832.0 0.0 0.0 0.0
"Or you could just use Steiner theorem for rotation around the point on the circumference, and do it in 10 seconds ;)" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8135.0 0.0 0.0 0.0
"The guy wrote the series wrong! The actual series should have been 1/2+1/4+1/8+1/16... And he cannot go any further than double the length of one block, measured from left end of the top block to the right end of the bottom block. And this means he would actually need infinitely many blocks to align the ends of the top and bottom blocks. So the guy actually couldn't pass the bottom block, it just seems like it from that angle. (Trust me, I solved this question in physics class in high school.)" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10136.0 1.0 1.0 0.0
"Zdalo sa mi že slnko ☀ ma svoju abecedu videl som písmenká a maľovanie a tuším aj zvuk písmenká  staré" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 12271.0 0.0 0.0 0.0
"It is crazy... really amazed... (tears drop)" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 6942.0 0.0 0.0 0.0
Thanks VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 9576.0 0.0 0.0 0.0
"can someone shed a light on how is nds = <-f_x, -f_y , 1>dxdy @47:00" phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12631.0 0.0 1.0 0.0
"Teşekkür ederim Dr. Strang. Eğlenceli bir eğitim oldu." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 9038.0 0.0 0.0 0.0
"Then can i write error matrix as 1 - the projection matrix?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 10342.0 0.0 1.0 0.0
"Should we not use A0 = QR ,  A1=RQ => A0 = QRQ^-1 since we know Q is orthogonal and hence invertible? Where as R is not invertible unless A is?" d32WV1rKoVk "12. Computing Eigenvalues and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8643.0 0.0 1.0 0.0
"The eigenvector calculation around  minute 33 confused me until I saw how the zero in row three gives an extra degree of freedom in choosing the vector. The check is to multiply by row 2. A nice trick." lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 10084.0 0.0 0.0 1.0
"bed finishing" 3eiio3Tw7UQ "19. Weak Law of Large Numbers" "6.041 Probabilistic Systems Analysis and Applied Probability" 12529.0 0.0 0.0 0.0
"Thank you MIT, thank you Mr. Strang, this is the way EVERYTHING  should be taught!!!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9158.0 0.0 0.0 0.0
"i am big Aylin" 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 13327.0 0.0 0.0 0.0
"Why would someone dislike this?
" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11935.0 0.0 0.0 0.0
"Thank you so much" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9339.0 0.0 0.0 0.0
"the best professor on linear algebra and free class, you don't pay anything you get the best educated in the world, god bless America and the bad professors in the university should've think about themselves too, if they don't really like teaching and love students want to help students to make sense,they can always just leave, we have a lot of good professors looking for jobs!!!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14668.0 0.0 0.0 0.0
"At 27:20 I have to guess the row since i don't wanna think so i took the row as [x,y,z] and then solve it manually to find that x+z = -3 will solve it. I thought i am so smart but..
...
...
At 37:40 I couldn't solve it using taking the variables although matrix P was an easy one to think but at time of lecture it seems hard but i guess it comes through practice" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2628.0 0.0 0.0 0.0
"I would like to have a test, please tell me where I can find it :)" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6261.0 0.0 0.0 0.0
"Professor Strang mentions that U and V form bases for the four fundamental subspaces of A, but it's not clear to me how C(A) = C(Ur) and C(A') = C (Vr'). I know that U and V were determined by the eigenvectors of AA' and A'A, respectively, but how are these related to the column and row spaces of A?" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 8358.0 0.0 1.0 0.0
"thank you MIT for open courseware
" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14481.0 0.0 0.0 0.0
"He's obviously French . 
" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4641.0 0.0 0.0 0.0
"who else thinks that mistake was done deliberately" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 15261.0 0.0 0.0 0.0
"Right hand rule 39:20" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8572.0 0.0 0.0 0.0
"Thank you MIT and Gilbert Strang sir,you made my studies simpler" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9135.0 0.0 0.0 0.0
"@UUUtub22 votre anglais est bon pour un francais!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1748.0 0.0 0.0 0.0
"Listening to him think his way through problems is the analytical education we need, and not just for algebra. His candor is well appreciated. He attacks very complicated ideas with a simple tongue. And in spite of all the newer technology, i am learning more from his approach than the newer educators." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 7387.0 0.0 0.0 0.0
"BEST MATHS TEACHER EVER SEEN.." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2801.0 0.0 0.0 0.0
"I WANT TO KNOW ALL THE MATH IN THE UNIVERSE!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5004.0 0.0 0.0 0.0
"cameraman sleeping?" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12594.0 1.0 0.0 0.0
"Is confusing notation a feature or a bug in maths?.." XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6765.0 0.0 0.0 0.0
"""Well it takes approximately for ever to compute these determinants""!! Wow, such great sense of humour!!" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 131.0 0.0 0.0 0.0
"This is pure gold." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10707.0 0.0 0.0 0.0
"Proof of TRL neglects edges inside clusters?" RD9AWDdj-Yk "7. Szemerédi's graph regularity lemma II: triangle removal lemma" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 8417.0 0.0 1.0 0.0
"Clear, concise, efficient, and most importantly doesn't make you take 1000 notes. Love his reviews to start off every lecture... sadly many professors are either too lazy, inept, or inefficient to spend time on review each class. I've watched many many math videos, and this Professor is probably the best math lecturer I am yet too hear. (Though Professor Leonard's calc series is wonderful as well.)" -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 3154.0 0.0 0.0 0.0
"If you activate the subtitles, it changes it to ""variety""." U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6534.0 0.0 0.0 0.0
"The ordinary light indirectly change because end phongsaly nod but a second energy. homely, godly drink" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 10218.0 0.0 0.0 0.0
"A statistics class focused on understanding statistics, not just scribbling equations.  Very refreshing." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 2157.0 0.0 0.0 0.0
"I Really Like The Video Graphs, Networks, Incidence Matrices From Your" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4973.0 0.0 0.0 0.0
"at 37:30 why we inserted the slope as 2y/x but not 2x? Since 2x is the slope of parabola" 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12446.0 0.0 1.0 0.0
"linear approximation is basically the equation of the tangent line at the point x0" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13803.0 0.0 0.0 0.0
"free lectures. I  love M.I.T, love america. Does any country do like that?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 12897.0 0.0 0.0 0.0
"apparently i tested high on my IQ test in school. but watching this makes me feel dumb." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12393.0 0.0 0.0 0.0
"Glad I decided to go all the way back to basic LA, such a great and thorough review" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 4052.0 0.0 0.0 0.0
"Thank you for posting this. These videos will allow me to pass my class!" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 9256.0 0.0 0.0 0.0
"vector spaces of matrices! mindblow!" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14995.0 0.0 0.0 0.0
"The final review is very helpful, making me realize that my memory of some materials is already fading away a bit. So I went back for refreshing.  " ZwpwmGP5ITM "Lec 34: Final review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10105.0 0.0 0.0 0.0
"""The job is to make some sense out of it."" He is funny haha." cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 118.0 0.0 0.0 0.0
"It's extremely helpful , thank you sir." EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 7038.0 0.0 0.0 0.0
"How is P(AnB)=0 but P(A)*P(B)=1/12?" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 4865.0 0.0 1.0 0.0
"Lol, I love being a high school junior, and doing this :D" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7402.0 0.0 0.0 0.0
"My mind was blown two times  in just 45 minutes ❗❗🤯🤯" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7774.0 0.0 0.0 0.0
"He is very interesting" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4552.0 0.0 0.0 0.0
"I respect the work you put into your videos. I find it truly disconcerting that all the major cryptocurrency YouTubers only look to pure waves and completely ignore the broader narrative of why BTC is pumping and why the future outlook may not be as optimistic as it seems. It's a bit irresponsible to ignore the fact that every ETF launch so far has caused a sharp spike in BTC's spike. Already on shaky ground with historically low volumes and nearly pure whale pumps, we narrowly avoided a long-term bear market. This is the worst time in history to invest as so many are not backing up their crypto assets. More attention should be paid to day trading as it is less affected by market unpredictability, ... I have gained over 11 BTC from day trading with Anthony Renato, insights and signals with great success in less than 2 weeks together with people around me, Mr. Anthony Renato Daily Trading Signals. This is one of the best tools to protect your wealth in case it starts to decline. 👉Email { Anthonyrenato @ financier.com ) Or WhatsApp ‪+1 (424) 377‑4036‬. It is very accurate and always offers a great positive return on your investment.
" cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 5953.0 0.0 0.0 0.0
"thanks MIT i'm from Colombia, i really  appreciate it !!" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14556.0 0.0 0.0 0.0
"This isnt exactly mathematical approach.. I see no theorems or proofs.. is this LinearAlgebra for physicist?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10777.0 0.0 0.0 1.0
"What a guy; Boss+" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11417.0 0.0 0.0 0.0
"36:04 maybe it's worth mentioning that all E[Xi] are equal" P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 1028.0 0.0 1.0 0.0
"Prof Strang can be quite the comedian - that comment about Lewinsky was hilarious." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 8270.0 0.0 0.0 0.0
"""Whether the rest of the world will realize I was in danger or not, we don't know.""  XD" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 134.0 0.0 0.0 0.0
"""well I shouldn't do this, but I will."" How many times has he said this in this course?" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 191.0 0.0 0.0 0.0
"someone needs to make a compilation of the students cheering for the professors erasing the blackboard!!" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 14363.0 1.0 0.0 0.0
"This is seriously good stuff but I feel the lecturer glosses over a lot of nuances and could spend more time imparting intuition and abstract mathematical reasoning / techniques. Of course that would require twice the number of lectures." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10714.0 0.0 0.0 1.0
"beautifully taught!" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12523.0 0.0 0.0 0.0
"SIGN BETWEEN    A.B   WILL ALSO BE POSITIVE IF  ANGLE THETA LIES BETWEEN 270 DEGREE TO 360 DEGREE( OPEN INTERVAL)   " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8580.0 0.0 1.0 0.0
"I'm literally binge watching these like a TV show. It's 03:15..." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6345.0 0.0 0.0 0.0
"I am absolutely in love with that accent" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5057.0 0.0 0.0 0.0
"the audio is soooo low, guys" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 14662.0 1.0 0.0 0.0
"Learning LA after graduation." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7254.0 0.0 0.0 0.0
"fuck me...you guys in MIT do differentiation in your FIRST YEAR??

I have done differentiation in my 11th grade(high school in your region, I suppose)...MIT is easy shit...I suppose
god, MIT is slow...

" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12902.0 0.0 0.0 0.0
"Great teacher. I'm 76. He makes a potentially abstruse subject simple." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 4342.0 0.0 0.0 0.0
"@ around 7:30 how is he finding the vector PoP..? is it just subtraction of co ordinates from x,y,z and how does subtraction gives us the result ? what is the logic behind it ??" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1488.0 0.0 1.0 0.0
"amazing lecture. loved it!" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12349.0 0.0 0.0 0.0
"he makes a comment in passing about doctors ""getting tests results wrong"", but his example about the radar doesn't readily translate into an example about medical testing. Even though a disease might be very rare, doctors don't just order a test for diseases at random. Drs order tests for a disease when a person has symptoms similar to those of others who have previously had the same disease. And so, even though celiac disease is suffered by less than 2% of the population, a patient for which celiac disease testing has been ordered will actually have a much higher chance of having it than a randomly chosen individual. While he's right the a priori chance of a random person having some rare disease is low, that same chance is much higher for a person that has been seen by a doctor and judged to be having symptoms of such rare disease." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 13109.0 0.0 0.0 0.0
"MIT Open Course ... WELL DONE.   Gilbert Strang   WELL DONE." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7508.0 0.0 0.0 0.0
"It was awesome to learn about the Jacobian. I've seen this here and there and never understood what it was. Thanks!!" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6997.0 0.0 0.0 0.0
"My mind got blown when I realized you could get the basis for the left null space from row transformation. I mean, it seems completely obvious after he points it out but I never thought much of it until then." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7773.0 0.0 0.0 0.0
"I like how the prof says factorial." 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 5669.0 0.0 0.0 0.0
"He gives the vibes of mr. Mackay from south park. ""Mkay? ""😛
Haha, he is an amazing prof. Though. ❤️" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 4485.0 0.0 0.0 0.0
"i looking for lol buddy in euw, alingerte add me guys" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13424.0 0.0 0.0 0.0
"Wow, this professor is so bad. The students already knowing this is the only way they'd get through." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12078.0 0.0 0.0 0.0
"Finished (17/03/21). To the exam!" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3802.0 0.0 0.0 0.0
" Never Seen someone like this.... Amazing!!!!" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 7.0 0.0 0.0 0.0
"Why do we set the free variable to 1? What if we chose like 7 or 10 or any non zero value?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 11833.0 0.0 1.0 0.0
"the pseudoinverse part is unclear, the book tells more details and it relationship with the normal solution" ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14734.0 0.0 1.0 0.0
"why we have to write dx in an integral ??" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15376.0 0.0 1.0 0.0
"I'm brazillian, and I've been watching all the 18.02 lectures with Aurox as Instructor... And I can say that I am understanding every single word that comes out of his mouth. He's brilliant! Respect for him." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6309.0 0.0 0.0 0.0
"You have to learn calculus regardless of where you live...well I mean it depends on what kind of major you are going in to." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12213.0 0.0 0.0 0.0
"Now i can say i have a ""strang"" understanding of linear algebra" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 7958.0 0.0 0.0 0.0
"For anybody wondering d/dy tan y = 1/cos^2(y) due to Cos^2(y)+Sin^2(y) being in the numerator of the answer. This is a trig identity that simplifies to one." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3852.0 0.0 1.0 0.0
"@Phughy Your point? Not everyone has the luxury to have taken or even knew they wanted to take calc or above in high school" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1702.0 0.0 0.0 0.0
"Great lecture- thanks" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4285.0 0.0 0.0 0.0
"He teaches the way mathematicians do math, lol.  It comes to him as he goes along.  Such a natural teacher. How I wish I had him..." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4613.0 0.0 0.0 0.0
"Graph and Tree are concepts used in Computer Science frequently" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4186.0 0.0 0.0 0.0
"I think that choosing the distrib on Y is mostly done based on MaxEnt principle, not arbitrarily as said around 19:45." X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 6041.0 0.0 1.0 0.0
"Wow, wow and woowwww. 18:35 he really shows why we introduce this well known notation explicitly defining the constant variables. Never knew it had such a precise reason." 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12080.0 0.0 0.0 0.0
"Audio channels fixed!" 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 2734.0 0.0 0.0 0.0
"Diffrerentiation of logarithmic and exponential functions." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3401.0 0.0 1.0 0.0
"you ate the best" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15496.0 0.0 0.0 0.0
"My dreams come true. I just want to watch some lectures about functional analysis." uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 7746.0 0.0 0.0 0.0
"I love this movie." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5830.0 0.0 0.0 0.0
"It does - there is a generalized Stoke's theorem of which the Divergence Theorem, Green's Theorem, Stoke's theorem as it appears here, and the Fundamental Theorem of Calculus are all special cases. This generalized theorem works in any dimension!" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6911.0 0.0 0.0 0.0
"I have a question to all the people talking about ""how bad american education is"", why does everyone from around the world want to come to MIT? Why are MIT graduates so succesfull?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5503.0 0.0 0.0 0.0
"15:55 d|r|/dt does make sense to me: r is the position vector and it is a function r(t) of t; hence also |r| is a function of t and can be differentiated wrt t." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 460.0 0.0 0.0 0.0
"@iDiViNeXx sounds French" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1885.0 0.0 0.0 0.0
"lol that loud applause startled him a bit" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13831.0 0.0 0.0 0.0
"Emergency question! Can we describe a basis for non-subspaces? For example a plane doesn't go through the origin???" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 3563.0 0.0 1.0 0.0
"Professor Strang: You have the amazing ability to bring out new rabbits out of old hats! Hats off!" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 8390.0 0.0 0.0 0.0
"Thank you very much for posting !!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9439.0 0.0 0.0 0.0
"for those who understand in one lecture, good for u but u will never really able to use it in real world application if u only understand cos u need to apply
" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12892.0 0.0 0.0 0.0
"Hello very good" cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 4661.0 0.0 0.0 0.0
"how can we calculate that Expected value without actually finding distribution of that function? at 21:38" H_k1w3cfny8 "10. Continuous Bayes' Rule; Derived Distributions" "6.041 Probabilistic Systems Analysis and Applied Probability" 13202.0 0.0 1.0 0.0
"Gradient, from functions to vectors.
Divergence, from vectors to functions.
Curl, from vectors to vectors." wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 4183.0 0.0 0.0 0.0
"Why did MIT hire a paparazzi shoot OpenCourseWare video ?" CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11806.0 0.0 0.0 0.0
"Please tell me best books for linear algebra" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8215.0 0.0 1.0 0.0
"this actually isn't too bad" ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14794.0 0.0 0.0 0.0
"Damn, I misread this. I thought this was the lecture on Dilbert space!" EBdgFFf54U0 "Lecture 14: Basic Hilbert Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 3303.0 0.0 0.0 0.0
"find someone who can explain it to you well. especially with calculus, the best thing to do is understand each topic conceptually first, then equations come next. " jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12860.0 0.0 0.0 1.0
"wohooo, all makes sense now :D" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 15389.0 0.0 0.0 0.0
"11:15 who the fuck eats in a class and sits in a front row ." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 368.0 1.0 0.0 0.0
"Khan's all about giving intuition and nothing else.If you really want to learn then go for a complete university course and that's the way you should learn imo.I used to rely heavily on khan to buy some time and excuse which resulted in me FAILING IN MATH EXAM TWICE." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7213.0 0.0 0.0 0.0
".......id drop out
" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 264.0 0.0 0.0 0.0
8:18 QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1418.0 0.0 0.0 0.0
"So glad I came across this!! Thank you so much MIT!" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 8759.0 0.0 0.0 0.0
Savage!! 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 8601.0 0.0 0.0 0.0
"Introduction to brain damages." C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 6736.0 0.0 0.0 0.0
"It's my honor to have met you even virtually, sir!" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7059.0 0.0 0.0 0.0
"the way he solved that limit at the end by using the derivative was absolutely brilliant : ) thx : D" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14749.0 0.0 0.0 0.0
"Thank you MIT professors. Thank you MIT so much. Such a wonderful job. I really appreciate it. " PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9151.0 0.0 0.0 0.0
"Thanks MIT
" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9601.0 0.0 0.0 0.0
"Hug you , professor. Thanks a lot." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4913.0 0.0 0.0 0.0
"God bless Linear Algebra 🙏thanks y'll guys" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 4072.0 0.0 0.0 0.0
"Protip: Only listen to the right earbud." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8454.0 0.0 0.0 0.0
"Great teacher!  he explained many concepts in Statistics far much better than my previous learned, cleared out many doubts.  I'm following his series also.  Only this Lecture 12 I'm not full understanding yet, need more practice." P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 4338.0 0.0 0.0 1.0
"i think I have a pretty good basic on that deteminant = area thing since we were just talking about it in my linear algebra class :D" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13466.0 0.0 0.0 1.0
"I am currently a software engineer in 3rd year. I watched a couple of these lectures back in first year when I was taking linear algebra and found it extremely confusing because that was my introduction and these lectures expect you to know the basics. Now that I know the basics and am currently reviewing what I've already been introduced to, these lectures are super insightful." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 5082.0 0.0 0.0 0.0
"Thanks again Prof Strang." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 9674.0 0.0 0.0 0.0
"When differentiating the sine and cosine functions, he mapped delta x to 0 on the first term, and 1 on the second term. How does this work?" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11613.0 0.0 1.0 0.0
"Gram-Schmidt portion of the lecture begins at 26:07 for anyone only interested in that" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 4184.0 0.0 0.0 0.0
"padma laxmi is hot" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 14165.0 0.0 0.0 0.0
"@aVerKePedo So the thing that's happening here is that he's not finding the area of a circle, he's finding the volume of a region above a surface that 'looks' like a circle. What he plots there is the base of the surface, which is where you get your bounds of integration from.

If he was finding the area of a circle, the double integral of r*dr*dø with those bounds would indeed be correct and would yield pi/4 because the formula for the circle would be sqrt(x^2+y^2) = r = 1." 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1763.0 0.0 1.0 0.0
"Awesome video series" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2773.0 0.0 0.0 0.0
"Thank you Dr. Strang. I have greatly enjoyed these lectures I hope they have prepared me for taking Linear Algebra in the fall. I'm a 21 year old from Iowa City, Iowa and I attend The University of Iowa." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9104.0 0.0 0.0 0.0
"Argh... who da fook hires cameraman, that has no mathematical backgroud!.." XtNXQJkgkhI "22. Bayesian Statistical Inference II" "6.041 Probabilistic Systems Analysis and Applied Probability" 2545.0 1.0 0.0 0.0
"is this the full course? thank Prof." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13666.0 0.0 0.0 0.0
"Boost your knowledge of core engineering subjects here 💯🇺🇲" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 2909.0 0.0 0.0 0.0
"U need to improve the voice quality like the first one ." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11112.0 1.0 0.0 0.0
"God bless MIT!!!❤" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4078.0 0.0 0.0 0.0
"in r11 column after two transitions the value should be .225 not .35... @34.50minutes" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 13595.0 0.0 1.0 0.0
"@muslim86mus Are partial derivatives related to PDEs in the same way that derivatives are related to ODEs? I know about a semester's worth about ODEs, and so I assumed that the relation between derivatives and ODEs was the same as with partial derivatives and PDEs. I don't really know anything about PDEs though." ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1955.0 0.0 1.0 0.0
"bitch that's what i thought; too bad i finished this class last semester" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 12543.0 0.0 0.0 0.0
"This is just amazing, how much you appreciate this lecture largely depends upon how much you paused during the previous ones." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 10681.0 0.0 0.0 0.0
"the best maths teacher ive come across!" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 14666.0 0.0 0.0 0.0
"I didn't get it about  the deeper understanding about radians! :(" TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5265.0 0.0 1.0 0.0
"The part I found confusing is when we write [I F]*[-F,I] = 0 F and -F are the same dimension but the identity on the left hand side is rxr and on the right hand side (n-r)x(n-r),

Thinking it through, it makes sense. The RHS has the same number of columns as the number of free variables. It's just a little unusual to see the same letter on both sides meaning slightly different things." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 10219.0 0.0 1.0 0.0
"For the proof that built on why lim x goes to 0 that sin(1/x) does not exist, isn't that is applying the fact that sin(1/x) is a continuous function hence convergent sequence will be mapped into a convergent sequence under this mapping hence we have he contradiction?" bBESL68iX6s "Lecture 14: Limits of Functions in Terms of Sequences and Continuity" "MIT 18.100A Real Analysis, Fall 2020" 3894.0 0.0 1.0 0.0
"7:51. Really good question." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 1405.0 0.0 0.0 0.0
"What is wrong with most of you commentators?  If you are too smart or too good for these lectures then go somewhere more challenging.  No need to show off how smart you are by stating how simple the work is for you." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11545.0 0.0 0.0 0.0
"this guy reminds me of Donald Duck" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14837.0 0.0 0.0 0.0
"Sir here along which vector u are taking projection u have specified nothing" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 8695.0 0.0 1.0 0.0
"How did I end up here? X_X" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4832.0 0.0 0.0 0.0
"I love how you can reach the same answer also using a calculus approach.. and I LOVE the two pictures for the least squares regression. Beautiful stuff and amazing lecturer." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 5756.0 0.0 0.0 1.0
"http://mathworld.wolfram.com/Gram-SchmidtOrthonormalization.html

 https://en.m.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process" MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13254.0 0.0 0.0 0.0
"thank you soo much for making me see vectors as a reality!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14519.0 0.0 0.0 0.0
"Fibonacci numbers being solved for as an algebraic equation with linear algebra was pretty cool." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 3756.0 0.0 0.0 0.0
"Camera man is so professional" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 2997.0 1.0 0.0 0.0
"13:30 don't tell me the flat-Earther are at MIT now..!!!" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 417.0 0.0 0.0 0.0
"das hab ich mit 16 in der 10 klasse gelrnt..das gechillteste was es gibt :D" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12722.0 0.0 0.0 0.0
"square shaped system with non-zero numbers in main diagonal (pivot position) and only zeros below diagonal. above the diagonal you can have any numbers you want.
" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14390.0 0.0 1.0 0.0
"Few comments:-
(1) As a mathematician I never referred to sign change in a function when taking derivative order two as concave up or down - the way I learned and always described to other people was as concave or convex function.

(2) At minuet 44:00, I noticed in few occasions saying the range of the function instead of domain when the intervals were written on the black board. Furthermore 0 < x < e^2 is the same as 0 < x < e and hence the confusion later on with points of inflection when in fact it should have been said that: in the interval 0 < x < e (subset of the entire domain) the function is decreasing since df^2 is less than zero and then from e < x < +infinity, the function is increasing since df^2 is greater than zero.

Apart from these issues, the lecture is very good." twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3753.0 0.0 1.0 0.0
"What are the Prerequistics for learning this course.Please tell me. I want to learn this and also tell the reference book for it.Please tell me" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11465.0 0.0 0.0 0.0
"if  A  is surjective  then the range of  A  is closed. because  it is  equal to  H." BctaYoR9tOY "Lecture 18: The Adjoint of a Bounded Linear Operator on a Hilbert Space" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 13527.0 0.0 0.0 0.0
"24:40 wtf is it halloween" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 750.0 0.0 0.0 0.0
"How do u get (1 2 3 1) with a zero row (0 0 0 0) and (1 0 1 1)

u said u reserve the steps.." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4848.0 0.0 1.0 0.0
thxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14939.0 0.0 0.0 0.0
"Can someone help me with a math test I really need help please" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3082.0 0.0 0.0 0.0
"Excellent lecture!!!" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3653.0 0.0 0.0 0.0
Good 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4107.0 0.0 0.0 0.0
"These students don't know how lucky they are sitting in that classroom. Perhaps a future research  person sits there who perhaps by standing on the shoulders of past gifted people will help find a cure for some of these dreadful diseases from learning how to apply his way of thinking. Courses such as these train young minds for concepts that will challenge them when they become age 30 and beyond with a a decade or more of real life knowledge. All you youngsters this is your wake up call, BEGIN!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10426.0 0.0 0.0 0.0
"The goat no cap" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10121.0 0.0 0.0 0.0
Ez VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3713.0 0.0 0.0 0.0
"Wonderful lecture" H_k1w3cfny8 "10. Continuous Bayes' Rule; Derived Distributions" "6.041 Probabilistic Systems Analysis and Applied Probability" 11988.0 0.0 0.0 0.0
"So if col 3 = col 1 + col 2, then x=[1 1 0] and x = [0 0 1] produce the same vector b, which is what - a paradox?  Alternatively, you can't reduce 3-2 to 0 without also reducing 3-3 to 0.    I know that happens thru elimination.  Not yet seeing why that follows logically from col 3 = col 1 + col  2.  But it means z can only equal 0, so the column space can't fill R3." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8771.0 0.0 1.0 0.0
"I actually finished the course. Thank you so much OCW" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5014.0 0.0 0.0 0.0
28:35 j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 839.0 0.0 0.0 0.0
"Love him so much." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 7439.0 0.0 0.0 0.0
"A is reducible to co-A implies that Atm is reducible (general) to co-Atm. Is this really the case?" N28g_YBXY8Y "9. Reducibility" "MIT 18.404J Theory of Computation, Fall 2020" 2127.0 0.0 1.0 0.0
"damn subtitle, my exam is in a couple of days and I need to watch this seriously, but the subtitle just keeps making me giggle ^^haha" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 12713.0 0.0 0.0 0.0
"Such cool stuff." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8949.0 0.0 0.0 0.0
"So we're talking about 4D object😶" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 8800.0 0.0 0.0 0.0
"Thank you for this lecture, I found it very helpful and informative.Great lecture and good filiming. Much appreciated." 4UJc0S8APm4 "23. Classical Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 9281.0 0.0 0.0 0.0
"This was amazing, thank you so much for all of the content made available for everyone!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 10967.0 0.0 0.0 0.0
"Excellent lecturer!" PnPIqh7Frlw "Lec 24: Simply connected regions; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3663.0 0.0 0.0 0.0
"These MIT math professors have their shit together. " MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10393.0 0.0 0.0 0.0
"13:20 course start" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 411.0 0.0 0.0 0.0
"Helped to understand" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4671.0 0.0 0.0 0.0
"indian ascent is much more clear and understandable then this." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13607.0 0.0 0.0 0.0
"@southsidesman Keep your crap out of videos like this. You're really going to spam MIT math lectures? Nut." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2023.0 0.0 0.0 0.0
"I like your content of sharing your knowledge about statistics...hope my channel would also benefit from this channel by following you. https://www.youtube.com/channel/UCYiQ3ujdiWfpi3LZhM4Do_Q" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 5699.0 0.0 0.0 0.0
"This is truly golden knownledge. Gilbert Strang is incredible. I love this linear algebra course so much" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 10761.0 0.0 0.0 0.0
"Strang if a gift from God ❤️" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8904.0 0.0 0.0 0.0
"This lecture answered my whole life question which noone answered me
Thank u mit ❤️" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10784.0 0.0 0.0 0.0
"I've been watching these lectures and this is my favorite so far. To finish with the numerical calculation of the ""mystery number"" e was brilliant." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6411.0 0.0 0.0 0.0
"This goes to show that you can be a brilliant person but a crap teacher.

MIT or not I'm going to stick with Khan Academy." yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 10504.0 0.0 0.0 0.0
"Why is it that f is taken as X^2 + Y^2 and not something else?" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11878.0 0.0 1.0 0.0
"i think the whole course took me from 1.5 to 2 months to complete it (im first high school i barely knew what a matrix is) and i cant believe how awesome the whole course i just want to say thanks 
im studying this so i work in the ai field and i know how to compute all of this using python (learned programming first) and what i can do now is pretty incredible now two more courses to finish before university 
single and multi variable calculus
THX MR.GILBERT STRANG<3" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 13478.0 0.0 0.0 0.0
"Thank you MIT for making these lectures publicly available. Will always be grateful to you. One day I will make sure (if not certainly,but will try to) to get my PHD. from you." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9144.0 0.0 0.0 0.0
"Thank you so much for this amazing course!!!" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9372.0 0.0 0.0 0.0
"wow i am glad that i go to a university where they give the notes after the class because i would not be able to copy ALL of that.
i would get flustered and throw my pencil." MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15416.0 0.0 0.0 0.0
"This is awesome. That column picture analysis is new to me. Great lecture my dude" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10645.0 0.0 0.0 0.0
"what is the definition of saddle point?" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15164.0 0.0 1.0 0.0
"This is amazing!

I studied chemistry at university few years ago, and that definition of Markov Chains really makes me think of what we did with the equilibrium of the reactions with the different molecules. This is exactly the same kind of definitions: the different states are our different molecules, the probabilities have exactly the same role as our ""reaction speed"", and the conclusion is the same: the equilibrium is unique for a given system.
Actually during the lecture I was trying to guess just from the diagram what the equilibrium would be hahaha.



I feel sad that we were not even given a mention about markov chains back then.


I was struggling with the last 3 lectures in this course, and even more in the assignments, but I'm so happy to see these descriptions I am already intuitively familiar with that my pain just flew away!" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 10614.0 0.0 0.0 0.0
"Can somebody tell me why at 7:50 the second ∆x tends to 1 and not zero please ?" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3066.0 0.0 1.0 0.0
"At 44:40 the girlfriend broke up with the guy with the cell phone or the class was too hard  to understand?" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 2677.0 0.0 0.0 0.0
"The akward moment when free knowledge is given and you complain about quality of video" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9980.0 0.0 0.0 0.0
"I love his accent!! =D By the way, he teaches well too!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5736.0 0.0 0.0 0.0
"This is really an exellent teacher, wonderful class" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10712.0 0.0 0.0 0.0
"He's  still wearing the same shirt, has the same humor, same energy and 15 years have passed. This guy is just amazing." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4622.0 0.0 0.0 0.0
"I was expecting more from this lecture. Nevertheless ready for the next lecture on eigen value and eigen functions." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 6152.0 0.0 0.0 0.0
这个老头教的不错 CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15663.0 0.0 0.0 0.0
"Thought it was Jimmy Dore for a second in the thumbnail." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 10998.0 0.0 0.0 0.0
"Me after reading that class was empty, 😲" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 7644.0 0.0 0.0 0.0
25:05 YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 763.0 0.0 0.0 0.0
"He is slow but packs a punch all the way to the end of the lecture." KcI2_r51Eb8 "Lecture 17: Minimizers, Orthogonal Complements and the Riesz Representation Theorem" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 4536.0 0.0 0.0 0.0
"Why do we do square deviation, but not ordinary one? I don`t understand the precondition for squares. If anyone can explain, do it, please." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11828.0 0.0 1.0 0.0
"I'm so confused. Do MIT students go to each lecture multiple days per week since each lecture in this playlist is only an hour long, compared to the standard 3-hour long class in other colleges and what I've read about them, and the professor seems to say goodbye after each of his lectures ends." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6371.0 0.0 0.0 0.0
Magic rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7561.0 0.0 0.0 0.0
"Pretty sure he's French !" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8251.0 0.0 0.0 0.0
"It's feeling like I m in MIT and great respect for prof.Strang" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7039.0 0.0 0.0 0.0
"@javyel13 yo creo que con que subir los videos ya estan haciendonos un favor. Ademas su ingles es re claro, asi que no deberia ser un problema el entenderlos. Soy de Bolivia, por si te interesa para compartir algo de esta materia, mira que esta buenisima." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1898.0 0.0 0.0 0.0
"This teacher is so amazing.. thank you!" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10938.0 0.0 0.0 0.0
"One thing in question in the lecture is that Ui but not Vi is in the column space of A. Vi should be in the A's row space." ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8110.0 0.0 1.0 0.0
"thanks a lot :" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 14566.0 0.0 0.0 0.0
"A great lecture showing us the wonderful secret behind linear algebra" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 2120.0 0.0 0.0 0.0
"watch this at x2" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15065.0 0.0 0.0 0.0
"''HHHrwhhhaat is the sum.'' Great lecture." 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 207.0 0.0 0.0 0.0
"Excellent video Professor" ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3679.0 0.0 0.0 0.0
"He looks like Mr. Earnie from my 10th year. He was cool." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4569.0 0.0 0.0 0.0
"Can one of you ""smart"" ""engineers"" please learn how your great grandparents or older could make machines without gas or batteries. Like wind up or something. The globe is almost out of gas because ""smart"" or ""intelligent"" people are still drooling over something simple someone said over almost 100 years ago. I understand it's your religion. However can someone please aim for some progress." cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 3059.0 0.0 0.0 0.0
"The video series is a great and fast review of linear algebra." Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10314.0 0.0 0.0 0.0
"i loved it!" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13440.0 0.0 0.0 0.0
.4 rLlZpnT02ZU "4. Parametric Inference (cont.) and Maximum Likelihood Estimation" "MIT 18.650 Statistics for Applications, Fall 2016" 271.0 0.0 0.0 0.0
"We know that the first three rows of A form a loop. So, the rank of the matrix should be 2, right? We know that there are maximum 2 rows that are independent in A. Please explain." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11322.0 0.0 1.0 0.0
"Where did M(e)=1 come from?" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11672.0 0.0 1.0 0.0
"I agree Sprang is great but you could have recognized the golden ratio 1/2(sqrt5 +1) and every mathematician knows this number. It's like being baffled if someone tells you pi equals 3,14159265...." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 5023.0 0.0 0.0 0.0
"Thoroughly enjoyed these lectures, much easier to understand than my lecturers in college. Thank you Professor Strang!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 10986.0 0.0 0.0 0.0
"how would the shape look like for p, 1<p<2" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13252.0 0.0 1.0 0.0
"Is x^t*y a 1-D matrix or a number?" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6889.0 0.0 1.0 0.0
"I want to use chalk." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6145.0 1.0 0.0 0.0
"Just the best.... MIT lov it

" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7196.0 0.0 0.0 0.0
Love.... rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7475.0 0.0 0.0 0.0
"Can someone please explain to me, Why do we get all the Null space of A just by taking all the combinations of only two special solutions. What is the proof of this?. Shouldn't we take all possibilities of special solutions." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 3089.0 0.0 1.0 1.0
"(note for myself)
. If v is a column vector, is v^T times v a 1x1 vector or a number(scalar)?
. Can a 1x1 matrix be treated like a number? What about the commutative law?
. The fact that ""1x1 matrix is isomorphic to a number"" means they're interchangeable in math equations?" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 225.0 0.0 1.0 0.0
"@cuinuc 
I think they are actually the same, because LAMBDA is a diagonal matrix, you can have a try." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 1819.0 0.0 1.0 0.0
"I just started loving physics after seeing your lecture" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5619.0 0.0 0.0 0.0
"Amazing explanation! " 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2360.0 0.0 0.0 0.0
"can anyone explain how the 5th column of w8 came out to be?" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12600.0 0.0 1.0 0.0
"where are the online programming assignments ?" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15219.0 0.0 0.0 0.0
"many thx for these wonderful resources out there" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13910.0 0.0 0.0 0.0
"Prof Strang spoke so much about errors and he did make one ! :P" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 8274.0 0.0 0.0 0.0
"This is a great series and I've learnt so much from it. But if anyone (like me) is a little bit confused about maxima, minima, saddle point and why they can be calculated that way, here's some amazing videos from Khan Academy that'll definitely help you out:
https://www.khanacademy.org/math/multivariable-calculus/applications-of-multivariable-derivatives/optimizing-multivariable-functions-videos/v/multivariable-maxima-and-minima" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10594.0 0.0 0.0 1.0
"17:26 ""That 7 is no accident...that 11 is no accident..."" And I live over a 7-11...spooky, Dr. Strange." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 505.0 0.0 0.0 0.0
"This fellow makes things crystal clear." _CdoRiNSrqI "Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10502.0 0.0 0.0 0.0
"There are three typographical errors on the notes that I just want to point out, in Fig. 3. The scant line from (-1/2,1/2) to (0,1)  in the notes it says (1,0). If you work out the slope (y2-y1/(x2-x1) it comes out right if the points are (-1/2,1/2) and (0,1)
The same error is repeated in the actual figure, the y-intercept should be (0,1) and not (1,0)
The last typo is on page 4 in a both in the center it say e^x = w it should read e^w =x as is correctly expressed 5 lines after. 

" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10357.0 0.0 1.0 0.0
"For any x=e^n, it is clearly possible to know the value of Ln(x), which is n. For a particular case when n=o, therefore Ln(e)^0=0. 
I am just saying that the teacher should not say that x=1=e^0 is the only number we can know for sure the value of Ln(x)." 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3851.0 0.0 1.0 0.0
"Thank you so much, Prof. Strang and MIT for making the linear algebra (straight) and simple." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9395.0 0.0 0.0 0.0
"...one of the best lectures I ever had.
...and I've out of school for tens years." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 269.0 0.0 0.0 0.0
"From this lecture,  I understand Singular Value  Decomposition in linear algebra. Dr. Strang really   explained this topic  and the examples very well." TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 3937.0 0.0 0.0 1.0
"already know all of this from school" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12330.0 0.0 0.0 0.0
"Hahaha, ""33:33 This orgy of greek letters""" sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4415.0 0.0 0.0 0.0
"It is very sad to see Professor turning older and older. He is a great teacher!" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6972.0 0.0 0.0 0.0
"Shouldn't He have multiplied the 0.3 by sigma=sqrt[373] around 18:40 ?" phbw9r1iUDI "7. Parametric Hypothesis Testing" "MIT 18.650 Statistics for Applications, Fall 2016" 8644.0 0.0 1.0 0.0
"Great lecture gilbert strang.. 
You are my saviour for final exams. " 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4253.0 0.0 0.0 0.0
"good video, good explanation, good fun" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12954.0 0.0 0.0 0.0
"Guys about the problem on 16:12 , the integrand fuction  is continious for both x = <0  and x>0  so  i assume domain of the integrand fuction is R-0 (there was no other restrictions) but  the undoing trig sub part  (24:21) he assumed theta is <90 so that solution works for x=positives.Did he solve that problem for only x >0 or somehow its related with x<0 too but im missing it ?" CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4388.0 0.0 1.0 0.0
"This is amazing!!!!!!!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10617.0 0.0 0.0 0.0
"Greetings from New York City!

Prof. Strang was my Linear Algebra 18.700 professor during my sophomore year at MIT in Spring 1973.  I loved his teaching style, did well on the tests, and received an “A” in the class." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 4382.0 0.0 0.0 0.0
"hey um..., for some reason i cant watch any of the video in the web site you posted here. Whenever i click on the video icon it just loads but never get there." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13150.0 0.0 0.0 0.0
"17:46 ""Math starts counting with one and electrical engineers start counting at zero. Actually, they're probably right.""" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 516.0 0.0 0.0 0.0
"Believe me it's really helpful.
If you really wanna grasp the whole lecture, then click the link below before going to the next 24th Lecture.
https://www.youtube.com/watch?v=dZfdKXxhnTM" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 2845.0 0.0 0.0 0.0
"@007seppy so schwer kommt mir das auch nicht vor und ich bin 10. real :D" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1491.0 0.0 0.0 0.0
"One thing that I find confusing is that because the sigma matrix is left multiplied by V transposed, it is not pure scaling. This is because the sigma values are multiplied by the rows of V transposed and not the columns. This will cause additional rotation and changes in dimensionality." rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8112.0 0.0 1.0 0.0
"The corn field explanation blew my mind! Thanks, now I understand vector fields!" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10060.0 0.0 0.0 0.0
"mit chalk company hai keya.hamari desh me bhi aisi chalk chahiye." wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13950.0 1.0 0.0 0.0
"Starts at 10:00" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 8886.0 0.0 0.0 0.0
"Good. But I wish proof was given" Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4163.0 0.0 0.0 1.0
"Thankyou professor" rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 9872.0 0.0 0.0 0.0
"Thank you very much, Professor Gilbert Strang. You are a legend of linear Algebra." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9452.0 0.0 0.0 0.0
"love this course" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13879.0 0.0 0.0 0.0
"Dr. Stranglove or ""How I Learned to Stop Worrying and Love Numerical Linear Algebra""" z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3517.0 0.0 0.0 0.0
"@3:30, why is he omitting the sigma scalars (singular values) in this sum of left & right singular vectors to produce X? Is that right?" 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1551.0 0.0 1.0 0.0
"the least viewed lecture of the entire series :D This is a hard topic. Thank you, Professor Strang." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 14706.0 0.0 0.0 0.0
"Where can I see the solutions to the problem sets? Thanks!" phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11663.0 0.0 0.0 0.0
"Wow, this is just awesome!" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 12075.0 0.0 0.0 0.0
"Thank you so much, dear Professor Strang, all TA's, the camera personnel, and all other supporting staff. Started learning this course about ten years ago. After graduating from my program and working now, I finally managed to finish watching and reading the lecture notes. The whole system of linear algebra shown in this course is so beautiful. Will go through the exercise, problems, and exams also, all necessary steps to refresh memories and memorize essential details. Will continue to finish  Professor Strang's Highlights of Calculus, differential equation, and three other linear algebra courses. You are a blessing to humanity, Professor. God bless you and your family." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9400.0 1.0 0.0 0.0
"good luck" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12948.0 0.0 0.0 0.0
"Oh.. my god.. the board and chalk are phenomenal..!" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8034.0 1.0 0.0 0.0
"this is the last, im sad, because these lessons are great, thank you ! I proceed ..." rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14882.0 0.0 0.0 0.0
"Thank you so much sir, your effort in this age" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9380.0 0.0 0.0 0.0
"Man, this guy is soo much better than my own prof.. It's just that he's able to explain ideas much more clearly and at a reasonable pace! " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7588.0 0.0 0.0 0.0
"In the minute 10:20 the teacher talks about a third method to multiplicate matrices. It should be multiplying every row of A by all the columns of B, isn't it? I didn't get it at all. If someone knows I'll read haha." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6678.0 0.0 1.0 1.0
"At the end I remembered I never read about fourier transform only fourier series. Thought I was going insane for a second." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 2726.0 0.0 0.0 0.0
"every math loving student would love this great man" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 12806.0 0.0 0.0 0.0
"By far, Denis Auroux has explained the lecture really well, and it has really been helping me out with the application of 3 by 3 det. to find equations of planes. Thanks for providing these free videos M.I.T." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2974.0 0.0 0.0 1.0
"An Indian edition of this book is available only in India
http://www.wellesleypublishers.com/buy.html" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 2420.0 0.0 0.0 0.0
"Best professor ever seen.... Wish my dumb prof is like him mate" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2873.0 0.0 0.0 0.0
"awsome lecture i think i'm falling inlove with maths......
" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12500.0 0.0 0.0 0.0
"equation @ 33:07  i.e.  E32(E21A)=U  ;that might be wrong bcoz I multiplied to get LHS which is not equal to RHS =U .
please help I can't figure out what is wrong." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12798.0 0.0 1.0 0.0
"Nothing is broken - go to the URL link get the lecture slides , get the HW assignments and everything you need to understand what is going on is there. Phillipe Rigollet is excellent and discusses with ease fairly complicated material. Excellent job. My two complaints are that the sound volume is a way too low - whoever recorded the first lectures did lousy job. Also the slides are not properly exported to pdf - there are some missing math  symbols in some of the equations" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 7943.0 0.0 0.0 0.0
"Thank you for the wonderful lectures. 
I didnt catch, if dimension of column space is same as rank of matrix. By doing row operation, Row space seems to be the same, but the column space changes. How do we know that the dimension of column space of row reduced matrix is same as the original matrix?" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 9271.0 0.0 1.0 0.0
"what if someone fart" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15145.0 0.0 0.0 0.0
"(note for myself)  23:46) if the two eigenvalues are complex numbers, they'll be conjugates of each other(sum becomes a real number).
31:47, 33:26) Search what 'matrix exponential' is. It's *NOT* just a simple notation of element-wise exponential operation.
* Also note that this lecture does *not* cover  the entire rigorous mathematical proofs, as well as other lectures of Prof. Strang (At least this series of Linear Algebra lectures so far).
* The solution using ""matrix exponential"" notation (31:55) can be understood if you see 44:30, given the Taylor series of the matrix is the _'definition'_ of the matrix exponential notation." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 226.0 0.0 0.0 1.0
"Thanks!!! Excelent. Is there a text book about this?" P3tGiT72APw "14. Graph limits I: introduction" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 9837.0 0.0 0.0 0.0
"I really like his teaching. Perfect." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 5923.0 0.0 0.0 0.0
"I love when he's building up to property 3.  You can tell how excited he's getting (adjusting his hair, taking little pauses).  Very cute" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 5843.0 0.0 0.0 0.0
"47:56

can someone explain to me how he got f'(Xo) ?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1286.0 0.0 1.0 0.0
"I'm liking these videos a lot, but I admit that if this was my first introduction to Linear Algebra, I would  be confused. I have already had a LA course before, and these videos are just great for me to think about things differently and connect the concepts in different ways. Have had a few ""aha!"" moments with things I only did mechanically before." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6344.0 0.0 0.0 0.0
"Audio starts at 1:14" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 2742.0 0.0 0.0 0.0
"""si alguien se animara a traducirlo...""" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 173.0 0.0 0.0 0.0
"still don't understand however i feel that i need to do some e.g.'s and i'll get there..
great lecture regardless" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14398.0 0.0 0.0 1.0
"I watched all 36 videos of linear algebra. DR. Strang you are an amazing and a ionic professor at MIT. I  really learn linear algebra from watching these videos  and doing problems from different linear algebra textbooks. I watched all your videos from 18.085 and 18.086., however linear algebra is the best. I will be watching the rest of your videos on linear  algebra. DR. Gilbert Strang, thank you so much for all your contribution to advanced mathematics." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 6183.0 0.0 0.0 0.0
"A random thought on the string problem-- y'(x_0)=0 because it minimizes the total mechanical energy (mgy=min; lagrangian mechanics). Also, don't confuse x_0 which makes y'(x_0)=0 possible with the variable x, as the former is just a random value for the lowest point on that elliptical curve." sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2153.0 0.0 0.0 0.0
"This guy loves telling really really subtle jokes." -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10552.0 0.0 0.0 0.0
"I know this is math From India" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5643.0 0.0 0.0 0.0
"I don't understand how David Jerison can take the natural log of a negative number, the domain of the function doesn't exist for negative numbers. Am I missing something?" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5341.0 0.0 1.0 0.0
"A probability paradox?
If I construct the sample space in this way: E1= king boy & king's sibling boy, E2= king boy & king's sibling girl, it would seem that the probability of E2 is 1/2. 
But if I construct the sample space in this way: E1'= BB, E2'= BG, E3'= GB, E4'= GG, it seems the probability that the king's sibling is a girl is 2/3.
But only in the second case can I assume all events are equiprobable: E1 can happen in just one way; E2 can happen in two: E2 = E2'UE3'." 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 2147.0 0.0 1.0 0.0
Terrible WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 9028.0 0.0 0.0 0.0
"Great lecture! Thank you, Professor Strang!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4270.0 0.0 0.0 0.0
"Does anyone know why we write only ""1"" for the value of ""I"" (identity) in the final matrix of this video? The equation was that x=c[-F ; I]. Why do we plug in a vector of F but only a scalar of I?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 3447.0 0.0 1.0 0.0
"khan academy " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13751.0 0.0 0.0 0.0
"""How many of you have seen spherical coordinates before?""
*Half the class raise their hands*
""I see that's not very many.""

- The legendary Auroux, 2007" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 52.0 0.0 0.0 0.0
"When he speaks I'm able to download mathematical facts just by watching 👽" feb9j65Iz4w "24. Linear Programming and Two-Person Games" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11626.0 0.0 0.0 0.0
"thanks MIT" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14554.0 0.0 0.0 0.0
"Couldn't the commentary at 30:19 about 'quarter' lead to some misunderstanding about cardinality of R^2?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 3248.0 0.0 1.0 0.0
"Hard stuff" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4424.0 0.0 0.0 0.0
"25:57
Why he wrote f(-1,0)?" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 791.0 0.0 1.0 0.0
"lol he doesnt explain shit worst lecture ever,waste of time" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 13826.0 0.0 0.0 0.0
"Thanks professor for these amazing lectures.  
I would like to give a suggestion- please write the name of topic in the description/thumbnail, so it will be easy for us to find the specific lecture.
By the way 😊 Thanks again for the lecture. ❤❤" 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9764.0 0.0 0.0 0.0
"Improper integrals start @6:49 roughly" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6587.0 0.0 0.0 0.0
"Do they all know where is Mumbai at 1:38?" MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3414.0 0.0 0.0 0.0
"my calc teacher never taught me these kinds of things" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13972.0 0.0 0.0 0.0
"good stuff" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12951.0 0.0 0.0 0.0
"This guy is faaantastic ❤️ 20:34" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10529.0 0.0 0.0 0.0
"""Maybe I wanted you to figure out yourself ""  He is funny" OYcdw5vOgIc "23. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 83.0 0.0 0.0 0.0
"Thanks Coronavirus... finally done. BUT WAIT THERE’S MORE" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9585.0 0.0 0.0 0.0
"My class uses stewart's multivariable calculus and I don't like that book. These videos and ostebee's multivariable calculus make me one of the best in class." z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7740.0 0.0 0.0 0.0
"Finally! Where did you end up finding this??? Cached in someone's IE?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 3791.0 0.0 0.0 0.0
"This is what we learn in 4 classes of same length" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 10771.0 0.0 0.0 0.0
"This guy is objectively the best teacher btw." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10538.0 0.0 0.0 0.0
"Tt want to be yur students whom already been MIT University." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11101.0 0.0 0.0 0.0
"43:41 Columns 1 and 3 don't form a basis, though? They span the subspace but are not independent? Column 1 can be found in column 3?

Wait, but no combination of 1 and 3 will ever cancel each other out, so their nullspace is only the zero vector. I would have made a major mistake if I didn't catch that, damn." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 1215.0 0.0 1.0 0.0
"The class is great, but can you add English subtitle on it? It will be easier for people from non-English area.😀" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10045.0 0.0 0.0 0.0
"Greek professor!!" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 4380.0 0.0 0.0 0.0
"Love you mit" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7466.0 0.0 0.0 0.0
"Perfect lecture 👌👌" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 8178.0 0.0 0.0 0.0
"I had to pause to figure out how he got the eigenvectors at the end. Plugging in Phi works but it wasn’t until I watched again that I noticed he was pointing to the lambda^2-lambda-1=0 relationship to reveal the vector." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 5474.0 0.0 0.0 0.0
"Great lecture. Thanks Prof. Strang. Thanks MIT." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4294.0 0.0 0.0 0.0
"Absolutely incredible. All of my teachers tried to explain this over the course of 3 class periods, keep in mind my classes only have 20 students. He accomplished a thorough, easy to follow explanation in 30 minutes. Absolutely incredible teacher." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2206.0 0.0 0.0 0.0
"Great lecture." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4286.0 0.0 0.0 0.0
"@chesteronline2010 really :O ?? then i wont study" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1816.0 0.0 0.0 0.0
"19:38 your lecturer is not Rembrandt.... hahaha... professor got some humor!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 563.0 0.0 0.0 0.0
"Yale better" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12112.0 0.0 0.0 0.0
"In my calculus class FTC2 was told to be the simplest one which just showed the change of variable. Here I gotta know the big picture behind it." Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6645.0 0.0 0.0 0.0
"I came here to see his art on the board." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5182.0 1.0 0.0 0.0
"Will this witchcraft allow me to build a Star Trek replicator?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11952.0 0.0 0.0 0.0
"15:35 when you circle the wrong thing" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 454.0 0.0 1.0 0.0
"feel sorry for those who didn't study ODEs before" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 12853.0 0.0 0.0 0.0
"in the discussion of the falling pumpkin, the average speed should, i feel, actually be the average velocity since there is a sign in front of the numerical answer. i think he just forgot to mention that. anywho, nice vid" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13598.0 0.0 1.0 0.0
"This is Analytical Maths,in short the analysis moves from variable and ends at the clarity of the function....." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10578.0 0.0 0.0 0.0
"energetic professor." UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 12795.0 0.0 0.0 0.0
"This is boss...Great Lecture !" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10650.0 0.0 0.0 0.0
"@matanorland1  It's because not all of the students pay all of that $50K (that's what it is now). About 85% of the students receive some sort of grants  from MIT. In order to maintain and make sure that future students will get those those scholarships they need donations." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1936.0 0.0 0.0 0.0
"I cried a bit when I saw the inverse appeared in the augmented part of the matrix @40:51.  Dang this is beautiful" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5254.0 0.0 0.0 0.0
"wow actually explaining where rdrd(theta) comes from........." 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15412.0 0.0 0.0 0.0
"That's because you suck at this." 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 9931.0 0.0 0.0 0.0
"26:37 this is for those who did not understand the first reasoning behind why the inverse was not possible.
A=[1 3;2 6]  
X is supposed to be the identity matrix so that A^-1A=I
You can approach it this way:
A*(1st col. of X)= [1;0]
which is same as 
1st col. of A* X11+ 2nd col of A*X12
but the problem is that since the first column and second column of A are dependent vectors (that is [1;2] and [2,6] differ only in length and not in the direction. It's impossible that a linear combination of them can result in a vector that has a different slope (as is [1;0])
I hope this helps." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 805.0 0.0 1.0 1.0
"for anyone interested in the proof of the law of cosine https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-law-of-cosines/v/law-of-cosines" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12880.0 0.0 0.0 0.0
"Yea see you on Wednesday" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 12118.0 0.0 0.0 0.0
amazing! vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 12356.0 0.0 0.0 0.0
"well explained!!. no jumping from equation to equation and well paced." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 15087.0 0.0 0.0 0.0
"gets old" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12917.0 0.0 0.0 0.0
"*silly. seriously? Complaining about boards during a brilliant  lecture?
@jphotguy" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 247.0 1.0 0.0 0.0
"I hope the Flying Spaghetti Monster blesses them too :)" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5591.0 0.0 0.0 0.0
"1:49 ""PERPENDIC---ULA---R""" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 601.0 0.0 0.0 0.0
"Great lecture!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 4259.0 0.0 0.0 0.0
"Pretty bad proof for the product rule. The u's and v's are really confusing and his second step wasn't explained well. If you want a good proof, watch Khan Academy's proof for the product rule. Makes a lot more sense." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8247.0 0.0 1.0 1.0
"31:00 PCA" Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 903.0 0.0 0.0 0.0
"what is pivot row" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 15158.0 0.0 1.0 0.0
"Too bad I cant donate using pay pal." 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11057.0 0.0 0.0 0.0
"Im kind of disappointed to see that at no point during this did he make the connection between WHY the integral from a to b of f(x) equals its antiderivative of F(b)-F(a). Basically, why does the area under the curve only appear to depend on its end points? this always confused me during calculus, because the answer isnt very obvious, but its stunning whats you see the conneciton. using riemann sums as well, at some number b-a/n as n goes to infinity. " Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6575.0 0.0 1.0 0.0
"25:00. That is definitely *not* a proof of the chain rule. Don't be misled into thinking so." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 761.0 0.0 1.0 0.0
"at 31.20 when making the columns orthonormal by dividing by 1/2 , F4 should also be divided and the new matrix 1/2(F4) is orthornormal. Then the new matrix and its hermitian are equal to the Identity, which means F4^H x F4 = 4I. Right?" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 12436.0 0.0 1.0 0.0
"My high-school professor never solved it via variables all the way to -1/(Xo^2). He went to the point of showing the
Xo - (Xo ΔX)
ΔX
and then showing how inserting numbers would cancel out the delta." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7763.0 0.0 0.0 1.0
"It is mentioned that ""phi is known positive value"" (16.28 min). I am wondering,  if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" OYcdw5vOgIc "23. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 6955.0 0.0 1.0 0.0
"Largest hall on our planet! with largest blackboard and several! Where and how many students😂" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 7249.0 1.0 0.0 0.0
"nice video" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14053.0 0.0 0.0 0.0
BEAST! xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2799.0 0.0 0.0 0.0
"@porta123stella tan^(-1)(x) is a very common notation for arctan(x), I see it used all the time. Ever seen a Texas Instruments graphing calculator?" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1976.0 0.0 0.0 0.0
"yeah... why do u think that happen?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 15476.0 0.0 0.0 0.0
"I think the last problem is incomplete: the sum is not always a projection matrix because if A was -I or I then the sum is not a proyection matrix but either 0 or the identity. I and -I are both symmetric and orthogonal." HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 6057.0 0.0 1.0 0.0
"Thank you professor for this excellent lecture." uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 9323.0 0.0 0.0 0.0
"my calculus 3 professor taught us,  think of a saddle point as a point on a ""pringles chip"" a lot of people know exactly what it looks like." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 13973.0 0.0 0.0 1.0
"one of the best teacher in the world thank you professor Gilbert Strang  god bless u" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 14150.0 0.0 0.0 0.0
"@29.30 the clapping was classic first time i heard applause in a calculus class" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1529.0 0.0 0.0 0.0
"""You start from the origin and you blow up the norm until you get a point on the line that satisfies your constraint, and because you are blowing up the norm, when it hit first, that's the smallest blow up possible, that's min, that's the guy that minimize"" (31:23-31:42) that's 2-D optimization in a nutshell...clear and simple, thanks very much Professor Strang.." NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 139.0 0.0 0.0 1.0
"OMG ITS THE THERAPIST FROM ANIMANIACS" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7984.0 0.0 0.0 0.0
"Long live your kindly,mild professor" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7410.0 0.0 0.0 0.0
"Anthropomorphizing the machine" m9eHViDPAJQ "4. Pushdown Automata, Conversion of CFG to PDA and Reverse Conversion" "MIT 18.404J Theory of Computation, Fall 2020" 2465.0 0.0 0.0 0.0
"To all of the people saying that American schools suck, they don't, not that much anyway.  I'm American, and I learned this in high school too.  The thing is that MIT is very forgiving about what background each student has, since some American schools (inner city) actually do suck.  I guarantee 18.06 (linear algebra) and 18.100C (Topology, Real Analysis) are way, way above anything taught in secondary school anywhere in the world.  Please note the "".01"" in the title.  This is a day one course." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11020.0 0.0 0.0 0.0
"the lecture is awesome but my head started spinning now!!!" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 14709.0 0.0 0.0 0.0
"Is there a special channel for Professor de is auroux??" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6824.0 0.0 0.0 0.0
"Que exageracion de PUNTOS" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8473.0 0.0 0.0 0.0
16:53 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 490.0 0.0 0.0 0.0
"I love the sarcasm of his voice in 27:50  ""In case you care"" xd" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 5783.0 0.0 0.0 0.0
"❤️ thank You so much ❤️... 🙏🙏🙏🙏🙏" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15611.0 0.0 0.0 0.0
"Why am I watching this ..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11773.0 0.0 0.0 0.0
"37:03 No BADBADNOTGOOD ?? lol" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 1053.0 0.0 0.0 0.0
"WOW🥺 I am not at all a math person, I just like watching these videos because it’s fascinating how smart people are. I understand nothing this professor is saying. This is about as far over my head as the moon is.  Amazing." eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11249.0 0.0 0.0 0.0
"how is d/dx (x^2+y^2=1) = 2x+2yy' = 0 ? everything is clear except y', where does it come from?" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13233.0 0.0 1.0 0.0
"@shakesbeer00 Because it's over the unit circle." WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2009.0 0.0 0.0 0.0
"you have to respect this man 🙏" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15507.0 0.0 0.0 0.0
"Good use of Zorn's Lemma on expansion." KlAjiDivJoQ "Lecture 5: Zorn’s Lemma and the Hahn-Banach Theorem" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 4159.0 0.0 0.0 0.0
"Plz upload complex analysis." OHiu2F18dFA "Lecture 7: Sigma Algebras" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 8224.0 0.0 0.0 0.0
"Who the fuck still uses a blackboard in this day and age? Someone as absolutely legendary as this guy. Old school is best school." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 11752.0 1.0 0.0 0.0
"This is MIT freshman math - all students in all departments are taking it and the next level of treatment starting 2nd year gets into the real meat." 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10580.0 0.0 0.0 0.0
"Great video,  but there is a big error.
6:13
""Do I have a subspace if I take all the vectors on the plane and all the ones on the line? No.""
False. In general you don't have a subspace, but it depends, sometimes you have one.
The correct answer would be ""If the plane contains the line yes, otherwise no"", another correct answer would be ""in general no"". 
But answering just ""No"" you are implicitly saying ""Always no"" which is false and incorrect." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 4356.0 0.0 1.0 0.0
"This man is extremely clear, excellent lecture!" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 10866.0 0.0 0.0 0.0
"Thank you for sharing the excellent lectures. " j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 9258.0 0.0 0.0 0.0
"To much time wasted writing on Chalkboard.   He could have written everything on the boards Before class and then faced the class and explained it.  Much time would be saved." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11041.0 1.0 0.0 0.0
"how is he ""cheating"" at 6:50 ? i've taken physics before but not sure what small details he's talking about" BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 13234.0 0.0 0.0 0.0
"35:46 Something about the exam also a review of this unit" BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1018.0 0.0 0.0 0.0
"At 59:57 defining the Brownian bridge, I believe there might be an error. An expectation of R.V's can't have a distribution. Therefore, I think he may have meant X_t | X_S ~N(0,t-s) instead of the expectation." a66tfLdr6oY "11. Parametric Hypothesis Testing (cont.) and Testing Goodness of Fit" "MIT 18.650 Statistics for Applications, Fall 2016" 2691.0 0.0 1.0 0.0
"23:30 Is this supposed to be ""A"" instead of ""dA"" on the LHS ?" XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 713.0 0.0 1.0 0.0
"34:13 is a beauty" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 978.0 0.0 0.0 0.0
"I have a math degree and I still enjoy these lectures. Auroux is a great lecturer." tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5494.0 0.0 0.0 0.0
"e^At does not converge as t tends to infinity....why does he say that?" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 12784.0 0.0 1.0 0.0
"Which book is used in this series. Or is there preferred book" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11711.0 0.0 1.0 0.0
"Newton rocks!" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7825.0 0.0 0.0 0.0
"Thank you for the lectures!!! Please, add the 16th lecture." V4xOdtqic3o "15. Regression (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 9267.0 0.0 0.0 0.0
"is it possible that i didn't get anything because i do not know physics" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13639.0 0.0 0.0 0.0
Amazing rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2347.0 0.0 0.0 0.0
"nothing makes me happier than seeing Dr. Casey Rodriguez eating a cookie and drinking a can of liquid" os_XGBNPllM "Lecture 8: The Squeeze Theorem and Operations Involving Convergent Sequences" "MIT 18.100A Real Analysis, Fall 2020" 14087.0 0.0 0.0 0.0
"I have a question, do we have to solve the psets by hand, or are we allowed to use a program like sagemath?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 5504.0 0.0 0.0 0.0
"Very Good Content !!!!!!!

🤙👌💪

👏👏👏👏👏👏" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 11154.0 0.0 0.0 0.0
(y) YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 227.0 0.0 0.0 0.0
"At 4:43 , why does he divide x= (aT b)/(aT a) ? Those are matrices, and I always thought that it is not possible to divide a matrix by a matrix, that was the reason as to why we instead multiply by the inverse but not divide?" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2688.0 0.0 1.0 0.0
"Just finished the whole Single Variable course. This really helped me put all these pieces of knowledge on calculus I got in high school together. Professor Jerison is the best teacher I ever had.
Thanks to MIT OCW for this opportunity!
Russia, 2016." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7176.0 0.0 0.0 0.0
"I've watched the first 3 videos so far and I find it's not easy to follow the professor. It looks like I should read through all the slides before coming back to the videos.." TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 6438.0 0.0 0.0 0.0
"“I’m sorry for teaching you algebraic theory”" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 15593.0 0.0 0.0 0.0
"I’m in engineering and still, this is too advanced for me, and most of my classmates. God, this is a great opportunity to learn. Thank you so much MIT!" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7111.0 0.0 0.0 0.0
"4:48 Albegra 😂" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1325.0 0.0 0.0 0.0
"the hall needs more chalk boards" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14699.0 1.0 0.0 0.0
"Is my understanding correct? That we are solving for the volume under z = exp[–(x^2+y^2)] and above the z = 0 plane? If yes, then I'm not sure why the professor avoided mentioning this. I guess it is because he didn't want to make the problem seem like a problem in multivariable calculus. Nonetheless, I think it would have made the discussion clearer." zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6800.0 0.0 1.0 0.0
"It took me 15 seconds to realize that he was speaking English! " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6989.0 0.0 0.0 0.0
"We ask owl selves, in a given dilection, a vectill" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11313.0 0.0 0.0 0.0
"Thank you Prof.Strang 🇨🇳" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 9203.0 0.0 0.0 0.0
"Thank you MIT OpenCourseWare!" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 9132.0 0.0 0.0 0.0
"You can find detailed information,  formulas and calculators for ""Bernoulli distribution"" and many more on trignosource - ""https://trignosource.com/bernoulli%20distribution.html""" gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 12188.0 0.0 0.0 0.0
"Sorry to break it to you, Strang, but you've lost me at this point. " IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 8857.0 0.0 0.0 0.0
"are you saying that this lecturer looks like Linear Algebra??? " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12401.0 0.0 0.0 0.0
"Can't wait for our classes to end so that I can binge watch lectire series." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3128.0 0.0 0.0 0.0
"First time I ever see an explanation on why we have y_general = y_particular + y_homogeneous, which somehow makes everything make sense." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 3819.0 0.0 0.0 0.0
"13:11 ""those give you junk; they give you an extra factor of ln2"". Actually I think they give you an extra factor of 1/ln2. Proof:
(log2p)'=(lnp/ln2)'=(1/ln2)*(p'/p)" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 406.0 0.0 1.0 0.0
"woohoo integration by parts...how exciting...reminds me of the lecture I had a week ago!" aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15400.0 0.0 0.0 0.0
♥️ t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15604.0 0.0 0.0 0.0
"Maths legend. Thank u sir for your love towards students and teaching maths" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7619.0 0.0 0.0 0.0
"This teacher knows what he's doing!" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10939.0 0.0 0.0 0.0
"Thank you...I enjoy how Professor Strang reveals the beauty of the subject, step-by-step." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 9566.0 0.0 0.0 1.0
"Thank You MIT OCW for this Amazing course. And thank you Professor David Jerison for being such an amazing teacher. So finally to 18.02!" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9048.0 0.0 0.0 0.0
뀨 PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15671.0 0.0 0.0 0.0
"This guy is awesome! Really enjoy the lectures." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10524.0 0.0 0.0 0.0
"I do not understand the fact that why the summation of expected values gives mean?? Could u please help Thanks in advance." 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 5291.0 0.0 1.0 0.0
"I don't want to write down a big definition, you can see what it is."" 
how much we need teachers like this." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5361.0 0.0 0.0 0.0
"so far the examples given for subspaces are all n+1 * n matrix. How comes that? Is it just a coincidence or does the 'missing' column represents zero vector?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 14330.0 0.0 1.0 0.0
"lol i watched the entire playlist just for this video" BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 13827.0 0.0 0.0 0.0
"50:00 the important/biggest/principal part of matrix" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1336.0 0.0 0.0 0.0
"we only live so long...lol, amazing professor!!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 15078.0 0.0 0.0 0.0
"well... How old are these students ?" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15095.0 0.0 0.0 0.0
"30:25 I had to pause for a bit and take a deep breath" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 887.0 0.0 0.0 0.0
"35:55 Size of identity matrix should be be nxn so that its conformable, shouldn't it?" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1023.0 0.0 1.0 0.0
Gracias. j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 4179.0 0.0 0.0 0.0
"god bless gilbert strang
and also thanks to MIT for putting them on  the web
what on earth  did we do before the internet  ?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 12927.0 0.0 0.0 0.0
"He builds to the adjoint for trivial means. Well done." QTg7040uSc0 "Lecture 23: The Dirichlet Problem on an Interval" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 4463.0 0.0 0.0 0.0
"why are  free variables with value 1 and 0 so special?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 15281.0 0.0 1.0 0.0
"this guy is awesome" phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14820.0 0.0 0.0 0.0
"Can we have access to programming assignments made for this course?" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3114.0 0.0 0.0 0.0
"Hlo sir 
 My question is that 
Why we use exponential" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4771.0 0.0 1.0 0.0
"Can anyone explain why he add OA,AB,BP and get OP?
And why AB is < 0 ，a>?" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3032.0 0.0 1.0 0.0
"18:04 and 28:12 
It proves Prof. Strang is a man of his words." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 527.0 0.0 0.0 0.0
"Thank you" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9082.0 0.0 0.0 0.0
"I'm unclear about the following statement 04:21 ""[Singular] means [matrix A] takes some vector X into zero"". I know if matrix A is singular, it means matrix A cannot be inverted. However, I don't understand how multiplying vector X by a singular matrix A will result in zero. I was wondering if anyone can help me understand this." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 6394.0 0.0 1.0 0.0
"Voice ❤️" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11237.0 0.0 0.0 0.0
"I undersand now why American suck in math damm
 (Yes I'm French)" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6117.0 0.0 0.0 0.0
"Camera guy if you're reading this, please keep camera on the board and stop following the professor unless he is physically making demonstration
" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2994.0 1.0 0.0 0.0
"This is so bad ...." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10715.0 0.0 0.0 0.0
"you are good teacher ever i have seen so keep it up
" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15492.0 0.0 0.0 0.0
"I have been thinking about the geometric proofs but i just can not visualize them , it has been many hours but i fail to comprehend the geometric proofs. Although i can say that the 2nd proof was a bit more feasible, but the first proof; especially the one which is related with A ( d/dx sinx = cosx ) is just nightmare.. " kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5519.0 0.0 0.0 1.0
"One of the silver linings for covid. Thanks." 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 8101.0 0.0 0.0 0.0
"Not under CC license 🤔" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7933.0 0.0 0.0 0.0
"Inverses --> add 3 times of row 1 to row 2::: Doesn't make row 2 as 3 1 0 it makes it 0 1 0

Row -1 --> 1 0 0
Row -2 --> -3 1 0
3 times row -1 ..> 3*1 0*3 0*3  --> 3 0 0
add above row to row 2 -3+3 1+0 0+0 --> 0  1  0" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6742.0 0.0 1.0 0.0
"To find this course on the web is tantamount to finding massive gold treasure." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 11036.0 0.0 0.0 0.0
"Now this helps me realise my mistakes in A level which I don't know before ... Amazing n good lecture solidly explained those tables n rules will surely help much" CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7960.0 0.0 0.0 1.0
https://www.youtube.com/watch?v=uy8Jcwl2YnU&t=7s VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 13283.0 0.0 0.0 0.0
"Hi, relative to undergraduate curriculum, would this be considered Intermediate Statistics / Statistics II, following an intro-level college stats class? Thanks!" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 4729.0 0.0 1.0 0.0
"Just like Lil Pump taught... B rows B rows B rows B rows B rows...." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7186.0 0.0 0.0 0.0
"That's some nice handwriting." dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 9939.0 0.0 0.0 0.0
"Prof. Auroux is awesome,,what a style" _CdoRiNSrqI "Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8288.0 0.0 0.0 0.0
"5:08 - Therefore, every King should have his two Queens.  ;-)  Totally logical to me.  Or perhaps Q is the queen that's a lady by day, and Q-transpose is the queen who's on her back.  :-|
   
Sorry guys - couldn't resist." or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1357.0 0.0 0.0 0.0
"The proof is so obvious it yells ""RAR!"" at you 🤓" d32WV1rKoVk "12. Computing Eigenvalues and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10258.0 0.0 0.0 0.0
"sorry but not sorry 38:25" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 14372.0 0.0 0.0 0.0
"love how many small extra's he throws in constantly, as small ""notes"" to know ^^ keeps the mind awake and entertained in wonder :D
wish my professors was as invested in their lectures :)" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13865.0 0.0 0.0 1.0
"3:10
A is the matrix of coefficients
6:23 
The line of solutions to this equation
23:44
26:00 big picture
29:30 multiplying a matrix by a vector. AX" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 1111.0 0.0 0.0 0.0
"In many linear algebra courses that I have seen, the student is simply told about the various relationships between the fundamental subspaces. But in this course these ideas are convincingly yet accessibly presented. This is very important because it allows students to really understand such key ideas of linear algebra to the point where they become intuitive, instead of simply memorizing properties and formulas. Another great lecture by professor Strang!" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6641.0 0.0 0.0 1.0
"that's was amazing." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 14649.0 0.0 0.0 0.0
"This video was recorded on a Saturday and I am watching it on a Saturday. The Professor caught me off guard when at the end, he said, ""have a great weekend. See you on Monday""" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 10961.0 0.0 0.0 0.0
"What an amazing lecture, thank you!" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 11451.0 0.0 0.0 0.0
"12:11  similar matrices
31:10 Jordan Form" TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 389.0 0.0 0.0 0.0
"I believe Prof. Strang deliberately made the mistake at the end of Lec 9, in order to transition the focus from column space to row space. The transition was too smooth for this to be an accident. This is also a great show of humility that he didn't mind being perceived making a mistake!" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5166.0 0.0 0.0 0.0
"explanations of counting is great by a geneous  prop..." 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 12834.0 0.0 0.0 0.0
"This is MIT. Great lecture" 0Va2dOLqUfM "5. Maximum Likelihood Estimation (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 10581.0 0.0 0.0 0.0
"Well I don't think I'll be humbled because in 6 months time I will have reached a higher level of Linear Algebra than MIT undergrads (actually doing a maths project in coorporation with my high school and a local university, in april I'll be finished.. L.A. is not exactly tough compared to other fields of maths)." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11344.0 0.0 0.0 0.0
"Can someone explain why the computatinal expense is roughly 100^2 for the first step? I thought it would be roughly proportional to n = 100" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 3077.0 0.0 1.0 0.0
"interesting topic, he is a good teacher for sure" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13618.0 0.0 0.0 0.0
"You should really rerecord the previous 5 classes with functions on the place of numbers and call it tensor calculus - introduction" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12238.0 0.0 0.0 0.0
"Beautiful... lovely.." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2826.0 0.0 0.0 0.0
"Guys i am 18 years old and i am learning some of that stuff at school right now... I am sure that they learn more advanced things there but it's alitle strange :/ Shouldn't all that be supposed to be known??" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4389.0 0.0 0.0 0.0
legend!!! 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 13780.0 0.0 0.0 0.0
"I'm out. I made it 21.5 minutes. It wasn't my nap time yet so I had to walk away." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 6361.0 0.0 0.0 0.0
"but good video by the way explains the basics, which is vital after all" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12569.0 0.0 0.0 0.0
"That's some high quality chalk he's using there." MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9938.0 1.0 0.0 0.0
"Thanks for the comments. Here is what I thought. If both the objective f and the constraint function g are smooth, the constrained min/max must also occur at some critical points (if we extend its definition a little), as indicated by some directional 0 derivative. The question is how to define this directional derivative of f by incorporating the constraint g=c. If this could be done, then the second directional derivative could surely be used to test for min or max. " 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9707.0 0.0 1.0 0.0
"Excellent lecture.  Dr. Strang goes a bit too fast.  But that is par for the course at MIT." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3661.0 0.0 0.0 0.0
"@ Rahul Duggal, the prof doesn't mean to change the column, he's just highlighting it to be obvious." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 1486.0 0.0 0.0 0.0
"thank you prof. Strang" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14504.0 0.0 0.0 0.0
"great teacher" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13004.0 0.0 0.0 0.0
"My neurons are enjoying..." 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 7777.0 0.0 0.0 0.0
"+Osman ÇALIŞIR All the lecture notes, exams with solutions and assignments are available on the MIT OpenCourseWare site at: http://ocw.mit.edu/18-01F06" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 255.0 0.0 0.0 0.0
"Thank you so much for sharenig  knowledge with a rest of the world. Thank you..." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9367.0 0.0 0.0 0.0
"Wow! Thanks so much for uploading this! What an engaging professor." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12052.0 0.0 0.0 0.0
"Is there any other statistics course from MIT" TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 6836.0 0.0 0.0 0.0
"It is a pure joy watching these lectures. Many thanks to Prof. Gilbert Strang and MIT OCW." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6926.0 0.0 0.0 0.0
"The Professor dusting the blackboard is so satisfying." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9975.0 1.0 0.0 0.0
"can we call him ""Mr. strang"" of probability?" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 12634.0 0.0 0.0 0.0
"he is actually a doctor takiing math may be ???" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13092.0 0.0 0.0 0.0
"Can anyone explain 32:18 why u(t)= s e^(lambda* t)  s(inverse) * u(0) = e^A*t *u(0)?
From 9:33, for example u(0)= c1* 1*x1,  c2*1*x2 (t=0, so e^lambda 1 or 2 * t, are 0)" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 3018.0 0.0 1.0 0.0
"MIT may have cheap black board but not have high quality education.....any way its lecture from 2005 .......now there will be high quality equipments there" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 7535.0 1.0 0.0 0.0
"Thank you professor Strang" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9314.0 0.0 0.0 0.0
"@IAmBenyamin Fantastic that you feel that way! However, when you get to college, you might encounter a professor teaching this that isn't anywhere near as good as this guy is .Don't let that discourage you, though! This guy alone got me through calculus. :)" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1635.0 0.0 0.0 0.0
"why the camera not following the writing at 36:30..." 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15366.0 1.0 0.0 0.0
"For the determinant, we can also represent each vector as a column. It will give the same answer." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3886.0 0.0 0.0 0.0
"I get so happy when things like that look kinda hard in the beginning solves that easy just because you know how to do it :)" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5435.0 0.0 0.0 0.0
"this guy is really good at the 3D drawings" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 14830.0 0.0 0.0 0.0
"Professor Gilbert Strang is one of my favorite heroes 🦸‍♂️ 🙌🏽❤️✨" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8328.0 0.0 0.0 0.0
"Everybody praising Money Heist's Professor....Because they haven't seen Gilbert Strang.The Professor  👏👏👏" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 3608.0 0.0 0.0 0.0
"where is he giving this lecture? A train station? geez can't the students shut up?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 15232.0 1.0 0.0 0.0
"""shuffle"" in practice or ""random pick"" in theory on 42:00" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 172.0 0.0 1.0 0.0
"Thanks! Professor. Taking half month to enjoy this course. A total new sight of math!!! Inspire my attention for research,for study again!!!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9833.0 0.0 0.0 0.0
"This is real education." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 10710.0 0.0 0.0 0.0
"he has a point" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13080.0 0.0 0.0 0.0
"43:25 how did he do that..." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 1208.0 0.0 1.0 0.0
"I liken mathematics lecture examples to this: 

You start at A and work out how to get B.  But A and B could be anything.  Arbitrary values are put through the motions to vaguely solidify the concept during a ""problem"".  My issue with this method is its distance from practicality making a weak attempt to bridge the abstract.  It is generally impossible to measure and extrapolate predictions from these vague examples to help verify one's understanding of the underlying concepts." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5705.0 0.0 0.0 0.0
"I'm a physics eng. student from Turkey. Thanks a lot for videos!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6299.0 0.0 0.0 0.0
"These videos finally make me realize that I wasn't stupid, my undergrad professor was!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 10433.0 0.0 0.0 0.0
"Thank you Sir, Just wanted to say thank you, for giving me a deeper insight into probability. I studied this from the 1st lecture to this. I will study the last 5 lectures later on." Tx7zzD4aeiA "20. Central Limit Theorem" "6.041 Probabilistic Systems Analysis and Applied Probability" 9236.0 0.0 0.0 0.0
"Can we say Wx + Xt ?   The x and t are subscripts. Or... does that imply a partial derivative only?" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 3117.0 0.0 1.0 0.0
"""Any space with those vector in it must have all the combination of those vector in it. And if I stop there then I have got the smallest space and that is the space they span"".  Got a feel. ☺️ Amazing Person." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 30.0 0.0 0.0 0.0
"34:52
I'm going to violate my own hole" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 988.0 0.0 0.0 0.0
"Thank you MIT OCW and Professor Gilbert Strang.
After I had watched this lecture for the 1st time, I had to build up my understanding on Differential Equations and Taylor series, then I watched this Lecture one more time with carefully thinking through each step, and hence, I'm able to understand. Great lecture." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 9129.0 0.0 0.0 1.0
"But (with some help from Taylor expansion) he used that specific case to justify what he claimed about general case. So it's only irrelevant if you only need to know how to compute stuff and don't strive for deeper understanding of the subject." 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2954.0 0.0 0.0 1.0
"What's a pivot?" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 11573.0 0.0 1.0 0.0
"The end almost made me cry, we lived together something wonderful, Thanks MIT" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10087.0 0.0 0.0 0.0
"Why didn't any students notice to the professor that he forgot to take the square of (2b/n)?" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11816.0 0.0 1.0 0.0
"Great lecture. i like this guy. Other teacher is good too, but this guy writes fast and explains things clearly for me." Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4297.0 0.0 0.0 0.0
"Why is it that a 1x3 row matrix has to be on the right of a 3x3 matrix for multiplication?(  I'm aware of the  mxn times nxp rule, just wanted to know the intuition )" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11877.0 0.0 1.0 0.0
😍🤤🤓🥳☺️🙏 Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15735.0 0.0 0.0 0.0
"how can a senior professor of mit be so wrong he didn't put -a^3/3  with b^3/3  to find the area between a and b so this mit" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13195.0 0.0 1.0 0.0
"I loved this lecture and yeah I integrated cos^4x .. ...it felt like a live classroom it was not boring like other video lectures on YouTube it was lovely 👌👌👌" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5860.0 0.0 0.0 0.0
"Thanks Prof. Gilbert Strang for such a nice topic to discuss" 0Qws8BuK3RQ "34. Distance Matrices, Procrustes Problem" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9632.0 0.0 0.0 0.0
"just i can say great" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 13738.0 0.0 0.0 0.0
"this is all good but maybe breaking up the lecture into sections and many different videos instead of 50 minutes would work great. but he teaches very well" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14851.0 0.0 0.0 0.0
"Years ago I decided to study Linear Algebra. I done a Cert in Engineering and we hadn't done many matrices or enough. So I was really struggling. But I passed as I used the formulae (the course book I had was for Stage 2 and I should really have being Stage 1. But for all that time, out of curiosity I wanted to know what they actually were. I couldn't easily see then how they were vectors. The lecturer makes it clear. I could follow up to finding the eigenvalues. I had always been puzzled how they ignored the other numbers not on the diagonal. Trying an identity as he had and changing the numbers I realised what that diagonal - the trace he called it - was. Amazing! I realized that the 3  1 / 1  3  was 3 x  1 1 /  1 1   It doesn't change except in the amount, not the direction. But in effect only the diagonal from top left to bottom right are significant." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 12132.0 0.0 0.0 0.0
"Lecture 1: Dot Product
Lecture 2: Determinants
Lecture 3: Matrices
Lecture 4: Square Systems
Lecture 5: Parametric Equations
Lecture 6: Kepler's Second Law
Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds)
Lecture 8: Partial Derivatives
Lecture 9: Max-Min and Least Squares
Lecture 10: Second Derivative Test
Lecture 11: Chain Rule
Lecture 12: Gradient
Lecture 13: Lagrange Multipliers
Lecture 14: Non-Independent Variables
Lecture 15: Partial Differential Equations
Lecture 16: Double Integrals
Lecture 17: Polar Coordinates
Lecture 18: Change of Variables
Lecture 19: Vector Fields
Lecture 20: Path Independence
Lecture 21: Gradient Fields
Lecture 22: Green's Theorem
Lecture 23: Flux
Lecture 24: Simply Connected Regions
Lecture 25: Triple Integrals
Lecture 26: Spherical Coordinates
Lecture 27: Vector Fields in 3D
Lecture 28: Divergence Theorem
Lecture 29: Divergence Theorem (cont.)
Lecture 30: Line Integrals
Lecture 31: Stokes' Theorem
Lecture 32: Stokes' Theorem (cont.)
Lecture 33: Maxwell's Equations
Lecture 34: Final Review
Lecture 35: Final Review (cont.)" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7274.0 0.0 0.0 0.0
"Where is the timestamp guy?" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 11693.0 0.0 0.0 0.0
"thank you so much sir,you made learning very easy...." jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 14517.0 0.0 0.0 0.0
"""What's the long word for bowl?""" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 133.0 0.0 0.0 0.0
"The way he is teaching linear algebra by taking example of solving linear equations and not just throwing all the formulas without their incentive is really great." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10327.0 0.0 0.0 1.0
"to share this quality of things is incredible" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14948.0 0.0 0.0 0.0
"@adidasguy87 lol tryied to play it off? he immedietely listened to his students' opinion." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1767.0 0.0 0.0 0.0
"I think the 1st problem set of this course is not in the website. The website shows the ps1 of 18.01." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6048.0 0.0 1.0 0.0
"oh i am really sorry it was origin i didn't see and commented about a" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14106.0 0.0 0.0 0.0
"Thanks for pointing this out.

Also, when vectors (1, 1, 2), (2, 2, 5) and (3, 3, 8) are written as column vectors and placed in a 3x3 matrix A, A’s first two rows equal (1, 2, 3).

Hence the rank of A is 2 and its nullity is 3 – 2 = 1 > 0.

Thus A’s columns are linearly dependent.
" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 9691.0 0.0 0.0 0.0
TY TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 9004.0 0.0 0.0 0.0
"wow...maths is like making a discovery! many thanks for MIT fraternity.." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15436.0 0.0 0.0 0.0
"Is this intro calc? Like if you've taken advanced algebra and trig, is this the best place to start? I have a textbook and a fair bit of free time at the moment. Is this video the right way to begin? Thanks :)" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6875.0 0.0 1.0 0.0
"In the last geometric proof to show angle QPR is equal to theta, he could have drawn a line from R perpendicular to the horizontal radius, instead of making the ""rotation argument""." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6673.0 0.0 1.0 0.0
"@bnssapp  I like to think it gives me a reason to get out of bed in the morning." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1800.0 0.0 0.0 0.0
"Fantastic! Thanks for uploading." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 3742.0 0.0 0.0 0.0
"Thank you Dr. W. G. Strang, for all this knowledge you have all us favored of." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 9106.0 0.0 0.0 0.0
"For nearly three quarters of this lecture I was totally lost about each single word of it." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 3869.0 0.0 0.0 0.0
"@mrwideboy Well we done this at the start of september and im 16. But yeah i know what you mean..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1953.0 0.0 0.0 0.0
"What if number of people are 2 ,then the expectation that 1 person gets his own hat won't make sense 😓" EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 11505.0 0.0 1.0 0.0
"he is an amazing teacher. His lectures helped me a lot ." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 13094.0 0.0 0.0 0.0
"and the paradox lies in the very nature of curvature itself, which can't be exactly calculated using discrete math (I am claiming the entire real number line is discrete)." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12373.0 0.0 0.0 0.0
"43:36 that moment when your professor's computational abilities goes far beyond standart human capabilities" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 1214.0 0.0 0.0 0.0
"Why are these guys not wearing masks ?" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11782.0 0.0 0.0 0.0
"beautifully done" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12521.0 0.0 0.0 0.0
"Thought Id be watching for 5 minutes, ended up staying for the whole class..." ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10997.0 0.0 0.0 0.0
"aww he is so cute" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12502.0 0.0 0.0 0.0
"he came up with a really round about way of saying take the derivative dx/dy." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13069.0 0.0 0.0 0.0
"Thank you, professor and all the guys who insist from Lec1 to Lec34." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9525.0 0.0 0.0 0.0
"16:29 speaks for itself" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 476.0 0.0 0.0 0.0
"I'm 10 minutes in and I gotta tell you, in this 10 minutes you've done more than one semester of my course in linear algebra" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6290.0 0.0 0.0 0.0
"Like a todos los q el yutu nos haya traído por recomendación, jaja
Talvez es una señal de q no se nada y me falta verlo😔🔫" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7349.0 0.0 0.0 0.0
"Formulas? Formulae, professor." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3917.0 0.0 0.0 0.0
"@yonatanable Yep!  That's what the ∮ symbol indicates... an integral about a closed curve." tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2076.0 0.0 0.0 0.0
"My friend I love your channel 😍 fully watching 💟👍💟💟💟💟💟💟" cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 7754.0 0.0 0.0 0.0
"It's such a privilege to watch this honourable man delivering a lecture. Your lectures are helpful, especially, to the people living in a conflict zone like Kashmir, where the lockdown extends for months and this time it is almost a year with the continuous lockdown. Your 39 minutes lecture takes us more than 60 minutes to stream because of 10 months long high-speed internet restrictions enforced on us by the government's fascist approach. We have to make do with whatever we can with 2G networks. The board appears blurry because of slow networks.
Thank you, sir. Thank you, MIT. Thank you, America. ❤" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7073.0 0.0 0.0 0.0
"Sir, good night/day/afternoon. This video series look great, but I would like to know, what kind of mathematical background do I need to understand this course. Thanks." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 8713.0 0.0 1.0 0.0
"I just wanted to say Thank You Prof Strang.  Your videos were very informational, and I've learned a LOT.  I appreciate all of your hard work." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5627.0 0.0 0.0 0.0
"Absolutely legendary. Professor Strang explains linear algebra 10 times better than my own professor at school. : )" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 2207.0 0.0 0.0 0.0
"Riemann sum - 37:44
Trapezoid method - 38:47
Simpson's rule - 43:47" jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8571.0 0.0 0.0 0.0
"@9:33 how column space C(A) is in R^m ?? It should be in R^n . Am I right?" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1578.0 0.0 1.0 0.0
"If you want to know the concept of graph filtering with in 5min check this and comment your opinions 
https://youtu.be/AlpVGHMONI0" cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6559.0 0.0 0.0 0.0
""" so what's up?"" lol" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 15.0 0.0 0.0 0.0
Thanks! 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9820.0 0.0 0.0 0.0
"Professor Strang thank you for breaking down and explaining Singular Value Decomposition in linear algebra." rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8366.0 0.0 0.0 0.0
"I think he didn't explain an important  bit: why are the row picture and the column picture  equivalent? As in how do they both yield the b vector?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6011.0 0.0 1.0 0.0
"Are all professors at MIT this good..." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2520.0 0.0 0.0 0.0
"Professor Strang might be the best teacher I’ve ever seen" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 8360.0 0.0 0.0 0.0
"I've finished all the lectures from 1 to 34 completely and I'm in awe of such a wonderful teacher. Thank you for your lectures Prof. Strang and MIT I've learned a lot. 
Forever grateful." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 6414.0 0.0 0.0 0.0
"24:23 THUG LIFE 😎😎😎" -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 732.0 0.0 0.0 0.0
"Craig's mother was a sine function.... she let dudes in from every angle." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3255.0 0.0 0.0 0.0
"48:53 hand-waving. ;p" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 1300.0 0.0 0.0 0.0
"Church lived 2 of Turing's lifetimes 92 vs 42" TTArY7ojshU "6. TM Variants, Church-Turing Thesis" "MIT 18.404J Theory of Computation, Fall 2020" 3149.0 0.0 0.0 0.0
"Never been this satisfied of something I watched since the purple wedding" XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 7813.0 0.0 0.0 0.0
"It is amazing that MIT students can be smart enough to understand this, and yet be so STUPID as to believe the leftist, self-destructive insanity that the TV pounds into their little heads every day.  How about this for a Basian analysis: What is the probability that a student makes it into MIT (assuming through hard work rather than by having a fasionable skin color) and yet votes for Democrats?  My first Prior would be very low.  But based on the high rate of the decline of America as a civilized nation, I would bet that many iterations later we would find that this initial Prior was far off the mark. 😯" bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 6934.0 0.0 0.0 0.0
"This is where computers are born ...set theory" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 10773.0 0.0 0.0 0.0
"Absolutely well done and definitely keep it up!!! 👍👍👍👍👍" lWW54ts9Ubo "24. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 2216.0 0.0 0.0 0.0
"I Really Like The Video Trigonometric integrals and substitution From Your" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5000.0 0.0 0.0 0.0
"thanks a lot" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 14564.0 0.0 0.0 0.0
"great video thanks" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13013.0 0.0 0.0 0.0
"In Brazil, we don't do that in the public high school, only in college. A 15 years old brazilian kid  learns introduction to functions. Because of things like that,  this country still needs changes in education. It's a shame!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6607.0 0.0 0.0 0.0
"you mean earphones, since it would be a challenge listening only from one ear while using headphones." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 15511.0 0.0 0.0 0.0
"It seems there are hundreds of blackboards hidden in this classroom." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 6985.0 1.0 0.0 0.0
"Simply the best" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8670.0 0.0 0.0 0.0
"Really extraordinary lecture.  Very lucid but highly interesting.  My research is on 'Adaptive signal processing'. However, I enjoyed this lecture most. Thank you." k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8512.0 0.0 0.0 0.0
"My Ears are already blasted out so, I cant feel the difference, dont use earphones anymore." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7731.0 0.0 0.0 0.0
"People absolutely hate Taylor series lmao" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8162.0 0.0 0.0 0.0
"It is a honor watching this. Thanks" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6925.0 0.0 0.0 0.0
"Is there someone similar for Data structures and algorithms?Please let me know.Cuz this guy is bomb." mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 6845.0 0.0 0.0 0.0
echelon 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 12791.0 0.0 0.0 0.0
"What an amazing lecture and capturing lecturer he's. THANK YOU" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11449.0 0.0 0.0 0.0
"thought I was playing sims for a moment there.." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 14933.0 0.0 0.0 0.0
"just saying the link in the description is not working...
thanks  !" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 13742.0 0.0 0.0 0.0
"I'm grateful that I had found this course, the professor was pure love, and I managed to learn through the course. Thank you professor, it was an honor." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 6323.0 0.0 0.0 0.0
真是妙啊！ CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15642.0 0.0 0.0 0.0
"I had to clap at 39:33 and 40:51 ...respect🙏" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 5472.0 0.0 0.0 0.0
"Why do I learn this at school?!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11820.0 0.0 0.0 0.0
"this man is an amazing teacher.. i wish i had him!" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14902.0 0.0 0.0 0.0
"Perfect, it s good to know convention and formal language to start.

He drives very well the 'meditation' on each step in a matematical way." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8182.0 0.0 0.0 1.0
"I love this man. He is so concise" sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5828.0 0.0 0.0 0.0
"I don't get the block example, why is it 1 + 1/2 + 1/3? shouldn't it be 1 + 1/2 + 1/4 since the new center mass is the current centre mass plus half of the current mass before ( whichi is 1/2)?? can someone explain " wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5310.0 0.0 1.0 0.0
"@AnimeBelover begining of the year... nobody knows nobody" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1585.0 0.0 0.0 0.0
"I dont know why but there has to be some examples to be solved to prove and get the better understanding of the equations he is putting up.
Otherwise it a awesome series." 4UJc0S8APm4 "23. Classical Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 5367.0 0.0 0.0 1.0
"The way he connects the flow of ideas.........." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 10324.0 0.0 0.0 0.0
"Lol I don't need to go to school, hahah I feel sorry for you all." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7395.0 0.0 0.0 0.0
"Protect this man at all cost! Now we know, what an angel looks like!" Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8453.0 0.0 0.0 0.0
"and a critical point is a point where first partial derivatives all equal zero. In this lecture Prof. Auroux talks about ""critical points"", but it is only to tell that these points can be minimum or maximum." 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12366.0 0.0 0.0 0.0
"All my respect, professor." MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2303.0 0.0 0.0 0.0
"13:54 why did the students write ""homecoming"" there?" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 421.0 0.0 0.0 0.0
"He doesn't appear hard to me..." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4475.0 0.0 0.0 0.0
14:00 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 424.0 0.0 0.0 0.0
"This lecture was next level" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10833.0 0.0 0.0 0.0
"this man is a legend" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 14901.0 0.0 0.0 0.0
"The Camera guy fell asleep..." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 9959.0 1.0 0.0 0.0
"That homework he left, is from what book?, and what pages are those?? i really need to practize this!!!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 9891.0 0.0 1.0 0.0
"I guess we could also take the 3rd vector by the cross product of the 2 earlier ones." 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 5458.0 0.0 0.0 0.0
"@brilliantdiamonds 18.02 is a required class for all MIT graduates, so the professor doesn't always go into the details of the analysis and whatnot. 18.024 is a more rigorous class for mathy people.

On the other hand, I do have to say that this class is actually more rigorous than the calculus courses I took in high school; certainly more so than AP Calc, which was mostly formula dumping." z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1806.0 0.0 0.0 0.0
"The bus crowdedness experiment is great." XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 10026.0 0.0 0.0 0.0
"Thank you." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 9544.0 0.0 0.0 0.0
"There are a lot of comments that some of the Prof.'s explanations are not rigorous enough. MIT has 2 or 3 levels of introductory calculus. This one is for freshmen with little or no high school calculus, and who will probably major in eng. where the key is to get the right answer rather than to be rigorously correct. If you go to the OCW website, you can find the one aimed at students who want to major in math or physics. It's totally different and much harder." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10347.0 0.0 0.0 0.0
"baptistic: check out the transcripts of this lecture on the course page.. maybe you´ll find it less ""sloopy""" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12508.0 0.0 0.0 0.0
"This man has my respect." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10853.0 0.0 0.0 0.0
"I cant get over the chalk! send some down to UNCC! Anyone know where to find higher levels of calc.. Im well past intro to multivariable looking to get ahead next semester " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5232.0 1.0 0.0 0.0
"I see the space of no negotiations why don’t mind 🙏🏻? No consciousness of living togetherness in the wild . No truth no talking no incident on the wide😟." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5961.0 0.0 0.0 0.0
"Thank you Prof. Strang" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9193.0 0.0 0.0 0.0
"Oh no! Part 1 is missing! :(" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 8022.0 0.0 0.0 0.0
"In 25:50 , An alternative way to understand that matrix A doesn't have an Inverse is to visualize the matrix in a cartesian plane. 
The matrix is composed of two vectors: (1,2) & (3,6). Plotting these two vectors you will realize that they are parallel. Thus, they don't create a 2D area. They are a 1D line, one on top of the other. Reversing such vectors (applying the inverse matrix) would result in a  zero-D point, specifically (0,0). Thus, there is no inverse matrix for matrix A. 

Note: Finding that the determinant of the matrix A is equal to 0 would quickly depict this same process." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6596.0 0.0 0.0 1.0
"hopefully this is 100 level because i knew all this in high school" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13186.0 0.0 0.0 0.0
"These course works are amazing!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10399.0 0.0 0.0 0.0
"nice trike bro" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 14051.0 0.0 0.0 0.0
"@17:57 , what was that sound ? some one with a flu ?" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1502.0 0.0 0.0 0.0
"Doesn't the number of flat pieces depend on how we fold the plane. Because if the second fold is parallel to the first fold then we get 3 flat pieces rather then 4 and the same argument holds for 3,4,... folds. 
So how we rely on that formula which gives incorrect answers when we change our fold keeping the no of folds same as it doesn't consider the spatial pattern we use to have a fold. 
Is I am right or I just missed something important?" sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3469.0 0.0 1.0 0.0
"Who is the first one who dare to dislike this video?" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11741.0 0.0 0.0 0.0
"Thank you so much! This is amazing!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 9387.0 0.0 0.0 0.0
"29:46...Upper-middle, square, beginning of 2nd, line." QeYUHA0UMVg "Lecture 21: The Riemann Integral of a Continuous Function" "MIT 18.100A Real Analysis, Fall 2020" 858.0 1.0 0.0 0.0
"Thanks for this opportunity 😊😽🙂" XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9735.0 0.0 0.0 0.0
"19:08. :D" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 556.0 0.0 0.0 0.0
"Regarding the typo https://youtu.be/l4NoMKEHQwM?t=2785 (45:25), it's subtle. Namely, Var(X1+X2) = Var(X1) + Var(X2) + 2Cov(X1,X2) = Var(X1) + Cov(X1,X2) + Var(X2) + Cov(X2,X1). In case of Var(X1+X2+...+Xn) = Var(X1) + Var(X2) + ... + Var(Xn) + Cov(X1,X2) + ... Cov(X1,Xn) + ... + Cov(X2,X1) + ... + Cov(X2, Xn) + Cov(Xn,X1) + Cov(Xn,X2) + ... . Thus, the pairs of covariances are ordered, but if we selected non-repeated all possible pairs, then there would be this 2." l4NoMKEHQwM "11. Derived Distributions (ctd.); Covariance" "6.041 Probabilistic Systems Analysis and Applied Probability" 8544.0 0.0 1.0 0.0
"Nice video" 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7863.0 0.0 0.0 0.0
"He's a good lecturer." P3tGiT72APw "14. Graph limits I: introduction" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 4626.0 0.0 0.0 0.0
"Auroux is THE MAN. One of the best professors I've had so far." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2745.0 0.0 0.0 0.0
"I see why this was made free." WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 5962.0 0.0 0.0 0.0
"How could the they prepare to leave the class before he finish the lecture , I would stay whole day to listen his lecture !!!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4831.0 0.0 0.0 0.0
"I Really Like The Video Lagrange multipliers From Your" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4980.0 0.0 0.0 0.0
Yo. CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12159.0 0.0 0.0 0.0
"Thank u all" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9070.0 0.0 0.0 0.0
"For finding basis for N(A), Why can't we use similar approach of finding basis for left nullspace. 
1) trans(A) - - - ->  RREF
2) E' × trans(A) = RREF
3) finding basis from E'" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3865.0 0.0 1.0 1.0
"There are people who can nail every complicated computational problems of single variable differentiation and integration, while at the same time have no clue about limits and continuities, and how continuity and differentiability differ in higher dimensions. Come back again when you fail mathematical analysis." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10355.0 0.0 0.0 0.0
"Thanks Prof. Auroux :)" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9629.0 0.0 0.0 0.0
"For property 3b should the top row be    (a+a'   b)  -->  (a   b) + (a'  b)" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 3872.0 0.0 1.0 0.0
"Is Alex still okay?" 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6745.0 0.0 0.0 0.0
0-15.62A=(B). 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 275.0 0.0 0.0 0.0
"nice example of seeing matrix in perspective of stat" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 14032.0 0.0 0.0 0.0
"Congratulations to this great Professor!  Bravo!!!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 3202.0 0.0 0.0 0.0
"My favourite sports team is the Seattle Submatrices" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 7752.0 0.0 0.0 0.0
"anyone who is interested in knowing what is he doing, or who wants to enjoy the beauty of mathematics . 

of course you don't ... but you will never come out of the cave" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12390.0 0.0 0.0 0.0
"It's 1:30 am, I'm after a couple of cans of beer, I couldn't figure out the lower maths 40 years ago in school and left college after a year........... I could be wrong but I have a sneaking suspicion that my suggestions algorithm may have fucked up big time." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7011.0 0.0 0.0 0.0
"sir is explaning gud.. but slides are not visible properly.. can someone plz provide me it's soft copy?. it will be really helpful to me.. thank you." 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 14309.0 0.0 0.0 0.0
"somehow i dont find the fact that the number of pivot columns is the same as the dimension of the column space obvious - the only way I could think of getting around this right is to get the row space involved.... would this do?" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14362.0 0.0 1.0 0.0
"i wouldnt mind walking through a wall :)
" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13509.0 0.0 0.0 0.0
"@ 8:47 , shouldn't that be a -5?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1483.0 0.0 1.0 0.0
"Thank you Professor Strang and MIT. This is fun and great! It boils everything down to the fundamentals. Best you can get!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9216.0 0.0 0.0 0.0
"Who  else  came   from   2003 spring lecture video 🥰" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11724.0 0.0 0.0 0.0
"It seems the audio from lecture 1 to lecture 2 transformed from R1-->R2" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6984.0 0.0 0.0 0.0
"Thank you for the video lectures Prof. Gilbert Strang, I learned a lot from them." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9270.0 0.0 0.0 0.0
"What a legend" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11420.0 0.0 0.0 0.0
"24:40 LMAO, the professor is very funny, ""keep walking away""" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 746.0 0.0 0.0 0.0
"Following his lectures since 2017, greatest teacher ." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3834.0 0.0 0.0 0.0
"unbelievable!!! he is 84 (when this video was recorded)" MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14978.0 0.0 0.0 0.0
"0:54

That's probably the hottest girl at MIT. " 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 309.0 0.0 0.0 0.0
"Please never die." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8209.0 0.0 0.0 0.0
"great lecture" 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 12973.0 0.0 0.0 0.0
"42:12 , the answer is rank(A) = rank(B) right ?" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 1173.0 0.0 1.0 0.0
"I watched this video hoping to learn what the row space and left null space were good for and learned nothing new. This lecture recounts only the definitions of the four fundamental subspaces and their dimensions and works on an example of finding their respective bases. Like in his book ""Introduction to Linear Algebra"", Dr. Strang takes so many shortcuts and skips over the precise definition of many concepts and proofs and precise definitions of so many important theorems that I find his lectures (and book as well) useful only to a limited extent. I appreciate the effort but I believe there should be a better way of teaching linear algebra." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6187.0 0.0 0.0 1.0
"3:15 upper matrix must have zeros up of the diagonal." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 1113.0 0.0 1.0 0.0
"@Lemnirot lol 1 + 2(5) != 8

so you're wrong" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 1658.0 0.0 1.0 0.0
"This class makes me so happy~" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10478.0 0.0 0.0 0.0
"I used to think I understood algebra..." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6128.0 0.0 0.0 0.0
"0:15 ""...Let's make this lecture immortal""" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 302.0 0.0 0.0 0.0
"1) I think strictly speaking the likelihood function (at 15:45) which we need to maximize is the joint density function of the W vector, not the joint density function of the Y vector. The notation and the wording are kind of confused there. But the idea is clear. 2) The parabola/model around 28:45 is first called a quadratic model, then it's explained that it's still a linear model (at 29:50). I assume the term quadratic refers to the X, while the linearity refers to the thetas. 3) I think it should be noted that by introducing h(x) (at 29:57) we get more free parameters (apart from theta0 and theta1) e.g. if h(x) = a . x . x + b . x + c we get also a,b,c as free parameters. So the minimization now happens not just over theta0 and theta1 but also over a,b,c. And that's what might lead to overfitting (the presence of too many free parameters). Right? 

Great series of lectures though! Many thanks to MIT OCW and to prof.Tsitsiklis! One just needs to listen with care, and question (to some healthy extent) everything one hears." tBUHRpFZy0s "24. Classical Inference II" "6.041 Probabilistic Systems Analysis and Applied Probability" 318.0 0.0 1.0 0.0
"awesome awesome awesome !!!!" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 12488.0 0.0 0.0 0.0
"I never knew what the background idea of e is, and now this wonderful lecture has enhanced my understanding of e, thanks a lot Prof. David Jerison!" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5880.0 0.0 0.0 0.0
"""Oh Kay"" " TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 93.0 0.0 0.0 0.0
"11.01 that boy with a hairstyle like a slice of watermelon." HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 359.0 0.0 0.0 0.0
"What the.. How did he even... Why did he even. What is life?" HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 11562.0 0.0 0.0 0.0
"That's a large class, must be a freshman class." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9929.0 0.0 0.0 0.0
"chain ghoul" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12647.0 0.0 0.0 0.0
"@25:00 Professor Strang manipulates V_1^t * (A^T * A) *V_2 into V_1^t * (∂_2 ^2) *V_2......

How does A^T * A = ∂_2 ^2 exactly?" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1518.0 0.0 1.0 0.0
"48:14 you change it by switching from Lagrangian mechanics to Hamiltonian :D" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 1293.0 0.0 0.0 0.0
"skip to 2:30" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14318.0 0.0 0.0 0.0
"Why is L always inverse of E? Like how can we see that geometrically?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 11863.0 0.0 1.0 0.0
"Absolutely delightful to see another of Prof Strang lectures...,
PS A busy and working minds is like a brain exercise that will keep you mentally healthy for a long long time!!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2203.0 0.0 0.0 0.0
"I agree. Ive been taking calculus for 3 years now and this is the first time I truly understood the concept of a differential. " 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5029.0 0.0 0.0 0.0
"Prof. Strang is a magician. the way he pulls out tricks from his hat and makes sound Linear Algebra concepts fun to students. Respect Respect, only 75% through this video and mesmerized. Charismatic teacher. raw suave, trickery from the magician teacher." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8303.0 0.0 0.0 0.0
"@Lemnirot He corrects this in Lecture 10" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 1657.0 0.0 1.0 0.0
"mit disculpa soy de peru y no se te importaria mandar tus videos en español
x fa no seas malo " 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13952.0 0.0 0.0 0.0
"@ 21:55 Jerry Seinfeld" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1470.0 0.0 0.0 0.0
"Simply amazing!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8662.0 0.0 0.0 0.0
"Thank you so much for this lectures. Completed all my linear algebra classes like 3 semesters ago so Im here at my own leisure." Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9375.0 0.0 0.0 0.0
"24:37 shouldn’t the reason for being half be because we define theta strictly? I mean we would get the other half by 180 + theta." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 739.0 0.0 1.0 0.0
"He is my best prof." cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4525.0 0.0 0.0 0.0
"Useless Freemason math." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11137.0 0.0 0.0 0.0
fantastic 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12842.0 0.0 0.0 0.0
"Finally Completed :)" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 3760.0 0.0 0.0 0.0
"the teacher is himself not sure of formulas ,highly under confident my local teacher have better knowledge than him,MIT needs to improve here" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14744.0 0.0 0.0 0.0
"Thank you sir! Thank you!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9334.0 0.0 0.0 0.0
"Great guy in the planet" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 4229.0 0.0 0.0 0.0
https://www.youtube.com/watch?v=Ot87qLTODdQ QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 13274.0 0.0 0.0 0.0
"this guy knows his stuff. i enjoyed his class very much. Fair grader too, not tough, but fair." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 14836.0 0.0 0.0 0.0
21:00 ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 667.0 0.0 0.0 0.0
"thinking back of my statistics course in university, i feel like i've been conned. This is so much better" P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 14792.0 0.0 0.0 0.0
"Great intro to orthogonal complements towards the end of the lecture! 44:20" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 4236.0 0.0 0.0 0.0
"0:32 Exponentials (properties and differentiation)
    - 5:30 derivative of exponentials
    - 8:57 M(a) --- later on defined as ln(a)
    - 13:39 Introduction of e as basis for the exponential
20:54 Natural logarithm (using implicit differentiation)
27:42 Derivatives of exponentials in general (a^x)
     - 28:48 First method (using conversion a^x = (e^ln(a))^x
     - 33:37 Second method (using logarithmic differentiation)
38:45 First Example with log differentiation ( derivative of x^x)
41:31 Second Example with log differentiation (definition of e)" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 306.0 0.0 0.0 0.0
"Free AI Python Course on Youtube : https://www.youtube.com/watch?v=5APYjKJfPek&list=PLi1BmHvgBkxKKdNkK_x8BTTj7vI_p3bSM&index=1" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3921.0 0.0 0.0 0.0
"When he presents Taylor's formula, it's not quite correct because the formula he presents is for MacLaurin Series since it is centered at 0. " wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11619.0 0.0 1.0 0.0
"@ycao19 yes indeed!" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 2075.0 0.0 0.0 0.0
"Love you Prof. Strang.....I am beginning to fall in love with Linear Algebra....You are a genius Prof. Strang...." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 7464.0 0.0 0.0 0.0
"you made me love linear algebra" TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 15508.0 0.0 0.0 0.0
"This has been helping in my Wits University MATH2011. Thanks MIT!" ZwpwmGP5ITM "Lec 34: Final review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10569.0 0.0 0.0 0.0
"Thanks Dr. Strang" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9587.0 0.0 0.0 0.0
"These courses are the best in the Math." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10401.0 0.0 0.0 0.0
"What an excellent teacher! I have that edition of his book (& the next). They're recommended texts in game programming." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11456.0 0.0 0.0 0.0
"The wrathful yoke relatively judge because appeal internally apologise than a electric edward. needless, nutritious maraca" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 10341.0 0.0 0.0 0.0
"Mit student don't know how to calculate determinant" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7680.0 0.0 0.0 0.0
"Thanks from india" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 9747.0 0.0 0.0 0.0
"You mentioned that Null space =[-F I]^T. But what about X=zero vector? Because [-F I]^T does not cover X=zero vector. Explain this please" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 12227.0 0.0 1.0 0.0
"Great lecture! However I have a doubt, can someone please tell me how to find the basis from row reduced echelon form?
The row reduced matrix according to me R = [(1 0 1 0 0), (0 1 1 0 -1), (0 0 0 1 1), (0 0 0 0 0)]
I have gone through lectures 1-11, but still I am not getting it. Am I missing something? Please help" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4265.0 0.0 1.0 0.0
"i get chills from the first 5 minutes of this" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13381.0 0.0 0.0 0.0
"I am watching in 2020 and I must say it is fresh as mortal. Long Live Prof." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5154.0 0.0 0.0 0.0
"Gracias excelente explicación" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4178.0 0.0 0.0 0.0
"this one lecture was hard." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14908.0 0.0 0.0 0.0
"i guess I am the lucky one since i've just started to watch this video lecture series today!" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 13383.0 0.0 0.0 0.0
"15:58  Gilbert, it is less confusing if you take a and b on the second row while doing the co-factor formula. lol" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 461.0 0.0 1.0 0.0
"@davestoj thanks :) " bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1823.0 0.0 0.0 0.0
"o pateras sas!" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 14096.0 0.0 0.0 0.0
"a teacher u really like 2 have" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12291.0 0.0 0.0 0.0
"56:29 subtitle correction instead of personality density, it should have been probability density. Thank you for the content =)" a66tfLdr6oY "11. Parametric Hypothesis Testing (cont.) and Testing Goodness of Fit" "MIT 18.650 Statistics for Applications, Fall 2016" 1352.0 0.0 1.0 0.0
"the notation with curly d's at 31:05 is wrong" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14721.0 0.0 1.0 0.0
"omg sir much obliged sir, so much obliged !!" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 14142.0 0.0 0.0 0.0
respect!!! 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 14266.0 0.0 0.0 0.0
38:38 YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1083.0 0.0 0.0 0.0
"I go to CSULB yet I pay more attention to these lectures and learn more. I should just pay you guys." 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 5438.0 0.0 0.0 0.0
"I'm here" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 6327.0 0.0 0.0 0.0
"@27:17 ""Why is this method valid?"" The question many ""teachers"" never explain (and sometimes discourage students who ask such question). This is one of the key differences between a teacher and someone whos job description is teacher." 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1522.0 0.0 1.0 1.0
"You gotta love the fact that this is MIT and the Volume quality is shite" X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 12208.0 0.0 0.0 0.0
"The way he tapping on the board with the chalk is  pissing me off." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10332.0 1.0 0.0 0.0
"why cant we assign free values to pivot variables" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 15294.0 0.0 1.0 0.0
"the quality of chalk is mesmerizing!" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14737.0 1.0 0.0 0.0
"Why are these lectures so short? Is 45 minutes a normal lecture time in the us?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11783.0 0.0 0.0 0.0
"Pretty sure he got this job solely because of his superhuman blackboard handwriting." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8250.0 0.0 0.0 0.0
"Good Job Professor, but blackboard work and video quality not up to mark." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4119.0 1.0 0.0 0.0
"I learnt these stuffs when i was 15-16 years old ...... good stuff ...... Maths rock in any age (means stone age till the computer age ).....
" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5657.0 0.0 0.0 0.0
"“If a matrix takes a vector to zero it’s no way an inverse can bring it back to life.” I  love it😇😇😎😎" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 15592.0 0.0 1.0 0.0
"@MrAnuarsh the infinitesimal length of r (so small it has no length) is the vector coordinates of the infinitesimal length of x, infinitesimal length of y, and infinitesimal length of z" seO7-TwXH_I "Lec 30: Line integrals in space, curl, exactness... | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1680.0 0.0 0.0 0.0
"In order to prove the existence of e, he should have proved ""for some a, M(a) is non-zero"" (or, M(2) is non-zero to take his choice of a) which he never did." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6648.0 0.0 1.0 0.0
"If the integers are infinite in number, then most of them must be big, like really big, so, in the standard proof that square root of 2 is irrational, how can we be so easily sure that we can find and cancel any common factors from p/q to get the ratio into lowest terms?" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 6520.0 0.0 1.0 0.0
"I love and love you. All the best for you sir." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 5727.0 0.0 0.0 0.0
"This teacher made fall in love with linear algebra thankyou ❤️" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 10940.0 0.0 0.0 0.0
"I cannot post. hmmm " _CdoRiNSrqI "Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5230.0 0.0 0.0 0.0
"24:39 Amen, brother!" gXPX29KfEc4 "Lecture 24: Uniform Convergence, the Weierstrass M-Test, and Interchanging Limits" "MIT 18.100A Real Analysis, Fall 2020" 742.0 0.0 0.0 0.0
"I can't understand why A(xp + xn) = 0 are all the possible solution we can have multiple xp how can we show that we can't comeup with an xp which is not xp+xn" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 5226.0 0.0 1.0 0.0
<3 FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1456.0 0.0 0.0 0.0
"The sound level is too low, maybe re-upload with increased volume?" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 10284.0 0.0 0.0 0.0
"What if any Eigen value is repeated??? 
I guess that we still get 
n-orthogonal Eigen vectors. 
The reason:
We can relate it to the algebraic multiplicity and geometric multiplicity of an Eigen value. 🙂" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 11503.0 0.0 1.0 1.0
"Prof Gilbert Strang is a teaching artist." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8264.0 0.0 0.0 0.0
"We can have infinite possible set of Eigen vectors.
But in this problem,  we know from the definitions 
Sigma×u =  A v.
So we have to choose u according to the v chosen.
So in this case that u2 = [0, 1] is not corresponds to v2 chosen. 
The corresponding 
Sigma2 ×u2 =  A v2
==>  u2 = [0, -1]." TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 11316.0 0.0 1.0 0.0
"omg i watched some of the MIT lectures
they all are so simple and dont go deep into stuff. its like school...extremeley easy related to our universities oO" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14137.0 0.0 0.0 0.0
"Thanks a lot for posting these videos!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9657.0 0.0 0.0 0.0
"4:26 norm" Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1319.0 0.0 1.0 0.0
"helped me out a ton, thanks" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13137.0 0.0 0.0 0.0
"The most beautiful part of calculus that I got!" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10193.0 0.0 0.0 0.0
"Thanks MIT!" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9613.0 0.0 0.0 0.0
"Thanks for your presentation. Please in the case we use ordinal logit , should we report pearson correlation and omnibus test value? if it is the case, how to interpret them (for exemple, under or above p value, what it is the meaning). Also shoud we consider the sig level from the table 'Test of model effect' or 'Parameter Estimates' table to say that a relationship between the predictor and outcome variable is significant. I am really looking for ways to interpret, your answer will really help me. thanks." X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 9745.0 0.0 1.0 0.0
"MIT what book do you prefer for this course and thank u very much for uploading it" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 7550.0 0.0 1.0 0.0
"If i had some powers vested in me, I would declare him the greatest teacher of all times." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6503.0 0.0 0.0 0.0
"What is the difference between space and subspace?

The dimension of both row and column space of B =[0 1; 0 0] are same, right? So they are both in the R1 subspace. So the subspace of both row and column space is equal, am I right?  " l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 11523.0 0.0 1.0 0.0
"he is such a great teacher!! thankyou professor strang!!
" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 13100.0 0.0 0.0 0.0
"17:49 I like the word rangle" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 519.0 0.0 0.0 0.0
"I wish I had this prof for Calc...  So much better at explaining what he's doing than the one I had" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6204.0 0.0 0.0 0.0
"Why people laugh on every lecture multi variable Calculus for no good reason. MIT students on drugs or something? " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11905.0 0.0 0.0 0.0
"Mit cant afford dry erase...." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7675.0 1.0 0.0 0.0
"Thanks sir" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9774.0 0.0 0.0 0.0
"Even at old age he is razor sharp. I've seen old lecturers get confused; this man is extremely sharp. Great lecturing and teaching." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 3584.0 0.0 0.0 0.0
"My deam is to enroll in the Institute." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7742.0 0.0 0.0 0.0
"'Differentiability is a miracle when it happens' -- Dr. Casey Rodriguez
' Assume f,g,h,... are all continuously differentiable' -- Me as an engineer" PuRJ9IgUW-M "Lecture 18: Weierstrass's Example of a Continuous and Nowhere Differentiable Function" "MIT 18.100A Real Analysis, Fall 2020" 208.0 0.0 0.0 1.0
"Can anyone explain to me how he wrote the inverses at 21:42" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 3027.0 0.0 1.0 0.0
"Well when go in Bracket in Calculus make sure to stay consent don't come out that the mistake that can mess everything up in Hoptel" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11362.0 0.0 1.0 0.0
"I struggled for the longest time with the discussion around 40:39 about ""how many cases"" there are. I believe what confused me was the instructor (who is excellent) started an approach with conditional probabilities, and then changed back to an approach with counting. (""If you're told that the first two are heads"" sounds like a description of a conditional probability on HH in the first two spots, when we're really conditioned on ""3 H total."") What I _think_ he means is that he's counting every instance in which HH are the first two options. The ""the only uncertainty"" phrase leads you , again, to think he's going to talk about probabilities. However, he seems to mean something more along the lines of ""there are 8 cases where the first two of the three Hs are at the start, namely one case for placing the remaining H in each of the eight remaining positions in the list."" Hope this helps someone!" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 5976.0 0.0 1.0 0.0
"love this course" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 13880.0 0.0 0.0 0.0
"31:40  In the case of A = [2, 6; 6, 7] for example, when setting z = 0, what we actually get is a cross (an 'X' shape) ; when z euqals other values, then we get a hyperbola." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 914.0 0.0 1.0 0.0
"At 14:00 that’s *not* true in general. The number of basis vectors of C(A) is rank(A) *yes* but said basis vectors are not the pivot columns. The professor probably misspoke or something.

Doing rref(A) of a matrix means we’re taking linear combinations of the rows of A, so there’s no reason to believe the column space will be preserved during the row-reduction operations. In general, C(A) is not equal to C(rref(A)).

Let A^T stand for transpose of matrix A. Then the following is always true: *C(A) = C( ( rref(A^T) )^T )* . He’s kind of implied this already in previous lectures without using the rote notation, I’m just connecting the dots like a game.

Edit:

A simple example is A = [1,2; 2,4]. rref(A) = [1,2; 0,0]. The column space of rref(A) is along the “y” axis whereas the column space of A is along the line “y” = 2 ”x”. It should be clear that aside from the zero vector, they have no other vectors in common. Further, rref(A) has one pivot column, so the dimension of A should be 1. 2*[1;2] = [2;4] (columns are linearly dependent, so we really only have *1* vector to scale. Hence, dimension of C(A) = r = 1, as earlier predicted 😊

Hopefully this helps someone. Professor Strang is one of the best educators out there, I see why people admire MIT! This playlist in linear algebra is the perfect way to prepare for the vectorized implementations of machine learning (if you actually wanna understand what you’re doing, that is). Best wishes to you all. 👨🏽‍🏫" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2589.0 0.0 1.0 0.0
ك phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15575.0 0.0 0.0 0.0
Excellent. 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3692.0 0.0 0.0 0.0
"An Indian edition of this book is available only in India
@t" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2415.0 0.0 0.0 0.0
"Thanks! Great lecture :)" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9830.0 0.0 0.0 0.0
"The negative just shows the direction, in this case down." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10201.0 0.0 0.0 0.0
"The invention and development of Google is due to Markov Matrices. The things that we see and use everyday in our lives is built on mathematical theory and concepts." lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 10145.0 0.0 0.0 0.0
"at 19:56 the conclusion  about ""the short curves are nearly straight"" is such a non-rigid statement ... totally disappointing. In stead, the professor should use 1 < ( sin(x)/x ) < 1 to give mathematical proof the limit.  At 28:03, hahaha... how could MIT student not know the basics about arch length on unit circle equals to the angle in radiance? we all learned this in 7th grade when we were about 14 in Asia. At 31:20 the girl raised a good question, since the professor did not prove the limit of ( (1-cos x)/x) ratio in mathematical way, instead he used an intuitive way. I think, from 19:56 to 34:30 is a disaster that can be avoid in MIT class room." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12422.0 0.0 1.0 0.0
"Do not get too excited, he is not wearing a different shirt, he is wearing a coat, you can see the over-loved shirt under it." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 3411.0 0.0 0.0 0.0
"If you invert a tangential eigen value relative to the elliptical transfraction of its angular differential momentum are you going to end up with an algebraic postulate equal to the original eigen value or will it invert the transfraction into a post eigen mutation?

This has always bothered me.

The math, as I'm sure you'll agree, is not elegant - but is, at least, functional. 

Eigen (e)

e~n× t4.046 = a2 + a2r + a3 + a4 ÷ (integer extrapolate) ie 44 × Aa + aA2 (t4 f44)" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 6550.0 0.0 0.0 0.0
"Fantastic lecturer. Thank you Professor Aurox!" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3735.0 0.0 0.0 0.0
"These lectures online never make sense." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10419.0 0.0 0.0 0.0
"i wish i had this kind of professor at my university" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13499.0 0.0 0.0 0.0
"Being accepted to MIT does not grant superior knowledge. This is a freshman course." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 2841.0 0.0 0.0 0.0
"HE NAILED IT 43:18" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4399.0 0.0 0.0 0.0
"DR. Strang, thank you explaining and analyzing Norms. I understand this lecture from start to finish." NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3287.0 0.0 0.0 0.0
"Surprised that MIT prof made so many mistakes in basic algebra." yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 8973.0 0.0 1.0 0.0
"Why did he write f(x0) instead of f(x)" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11812.0 0.0 1.0 0.0
"He doesn't even cares to rub the board properly 😅😅😅😅" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 4476.0 1.0 0.0 0.0
"DAu knows students capacity, & send u to yr home, excellent!!!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3270.0 0.0 0.0 0.0
"This lecture is like opium to me !!❤️❤️❤️" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10805.0 0.0 0.0 0.0
"that moment when you can answer the questions professor Gilbert asks but none of them MIT students can :D :D" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 14638.0 0.0 0.0 0.0
"what would happen as y tends to infinity won't the both slopes be = 0" 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15190.0 0.0 1.0 0.0
"Lecture 1 of calculus he uses Limit, but he doesn't define it anywhere ... was that done in a previous course? otherwise I believe the course is incomplete..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7263.0 0.0 1.0 0.0
24:09 dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 727.0 0.0 0.0 0.0
"Lost me at matrix rotation dot product 🤪😜🙄" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7426.0 0.0 0.0 0.0
"how did you factored that 19:53 diference equation?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13220.0 0.0 1.0 0.0
"Dr. Strang this lecture uses some abstract methods which help me   understand projections onto subspaces much better." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3511.0 0.0 0.0 1.0
"great lecture. i wanted to give a standing ovation when the video finished. lol." IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 12987.0 0.0 0.0 0.0
"how did we get 32 and 18 as squares of sigma1 and sigma2 ?" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 13219.0 0.0 1.0 0.0
"I am from India and we learn this in school, isn't it easy??? IIT is way tougher than this..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5092.0 0.0 0.0 0.0
"83 dislikes from dumb people who hate math. 

410 likes from the future innovators of this world." 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1410.0 0.0 0.0 0.0
"Am I the only one to feel that cameraman is obsessed with zooming in things? That's really annoying - I am more confident in his camera('s resolution w/o zooming) than he is..." WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2336.0 1.0 0.0 0.0
Nice or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7836.0 0.0 0.0 0.0
"It seems that there's more to say by Prof. at the end of the video" 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6982.0 0.0 0.0 0.0
"Great intuition..." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4237.0 0.0 0.0 0.0
"the logicality is unreal" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 14714.0 0.0 0.0 0.0
"I wonder where these students are now." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6251.0 0.0 0.0 0.0
"44:25 ""orthogonal matrices don't change the length of x"" I guess he meant orthonormal. [Gilbert Strang uses orthogonal and orthonormal interchangeably]" HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 1235.0 0.0 1.0 0.0
"Yes! Most charismatic calculus lecturer I've seen on youtube. I'm biologist and enjoy improve my math skills in my free time. Many thanks from Russia. I'm very grateful. ." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12141.0 0.0 0.0 0.0
"Thanks professor." xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9769.0 0.0 0.0 0.0
"My doubt is what were we trying to prove while calculating the cost of operation during elimination. And how EA is costlier than LU?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 7744.0 0.0 1.0 0.0
"Good lecturer, not sure I would want him as a professor. Explain man!" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4140.0 0.0 0.0 0.0
"Around 33:30, how do we know that x=xp+xn gives a complete solution of Bx=b? The way I think of it is that B*xp+B*xn=b+0, so we only get one particular solution that we chose arbitrarily. Can I make linear combinations with the null space basis vectors to obtain all the other solutions or what am I missing? Thanks" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 2554.0 0.0 1.0 0.0
"Respect from China" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8558.0 0.0 0.0 0.0
"Hard to believe that professors getting paid this much are still doing presentations using chalk on a blackboard like something out of the 18th Century. Their lazy asses should be fired, actually." uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 4426.0 1.0 0.0 0.0
"Mi like it already" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7660.0 0.0 0.0 0.0
"That's the end of these lectures. It took 10 months with a text book of the professor which is translated into Korean. I was very lucky to watch these videos with the textbook.  I can't say that I understand all but I am very happy because  I have finished his all 35 lectures. Thanks professor!! Thank MIT!!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9942.0 0.0 0.0 0.0
"@SuperMafioBrother pre-calc is nothing like true true calculus." jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1732.0 0.0 0.0 0.0
"向Mr Strang致敬" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 15618.0 0.0 0.0 0.0
"Are eigen vectors of a symmetric matrix already unit vectors, or we need to normalize them?" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2522.0 0.0 1.0 0.0
"oh ok, that's right, there are not 6 different row swaps but there are 6 different ways to ""reorder the matrix.""  thanks. lande" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14110.0 0.0 1.0 0.0
"I feel like a tired octopus" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5394.0 0.0 0.0 0.0
"Hit Like if you got to know now from where dot product have originated" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4769.0 0.0 0.0 0.0
"11:03 why the column vector is drawn on  x, y plane despite they are coefficients of x?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 363.0 0.0 1.0 0.0
"Congratulations  to everybody who finished this course! You are all great students, and you can be proud of yourselves." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 3198.0 0.0 0.0 0.0
Gorgeous 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4166.0 0.0 0.0 0.0
"love it
" P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 13866.0 0.0 0.0 0.0
"God, I love this guy!!!!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 4099.0 0.0 0.0 0.0
"start vector spaces at 20:18 by taking a deep breath ....." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14393.0 0.0 0.0 0.0
"Lewin and Auroux are especially awesome lecturers !
Thanks for uploading " 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7344.0 0.0 0.0 0.0
"This guy is incredible." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 10537.0 0.0 0.0 0.0
"This is so not physics bro" MlYhHsq_tOU "25. Structure of set addition V: additive energy and Balog-Szemerédi-Gowers theorem" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 10723.0 0.0 0.0 0.0
"Thank you so much for making these lectures publicly available. I enjoy doing math and I don't have the opportunity to properly train in it. I am so far thoroughly enjoying these free lectures." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9362.0 0.0 0.0 0.0
"And how does someone look like Linear Algebra?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2444.0 0.0 0.0 0.0
"Thank you MIT for making this marvel an open courseware !!!" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9145.0 0.0 0.0 0.0
icon 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 13524.0 0.0 0.0 0.0
"I'm 1 year old and I learned that 2 years ago...hehehe! bastards" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6289.0 0.0 0.0 0.0
"I think many of the videos has been updated recently to a better quality though. So the views of the previous video may not show anymore." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 6034.0 0.0 0.0 0.0
"33:24 His sun is apparently ""female"" lol" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 958.0 0.0 0.0 0.0
"Sehr gut professor" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8622.0 0.0 0.0 0.0
"@fatecguaratingueta hehe, muito bom os videos." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1834.0 0.0 0.0 0.0
"grateful to mit" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12962.0 0.0 0.0 0.0
"Never thought calculus could be so beautiful." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7822.0 0.0 0.0 0.0
"At 1:57 ""Died Earlier Too"" : Epic :) ." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2604.0 0.0 0.0 0.0
"There are 10 types of people. Those who understand binary and those who don't ;)" wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 10345.0 0.0 0.0 0.0
"Life is hard." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7348.0 0.0 0.0 0.0
mindblowing MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 13946.0 0.0 0.0 0.0
"I Really Like The Video Flux; normal form of Green's theorem From Your" _CdoRiNSrqI "Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4948.0 0.0 0.0 0.0
"Which book would be suitable with this lecture series??" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11714.0 0.0 1.0 0.0
"In order to understand the A= QR part, my suggestion is to take advantage of the fact that Q^T is equal to the inverse of Q. So, multiply the both sides of the primary equation with the Q^t from the left. You will get Q^t A = R.

In this form, you will see more easily that why the elements of R matrix should be what they are and why R is an upper triangular matrix." 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 6649.0 0.0 0.0 1.0
"Did a crash course on Lin Algebra that purely calculated these. I knew all the steps. But did I really know it? Now i do.. Thank you Gilbert Strang. I endeavour to do ALL your courses that you have available on the internet. What a remarkable world we live in today.." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 3366.0 0.0 0.0 0.0
"49:46 It seemed for a second that the floor was falling Xv." sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1310.0 1.0 0.0 0.0
"pulling an all nighter studying linear algebra and I would have never done that if I hadn't stumbled across his lessons, hands down best teacher I had ever witnessed. I might fail in the exam but these lessons have helped me follow and understand much more than  ever." 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 14230.0 0.0 0.0 0.0
"thank you teacher" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 14521.0 0.0 0.0 0.0
"Thank you for these lecture" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9272.0 0.0 0.0 0.0
"I think you should rename the title as ""MIT 18.01 Single Variable Calculus, Fall 2007 "" not ""MIT 18.01 Single Variable Calculus, Fall 2006"" << thank you mit for these great lectures" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6084.0 0.0 0.0 0.0
Interesting 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6724.0 0.0 0.0 0.0
"very interesting stuff" EBdgFFf54U0 "Lecture 14: Basic Hilbert Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 15024.0 0.0 0.0 0.0
"Great teacher in the world" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 4337.0 0.0 0.0 0.0
"37:17 that's what she said. . ." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1060.0 0.0 0.0 0.0
"https://en.m.wikipedia.org/wiki/Computational_thinking 
https://en.m.wikipedia.org/wiki/Jeannette_Wing" 2K7CvGnebO0 "19. Saddle Points Continued, Maxmin Principle" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13259.0 0.0 0.0 0.0
"Camera man terrible." bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 2999.0 1.0 0.0 0.0
"Thank you professor Gilbert! What you did is incredible, this help take me where I want to be in life!" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 9312.0 0.0 0.0 0.0
"I appreciate how he thoroughly erases the blackboard." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5158.0 1.0 0.0 0.0
"I can understand why MIT is world's best
" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 5202.0 0.0 0.0 0.0
"@hellomate639 in a quite plainly condescending pompous way... That's all." dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 1866.0 0.0 0.0 0.0
"Thank you Prof. Strang
Best wish for you!
Good bless you!
God of 18.06!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9194.0 0.0 0.0 0.0
"11:10  the guy in the first row is eating!! Omg, this doesn't happen in our country" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 364.0 1.0 0.0 0.0
"I don't care about Clinton or some others, the best thing for me is the distance between Dr. Gilbert and me is just 1." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 5297.0 0.0 0.0 0.0
"For 13 minutes (21:00-34:30), Professor Jerison tries to justify (1-cos x)/x goes to zero, without, I think, making the case. While he convinces me that the ""1-cosx gap"" goes to zero faster than the arc length, he doesn't show that it goes to zero fast enough. For example, if it went to zero 10 times faster than the arc length, the limit would approach 1/10, not zero. 

I'm comfortable with his argument about (sinx)/x going to 1 and have in fact used that argument to defend the ""small angle"" approximation in Physics. (Larson 3rd edition, pg. 81 however, gives a rigorous explanation using limiting cases of  triangular areas bounding the section of the circular area swept out by the angle, and then applying the squeeze theorem, (1-cosx)/x is left as an exercise. 

But once you have the limit of (sinx)/x going to 1, just multiply top and bottom of (1-cosx)/x by (1+cos), the numerator becomes (sinx)^2  and the expression becomes: 
[(sinx)/x] [(sinx)/(1+cosx)], first factor goes to 1 and the second to zero. It's good to review properties of limits for this.

Where fault can be found, the good is often ignored. MIT and the professors involved are doing a GREAT public service by constructing these online courses. I'm amazed at the breadth and complexity of the courses offered. I deeply thank all of the MIT people involved in this. The examples and problems done in the class are excellent. I find many of the proofs easier to follow than in some texts. Thanks Professor Jerison!." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3835.0 0.0 1.0 0.0
"Well, this lecture is hard for me to understand, it confuses me. But I'm trying to see the big picture. Here's what I think:
The whole lecture is about how to use iteration methods to solve Ax=b, Ax=λx, Av=σu. Since for large matrix, it will cost a lot if we try to solve things like det(A-λI)=0 or do multiplication A*A.T,  we need to use iteration to solve it fast. And in the lecture, several iteration methods are mentioned: Arnoldi iteration, Lanczos iteration, and QR iteration. But I  do not understand many details in these algorithms, and I think I don't need it now, so I will leave these questions to the future." d32WV1rKoVk "12. Computing Eigenvalues and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11372.0 0.0 0.0 1.0
"You rock Professor Strang!!!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12235.0 0.0 0.0 0.0
"the last example could be solved easier when integrated over dtheta first" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14704.0 0.0 1.0 0.0
"AMAZING Lecturer! Easy steps to follow and talks slow enough to understand. Thank you MIT!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 2181.0 0.0 0.0 0.0
"Shouldn't the small amount of heat required to raise the temperature of water be something like dQ= mcdT, where m=density*volume and c is the specific heat capacity of water?? Why does he just write energy = temp*volume?" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8653.0 0.0 1.0 0.0
"@zamaxx 

MIT has one.  18.01 is the physics 1 videos.  I believe there is also 18.02 and 18.03" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2079.0 0.0 0.0 0.0
"can anybody explain me the logic/proof behind rref algorithm?it completely went over my head lol.." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 12598.0 0.0 1.0 1.0
🤔🇺🇳🗣️🇺🇳🗣️🇺🇳🗣️🇺🇳🗣️🇺🇳🗣️🇺🇳🇺🇳✍️🤳🤔🤳🤔✍️🇺🇳🗣️🇺🇳🗣️🇺🇳🗣️🇺🇳🗣️🇺🇳🗣️🇺🇳🗣️🇺🇳🗣️🇺🇳🗣️🇺🇳🇺🇳🗣️🇺🇳🗣️🇺🇳🗣️🇺🇳🗣️🇺🇳🤔🤔🤔🏋️🏋️🏋️🏋️🇺🇳🗣️🇺🇳🗣️🇺🇳🤔🇺🇳🗣️🇺🇳🏋️🗣️🇺🇳🤔💞💝💞💝💞💝💞💝💞💝💞💝💞💝💞💝💞💝💞💝💞💝💞💝💞💝💞💝💞💝💞💝💞💝💞💔💞💞💝💞💝💞💝💞💝💞💝💞💝💞💝💞💝💞💝💞💝💞💝💞💝💞💝💕💝💞💞💝💞💝💞💝💞🧠💅🙏🤳✍️🍔=🍞🥩🥦🍅🍞 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15743.0 0.0 0.0 0.0
"MIT Opencourseware,

In his explanation on the (1-cos (theta))/(theta) for the long piece (31:25) in answer to the lady's question, does the cos theta value as it goes out further becomes 1, so that (1-1)/theta yields 0 as the answer?" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7509.0 0.0 1.0 0.0
"Finally understood Jacobian :)" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3783.0 0.0 0.0 0.0
"This is magnificiant!! I have no words to express how thankful I am towards the exposure of this video" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 10687.0 0.0 0.0 0.0
"@59:25, what do we mean by confidence and how can one compute it?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 1569.0 0.0 1.0 0.0
"I hope most of you noticed that at 42:21 we were dealing with a ""toilet function"" ;)" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 5587.0 0.0 0.0 0.0
"Thanks from bottom of heart, Prof Strang!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9746.0 0.0 0.0 0.0
"I considered that my abstract vector goes... away." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5247.0 0.0 0.0 0.0
"17:46 He states ""mean is at distance 1/sqrt(n) from the expectation"" but I guess it should be 1/sqrt(n) x sigma: 
edit: I guess it's the same question by SuperChrzascz" phbw9r1iUDI "7. Parametric Hypothesis Testing" "MIT 18.650 Statistics for Applications, Fall 2016" 517.0 0.0 1.0 0.0
"Almost anyone in the comments are those who needed to learn linear algebra but couldn't because of all the horrible lectures out there and then they found this one. What a lovely wonderful course. I'm not even tired a bit. My first ever comment on a youtube video I guess so: Thanks a lot for the amazing lectures." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2319.0 0.0 0.0 0.0
"20:25 a gangsta with brains? :-\" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 650.0 0.0 0.0 0.0
"great lecture as always with very instructive example. Thank you so much" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12980.0 0.0 0.0 0.0
"This man works miracles. 

THANK YOU PROFESSOR GILBERT." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 10880.0 0.0 0.0 0.0
"That beautiful R at https://youtu.be/VPZD_aij8H0?t=2748" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 9877.0 0.0 0.0 0.0
"No, I was talking about numerical mathematics, solving stuff like polynome interpolation, numerical integration, solving ODEs by approximation etc :)" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7899.0 0.0 0.0 0.0
"who's that eager student answering every question for everyone else on every class?" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15271.0 0.0 0.0 0.0
"Thank you professor Gilbert!" cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9311.0 0.0 0.0 0.0
"he teaches excellently! make complicated things easy to understand, that's the magic!" jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 13115.0 0.0 0.0 0.0
"Brilliant lecturer! Thanks a mill" ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 2930.0 0.0 0.0 0.0
"this prof -> the man" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14910.0 0.0 0.0 0.0
"Thank you so much. My video on Eigenvalues 
 https://youtu.be/EZwBkwSVGO4" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 9412.0 0.0 0.0 0.0
22:20 j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 697.0 0.0 0.0 0.0
"@RickRubik At what time index?
" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1708.0 0.0 0.0 0.0
"Thanks Gilbert...love your work. JS" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 9590.0 0.0 0.0 0.0
"Why should we choose only between zero and one for the free variables? Can we not choose any set of variables for these? Is it impossible for these free variables to be any thing else? If I choose 0, and 0 as the free variables, I get [1, 1, -2. 1 ]T as the solution in the case under discussion, and that fits too. However, as suggested, that becomes a combination of these special solutions. Ok. Would it always happen to be this way, irrespective of which free variable I choose? For example, if free variables were to be 1 and 1, it does not fit a solution." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 11908.0 0.0 1.0 0.0
"Nothing special :) Thought MIT is much more difficult." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7945.0 0.0 0.0 0.0
"guys this guy is the best no cap." IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 13027.0 0.0 0.0 0.0
"It is mentioned that ""phi is known positive value"" (Lecture 23: 16.28 min). I am wondering,  if exponential dist. comes under canonical exponential family (or not), where theta = lambda, b(theta) = ln(theta) and phi = -1?" X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 6956.0 0.0 1.0 0.0
"Where is Lec 8" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11679.0 0.0 0.0 0.0
"whats the professors name" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15201.0 0.0 0.0 0.0
"И Луна с Марсом чистим образы." vMaKx9fmJHE "12. Testing Goodness of Fit (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 15553.0 0.0 0.0 0.0
"easy as fk wtf!" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12789.0 0.0 0.0 0.0
"I just can't thank you enough for showing such a clear picture of these concepts. I was struggling to understand 3D Computer Vision and how the linear algebra involved in it. Your lecture series has connected all the points which I have tried very hard enough to understand but I couldn't until I followed your lecture series. You have shown the whole picture by explaining the logic behind each and everything. You are an awesome professor. Thank You so so much. The way you explain is incredible, brilliant." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5598.0 0.0 0.0 1.0
"هو انا الوحيد الي حاسس ان الراجل دا بيفسي ؟" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 15576.0 0.0 0.0 0.0
"It is 3 am, I am hungry and I should have really taken care of washing today but I watched this 12 year old lecture on calculus instead. No regrets though." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6923.0 0.0 0.0 0.0
"My right ear is so educated" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7785.0 0.0 0.0 0.0
"I believe the instructor from Thinkwell teaches Calculus much more better" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5172.0 0.0 0.0 0.0
"funniest lecture ever XD" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12910.0 0.0 0.0 0.0
"Why so few people at the lecture?" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 11910.0 0.0 0.0 0.0
"God bless him and keep him safe! Great teacher." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4079.0 0.0 0.0 0.0
"Brilliant insights about teaching. Expected nothing less from the master, Mr Strang! He gives so fully to his students. It is privilege to watch his teach. Also great interviewer and a good pick of questions. Thank you for the video!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 2927.0 0.0 0.0 0.0
"Definitely perfect final!!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3341.0 0.0 0.0 0.0
"how can i find rank of a matrix ?" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 13198.0 0.0 1.0 0.0
"lol funny I'm just first watching this today and it was posted exactly 7 years ago xD
thanks for the video, really helpful! I was struggling with this concept for my current linear algebra 2 course since I took the non-specialist version of linear algebra 1 which didn't really test us on proofs at all. I think I have a better understanding of the four fundamental subspaces now! :)" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 13825.0 0.0 0.0 0.0
"Just finished the whole Single Variable Calculus course.
Thank you MIT OCW for making this possible.
USA, 3:20am 3/19/2019." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7173.0 0.0 0.0 0.0
"and it all ends in one" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12369.0 0.0 0.0 0.0
"Does the a used in p=ax refer to a being a unit vector?" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3459.0 0.0 1.0 0.0
"Completed today! Thank you Prof. Strang and MIT OCW." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 3186.0 0.0 0.0 0.0
"I want to learn Calculus....not ""VECTORS"".....whatever is given here is the very basic information of vectors....i think every body must have been knowing this.....
 " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6139.0 0.0 0.0 0.0
"I Really Like The Video Divergence theorem. From Your" WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4942.0 0.0 0.0 0.0
"4:12 This is something, I think, that's a little misleading. As far as I understand it (and I can be wrong of course), the eigenvectors are the same vectors. They just have different coordinates since by changing B to A, we switch coordinate systems/bases, but they still have the same direction and length, we are just looking at them from a different angle. Can somebody tell me if I'm wrong about this?" HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 1314.0 0.0 1.0 0.0
"See even before endgame people 'ohhhhhhhh'ed on mobius strip that is beauty of the shape......or maybe they are just nerds who am i to complain" sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8612.0 0.0 0.0 0.0
"what did students do before that man" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 15132.0 0.0 0.0 0.0
"Very good lecture Professor Strang thank you from Amazon Forest." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 11178.0 0.0 0.0 0.0
"Audio channels fixed!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 2735.0 0.0 0.0 0.0
"""What about the solution to Ax=b, what's the story on that one?"" hahahah he's adorable" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 132.0 0.0 1.0 0.0
13:20 VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 410.0 0.0 0.0 0.0
"girlbert is my homie" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 12921.0 0.0 0.0 0.0
"but i am still confused as to where and when at all would we encounter such a situation where we would be required to find eigen values and vectors ?? any domain aor example in mathematics , any example , where we would encounter situations like AX=LAMBDAX  ?? Why at all we had to develop a whole subject of eigen , what was the trigger ??" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 12570.0 0.0 1.0 0.0
"a day after i watched this lecture. the proff in my uni proved induction too. and i can say that this guy ROCKS." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 12281.0 0.0 0.0 0.0
"Thank you, Professor for your sincere intentions. This is the first course that I finished online and this content motivated me a lot to seek more. I believe you directed my path, Sir. Also, Thanks to the whole OCW family!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9515.0 0.0 0.0 0.0
"anyone mind explaining why, when we're trying to prove D  is not regular by contradiction, we can't take 010101 as a string, where the first 01 is x, the second 01 is y and the last 01 is z. We take the y and repeat it as much as needed and we still stay in the language.
why is that not possible? is it because 01 is same as 01010101...." KAySmSEGc9U "3. Regular Pumping Lemma, Conversion of FA to Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 12388.0 0.0 1.0 0.0
"great explanation, see below how you can use SVD to compress images in few lines of python :
https://medium.com/analytics-vidhya/compressing-images-using-linear-algebra-bdac64c5e7ef
https://www.kaggle.com/gauravsharma99/compressing-images-using-linear-algebra" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12971.0 0.0 0.0 0.0
"This man does not stop giving, many thanks." NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10849.0 0.0 0.0 0.0
"The matrix he was talking about was n columns m rows??" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 10185.0 0.0 0.0 0.0
"Anybody knows what the corresponding textbook is? Thank you very much!" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 2478.0 0.0 0.0 0.0
"Am I the only one who laughs at his jokes? Just me? The class attendants seem dead." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 2339.0 0.0 0.0 0.0
"Good to learn from the best matrix professor again!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4158.0 0.0 0.0 0.0
"camera angle !@#$!$, come on!" Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12589.0 1.0 0.0 0.0
"The lecture is incomplete? The lecture did not finish but the video did? WHY!?" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10162.0 0.0 0.0 0.0
"""Now how do I prove that?""
Me: Gilbert bruh, chill not necessary. I trust you with my whole life." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 92.0 0.0 0.0 1.0
"Amazing professor! Sometimes I just watch his 18.06SC from MIT for fun." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 2389.0 0.0 0.0 0.0
"In case 3 where m<n prof wrote min A+b. What does it mean? Is it stating the fact that pseudoinverse matrix does give minimum norm of vector A+b? Another version: it means that distance between A+b and b is minimal." Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6626.0 0.0 1.0 0.0
"i hear he was kermit's voice on sesame street for some time  0.o" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13401.0 0.0 0.0 0.0
https://youtu.be/7Ng4GCvOu24 cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 13286.0 0.0 1.0 0.0
"6:14 where is my yellow chalk? it is in your left hand ;)" PnPIqh7Frlw "Lec 24: Simply connected regions; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1380.0 1.0 0.0 0.0
Wow 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12017.0 0.0 0.0 0.0
"Matrix multiplication used to be so arbitrary to me. After 18.06 it's easy and intuitive." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7622.0 0.0 0.0 0.0
"38:56 Distribution of \hat{B}
54:45 MSE (Quadratic risk) of \hat{B} is the trace of the covariance matrix." JBIz7UadY5M "14. Regression (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 1088.0 0.0 1.0 0.0
"Did this professor ever lift?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3387.0 0.0 0.0 0.0
"Very well explained, and this chapter is quite important for you to understand gradient descent in machine learning. Thanks, professor" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 11232.0 0.0 0.0 0.0
"peek a boO!" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14170.0 0.0 0.0 0.0
"Denis Auroux for president !!!!" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3345.0 0.0 0.0 0.0
"I like this professor so much, listening his course is an amusement." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5692.0 0.0 0.0 0.0
"16:35 how I want to feel after the exam when I screw up" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 482.0 0.0 0.0 0.0
"21:46
""Cheap MIT blackboard loool""" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 684.0 1.0 0.0 0.0
"This has got to be one of the hardest lectures to follow - even the students are baffled. ""Where did that x^(-2n) come from?"", ""oh, well I just decided to perform 3 extra steps in my head without telling you what I was doing.""
Smart fellow, but man, he's jumping all over the place without a lick of explanation." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10571.0 0.0 1.0 1.0
"I don't know why i am crying" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5325.0 0.0 0.0 0.0
"I don't like this guy as much as the other prof, seems to skip some necessary explanation" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5328.0 0.0 0.0 0.0
"Can anyone explain to me why the answer for cost of B is $n^2$ around 40:00?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 3028.0 0.0 1.0 0.0
"I believe at 2:58 he said the angular velocity in radians per second not gradients per second." BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 5167.0 0.0 1.0 0.0
"I wonder if the couple at 15:03 in the second row is still together." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 6245.0 0.0 0.0 0.0
"very good lecture" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 15005.0 0.0 0.0 0.0
"28:55  Seems Accurate hahaha" X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 846.0 0.0 0.0 0.0
"Really clear lecture. Awesome job.
" mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 8508.0 0.0 0.0 0.0
"At my school(FIU) Linear Algebra is taught at the junior level. Its mostly proofs and is incredibly painful. These videos help, but I'm still fighting just to get a B." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2719.0 0.0 0.0 1.0
Agree! 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 2274.0 0.0 0.0 0.0
"perfect freshman course; amazing" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 14175.0 0.0 0.0 0.0
"amazing pedagogy david , thanks" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12351.0 0.0 0.0 0.0
"21th immortal lecture" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 690.0 0.0 0.0 0.0
"ooh am i the first one in 2020 quarantine to reach here ;P" aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14155.0 0.0 0.0 0.0
"i study at ETH and we are 0% allowed to do these geometric proofs so i was kind of shocked to see them" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13464.0 0.0 0.0 0.0
"amazing lecture. Thank you Professor Strang, Thank You MIT!" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 12348.0 0.0 0.0 0.0
"They still use chalk boards?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10443.0 1.0 0.0 0.0
"This vedio saved my life,I can't stand the counter-intuition way of learning anymore,human'thinking ability should be used in exploring way" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10949.0 0.0 0.0 0.0
"Leaving the proof as a cliffhanger, almost worse than Fermat…" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7258.0 0.0 0.0 0.0
"Incorporating MATLAB commands in the lecture  is a great way for students to learn about  matrices and linear algebra in context. The overall lecture  is another classic by DR. Gilbert Strang." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6700.0 0.0 0.0 1.0
"39:58 I don't follow this logic. Why do the number of upward transitions need to match the number of downward transitions? Won't it depend on the values of p_i and q_(i+1)?" ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 1108.0 0.0 1.0 0.0
"I remember I would watch this series of lectures while I was taking both Calculus I and II at my university. I dominated those classes, and I think I owe a big thanks to MIT OCW because I believe these lectures made a significant contribution to my understanding of Calculus. For me, these lectures have become as important and memorable as the real classes I've taken at my university. Thank You! " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5941.0 0.0 0.0 0.0
"the proof at 15:00 is the best geometric proof for sin(theta)/theta -> 1 as theta ->0 that i have seen....the bow thing will help me never forget....thanx" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14731.0 0.0 0.0 1.0
"I didn't watch the first one. I just checked this out real quick to see if I understood any of it." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5281.0 0.0 0.0 0.0
"these lectures are awesome, but as someone who didn't know anything about linear algebra, i DEFINITELY suggest watching these  videos by 3blue1brown instead or first, depending on amount of time avaliable: 

https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

One actually understands what ""matrix multiplication is a composition of linear transformations"" means and why that is really all one needs to know in order to truly understand matrix properties and operations (instead of just memorizing them)." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14777.0 0.0 0.0 1.0
"Thank you very much Prof. Gilbert" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9433.0 0.0 0.0 0.0
"Good Job Professor" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4113.0 0.0 0.0 0.0
"how do we know..?, when we do A*Inverse(A) gives an Identity Matrix before finding  inverse(A)?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13225.0 0.0 1.0 0.0
"Has the book he said he was writing completed ?" MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4435.0 0.0 0.0 0.0
"I find it really helpful to pause and try to proof the theorems before they are worked out in lecture." 9_xG0AGRa-w "Lecture 2: Cantor's Theory of Cardinality (Size)" "MIT 18.100A Real Analysis, Fall 2020" 5414.0 0.0 0.0 1.0
"24:21 unless you are using a brainfuck matrix calculator or some dark forbidden program of the type." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 731.0 0.0 0.0 0.0
"Great Job Professor" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4199.0 0.0 0.0 0.0
"haha soooo true" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13042.0 0.0 0.0 0.0
"Thank you 😊" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 9461.0 0.0 0.0 0.0
"question:
a bit before 10:45 when the student asked the question the prof replied that the same procedure will be followed to calculate the magnitude of the vectors.
But vectors are supposed to have a direction too, so how can you extend the dimensions to more than three (or is it possible?).
Time can be one but that will make things a hell lot complex." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14239.0 0.0 1.0 0.0
"이건... 전설이다. I'm so happy to finish this course although I didn't do any homework stuffs except exams. Prof. Strang will remain as the best professor about linear algebra forever in my heart. Thank you so much. And I specially thank for uploading these series on the web and opening to everybody in the world." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 15686.0 0.0 0.0 0.0
"44:40 - No, it's not making the mean zero that creates the need to use N-1 in the denominator.  That's done because you are estimating population mean via sample mean, and because of that you will underestimate the population variance.  It turns out that N-1 instead of N is an exact correction, but it's not hard to see that you need to do *something* to push your estimate up a bit." Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1239.0 0.0 1.0 0.0
"What are the prerequisites for this course ?" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11469.0 0.0 1.0 0.0
"Nice tie man 👍" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7856.0 0.0 0.0 0.0
"Professor Strang rules!" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8361.0 0.0 0.0 0.0
"epic moving chalkboard
wish my school had a few" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12797.0 1.0 0.0 0.0
"I am finishing my Linear Algebra class right now and am excited to check out further topics and applications. So beautiful how he explains column space and row space" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5089.0 0.0 0.0 0.0
"Surface area heat change occurs so it is d/dx2" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8972.0 0.0 0.0 0.0
excellent IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 12811.0 0.0 0.0 0.0
"at 25:17 when he says (row1)^T * x=0. This is wrong. Row1 is 1xn and x is nx1. Row1*x=0. row1^T is nx1 and you can't multiply a nx1 vector by x another nx1 vector." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12427.0 0.0 1.0 0.0
"I am not able to find the Functions of Two Variables Mathlets. MIT OpenCourseWare KINDLY HELP. Thanks!!" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 5119.0 0.0 0.0 0.0
Outstanding bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8139.0 0.0 0.0 0.0
"I've studied in university for 10 years and I haven't come across a better math lecturer. Best math teacher I've ever come across. He actually teaches but most lecturers just repeat stuff without connecting with students." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6430.0 0.0 0.0 0.0
"This  spans all my Spaces. Thanks to @lexfridman for pointing me in this direction again 30+ years after first taking and passing the course but not understanding anything." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 10454.0 0.0 0.0 0.0
"We can say that we were the first ones watching his great course! :)" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11317.0 0.0 0.0 0.0
"What are the chances that the joint pmf is 4/20 ?" -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 11467.0 0.0 1.0 0.0
"This is brilliant! I can see why MIT is one of the best universities in the world!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 10651.0 0.0 0.0 0.0
"Lecture timeline Links
Lecture 0:0
Method 1: Multiply matrix by vector 0:50
When allowed to multiply matrices 4:38
Method 2: Multiply matrix by COLUMN 6:12
Method 3: Multiply ROW by matrix 10:4
Method 4: Multiply COLUMN by ROW 11:37
Method 5: Block Multiplication 18:25
Inverse Matrices (Square matrices) 21:15
Invertible Matrix 22:0
Singular Matrix (No-inverse matrix) 24:39
Calculate Inverse of Matrix 31:52
Gauss-Jordan Elimination to solve Inverse of a matrix 35:20" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7297.0 0.0 0.0 0.0
"I don't understand the thing about the convergence rate :S ..You take the difference and then what..?" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5347.0 0.0 1.0 0.0
"very interesting thanks" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 15025.0 0.0 0.0 0.0
"Excellent as always and thx MIT." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 3635.0 0.0 0.0 0.0
"If the rank is only one, it can't get away from us." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 6523.0 0.0 0.0 0.0
"How can i just remember every bit of these lectures always? This is education in its true sense, sometimes i feel watching video is a better form of education than personal interaction, if you understand wat i mean" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4813.0 0.0 0.0 0.0
"""He was born earlier.. it was natural idea.. and died earlier too"" xD" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 51.0 0.0 0.0 0.0
"We're ""executing"" a determinant of formula here, ahhh I f-ing love professor, wish that I could attend his class huhu." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 11337.0 0.0 0.0 1.0
"I love you Gilbert" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5846.0 0.0 0.0 0.0
"super liked! worth watching last half to understand vector space clearly than reading hundreds of books.... " JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14418.0 0.0 0.0 0.0
"helps me understand what my teacher is actually talking about, thanks :)
" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13139.0 0.0 0.0 0.0
"@Zanco I agree, it's almost magical :-). Or as he puts it: elegant." Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 1760.0 0.0 0.0 0.0
"I'm taking this course (Linear Algebra) at the nacional university of Rosario, Argentina and this lectures were really helpful. We use Strang's book so this is perfect." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6388.0 0.0 0.0 0.0
"p(a and b) = p(a)*p(b|a).


The probability that both a and b occur, when only one event can occur is:
given that a occurs the probability that BOTH a and b occurs is the probability of a occuring multiplied by the probability that b has also occured given that a has occured.


On the other hand, if it given that B has occured, then the probability that both a and b have occured is the probability that b occured multiplied by the probability and a has also occured given that b has occured." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 14163.0 0.0 0.0 0.0
"43:00 Climax" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1194.0 0.0 0.0 0.0
"The lecture is amazing" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 10160.0 0.0 0.0 0.0
"Hi.  Is U the b in Ax = b?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 4731.0 0.0 1.0 0.0
"Answer of king question is 1/2. There is no ""GB"" option. it is not permutation. if you care about ordering, then you must choose another ""BB"" and ""GG"". ""GG"" is not important actually, but because of another ""BB"", the answer will be 1/2." 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 2463.0 0.0 1.0 0.0
"Hello, where does 8 come from?" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 4667.0 0.0 1.0 0.0
"I wish this guy was my Calc 2 instructor...  I guess in a way he kind is..." wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6230.0 0.0 0.0 0.0
"@huanyanqi Because he explained it well." _CdoRiNSrqI "Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1871.0 0.0 0.0 0.0
"can anyone explain these statements at 11:41 , rows of c are combination of rows of B. as we are multiplying a row of matrix A  by a matrix B to get the row of matrix C. It just i didn't get these statement what it is referring to?." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12601.0 0.0 1.0 0.0
"In what year is this subject taught?" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6694.0 0.0 0.0 0.0
"46:30, 46:45, 49:45" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 1272.0 0.0 0.0 0.0
"I hope that beyond the year 2050 somebody finds a way to upscale this masterpiece of lecture series to 1000K 3D holograms." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 5589.0 0.0 0.0 0.0
31=(34+28)/2 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 920.0 0.0 0.0 0.0
"@Prometheus4096 it seems yo dont ... Students from these course will be Enginers." eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1705.0 0.0 0.0 0.0
32.25 MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 921.0 0.0 0.0 0.0
"sec 2 = 1 + tan 2" CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14284.0 0.0 0.0 0.0
"36:22.
He missed a 2 in the denominator of u^-1/2" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1038.0 0.0 1.0 0.0
"""Automated motion tracking"" bro who u tracking here???" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 32.0 0.0 0.0 0.0
"Can anybody help me to see how is a vector time his transpose a projection? Thank you very much in advance :) 

Btw, amazing courses, you're truly lighting the way, Mr. Strang!" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 3012.0 0.0 1.0 0.0
"Best wishes to you!
祝您健康长寿:)" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 2883.0 0.0 0.0 0.0
"Muhammad ibn Musa al-Khwarizmi is a great scientist 
His name gave rise to the terms algorism and algorithm ." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7723.0 0.0 0.0 0.0
"wow how can this lecture be underestimated? watch his lecture from the beginning not just this part" yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 15415.0 0.0 0.0 0.0
"why is x_0y_0 = 1  ?
middle schooler here, please don't mock..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15349.0 0.0 1.0 0.0
"@Rumproast watch Nat Geo's My Brilliant Brain. There are 3 origins of genius" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1711.0 0.0 0.0 0.0
"So nodes are like some 0 dimensional thing; 
edges are 1 dimensional since they connect nodes;
loops are 2 dimensional since they have area.

I never understood that weird Eular's formula, finally linear algebra shed some lights on it ~" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8784.0 0.0 0.0 1.0
"Thanks, Prof. Strang! Rarely are teachers clear, quick and informative combined. Loved watching this course :3
Bravo!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9842.0 0.0 0.0 0.0
"800th upvote. Very good video!" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 1409.0 0.0 0.0 0.0
"Listening to your voice has been my priority these days." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 7388.0 0.0 0.0 0.0
"How did we arrive at Xpivot=-Fxfree" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 4844.0 0.0 1.0 0.0
"35:24 the moment of truth" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 1010.0 0.0 0.0 0.0
"If you think that you have much to learn. If you don't have much money, but you're capable, you get most of your tuition paid for." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6557.0 0.0 0.0 0.0
"this dude must get paid soooo muchhh" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14803.0 0.0 0.0 0.0
"I guess I don't understand how the last vector set creates a subspace / plane.  Since x, y, and z are utilized in both vectors, wouldn't the subspace essentially be all of R3 with linear combinations being able to extend through that plane infinitely due to z?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 5452.0 0.0 1.0 0.0
"36:15 why if we add semi definite matrix then the eigenvectors will be greater? Why it so obvious? Of course it's true for the largest eigen value, because we can use some maximum  property of first eigen value. Greatest eigen value equals matrix L2 norm - and the norm of matrix is the maximum of norm Ax, i.e. xAx ,so when we add uut we get much more ,is x(A+uut)x >xAx. But why it is true for second and other eigen values?" z3SmljnD_nQ "15. Matrices A(t) Depending on t, Derivative = dA/dt" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1033.0 0.0 1.0 0.0
"Not so illustrated. A lot of notions are not clearly defined" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7930.0 0.0 0.0 1.0
"guys, for the triangle doubt, people are confusing this with fx,y = 1/lx.
its not that, it's the distribution of y and x.
which means 0 <= y <= x <= l.
suppose if both y and x were to only go till l, then it would look like a square with length l. But now since y cannot be greater then x, we remove that upper half of triangle where y was greater than x and hence our triangle comes in the picture. It tells us the possible values of y when x goes from 0 to L. If we want a joint pdf of x and y, it just only depends on x. Here joint pdf = 1/lx . where we just put the value of given x.
Now, we have fx = 1/l and fx,y = 1/lx. We need to find the marginal pdf of y, which is the integration which results to log(l/y) / l  .
Now we have all three of them and can find whatever we want like  expectation and all." CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 13028.0 0.0 1.0 1.0
"Pretentious. MIT you can do better!" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 8245.0 0.0 0.0 0.0
"this lecture really puts together the concepts of pivot ranks, null space and special solutions, and complete solutions to Ax=b. I think we've also covered row reduction to get the augmented identity matrix to find an inverse and transpose." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 14896.0 0.0 0.0 1.0
"now i´m starting to learn something new, this teacher never insinuates that the questions that are posed are stupid or unapropried, this teacher is a good teacher....." BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14092.0 0.0 0.0 0.0
"Damn, I wish I had Gilbert Strang as a professor... oh wait... I wasn't smart enough to get into MIT's engineering program....lol" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3304.0 0.0 0.0 0.0
"This is the best lecturer I have ever witnessed! Everything is so smooth" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10741.0 0.0 0.0 0.0
AWESOME PnPIqh7Frlw "Lec 24: Simply connected regions; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2185.0 0.0 0.0 0.0
"STRANG GANG 2020" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8584.0 0.0 0.0 0.0
"like it" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13791.0 0.0 0.0 0.0
"@brayosaintdead note that the geometric proof is conditioned for theta = curve length in radians. that's why limit of sin(θ)/θ tends to 1 as θ --> 0, for the ratio between the vertical length of the cord (sin θ) and the curve lenght (θ radian) = 1. However for  (1 - cos θ) / θ, where the horizontal distance from origin to the cord is cos θ. The ratio between the gap (radius - cosθ) and curve length (in θ) ---> 0, for the gap is much shorter than the the curve length, and thus goes to zero faster" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1804.0 0.0 1.0 0.0
"39:12 NERDGASM" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1096.0 0.0 0.0 0.0
"Hi, did he say integral of 0 to infinity dx/(x^p) converges when p>1 or is it the other way around?" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4726.0 0.0 1.0 0.0
"wow ! That's Beautiful !!!" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 15409.0 0.0 0.0 0.0
"oh wow i'm 16 and taking Honors physics at my school. We are actually doing all this ( law of cosine, addicing vectors, etc.) for physics problems. I feel quite smart lol" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14115.0 0.0 0.0 0.0
"43:02 ""Fridi"" 
God I love this man." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 1197.0 0.0 0.0 0.0
"so, what is the word?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 14354.0 0.0 0.0 0.0
"Will return after I complete a good chunk of assignments." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 11945.0 0.0 0.0 0.0
"Software Engineer graduated in Electrical Engineering in 2006 - I watch these for fun, seriously :)" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8817.0 0.0 0.0 0.0
"this is the beauty of life, thank you so much Professor Strang and MIT!" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 14878.0 0.0 0.0 0.0
"I can't stop watching these lectures..." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 5222.0 0.0 0.0 0.0
"pls use hd cams mit! me and my friend donated what we cud pls use hd cam!!" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14194.0 1.0 0.0 0.0
"38:06 Professor spitting a fire line haha" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1075.0 0.0 0.0 0.0
"Great Professor!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4209.0 0.0 0.0 0.0
"I prefer to first divide the integration according to the path, then choose the appropriate coordinate system for each path. Thank you." z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5900.0 0.0 0.0 0.0
"what the hell did I just write.. I was just thinking out loud. with my fingers. and now I did it again. that's it I'm going to sleep" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15184.0 0.0 0.0 0.0
"6:12 ""Negative infinite"" should be undefined. Right?" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1377.0 0.0 1.0 0.0
"The students are really stupid. The professor is trying to teach how to setup the limit of the integrals but all the students want to do is to compute it. They keep on suggesting ways to ""simplify"" the computation missing the point that it is not in the least interest of the professor to actually carry out the integration." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10287.0 0.0 0.0 1.0
"Does anybody tell me the material link?" HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 3432.0 0.0 0.0 0.0
"Well, I'm getting puzzled here." z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11364.0 0.0 0.0 0.0
"All these videos are REALLLY REALLY helpful. Thank you so much, MIT!" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 2311.0 0.0 0.0 0.0
"03:15, 3:45" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 289.0 0.0 0.0 0.0
"I hope everyone realizes this is the beginning of calculus. I'am a freshman in high school watching out of pure interest. If your farther ahead of this; move along and don't comment on ""how easy this is""" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5584.0 0.0 0.0 0.0
"One of the best teachers the world has seen" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8095.0 0.0 0.0 0.0
"I'm really thankful to the people going through the trouble of making these subtitles, but in this video the subtitles were so full of errors of all kinds that it was really irritating :( I had to turn them off eventually because they distracted me so much." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 6366.0 0.0 0.0 0.0
"Prerequisite for this course and absolute must for amateurs like me https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8241.0 0.0 0.0 0.0
"Even Professor Tsitsiklis might stuck in the middle of the proof of Poisson distribution PMF...but the proof is perfectly written in his textbook, which is the BEST by far I've ever read in intro level probability and statistics. It took me a long time to fully understand Poisson process...thanks to MIT OCW and Professor Tsitsiklis." jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 3582.0 0.0 0.0 1.0
"@Taowhr yes, his handwriting is mesmerizing. " 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1738.0 0.0 0.0 0.0
"Great Classes..." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 4196.0 0.0 0.0 0.0
"Respected sir,you are the only one who made me fall in love with matrices and liner algebra,Thank you so much for your service ❤️" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8568.0 0.0 0.0 0.0
"A new intro stats series should be recorded either online (COVID baby!) or in person" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 2145.0 1.0 0.0 0.0
"0:00 Human Music" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 300.0 0.0 0.0 0.0
"Or Khan Academy which is a single person that teaches everything...better...for free..." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8133.0 0.0 0.0 0.0
"THANKS, Professor Gilbert and MIT for such a great course and clear illustration of Linear Algebra thanks is not enough though" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 8989.0 0.0 0.0 0.0
"32:45 How come both var(X | Y=1) = 1/12 and var(X| Y=2) = 1/12 
I didn't follow" P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 940.0 0.0 1.0 0.0
"It is lectures from 2005-2006 . Interesting what they thought now ." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6954.0 0.0 0.0 0.0
"Omg Professor, you are awesome,where is the abstract concept when you explain them in reference to reality!" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 8060.0 0.0 0.0 0.0
"  Dear Prof.    I took cal 1, 2 , 3  so many times  in 2 different part of the world, but this is the best  cal class ever in my life time.  please live longer to share your knowledge with us.

 " HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6.0 0.0 0.0 0.0
"THANK YOU MIT" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8980.0 0.0 0.0 0.0
"18.06 + 18.065 + Deep Learning Specialization = Great Combo" Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 523.0 0.0 0.0 0.0
"Why the position of A is changed in the projection (B = b - A(A^T.b)/A^TA ?) ?" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 11920.0 0.0 1.0 0.0
"Omg look at how clean those top boards are 🤩" AeRwohPuUHQ "22. Gradient Descent: Downhill to a Minimum" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8061.0 1.0 0.0 0.0
"I completed the course today. And like everyone, I feel like a different person than who I was 34 lectures before. For me whose weakness is being consistent, I enjoyed the course till the last minute. Thank you Prof Strang for giving me some valuable insights not only about Linear Algebra, but other topics as well (Graph Theory, Complex Numbers, Statistics, and so on). Thank you Prof Strang, and MIT OCW for sharing this treasure with the whole world! 
I can't say I will be missing you because I am all ready to see you in 18.065 :) God bless you Sir!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5241.0 0.0 0.0 0.0
"why do we need to make the eigen vector as small as possible ?" wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15306.0 0.0 1.0 0.0
"Thank you for these lectures, Dr. Strang." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9273.0 0.0 0.0 0.0
"If I had money i will purchase the book but the reality is that I'm umployee for the crisis and right now that I have free time after a long time, I´m trying to learn by myself because i want to renter to the collegue and get a phisycs degree to get a better job in the future, i really apreciate if someone could send me the  book ""multivariable calculus edwards, penney 6 edition"" to my email:   alejandro-hernandezramirez@outlook.es    thank you so much" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6465.0 0.0 0.0 0.0
"Treasure!  A true treasure!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11084.0 0.0 0.0 0.0
"Who knows for sure with deminsions. You do good to dream the Riemann." xaSL8yFgqig "Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11747.0 0.0 0.0 0.0
"He is the best!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4548.0 0.0 0.0 0.0
"thank you so much for sharing this course, I'm living in a country where buying things from other countries like online courses isn't possible due to sanctions. these free courses are the only things that let me learn, thank you again for your awesome website and courses." 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 14514.0 0.0 0.0 0.0
"@wasali31 just a few will understand it... You got the point." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2063.0 0.0 0.0 0.0
"bro helped me beat Zodiark. thanks man" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12559.0 0.0 0.0 0.0
"I am here to leave a like to the legend." xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5105.0 0.0 0.0 0.0
"This just so good to be true, fantastic!!!" H_k1w3cfny8 "10. Continuous Bayes' Rule; Derived Distributions" "6.041 Probabilistic Systems Analysis and Applied Probability" 10779.0 0.0 0.0 0.0
"One of the Best lecture for understanding Conditional Probability and Bayes theorem." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 8086.0 0.0 0.0 0.0
"From 1,012,547 views in the first lecture to 203,355 views in 27th...You belong to 20% who made it this far, Congrats!" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 3924.0 0.0 0.0 0.0
"This same material is covered in my grade 12 vectors and linear algebra course" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10916.0 0.0 0.0 0.0
"I Really Like The Video Cramer's Rule, Inverse Matrix, and Volume From Your" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 4938.0 0.0 0.0 0.0
"Can this procedure be expanded to deal with problems in multiple dimensions? So a, b, c, and d are not scalars but actually vectors themselves, representing the inputs x1, x2, x3 to a function f(x1, x2, x3). How would you form R that way, and would you have different condition numbers for each element of b?" wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3108.0 0.0 1.0 0.0
"The complexity of linear algebra has been reduced by him too." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 10054.0 0.0 0.0 0.0
"in the script i think it should have meant ""secant""? " RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13601.0 0.0 1.0 0.0
"at the start, with x^n, shouldnt it say n in R, not n = 1, 2, 3...? or does the binomial theorem only work for integers? I think it might, right--but then how are calculations like (x^e)' = ex^(e-1) justified? is there an alternate proof not using the binom. theorem, or is there an extension of it to R...?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12477.0 0.0 1.0 0.0
"Wow, I love this guy :D" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 12061.0 0.0 0.0 0.0
"30:30 i guess this should be at the beginning of the lecture
but it was a very nice lecture thank you for ur efforts <3" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 889.0 0.0 0.0 0.0
"I feel like I am in MIT!
. Sadly I 'm not :( " 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5392.0 0.0 0.0 0.0
"I love you Sir with the beautiful way of your learning" 2K7CvGnebO0 "19. Saddle Points Continued, Maxmin Principle" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5847.0 0.0 0.0 0.0
"You experience so many Ahha! moments in the lecture!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12205.0 0.0 0.0 0.0
"Which book does this class use?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11709.0 0.0 0.0 0.0
"Quite possibly the hardest lecture, so far." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 8484.0 0.0 0.0 0.0
"@Apvatar3000 You don't know what you are talking about." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1590.0 0.0 0.0 0.0
"This is not on the divergence theorem.." WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10699.0 0.0 1.0 0.0
"Isn't the proof a little sketchy if we have to differentiate more than once? I thought by definition the lim x-->a (f(x)-f(a))/(x-a) is f'(a)... So f'(a) is forced to exist. Otherwise aren't we arguing that lim x-->a (f(x)-f(a))/(x-a) = f'(a) = lim x-->a f'(x) which needs basically another proof? (Min 19-20) " PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6898.0 0.0 1.0 0.0
"Amazing! I like linear algebra a lot, I already had this class in college, I keep reading about it and ... I didn't even notice the passing of 40 minutes of the first class you! No wonder MIT is a world reference!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 2398.0 0.0 0.0 0.0
"Low D-High Minus High D-Low, all over Low Squared we go!!" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7489.0 0.0 0.0 0.0
"I take the risk of looking stupid. The professor said at 32:10 that density is probability of little intervals. But didn't he defined in the earlier lecture that density is probability of unit intervals? Am I getting anything wrong here?" CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 5989.0 0.0 1.0 0.0
"Fuck math!!! I hope all math burns in hell, its useless and to confusing and complicated I hate it so much!!!!!!!!!" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3941.0 0.0 0.0 0.0
"I survived!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5985.0 0.0 0.0 0.0
"I love how every lecture so far they managed to come up with a new and creative way to record sound. It's cute buy annoying." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5747.0 1.0 0.0 0.0
"Loved this lecture" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7481.0 0.0 0.0 0.0
"this prof is so good at lecturing" Tx7zzD4aeiA "20. Central Limit Theorem" "6.041 Probabilistic Systems Analysis and Applied Probability" 14911.0 0.0 0.0 0.0
"why do we go to lecture??" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15305.0 0.0 0.0 0.0
"What filthy language, can't believe MIT would allow this. 15:34" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11494.0 0.0 0.0 0.0
"i will make donation when i become succesful" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13494.0 0.0 0.0 0.0
magic! rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13895.0 0.0 0.0 0.0
"Couldn't we have used the chain rule?" AdTvkFsqcDc "16. Derivatives of Inverse and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3250.0 0.0 1.0 0.0
"He is much older now, but still incredibly sharp, up-to-date, and deeply on the money 😉, I might add." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4524.0 0.0 0.0 0.0
"41:00, (y=1/x)
Area of the triangle
2(x)(y)=
(substitute the original function (y=1/x) into the area of the triangle equation he arrived at and you get.
2(x)(1/x)=2" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1145.0 0.0 1.0 0.0
"oh I can't stop this class, I watch it all night." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 14101.0 0.0 0.0 0.0
"6:14 A Student has arrived late in the lesson." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 1379.0 0.0 0.0 0.0
"Thank you so much sir, for uploading this playlist on Linear Algebra. I need those concepts for Quantum Mechanics classes." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 9379.0 0.0 0.0 0.0
"25:46 Strang: ""I squared I cubed... I squared I cubed... ""
Me: ""You sure did :DDD""" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 787.0 0.0 0.0 0.0
"Who disliked this?!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 11731.0 0.0 0.0 0.0
"|A(n)|=|A(n-1)|-|A(n-2)|. Does this hold for only tridiagonal matrices??" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 15530.0 0.0 1.0 0.0
"For those confused like me regarding the fishing example:
for part d): The number of fish caught can be found in 2 ways
Consider 3 Random Variables:
F: No. of fish caught
T: Time (The values that time can take)
FishTime: FishingTime (The values that fishing time takes, note that this is different from Time r.v.)

1) E[F] = E[F|0<T<2] * P(0<T<2) + E[F|T>2] * P(T>2)
                (0.6*2)       * 1               + 1              * P(0,2)
 

2) E[F] = E[F|FishTime=2] * P(FishTime = 2) + E[F|FishTime>2] * P(FishTime>2)
                E       * (1-P(0,2))               + 1              * P(0,2)
Here E will not be = lambda * tau
This is because if he fishes for exactly 2 hours it means he will definitely not catch 0 fish.
So we need to calculate the conditional pmf. That is P(catches k fish|catches atleast 1 fish)
Then use this to find the new Expected value by multiplying with k and summing for k = 1, 2....
Then put this for E and calculate.

Gives the same answer." XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 3901.0 0.0 1.0 1.0
"How of any of this used in a real life? Like in as a job?" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 4891.0 0.0 0.0 0.0
"i don't get why c=a-b... seems like that would bring you somewhere in the top left by his previous example" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13364.0 0.0 1.0 0.0
"They make really easy topics bit more complicated" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10441.0 0.0 0.0 0.0
"Would they please stop calling Nesterov's algorithm ``descent''? It's not a descent method as Nesterov himself keeps repeating. Otherwise, a wonderful lecture, and an impressive feat for the lecturer given his age." wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12012.0 0.0 1.0 0.0
"What a legend!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11421.0 0.0 0.0 0.0
"you are not a clear teacher because you not clear any step" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15494.0 0.0 0.0 0.0
"I don't think I've seen a proof for (AB)^T = B^T A^T that he uses in proving A^T A = (A^T A)^T at 40:30 yet in this lecture series, so you'll need to google around. I recommend youtube ID# Uri_d6o5KNs" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5333.0 0.0 1.0 0.0
"the asshole filming this ruined the video...

it makes it really hard to watch when it zooms in zooms out zooms in zooms out. all they had to do was set the frame back far enough and not fucking touch anything." 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14660.0 1.0 0.0 0.0
"The best teacher" 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10008.0 0.0 0.0 0.0
"that tie looks cool tho <3" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 14641.0 0.0 0.0 0.0
"best differential lecture that will ever exist" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12538.0 0.0 0.0 0.0
"Teaching is just a paycheck to this guy." C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 9020.0 0.0 0.0 0.0
"Really helpful, this whole lecture is like a beautiful artwork." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8520.0 0.0 0.0 0.0
"Amazing course, I don't like the way of lecturer's n drawing, it's mixed with m." 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 2358.0 1.0 0.0 0.0
"woow im learning more abt the topics than my actual classes, this prof is da bomb" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15401.0 0.0 0.0 0.0
"15:10 special solutions" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 449.0 0.0 1.0 0.0
"Thank you MIT" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9120.0 0.0 0.0 0.0
"Thank you MIT for making these lectures public!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9143.0 0.0 0.0 0.0
"THANK YOU SO MUCH MIT!!!!! great help for reviews" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8984.0 0.0 0.0 0.0
"This lecture reminds me of a question I've always had. It seems like the operations of lim is not really rigorously defined and proved. For example, in the last example it is assumed that lim(a * b) = lim(a) * lim(b). But if we consider lim operation as a function then this is the same as assuming f(a * b) = f(a) * f(b), which doesn't seem so obvious to me..." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10825.0 0.0 1.0 0.0
"He's got me cornfused all over again." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4634.0 0.0 0.0 0.0
"@greekman234 not if you go into the deep theory. this sucks.
just applying it is a nobrainer tho" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 1859.0 0.0 0.0 1.0
"4:37 
Kirchoff's Laws || Potential, Potential Difference, Currents || An electrical network
5:10
Hydraulic network || Flow of water, Flow of oil || Design for a structure || Bridge || Dome
5:15
INCIDENCE Matrix 
5 Rows are 5 Edges" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1321.0 0.0 0.0 1.0
"Many Thanks Prof." bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7593.0 0.0 0.0 0.0
"linear algebra by gilbert strang >> this same guy" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13799.0 0.0 0.0 0.0
"fair enough it may be a review in some way but in my uni this is all very basic pre-requisites before your even allowed on the course!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12839.0 0.0 0.0 0.0
"Question
23:40 - so you have H2 and to build H4 you did H2(H2)
To get H8 you did H2(H4) but do H4(H2) = H8 as well?
Because I was thinking if you put H4(H4) you would end up with 16 terms and that should be the same as making H4(H2(H2)) since, well, H2(H2) = H4..." Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8475.0 0.0 1.0 0.0
"Thanks but it is not enough" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9676.0 0.0 0.0 0.0
"Is there an audience in the classroom or was this filmed in front of an empty class?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6831.0 1.0 0.0 0.0
"calculus is hard" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12585.0 0.0 0.0 0.0
"Is this what they learn in college in America? ... I learned this last year.. I'm 16 right now. " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6887.0 0.0 0.0 0.0
"@dylanhoggyt I get that, but that doesn't answer my question. What I mean, is that around minute 14:00 he says that the error is vertical instead of orthogonal to the line. I thought we were trying to minimize the error by orthogonal projection. I'm probably mixing things up, but I don't see it." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 1828.0 0.0 1.0 0.0
"lecture 13 is missing ..there has to be technical error" bBESL68iX6s "Lecture 14: Limits of Functions in Terms of Sequences and Continuity" "MIT 18.100A Real Analysis, Fall 2020" 13769.0 0.0 0.0 0.0
https://youtu.be/zK8ysTiHDl8 FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13310.0 0.0 0.0 0.0
"I'm no expert but around 15:30 
The prof. depicts the parallelogram in the UV plane ,but in reality the the sides are still on the axes in the UV plane because the axes them selves are sheared. But when we look at it from the vantage point of the XY plane ,they take the form such parallelogram." UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6350.0 0.0 1.0 0.0
"Despite knowing what he meant, all that talk about doing stuff ""in space"" made me chuckle not just once." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3358.0 0.0 0.0 0.0
"""always expect the unexpected"" 😅 This prof rocks!!!" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 144.0 0.0 0.0 0.0
"perfect teacher and professor!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 14176.0 0.0 0.0 0.0
"great course , thank you MIT!" XtNXQJkgkhI "22. Bayesian Statistical Inference II" "6.041 Probabilistic Systems Analysis and Applied Probability" 12969.0 0.0 0.0 0.0
"nah i honestley finished at 31:31. i hope im wroong but if you start with y in a expo in the first quadrant then you are looking for trouble. there is no y obviously. but i will look on and be proven that he is searching and will find me short falling" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14011.0 0.0 1.0 0.0
"Thank you Sir.
I was curious to know where you are from.Does anybody know?" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 9239.0 0.0 0.0 0.0
"@MikeDunn The names aren't fancy, they're explanatory. Single variable calculus is just what the name says it is, calculus involving only one variable. I'm sure you can figure out the other one. Calc 1 or calc 2 don't tell you what the subject is actually about." aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1679.0 0.0 0.0 0.0
"You just said something exactly as he stated it.  I know exactly what he did.  My whole point is that the logic of solving each limit independently is flawed." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12218.0 0.0 1.0 0.0
"the bit about 80 - 5t^2 is incorrect
the number 5 is not exactly right.
The gravitational acceleration is actually equal to 9.81 meters per second per second.
(or depending where on earth you are it might be 9,80 but never 10)" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14670.0 0.0 1.0 0.0
"This is just beautiful." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 10683.0 0.0 0.0 0.0
"At 7:24 he changed Ax=0 to ux=0, why?
Previously in lecture 4, he taught EA = u. Confused here, please enlighten." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 2697.0 0.0 1.0 0.0
"students who think changing the extension of word doc from .doc to .pdf = pdf conversion 😂." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 14406.0 0.0 0.0 0.0
"I did not understand the last step replacing dA by dxdy. The proof contained slanted plane with an angle alpha to only one axis and not a general slant in both directions. Does this proof apply when we are considering a general slant to both x and y ? Will dA=dS Cos theta still be applicable?" WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5261.0 0.0 1.0 0.0
"cosin of the angle = dot product of vectors divided by the product of the lengths

dot prouct is a1b1+ a2b2 + a3b3
product of lengths is sqrt(a1^2 + a2^3 + a3^3) times sqrt(b1^2 + b2^3 + b3^3)" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12682.0 0.0 0.0 1.0
"the education is, it's almost the same everywhere, but you can not overrate the students and the teacher, something you will understand if you look at achievement comparison between universities " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14685.0 0.0 0.0 0.0
" thanks thanks thanks thans thanks thanks thanks thanks thans thanks thanks thanks thanks thans thanks thanks thanks thanks thans thanks thanks thanks thanks thans thanks thanks thanks thanks thans thanks thanks thanks thanks thans thanks thanks thanks thanks thans thanks alot" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12.0 0.0 0.0 0.0
"This deserves to be in the Guinness book of records as the best introduction to determinants 🙏🙏🙏🙏" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 10497.0 0.0 0.0 0.0
"2:44 hmm what was he trying to draw?!?!" jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 869.0 0.0 0.0 0.0
Dream 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3519.0 0.0 0.0 0.0
"i hope that I be a student in this university...." U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13403.0 0.0 0.0 0.0
"that chalkboard is so clean..." xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14627.0 1.0 0.0 0.0
"@IIAOPSW Actually it is. Watt is energy/time, Watt hour is W.h (not W/h or Watts per hour), so it is equal to energy/time x time, which is equal to energy. For eg. a 100W light bulb which is ON for 1 hour uses 100W.H of energy.

And yes, metric rules!" jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1636.0 0.0 1.0 0.0
"Thank you, professor Srang
Thank you MIT" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9522.0 0.0 0.0 0.0
"change the order of integration.  upon doing this you should get limits on outer integral: lower=0, upper=3; limits on inner integral: lower=0, upper=y/3 where the integral is e^(y^2)dxdy.  now you get xe^(y^2) and evaluate that from 0 to y/3 to get y/3e^(y^2)dy.  Now use substitution u=y^2
du=2ydy du/2=ydy which gives 1/6e^u for the integrand, limits being 0 and 9, and when evaluated gives 1/6(e^9-1)" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12650.0 0.0 1.0 1.0
"39:56 It looks like that the professor Strang is teaching during corona" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 1107.0 0.0 0.0 0.0
"lol ""what function has that derivative!  okay.  it's a freshman course"" 

love this guy" lZrIPRnoGQQ "27. Backpropagation: Find Partial Derivatives" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13819.0 0.0 0.0 0.0
"17:44 

What he called ""geometric interpretation"" was actually the definition of a dot product and what he called definition actually follows from it. 

Am I correct? Correct me if I am wrong.

Edit: In short I want to know which definition is the fundamental definition." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 515.0 0.0 1.0 0.0
"The real problem for Physicists is Truth in Labelling. Putting individual's possessive names over the top of self-defining informational identification instead of behind it in the Bibliography,  ..no one knows what the reality of Actuality is." uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 10270.0 0.0 0.0 0.0
"Note: Videos of Lectures 28 and 29 are not available because those were in-class lab sessions that were not recorded." lZrIPRnoGQQ "27. Backpropagation: Find Partial Derivatives" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7937.0 1.0 0.0 0.0
"Shockingly bad pedagogy on so many levels." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8640.0 0.0 0.0 0.0
"This stuff is awesome !!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10929.0 0.0 0.0 0.0
"MIT really has the best professors 😃" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7540.0 0.0 0.0 0.0
"That is bs proofs of the sinx/x geometrical proofs aren't that good. What you should do is the use maclaurins theorem and make sin(x) into a polynomial function. Which in zero acctually equals sinx. Then it's real easy to see that sinx/x is equal to 1" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9896.0 0.0 1.0 1.0
"Why does he say his definition is ambiguous? In what ways does defining a function as some subset of AxB make the definition less ambiguous?" 9_xG0AGRa-w "Lecture 2: Cantor's Theory of Cardinality (Size)" "MIT 18.100A Real Analysis, Fall 2020" 11840.0 0.0 1.0 0.0
"BIG DEAL if you do it in high school, in the 6th grade or in grad school, freshman year, etc, BIG DEAL-A hundred years from now, you will all be DEAD as a rotting corpse. So who cares if you learned it sooner or later. A hundred years from now, you will be NOTHING!!!!" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2803.0 0.0 0.0 0.0
"With soo much attention this cameraman must have become engineer" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11969.0 1.0 0.0 0.0
"Prof: ""you are easily amused"" hahahahaha @35:47" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8319.0 0.0 0.0 0.0
"I start learning ordinary differential equation and Laplace transforms and I found the method of teaching was decent and clear( better than many uni professor)" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 5969.0 0.0 0.0 0.0
"is it common in physics to use angle bracket to denote vectors instead of standard matrix form?  how to differentiate a row vector from a column vector, or it doesn't matter, we just  assume the dot product is the product of two or multiple vectors with the same length yet orthogonal orientation?" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13635.0 0.0 1.0 0.0
"What would any if this be used for?" cqdUuREzGuo "Lecture 8: Lebesgue Measurable Subsets and Measure" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 11569.0 0.0 0.0 0.0
"8:26 Another good question is ""Could we have integrated from 0 to pi instead?""" BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1419.0 0.0 1.0 0.0
"Spectacularly potriated" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 8866.0 0.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8431.0 0.0 0.0 0.0
"Like that he starts with eigenvectors and their intuition" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 7361.0 0.0 0.0 1.0
"Wish I was there!(not)" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 11956.0 0.0 0.0 0.0
"A fantastic teacher and person! Thank you!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 2111.0 0.0 0.0 0.0
"28:55 LOL momlevel explanation" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 847.0 0.0 0.0 0.0
"Man this is the definition of LECTURE.....❤️❤️" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7577.0 0.0 0.0 0.0
"Peter Thiel on the Global Economy, the State of Our Technology, and Artificial Intelligence


44:46 independant non politician" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 8186.0 0.0 0.0 0.0
"What’s up with all coughing?" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11599.0 0.0 0.0 0.0
"Finally I watched the whole. Thanks MIT for all of its great lectures!" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3762.0 0.0 0.0 0.0
"What courses would be beneficial for applied economics and econometrics students? Thanks in advance!" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 11477.0 0.0 0.0 0.0
"I love blackboards, i dont know why i had to study in those white-shiny-boards :S" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5729.0 1.0 0.0 0.0
"Everything so simply explained.  thank you" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 3617.0 0.0 0.0 0.0
"Someone save me back I didn't use stop loss I didn't see it coming" cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 8841.0 0.0 0.0 0.0
"I love how the first lecture had 2+ million views and every other lecture after decreased just like in real life" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5753.0 0.0 0.0 0.0
"Not only is he going faster than what the syllabus calls for, but he managed to do that without loosing me. Dr. Strang is very good at what he does." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 7929.0 0.0 0.0 0.0
"I was kinda hoping that Prof. Strang started this lecture with his comment on ""Does DL usually work?"" from last lecture... Was that part edited out?" cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6156.0 0.0 0.0 0.0
"It is good lecture. But, about the example you used about kissing does not fit many, especially non west cultures. In some cultures and religions such things are not acceptable." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 6945.0 0.0 0.0 0.0
"this guy's chill i like him" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14844.0 0.0 0.0 0.0
"Proff i will hug you whenever i will meet you.." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8411.0 0.0 0.0 0.0
"He lost me at the inverse functions.  Is the purpose that it gives us a way to rewrite the function to make implicit differentiation easier?" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4574.0 0.0 0.0 0.0
"At 28:00 what is the intuition behind shape of the bowl and large/small eigenvalues? He made it sound like a quite obvious statement. 

Also at 36:50, given that S and Q-1SQ are similar implies they have same eigen values. However, how do you show S and Q-1SQ are similar? 
OK I figured out the 36:50 part. It is the spectral theorem which sir had covered in previous class. S = Q (lambda) Q-1. 
Lambda = Q-1 S Q. As, lambda is defined as the matrix of eigen values of S, this implies that S and Q-1 S Q are similar. 

Please explain the part at 28:00 . Thanks!" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2631.0 0.0 1.0 1.0
"yes!! its adamn shame because many of the other ocw lectures have excellent camera work. this guy is maybe the best professor ive seen, but the zoom-tastic camera work makes following along much more difficult!" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15484.0 1.0 0.0 0.0
"Do you think he purposefully stopped erasing boards while they were coming down simultaneously so that the students wouldn't cheer? Because throughout the lecture series it seemed to progressively happen less and less which makes me sad." tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3425.0 1.0 0.0 0.0
"I am not in MIT, lol. I'm a second year biochem student in the UK teaching myself maths for fun. I am trying to watch all the lectures for this, and understand them. The problems you can find online however are a bit beyond me!" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5124.0 0.0 0.0 0.0
"Now 549,213 people had attended your lecture, Mr.Strang" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 7947.0 0.0 0.0 0.0
"Oh he is a magician, hope our every faculty would be like him" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8007.0 0.0 0.0 0.0
"Why is the rank of matrix same as its transpose?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 11889.0 0.0 1.0 0.0
"Almost 40 years ago I had this kind of math but they didn’t serve us for 90 hours like here what they serve students for an hour.
Enjoyment. Professors are great." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2317.0 0.0 0.0 0.0
"@ViciousPancakesr1337 Not really." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1751.0 0.0 0.0 0.0
"Why is he using recursion but not a transition matrix, is it because recursion is a more general notation?" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 11873.0 0.0 1.0 0.0
"24:56 how did he figure out what the numerator had to be at 25:17? I am sure this is some simple algebra, but it's been a while :)" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 758.0 0.0 1.0 0.0
31:20 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 908.0 0.0 0.0 0.0
"Thank you MIT!!!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9153.0 0.0 0.0 0.0
"0:54 Outline
2:36 Random Variable
24:53 Expectation
43:00 Variance" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 310.0 0.0 0.0 0.0
"I'm confused. I think the euler's formula was V - E +F = 2 not 1." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6313.0 0.0 1.0 0.0
"The 2 players could be called Xavier and Yasmin, so X is for Xavier and Y is for Yasmin :-)" feb9j65Iz4w "24. Linear Programming and Two-Person Games" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9955.0 0.0 0.0 0.0
"watching it with speed - 2X option is highly recommended! :D" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 15068.0 0.0 0.0 0.0
"Watching this lecture is a treat. Thank you so much Prof. Jerison and MIT!" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11304.0 0.0 0.0 0.0
"Thank you for this video" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9285.0 0.0 0.0 0.0
"Excellent lecture, but his ""proof"" of the dot product interpretation from the cosine rule was a bit of a circular argument, ie. dot product if and only if cosine rule. I would say a better approach would be to DEFINE dot product as A.B = |A||B| cos (theta) and then DERIVE A.B = a1b1 + a2b2 + a3b3 from this, which can be done algebraically without reference to the cosine rule. Otherwise, good stuff; he seems a good teacher." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3654.0 0.0 1.0 1.0
"This professor is an artist and I can't understand why some people disliked this video. Thank you from Brazil :)" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10900.0 0.0 0.0 0.0
"40:09 zeros sum games: No lawyers involed :)" feb9j65Iz4w "24. Linear Programming and Two-Person Games" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1125.0 0.0 0.0 0.0
"This guy really is a good teacher." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 10558.0 0.0 0.0 0.0
"That cos 4 theta integral is very simple with reduction formulae. :) 
2/3* ( 3/4 * 1/2 * pi/2 ) = pi/8." YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9880.0 0.0 0.0 0.0
"Amazing! 
Thanks MIT" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2396.0 0.0 0.0 0.0
"Professor Strang is a god among mere mortals." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 8347.0 0.0 0.0 0.0
"For Check-in 21.2, how comes D rejects <D>1000000 on Step 1?

On input w, mark off f(n) tape cells where n = |<D>1000000|. Then what happens?" vqFRAWeEcUs "21. Hierarchy Theorems" "MIT 18.404J Theory of Computation, Fall 2020" 3839.0 0.0 1.0 0.0
"This 12th lecture is really confusing me." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10455.0 0.0 0.0 0.0
"maybe MIT students are too smart to focus on the algebra detail on matrices operations, but that was some fk up algebra work." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13926.0 0.0 1.0 0.0
"The lecture on Complex  Matrices and Fast Fourier Transform are excellent. DR. Strang also explained these two subjects in  Computational Science and Engineering I and  II at MIT." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 10165.0 0.0 0.0 0.0
"LONG LIVE PROFESSOR STRANG!!!!!" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7241.0 0.0 0.0 0.0
"OMG
I was dreaming about this course
Thank you Great Professor Gilbert Strang <3" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7978.0 0.0 0.0 0.0
"Seriously, the details of little things shape the masterpiece, Prof. Strang Rocks!!!!!!" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 8631.0 0.0 0.0 0.0
"I guess the girl at 50:06 going towards the blackboard is the one who finds the error which Professor talks about in the next lecture." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 5455.0 1.0 0.0 0.0
"Thank you professor Gilbert! You are amazing! you can make math really fun!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9313.0 0.0 0.0 0.0
"I Really Like The Video From Your Parametric equations, arclength, surface area" TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4965.0 0.0 0.0 0.0
"Fuck vectors..people need to teach stuff that is related to real life not some made up fake bs" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3944.0 0.0 0.0 0.0
"I created an interactive table that reproduces the simple example described in this lecture! https://dl.dropboxusercontent.com/u/2642357/markov.html" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 5253.0 0.0 0.0 0.0
"The best❤
Love From Pakistan🇵🇰" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 10015.0 0.0 0.0 0.0
"Come on the accent got killed me" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3167.0 0.0 0.0 0.0
"RECIPROCAL  IN
MIXED OPERATION
PROBLEM TO SOLVE 
WITH  WHAT  IS 
TRUE?, WORLD  NEED  TO KNOW 
ISN'T IT." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8486.0 0.0 0.0 0.0
"This was so enlightening!" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 10974.0 0.0 0.0 0.0
"i notice the 25 dislike are they genius or average people?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13447.0 0.0 0.0 0.0
"Awesome..Massive respect" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2791.0 0.0 0.0 0.0
"He's creating a ratio of a complete circle. Kind of like saying 90/360 = 1/4. Another way to get his equation is to integrate the equation for arc length:

Arc = rθ
∫Arc = Arc area = ∫rθ dθ = 1/2 r^2 θ" BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4633.0 0.0 0.0 1.0
"Great lecture. Thanks for uploading." WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4296.0 0.0 0.0 0.0
"god please name lectures by the topics!!!!" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 12933.0 0.0 0.0 0.0
"Can anyone here care to explain how in the example in one dimension, when choosing a scalar outside R it grants that the stochastic gradient and the full gradient has the same sign? (corresponding to 30:30 - 31:00 ish in the video) Thanks in advance!" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3038.0 0.0 1.0 0.0
"I'm afraid this video doesn't seem to provide any proof of the significant theorem on the blackboard which insists:
========================
=
  N((A*)A)=N(A), i.e., the nullspace of (A*)A is identical to that of A, 
where A* denotes the transpose matrix of A. 
(For convenience, let * substitute for the conventional superscript T meaning ""transpose"".)
  ========================
I'd prove it my way, at least for all real number matrices A and real number input vectors, like this:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Proof.   Let A be a m-by-n real number matrix.  And then, for any input vector x in R^n
  Ax=0　⇒  ((A*)A)x = (A*)(Ax) =0,
so that if x is in the nullspace of A, then it is also in the nullspace of (A*)A, that is,
  N((A*)A)⊇N(A) ...(1).

On the other hand, let
  a[1], ..., a[n]
 be the column vectors of A.   In other words, let
  a*[1], ..., a*[n] 
be the row vectors of A*.   And then, for any input vector x in R^n, for each of i=1, ..., n, the i-th component of the product vector
  ((A*)A)x=(A*)(Ax)
is the dot product a*[i](Ax).   Therefore, ((A*)A)x=0 implies that for each of i=1, ..., n
  a*[i](Ax)=0,
so that Ax is perpendicular to any linear combination of the column vectors a[1], ..., a[n], i.e., to every vector in the column space C(A) of A.   However, as a linear combination of column vectors
  a[1], ..., a[n],
Ax is also in the column space C(A), which combined with the previous statement means that Ax is in C(A) and at the same time orthogonal to C(A).  This is possible if and only if Ax=0, because otherwise Ax is not perpendicular to itself (see note at the bottom for another reason).   

Thus, after all it has been found that, for any input vector x in R^n
  ((A*)A)x=0 ⇒ Ax=0, 
so that if x is in the nullspace of (A*)A, then it is also in the nullspace of A, that is,
  N((A*)A)⊆N(A) ...(2).

(1) and (2) combined, implication is that N((A*)A)=N(A).　QED.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

(Note):  If C(A) = {0}, then trivially Ax in C(A) is the zero vector.   Otherwise, by the so-called Gram-Schmidt orthonormalization, an orthonormal basis can be chosen for the column space C(A) such that all the basis vectors are normalized and mutually orthogonal.  Then, the vector Ax in C(A) may be expressed as a linear combination of those basis vectors, namely
  Ax = s[1]n[1]+ ... + s[r]n[r],
where
  n[1], ..., n[r]
are the orthonormal basis vectors, 
  s[1], ..., s[r]
are real numbers, and
  r=rank(A). 
However, since being orthogonal to C(A), Ax is perpendicular to each of the basis vectors.  Thus, for each of k=1, ..., r
  0 = n*[k](Ax)
    = n*[k](s[1]n[1] + ... + s[r]n[r])
    = s[1](n*[k]n[1]) + ... + s[k](n*[k]n[k]) + ... + s[r](n*[k]n[r])
    = s[k], 
implying that Ax = 0.  QED.

Thanks.   Was I correct?   Are there any simpler proofs?" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6304.0 0.0 1.0 0.0
"My right ear enjoyed this" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 7784.0 0.0 0.0 0.0
"damn it , i spent time in just two lecs for a week ,  because English is not my mother tongue" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12711.0 0.0 0.0 0.0
"He is so warm and enthusiastic." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4540.0 0.0 0.0 0.0
"23:13 HI MOM I'M ON TV" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 710.0 0.0 0.0 0.0
"Gauss thought of it before we did, only because  he was born earlier... and died earlier too.. :D" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3985.0 0.0 0.0 0.0
"stop panning the camera! stay on the balckboard" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14400.0 1.0 0.0 0.0
"What you call ""old school"" teaching, when teachers actually cared about their students and worked hard at the black board, instead of just ripping through a bunch of slides at warp speed. It is sad that students these days have to pay such ridiculous sums of money for that nonsense when you can get a gem of a man like this here." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11571.0 1.0 0.0 0.0
"@BarbierNicholas you have interesting idea. But your x never goes to zero. If we take y=sin(x) and (y/x)=1, well we'll get a graph of y=x which is a diagonal line of 45 degree; not x-->0. " kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1600.0 0.0 1.0 0.0
"An 'Indian summer' is used in the UK to describe a summer that lasts later than usual." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2413.0 0.0 0.0 0.0
"my mind was blown at 30:00" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 13993.0 0.0 0.0 0.0
Thanks! eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9823.0 0.0 0.0 0.0
"20:30 I guess it should be mentioned that X is uniformly distributed." l4NoMKEHQwM "11. Derived Distributions (ctd.); Covariance" "6.041 Probabilistic Systems Analysis and Applied Probability" 656.0 0.0 0.0 0.0
"what is the textbook this course is using?" 9_xG0AGRa-w "Lecture 2: Cantor's Theory of Cardinality (Size)" "MIT 18.100A Real Analysis, Fall 2020" 15174.0 0.0 0.0 0.0
"i like how clear his answers are !!! " 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13417.0 0.0 0.0 0.0
"Hard to appreciate how well presented this is in first go around. The more one learns LA the more one appreciates this style of presentation." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4425.0 0.0 0.0 0.0
"I don't understand even a tad concerning complex math.  But I did find out that any high school dropout, such as myself, can independently discover the Einstein's Special Relativity(SR) phenomena, and also derive the SR mathematical equations at the same time. Google "" KSP Special Relativity "" to see just how easy it is." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5339.0 0.0 0.0 0.0
"14:40 
or you can just prove that 1^2+2^2+...+n^2=(n(n+1)(2n+1))/6 not so hard" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 433.0 0.0 0.0 0.0
"such a great professor, Salute you" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 14414.0 0.0 0.0 0.0
"""*executing*""" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 16.0 0.0 0.0 0.0
"feels like too many things a squished into one lecture" EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 12854.0 0.0 0.0 0.0
"gilbert strang makes linear algebra fucking simple" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 12919.0 0.0 0.0 0.0
"""In a previous life"" lmaooo #mathGoneSpiritual" -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 71.0 0.0 0.0 0.0
"Wonderful 
👌" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11982.0 0.0 0.0 0.0
"I have visited here on date 16 August 2020" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 5568.0 0.0 0.0 0.0
"The eigenvector u_2 related problem in Example 1 is about the scaling factor. 

Dr. Strang said that all the scaling factors should be larger than 0.
But if you set u_2 as [0;1], like in this lecture, sign decision issue arises.

Av_2 = [ 4 4 ; -3 3 ] [ 1/sqrt(2) ; -1/sqrt(2)]  = [ 0 ; - sqrt(18) ] = - sqrt(18) [ 0 ; 1 ]
Incorrect -> sigma can't be negative sign

if we change sigma_2 to have positive sign,
Av_2 = [ 4 4 ; -3 3 ] [ 1/sqrt(2) ; -1/sqrt(2)]  = [ 0 ; - sqrt(18) ] = sqrt(18) [ 0 ; -1 ]
Correct! and obviously, u_2 we've got is [ 0 ; -1 ]" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 10085.0 0.0 1.0 0.0
"Amazingly good explained. Nice video. Like." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2410.0 0.0 0.0 0.0
"This is the 3rd time I am taking these lectures in the last 2 years. Thank you, professor, these lectures are amazing." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 10730.0 0.0 0.0 0.0
"the formula that he starts with, where do we know it from???" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 14694.0 0.0 1.0 0.0
"45:17 㠪 ;)" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 1252.0 0.0 0.0 0.0
"Happy Halloweens guys, from 2022 with love :D still very very very useful for a struggling student like me." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 4421.0 0.0 0.0 0.0
"Watched this at 1.5 speed and it was amazing. We are so privileged to be able to watch MIT classes! Thank you so much MIT.  Very helpful class." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11287.0 0.0 0.0 0.0
"Gilbert Strang and Barton Zwiebach are the two MIT professors who literally paved my way into Theoretical Physics" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4014.0 0.0 0.0 0.0
2022 Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 631.0 0.0 0.0 0.0
"Why is a transpose (b-xa) =0 and not a times b-xa" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 11867.0 0.0 1.0 0.0
"the limit of the log is the log of the lim" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14713.0 0.0 1.0 0.0
"That is by far the best explanations on dot product in YouTube!
By the way, have you heard of the new type of (discrete) derivativative from 2010?  You should try and search it on YouTube:  ""Eureka! a new approach to calculus"".  This video depicts a simple kind of derivative." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9897.0 0.0 0.0 0.0
"Why take angle as function instead of time?🤯" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11914.0 0.0 1.0 0.0
"the first 30 mins were ;/ ;/
and the next 20 mins were :)" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14690.0 0.0 0.0 0.0
"@35:25 top 10 anime comebacks" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1543.0 0.0 0.0 0.0
"I don't understand, when rolling 2 dice, the number 7 is the most likely to happen? The students agreed as well as the prof. agreed to that! I though all numbers have the same probability, of course considering the dice to be balanced, no cheating. I feel stupid! 30:50" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 5356.0 0.0 1.0 0.0
"I understand this more than discrete mathematics" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6122.0 0.0 0.0 0.0
Splendid. TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 8872.0 0.0 0.0 0.0
"this is such an awesome lecture, especially after I notice that Processor Strang was doing a re-recording without any audience" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14877.0 1.0 0.0 0.0
"Thank you for these lectures. I took Stage 2 Linear Algebra in 1980. These lectures make it sound simpler. I think Gilbert Strang is the Richard Feynman of linear algebra." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9274.0 0.0 0.0 0.0
"who the hell can put the deslike button in this ? 
its a free lecture, you become sick and you can find what you lost here!! 
thank you MIT!" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15268.0 0.0 0.0 0.0
"Are you kidding me?? As an engineering student that i am in spain, i consider this class an insult to our intelligence... how can america still have the greatest former engineers or economists with this education?? This won´t last very long though..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2541.0 0.0 0.0 0.0
"Dr. Gilbert Strang is really a master!" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 3499.0 0.0 0.0 0.0
"Welcome to the world of Spam^^" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 11343.0 0.0 0.0 0.0
"24:00 this answer can be simplified to y' = -y/(2x+4y^2)" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 725.0 0.0 1.0 0.0
"Damn this guy is amazing D: he explains really good." RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3298.0 0.0 0.0 0.0
"a great prof..   abstract maths can so easily taught .... Its amazing...... Great ..... hats off to u 
U should come up with simillar lect in analysis" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 12283.0 0.0 0.0 0.0
"david jerison is THE shit" TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12727.0 0.0 0.0 0.0
"Thanh you Professor and MIT OCW" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9040.0 0.0 0.0 0.0
"Great Professor but.. he still has not mastered the dotted lines like Walter Lewin has haha" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4208.0 0.0 0.0 0.0
"@Bluebox91 That's what I originally thought, but he is actually from France." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1602.0 0.0 0.0 0.0
"thank you so much MIT! this is amazing aid for students around the world struggling with their courses, or wanting to study the multivariable calculus on their own!" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14512.0 0.0 0.0 0.0
"I've been taking proper notes, doing the readings, and all the things you would expect of a student (short of taking the quizzes and final). I'm surprised at myself for having the will, interest, and sustained performance to get here. I'm tooting my own horn because I think I deserve it. Thanks to Professor Strang, I haven't just learned one of the most beautiful frameworks in mathematics. I have also proven that I can focus and get things done. If you knew me, you'd know that I'm unreliable, highly motivated at first, but that I ultimately lose steam and perform poorly. This class taught me that when I choose to do something to completion, and mean it, good things can happen. Thank you from the bottom of my heart, Professor G. Strang! Seriously, I'll always hold you in high regard. You gave me the MIT experience. You made me really wanna roll up my sleeves and learn deeply, learn how to think, which is impressive because I'm a college dropout who wanted nothing to do with education (well, schooling, you come across that line of reasoning, I'm sure). This course has improved my confidence. I just wanted to let you know, the special touch you placed on every lecture was precisely what I needed to start to see education in a whole new light. I've said it a million times now, but thank you Professor Strang! And of course, many, many thank you's to the MIT OpenCourseWare for making such high-quality, timeless content available to millions like myself for free. You're changing minds." Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 6406.0 0.0 0.0 0.0
"We shouldn't call the null matrix Zero. 39:12" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11333.0 0.0 1.0 0.0
"they sure have been eager for that friday night party!
https://media.tenor.com/images/6cc59dc71e354ee0eca6d4cc3415bcdb/tenor.gif" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 14786.0 0.0 0.0 0.0
"That was actually the coolest introduction to determinants ive ever seen and will ever see probably. Hopefully he brings in the physical intuition later" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 9918.0 0.0 0.0 0.0
"Thanks for the lecture!" 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 9715.0 0.0 0.0 0.0
"Legendary Teacher  <3 <3 <3" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7324.0 0.0 0.0 0.0
"He's an amazing teacher. He is actually one of the few teachers I know of who can DELIVER his train of thoughts to the students. I wish I had him as my teacher x] He makes calculus so fun lol." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4631.0 0.0 0.0 0.0
"It's very basic and a foundation for many courses such as advanced statistical probabilities. It's a 1st year course with  only basic calculus as a prereq" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7077.0 0.0 0.0 0.0
"I love this man, for he, by showing the meaning and relations, makes me love Linear Algebra, a subject that used to bother me." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5827.0 0.0 0.0 1.0
"HOW AM I MEANT TO LEARN THE MATERIAL WHEN THE CAMERA HARDLY SHOWS THE BOARD??!" CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4406.0 1.0 0.0 0.0
"The proof for (uv)' should be simpler: 
(u+Δu)(v+Δv) - uv = uv + uΔv + vΔu + ΔuΔv - uv = uΔv + vΔu + ΔuΔv. 
Dividing by Δx and taking the limit as x→0, we instantly obtain:
uv' + vu' + u' x 0 = uv' + vu'. It's more logical that way, and we can clearly see why the formula looks the way it does.

We can of course make the process lengthier by writing instead of Δu and Δv their full expressions: 
u(x+Δx) - u(x) for Δu and  v(x+Δx) - v(x) for Δv. By doing so we get:
(u+Δu)((v+Δv) - uv = [ u(x) + (u(x+Δx) - u(x)) ] [ v(x) + (v(x+Δx) - v(x)) ] - u(x) v(x). And the proof will take more space, while it is still gonna be exactly the same as the two-line proof I have written above. In fact I believe students should practice both writing the short proof and the longer version just to clarify things for themselves. 

Now then, by knowing the end formula (uv' + vu'), we of course can prove it as in this video by trying some adding and subtracting tricks to make the end formula uv' + vu'. That's mathematically correct but it conceals from you why the formula looks the way it does.  *That said, the lectures are otherwise superb and deserve kudos in my opinion and a huge like.*" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10256.0 0.0 0.0 0.0
"sounds a little german" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14385.0 0.0 0.0 0.0
"I wish I was a student of MIT!" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6209.0 0.0 0.0 0.0
"Almost French language" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2318.0 0.0 0.0 0.0
"Hey MIT, thank you so much for posting this! If you want to improve the sound, try using an expander (a compressor set to a less-than-one ratio). To make the chalk more visible, the contrast could maybe be turned up. Come to think of it, the expander is just like audio contrast! After expanding, you may want to apply a maximizing limiter. The Waves L2 plug-in works great ($30), and you can do all this audio work in Ableton Live ($250 for students).

My mentor at work told me a few months ago I need to learn analysis. Since then, I went through 18.01, 02, 03, and 06 to refresh, and to see this lecture series up now is just perfect--thank you again!!" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 4688.0 1.0 0.0 0.0
"Great lectures.  He should have done an example with more than 1 constraints though." 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4310.0 0.0 0.0 1.0
"respect for Prof.Strang" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 14263.0 0.0 0.0 0.0
"I always hated linear algebra, but Prof. Strang makes it fun." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 5042.0 0.0 0.0 0.0
"helped so much thanks!!" TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 13138.0 0.0 0.0 0.0
"Why are things like derivative mentioned at the MIT in this way? This is easy school mathematics." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11786.0 0.0 0.0 0.0
"Does anyone have a good proof for property 9?" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 3437.0 0.0 1.0 1.0
"what even is a fourier transform?" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 15138.0 0.0 1.0 0.0
"Could someone explain to me why do we wan't A^TA to be an invertible square matrix? at 22:00" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 3234.0 0.0 1.0 0.0
"除了买了我老板课的教材，就买了这位教授的书。
和Gilbert Strang教授相比，绝大多数中国关于线性代数的课程连做弟弟的资格都不配，剩下的也只能是个弟弟
线性代数教育世界第一人，非Gilbert Strang教授莫属" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 15667.0 0.0 0.0 0.0
"Prof. Jerison is such a nice guy in his lectures you don't even realise that you're studying mathematics . He makes it pretty simple and easy to understand 😄" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8299.0 0.0 0.0 0.0
"It's not hard once you wrap your head around it. The only thing that gets me is when the prof is on a roll and explains things really fast, but that's why he takes question breaks so that students can ask for a re-explanation. " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7061.0 0.0 0.0 1.0
"@janitarjanitar improve your english" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1897.0 0.0 0.0 0.0
"Its quite understandable when your english terrible like mine is;-)" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7090.0 0.0 0.0 0.0
"It you uploading these lectures on youtube make sure these lectures are visible" TXMCTAF6SEE "Lecture 10: Simple Functions" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 7010.0 0.0 0.0 0.0
"But that was a critical moment in the lecture... another one of prof. Auroux's famous ""speed erases"". :)" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2964.0 0.0 0.0 0.0
"This is the best. Thank you for this free quality knowledge! <3" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10748.0 0.0 0.0 0.0
"soooo this only means he's good at memorizing, put a student to do the same he's the goal and yes this is the same thing we learned in high school except he's got one of those chalkboards that make them feel important or scientific because it slides up. Don't tai me wrong props to the guy but I'm sure that only one student understood what was really going on " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14369.0 1.0 0.0 0.0
"THIS MAN IS A FUCKING GENIUS" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8995.0 0.0 0.0 0.0
"Thank you Prof. Strang for these wonderful lectures - From India" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9197.0 0.0 0.0 0.0
"If matrix has all connections, it eventually has cycles, but it is not a failure. What is a rigour correct criteria?" p-bXJIa7QVI "Lecture 30: Completing a Rank-One Matrix, Circulants!" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6508.0 0.0 1.0 0.0
"i love you mit." BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13438.0 0.0 0.0 0.0
"wonderful professor" gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 15397.0 0.0 0.0 0.0
"Nobody:
Literally nobody:
Gilbert strang: *OKAY*" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 7909.0 0.0 0.0 0.0
"at around 37:15 when the Sir is talking about difference in Least Squares and PCA. I think minimization will lead to same solution as perpendicular length is proportional to other line. Hypotenuse * sin(theta), where theta is the angle between vertical line and the line of least squares which must be fixed for a particular plane(line). I could not understand where I am going wrong." Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12471.0 0.0 1.0 0.0
"Bro, this professor is good, but he needs to speak up @MITOpenCourseWare" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 2950.0 0.0 0.0 0.0
"One easy way to actually derive the whole inverse matrix formula step-by-step is by creating an (n)×(2n) size matrix, then put arbitrary coefficients on the left side (columns 1-3), and then the identitiy matrix on the right side (columns 4-6), then row-reduce the whole thing until the left side has become the identity matrix.
If you do that then the right side should become the inverse matrix of whatever was on the left side in the beginning, and from there you can also factor out the determinant from all those coefficients." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8077.0 0.0 0.0 1.0
"I've done this whole course, none of it has been very hard. Except his third method of matrix multiplication. I'm totally stumped and its the only one he doesn't explain clearly. I can't find anything on matrix multiplication row by row. Does anyone have any other key words for this - maybe a big name like ""hyperporaboloid"" or ""quaternion tensors"" or something?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6413.0 0.0 1.0 0.0
"He totally messud up the GPS example...
" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4617.0 0.0 1.0 0.0
"What I am inferring from the comments is it is ideal to work from right to left when determining the decomposition" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 11383.0 0.0 0.0 0.0
"This guy is way too slow " ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10549.0 0.0 0.0 0.0
"Sometimes, i feel like answering the questions to the professor but can't." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8847.0 0.0 0.0 0.0
13:17 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 408.0 0.0 0.0 0.0
"I have a little question though.

In the union between the plane P and the line L, explained from 05:00. There are some cases in which the union can be a subspace. This case occurs if the L is a subspace of P, meaning if L lies in P and goes through the null vector (0,0,0).

Correct me If I am mistaken!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 5492.0 0.0 1.0 0.0
"This is amazing! 
This is overwhelming that u guys r providing lectures for free to the needed ones.
Great job MIT." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 10615.0 0.0 0.0 0.0
"Thanks a lot for the videos; they were really helpful in preparation for exams. Though, I would suggest the operator not to zoom in as much, because it makes it hard to follow the flow of the lecture." YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9659.0 0.0 0.0 0.0
"Hello Dr. Adler's class hope y'all can see my comment" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4654.0 0.0 0.0 0.0
"I am convinced that MIT 18.065 is  one of the best math courses in the world.  There is no exaggeration to say that it serves as the mathematical enlightenment to me    thanks Dr Strang" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5079.0 0.0 0.0 0.0
"I didn't know about Markov matrices, they are very interesting.  So all n x n matrices with each entry equal to 1/n are Markov matrices, with eigenvalues 0 and 1 (1 because they are Markov matrices, 0 because their rank is equal to 1)." lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 5273.0 0.0 0.0 0.0
"optimal non-success rate" X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 14159.0 0.0 0.0 0.0
"really enjoyed the lecture ! It is so relieving to know and understand the derivation of a formula you've been given without proof!" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14249.0 0.0 0.0 0.0
"Thanks for the wonderful contents :D Professor Strang is my role model. He has the beauty that doesn't rust by times." p-bXJIa7QVI "Lecture 30: Completing a Rank-One Matrix, Circulants!" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9725.0 0.0 0.0 0.0
"Have a small doubt,
Can anyone please resolve this.
As sir said that if we take 2 columns in matrix then sir got a plane as a subspace ..It means if we take the linear combinations of 2 columns then we get a 2-d plane which passes through the origin right?
And now I tried with 2*2 matrix taking 2-d vectors and I should get a line which passes through origin if we take linear combinations of those ..
But I again got a plane ?
Am I doing wrong in making the subspace of  R^2?

thanks " JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4445.0 0.0 1.0 0.0
"are the labs available somewhere?" 2K7CvGnebO0 "19. Saddle Points Continued, Maxmin Principle" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12398.0 0.0 0.0 0.0
"Thank you." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 9541.0 0.0 0.0 0.0
"For the ring thing,  if the curve  created by professor Jerison's hands could be thought of as a function ,  so naturally wouldn't the ting just settle down at that particular function's critical point" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3896.0 1.0 1.0 0.0
"Excellent professor!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3670.0 0.0 0.0 0.0
"@Lemnirot  Not sure if you someone told you or if you already saw the next video, he did point this out. Not be mean, just wanted to let you know." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 1656.0 0.0 0.0 0.0
"*12:23* he has a point, of all letters you choose u and v😂😂" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 230.0 0.0 0.0 0.0
"It's a little more into matrix theory than that. He's assuming that we've already done the elimination process, and if there were any repeated equation while eliminating, it would yield an entire row of just 0's -that is, no pivot. So in essence saying that there's no pivot in one of the columns is the same as saying that one of the equations was repeated. The rank, r, is the number of pivots, m the number of rows. So if r<m, there must be a column without pivots, and the solution is not unique." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 7021.0 0.0 1.0 0.0
"Thank you for this lecture: https://www.youtube.com/richcoast" u4qQ1oIQcW8 "Lecture 25: Power Series and the Weierstrass Approximation Theorem" "MIT 18.100A Real Analysis, Fall 2020" 9282.0 0.0 0.0 0.0
"Of course to be a real Electrical Engineer you should use j for imaginary numbers." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 7997.0 0.0 0.0 0.0
"@sahookah because proving is math and knowing the prove helps you understand the theorem
" phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1997.0 0.0 0.0 1.0
"why am i watching this?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15280.0 0.0 0.0 0.0
33:34 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 962.0 0.0 0.0 0.0
t=n.p-q.n/(q1.n-q0.n) 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14431.0 0.0 1.0 0.0
"This was beautiful." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10968.0 0.0 0.0 0.0
"35 hours well spent." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 991.0 0.0 0.0 0.0
"love it when he says in PAGHTICULA(in particular)" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13867.0 0.0 0.0 0.0
"@poyanator you learnt this in high school right?you need to shut up and continue with your further education if you are interested." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1979.0 0.0 0.0 0.0
"A'A = I. So if we find a matrix E such that, EA = I, then A' must be E. Why is this something to be discovered? The process of finding E is just elimination process. So what's new?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2170.0 0.0 0.0 0.0
"Wait! How string ab be accepted since q3 not accept state/final state? 14:" oNsscmUwjMU "2. Nondeterminism, Closure Properties, Conversion of Regular Expressions to FA" "MIT 18.404J Theory of Computation, Fall 2020" 11260.0 0.0 1.0 0.0
"""Linear Algebra"" ~ 3Blue1Brown 
https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 80.0 0.0 0.0 0.0
"Hay quá!" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 4456.0 0.0 0.0 0.0
"great teacher completed in nice way. salute you sir." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13008.0 0.0 0.0 0.0
"“Never be heard to uder  pivot in the zero position”, priceless 😀😵‍💫" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15596.0 0.0 0.0 0.0
"Statistics is for good overthinkers🤓" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8892.0 0.0 0.0 0.0
"work begins at 9:12" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 15402.0 0.0 0.0 0.0
"how did he get (Ax-b)T(Ax-b)?" ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13214.0 0.0 1.0 0.0
"At 31:20 , I don't think that automaton can be created with two states. If it is possible, please share answer." 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 2640.0 0.0 1.0 0.0
"It is always so sad to think about that an educational video 99% better than all the others only has 70k views 10 years after is was uploaded" PnPIqh7Frlw "Lec 24: Simply connected regions; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6931.0 0.0 0.0 0.0
"""And died earlier too..."" LOL" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 27.0 0.0 0.0 0.0
"I like this guy." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5689.0 0.0 0.0 0.0
"Prof. Psaltakis is better !!!" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 8300.0 0.0 0.0 0.0
"Why DA/dx replaced with zero at 46:00" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11765.0 0.0 1.0 0.0
https://youtu.be/DDUC23useww 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 13291.0 0.0 0.0 0.0
"sir cross product is a vector quantity and the cross product is area of vectors of parallelogram. Is there area have direction . plz sir clear my doubt" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14308.0 0.0 1.0 0.0
"After watching his earlier lectures it feels strang(e) to watch him in such high quality" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2263.0 0.0 0.0 0.0
"Great , great lecture because Prfof Strang elucidates and focuses on the key ideas and the  intuitive meaning - not just the mechanics as most books and tutorials do. Thanks Prof. Strang for sharing your great mind and your skills as a great educator!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4195.0 0.0 0.0 1.0
Legend TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 7315.0 0.0 0.0 0.0
"GILBERT STRANG FTW!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 3966.0 0.0 0.0 0.0
"What about non parameric testing ?" 4HRhg4eUiMo "8. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 11444.0 0.0 1.0 0.0
"Thank you." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 9551.0 0.0 0.0 0.0
"I often watch MIT
It was amazing😘" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5890.0 0.0 0.0 0.0
"This is another fantastic lecture by the ring master of MIT mathematics DR. Gilbert Strang. GRAM-Schmidt  is a classic topic in linear algebra. An individual student cannot have too much linear algebra." 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 10635.0 0.0 0.0 0.0
"These lectures are very helpful for those who need to understand the material in depth." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10415.0 0.0 0.0 0.0
"One question Prof. and guys, how comes sigma in the middle is diagonal (square)? shouldn't its dimension (m, n) ? Thanks!" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8107.0 0.0 1.0 0.0
"When's he going to get on to multivariable calculus? " YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11650.0 0.0 0.0 0.0
"I love it. I get to go MIT for free learning." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 5761.0 0.0 0.0 0.0
"At 31:18. The professor says that Fxy ALWAYS = Fyx. But  Fxy doesn't ALWAYS = Fyx  according to Khan Academy. Isn't Khan Academy right ?" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2638.0 0.0 1.0 0.0
"Due to the pandemic, I have to take LA at a local community college online. And taking a course online meaning you are on your own, learning by only reading notes and textbook. Before Prof. Strang's lectures, I was struggling with the class. Now I understand the subject much better. Thank you, professor!" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 3528.0 0.0 0.0 0.0
"It's a great video because I can review what I learned this year" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 7020.0 0.0 0.0 0.0
"I was totally astonished by the idea of computing left nullspace!
Thank you Dr. Gilbert." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6170.0 0.0 0.0 0.0
"30:48 it's all about the feel!" HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 895.0 0.0 0.0 0.0
"This class was pure art" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 10481.0 0.0 0.0 0.0
"4:37 to 4:42 Yeah, turn that off. It's distracting me." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1322.0 0.0 0.0 0.0
"The greatest instructor I have ever met!! Thank you, Dr. Strang!" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 10127.0 0.0 0.0 0.0
"Truly an exemplary human being" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11092.0 0.0 0.0 0.0
Mind=blown YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7670.0 0.0 0.0 0.0
"I think he presented gaussian elimination very clearly. It's important algorithm for example in the process of inverting matrices" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6019.0 0.0 0.0 1.0
"طيب مافي مترجم!؟.
ي جمآعه آبي موقع ولا روابط تفهم لماده التفاضل والتكامل ٢ ضروري" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15573.0 0.0 0.0 0.0
"Thanks very much for those videos. For the first time in my life I finally understand those concepts. Hopefully, statistics textbooks will become less scary from now on." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9817.0 0.0 0.0 0.0
"Is all of this course multi variable differential calculus? I am taking multivariable differential calculus next month and don’t want to learn multivariable integral calculus yet" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6758.0 0.0 1.0 0.0
"Lol, go through all of the videos to understand it, you can do it with Khan Academy to go through things you don't understand. Not as hard as it looks, just try to smooth out all the things you're confused by, step by step, and eventually it will make sense." _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7404.0 0.0 0.0 1.0
34:09 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 977.0 0.0 0.0 0.0
"O MIT OCW, please release videos onto YouTube of the 18.100B, 18.100C, 18.700, 18.701, 18.702, and 18.901 courses!!! And, also of the complex analysis courses taught at the MIT! Please do seriously consider this request." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 7965.0 0.0 0.0 0.0
"Yuxuan Wang
Congratulations on reaching here. Cheers!! :P" 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 12269.0 0.0 0.0 0.0
"Good visualisation of what he's trying to explain at the start: https://eli.thegreenplace.net/2015/visualizing-matrix-multiplication-as-a-linear-combination" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4160.0 0.0 0.0 1.0
"This is just amazing how clearly he explains the topics, big thanks to the professor.  I wonder which other courses he teaches at MIT that are available in OCW? Also I think the Prof. is an author of the stats book for this course which must be great as well so need to look into getting it!" 3eiio3Tw7UQ "19. Weak Law of Large Numbers" "6.041 Probabilistic Systems Analysis and Applied Probability" 10680.0 0.0 0.0 0.0
"@NiocoNiO Then find me the derivative of (45X^5)+144X+15+(1000X^3)-(4X^2)" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1690.0 0.0 1.0 0.0
"Is that video available or not? I'm following the course on you tube but I can't visualize this particular lecture (n° 27)." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 6806.0 0.0 0.0 0.0
"Dr. Rodriguez, in minute 53:58 you mentioned that the limit as n approaches infinity, how do we know that the series converges?  Thank you Professor, this has been the best Analysis class I've ever taken, I finally understand this." EBdgFFf54U0 "Lecture 14: Basic Hilbert Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 3501.0 0.0 1.0 0.0
"Does anyone else have a pet peeve with the mathematical notation used for numerical value generated by the random variable as g(x) at 41:00? The professor says at 9:10 that ""x"" (in lower case) refers to the numerical value generated by the random variable. Why does he use g(x) for it later? Loosely speaking, he could have referred to it as g(sample space) as well, and although it isn't strictly a function of the sample space, it at least honours the the initial conception of ""x"" as the value generated by the random variable (which can be thought of as a function of the sequence(s) of events that satisfy the constraint g(sample space)=x)." 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 3435.0 0.0 1.0 0.0
"Its funny how much better this class seems compared to my college....." twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7085.0 0.0 0.0 0.0
"LOL - those annoying computer-generated comments are all over the MIT videos I've been viewing. Any theories why they exist?" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7231.0 0.0 0.0 0.0
"Although it is true intuitively that the T2, T3,.... all will be independent exponential random variable but the pdf for K=2,3,4 is not exponential...How can you argue about that??? anyone?" jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 2327.0 0.0 1.0 0.0
"You complete me." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 12198.0 0.0 0.0 0.0
😍😍😍😍😍 yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 15734.0 0.0 0.0 0.0
"At 17:35,  Shouldn't either of cos(x) or sin(x) should be the basis because either of sin or cos can be generated from the other. (like cos(x) = sin(π/2 - x)" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 2597.0 0.0 1.0 0.0
"Nice topic and wonderful lecture! 👍 I like it!" cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 7862.0 0.0 0.0 0.0
"Which math course is better to do after this?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11717.0 0.0 1.0 0.0
"A quick observation for 39:45. We can also prove that det(2A)=2^n det(A) by noticing that 2A=2IA=DA, where D is a diagonal matrix with twos down the main diagonal. Then, det(2A)=(by 9)=det(D)det(A)=(by 7)=2^n det(A)." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 2152.0 0.0 0.0 0.0
"@l955382 it's like an identity matrix except the 1s don't go across the diagonal.  The 1s are moved here and there to denote row operations" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 1928.0 0.0 0.0 0.0
"He should provide a proof showing why dropping the terms is correct using product rule." eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4607.0 0.0 1.0 1.0
"This class is Beautiful." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10472.0 0.0 0.0 0.0
nice IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 14026.0 0.0 0.0 0.0
"I love him so much 
I don't believe in God but I prayed for his health" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5730.0 0.0 0.0 0.0
"Thank you sir!" mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 9333.0 0.0 0.0 0.0
"Even tho this is a good college but we wont like it" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3587.0 0.0 0.0 0.0
Great! RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 4367.0 0.0 0.0 0.0
"Ha ha :-) ""Gauss thought of it before we did, but only because he was born earlier""" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4409.0 0.0 0.0 0.0
"He's thinking ""I'm trying to teach these kids 3-dimensional calculus and yet they can't figure out which hand is their right hand...""" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4648.0 0.0 0.0 0.0
"is this course applicable for lab analysis of data using statistical methods ? im a physics student wondering if this is worth the time to learn" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 13659.0 0.0 0.0 0.0
"Curve sketching actually begins about 30:00 in.  Before that is a review/extension of linear and quadratic approximation techniques." eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3267.0 0.0 0.0 1.0
https://youtu.be/y9lNbNGbo24 EBdgFFf54U0 "Lecture 14: Basic Hilbert Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 13309.0 0.0 0.0 0.0
"Wow. I couldn't perceive till I see from this lect. that the Lagrange multiplier method,  example, that the maximum values of  f are found at infinity to the hyperbola. " 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12086.0 0.0 0.0 1.0
"17:10  ""you can see from the way I am speaking what the answer is going to be..."" 
--wish my profs spoke like him...
" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 502.0 0.0 0.0 0.0
"Thanks to Dr.Tsitsiklis for this course." rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 9799.0 0.0 0.0 0.0
"Great Lecture!! Helped me a lot." dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 4203.0 0.0 0.0 0.0
"There is a problem with Dr. Strang's lectures.
The problem is, he makes it so intuitive that I'm literally nodding in agreement the entire lecture. I've now watched the lectures once, read the book chapters, and watched the lectures a second time. And while I have a good grasp of everything discussed so far, they all sort of blend in. I couldn't list the things I learnt one by one for these 10 lectures. :D (well, I sort of can.)" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10367.0 0.0 0.0 0.0
"I don’t know why he left the forth column out from the elimination process and rather came back to it later." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5376.0 0.0 1.0 0.0
"The way you clean the blackboard is infuriating to me. I can practically smell the dust from here.

But great lecture." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10334.0 1.0 0.0 0.0
"When he asks a question how many people pause the video and try ?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11615.0 0.0 0.0 0.0
"this teacher is very very good." -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14918.0 0.0 0.0 0.0
"Thank you so much MIT and Professor Auroux!!! You guys really make the entire course so easy, so organized and so interesting." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9350.0 0.0 0.0 0.0
"Great lecture, this has help me a lot to understand the book" IycOPFmEQk8 "5. CF Pumping Lemma, Turing Machines" "MIT 18.404J Theory of Computation, Fall 2020" 4284.0 0.0 0.0 0.0
"brilliant! " yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 12556.0 0.0 0.0 0.0
"Tell Pr Strang he is an absolute legend and many people over the world have been immensely helped by his work. My God bless his soul!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9026.0 0.0 0.0 0.0
"at 27:00, how come you are just able to factor out the diagonals? If you take out d1, arent all the diagonals in the matrix from the 2nd row to the nth row,  dn/d1?" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 12431.0 0.0 1.0 0.0
"If anyone is still confused and wants to understand fully how to derive the product rule, check this lecture note from MIT OCW: ocw(dot)mit(dot)edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/1.-differentiation/part-a-definition-and-basic-rules/session-9-product-rule/MIT18_01SCF10_Ses9c.pdf" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6496.0 0.0 0.0 0.0
"Is it beneficial for iit?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6778.0 0.0 0.0 0.0
"Very very great." z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11230.0 0.0 0.0 0.0
"""Every linear transformation is associated with a matrix"":- Gilbert Strang." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 46.0 0.0 0.0 0.0
"i finally learn something" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 13378.0 0.0 0.0 0.0
"hes deriving the derivatives of different functions, just simple calculus stuff" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13145.0 0.0 0.0 0.0
"In 37:38, why lnu=xlna when u=a^x?" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6600.0 0.0 1.0 0.0
"note to self -a" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14084.0 0.0 0.0 0.0
"In 2007-2008 I was lost, starting a PhD, completely lacking of a solid math background. So I watched his linear algebra course videos. A few years later I followed the one of Stephen Boyd on Linear Dynamical Systems (and recently part of the one in Convex optimization). These resources have been fundamental in me becoming a well-earning professional that still enjoys learning. Now, when I interview young people for Junior Data Science positions, almost all of them put the cart before the horse, just interested in the trying the latest method, even though they really don't understand what it does. I try to recommend them to follow the same path (start from the basics, follow good-old video lectures) but most of the times this advice is received as an eccentricity: ""Linear Algebra is soooo far away from the cool stuff, man"". So, my guess is that a course like that will make my point easier. Looking forward to discover it :)" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6592.0 0.0 0.0 1.0
"I hold a very radical theory which I do not expect everyone to accept.   ""There is no such thing as a negative number"".  Elements are defined by the number of protons in their atoms from 1 up.   Temperature goes from zero Kelvins up. A person cannot have a negative age,  a duck cannot have a negative number of ducklings.   The square root of a minus number cannot be obtained.    If there are 14 apples in a box, you cannot take 15 out of it.  Food for thought." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5578.0 0.0 0.0 0.0
"Bless you, Dr. Strang. Your lectures should be part of an Arctic Vault/Time Capsule so that aliens can drink from the fountain of your knowledge." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2901.0 0.0 0.0 0.0
"He sounds like Senator Pat Geary from Godfather 2." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 4609.0 0.0 0.0 0.0
"Brilliant lessons !" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 2932.0 0.0 0.0 0.0
"Thanks Prof Strang, MIT!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9627.0 0.0 0.0 0.0
"can you please tell me why we took lagrange multiplier in the pyramid?(at the end of lecture)..why gradiend of both func have to be parallel?" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12637.0 0.0 1.0 0.0
"Transpose(a)*(b-xa) is a dot product because well you can clearly see Transpose(a) is a vector but what about this expression (b-xa)?! well (b-xa) is a vector because we know that (b) is the vector we also know (a) is vector and (x) is a scalar hence 
vector-scalar*vector=vector" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 11083.0 0.0 1.0 0.0
"Intro => Most of the lecture, we're going to concentrate on their steady-state behavior.
meaning, we're going to look at what does a Markov chain do, if it has run for a long time.
What can we say about the probabilities of the different states? 
So what I would like to repeat is a statement I made last time that Markov Chain is very very useful class of models.Pretty much anything in the real world can be approximately modeled by a Markov chain provided that you set your states in the proper way." ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 6735.0 0.0 0.0 0.0
"@pedroissler caught not catched
" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1967.0 0.0 0.0 0.0
"Let Aij be the cofactor of aij in A. Then by definition detA= ai1Ai1+...+ainAin. What would happen if the Aij were taken from another row?
let B be the matrix with the same rows as A except for the k-th row that is the same as the i-th row. Then, bk1Bk1+...+bknBkn=detB=0 cause B has two same rows. But bkj are aij and Bkj are Aij (cause Aij =(-1)^(i+j)Dij and Dij eliminates the column and the row so it'll be the same)

Consider C= A*(adj(A))^t. The position cii will be ai1Ai1+...+ainAin= detA. cij with i!=j will be 0 because of the lemma proved above. Therefore C=detA*In, and with some algebraic changes, A^-1=( adj(A)^t)/detA" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 7332.0 0.0 1.0 0.0
"at 2:12 i started laughing, because I remembered a line from ""the big bang theory"", from the first episode" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12435.0 0.0 0.0 0.0
"Ok I figured this out. Let B=CD.  if C is invertible then CDx=0 is equal to Dx=C^(-1)0 therefore Dx=0 is equal to CDx=0. that is why N(B)=N(D)." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 8041.0 0.0 0.0 0.0
"""soo...cramer found a rule"" sounded like we're talking about the one from seinfeld stumbling upon some deeper mathematical truth" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 175.0 0.0 0.0 0.0
"I'd never thought I would binge watch anything apart from movies and seasons but this course got me wrong. All Hail Prof Strang!!!" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 6281.0 0.0 0.0 0.0
"Dr. Casey Rodriguez __/\__" O0Tw47okZJM "Lecture 21: The Spectrum of Self-Adjoint Operators and the Eigenspaces of Compact Self-Adjoint..." "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 3497.0 0.0 0.0 0.0
"39:09 I AM" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1095.0 0.0 0.0 0.0
"hahahah I don't see one blonde in the class. " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13053.0 0.0 0.0 0.0
"Wow! Euler characteristics just came out of nowhere." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12050.0 0.0 0.0 0.0
"I love prof. Strang and I'm very grateful for his lectures, but I have to admit I don't find this proof convincing. Correct me if I'm wrong, but the project he starts out with (@3:32) is to prove that every matrix A has this decomposition. But @13:26, he starts out by **assuming** that A has this decomposition, and then he deduces what U, Σ, and Vᵀ must be. But that doesn't show that every matrix A has this decomposition. Instead, it shows that *if A has this decomposition*, then *that's what U, Σ, and Vᵀ must be*. Even if we were to argue that we can obtain such U, Σ, and Vᵀ for any matrix A, prof. Strang doesn't show that by multiplying UΣVᵀ we will get back A for any A. 

I struggled with this topic for months until I finally could arrange everything into what I believe is a proof for why every matrix A can be decomposed this way." rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5766.0 0.0 1.0 0.0
"sexy ass lecture! he made it so clear" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14289.0 0.0 0.0 0.0
"Simply brilliant!!!" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 8664.0 0.0 0.0 0.0
"many people do actually.. if you don;t may be dont watch this?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13909.0 0.0 0.0 0.0
"33:07 dude, there's something moving under the professor's desk." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 952.0 1.0 0.0 0.0
"Sinceramente pensé que el MIT era una chingonería, la gran verga erecta de la enseñanza científica y tecnológica de EU. Ya ví que no es así (al menos no en lo que respecta a matemáticas). Este maestro es un inepto; Casi podríamos decir  que es lo análogo al IPN en México, casi, porque desde luego la infraestrutura es infinitamente mejor  en MIT y en general ellos siempre van a enseñar un poco más y mejor; No hay tanta corrupción ahí. Pero es análogo en el sentido que siendo EU deja mucho que desear, es pues, mediocre igual que el IPN, en México. Pero esta mediocridad en el IPN, no es sino reflejo de precisamente la complexión intelectual y moral y expresión del retraso que en ciencia y tecnológía( y no se diga en la enseñanza en estos temas) tiene un pueblo como México y que éste ha colocado al IPN como ""pilar y baluarte"" de la enseñanza científica y tecnológica en el país y como ""palanca de desarrollo"", cuando, al menos, no es tal." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8682.0 0.0 0.0 0.0
"such a cute professor" MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14410.0 0.0 0.0 0.0
"My AP Calculus teacher rocks because I skipped ahead into the video and know exactly what the dude is talking about." BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7730.0 0.0 0.0 0.0
"Thanks prof. Strang 😍 these courses are real gems!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9759.0 0.0 0.0 0.0
"Sure we like it prof😍😍😍😍😍😍😍. God bless you." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8971.0 0.0 0.0 0.0
"so, if his explanation is correct, then the limit of x/2x when x->0 = 0 because x aproches faster to 0 than 2x. It sounds ridiculous" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14352.0 0.0 1.0 0.0
great j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 12966.0 0.0 0.0 0.0
"LEGENDS NEVER DIE - Maths' legendary person in the whole world - Sir Gilbert Strang" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7226.0 0.0 0.0 0.0
"thank you" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14471.0 0.0 0.0 0.0
"Wish my professors wrote as big as that too -__________-" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 11959.0 0.0 0.0 0.0
"00:00 Error from last lecture, row dependent.
04:28 4 Fundamental subspaces.
08:30 Where are those spaces?
11:45 Dimension of those spaces.
21:20 Basis for those space.
30:00 N(A^T) ""Left nullspace""?
42:10 New ""matrix"" space?" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 279.0 0.0 1.0 0.0
"37:40 نقطة أخرى مهمة" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1070.0 0.0 0.0 0.0
"It is my dream to meet prof. Gilbert strang . His voice , his words ,his action touch my soul . Please prof. Read my comment so that I can satisfy only by this And I pray You may live 1000 years ." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 6959.0 0.0 0.0 0.0
"Is it true that colleges such as MIT wouldnt look at a HS applicant if they didnt take calc in HS?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6798.0 0.0 0.0 0.0
"Very nice lecture. Informative and pretty self-explanatory." sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11209.0 0.0 0.0 0.0
"4:42 Terry?" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 1324.0 0.0 0.0 0.0
"ur such a bad teacher lulw" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14983.0 0.0 0.0 0.0
"who takes single variable calc at MIT....." 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15267.0 0.0 0.0 0.0
"Much better than the shit-ass lecturer I had for this module. If only I had discovered this before my exams last year...thank god I still managed to scrape my 2:1  :D" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7717.0 0.0 0.0 0.0
"Prof. said, ""zero pivot"" twice doe." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8317.0 0.0 0.0 0.0
"Like like like no reason...." l4NoMKEHQwM "11. Derived Distributions (ctd.); Covariance" "6.041 Probabilistic Systems Analysis and Applied Probability" 7358.0 0.0 0.0 0.0
"mm don't know. for A=x, B=y and C=z i think you would get 0 for AxBxC, but there is a non zero volume.
or i might be wrong" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13956.0 0.0 1.0 0.0
"I understand nothing..." WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 6119.0 0.0 0.0 0.0
"Sadness is this man getting old..." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8593.0 0.0 0.0 0.0
"Thks for the lecture. But surprise to see you are still using blackboard and chalks in the states" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10982.0 1.0 0.0 0.0
"14:44 aren’t the odd numbers also negative" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 437.0 0.0 1.0 0.0
"41:51 what's up" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 1163.0 0.0 0.0 0.0
"@Kingarthur305 
Maybe you should donate" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1653.0 0.0 0.0 0.0
"THIS must reach YouTube top videos instead of a trash going on there." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8997.0 0.0 0.0 0.0
"awesome how prof. Strang uses an error in lecture 9 to draw attention to the fact that the R(C(A)) = R(C(A')) ... a lot of ego driven profs. would have simply shrugged it off." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12490.0 0.0 0.0 0.0
"brilliant 👌this is getting really interesting" EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 12555.0 0.0 0.0 0.0
"Why is abb not accepted considering that after ab, and you are on state q3, you can take an epsilon transition to q4, then read b again, or is this not allowed?" oNsscmUwjMU "2. Nondeterminism, Closure Properties, Conversion of Regular Expressions to FA" "MIT 18.404J Theory of Computation, Fall 2020" 11868.0 0.0 1.0 0.0
"19:02 SAVAGE!!! lol" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 553.0 0.0 0.0 0.0
"Thank you for this clean and concise demonstration about the cycloid motion." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9280.0 0.0 0.0 0.0
"An amazing first lecture, glad to see the audio is fixed, thanks for taking care of this course. It's beautiful to perceive people from all over the world gathering here to gain knowledge, Professor Strang is a great teacher <3" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 2435.0 0.0 0.0 0.0
"lols whats wrong with the Taylor expansion?" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13844.0 0.0 0.0 0.0
"@Mrhellzya How is it a ""waist"" of time?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1686.0 0.0 0.0 0.0
"dam this, whenever i see an MIT lecture i admire how those students are so lucky!
" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12706.0 0.0 0.0 0.0
"classic explanation" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 12654.0 0.0 0.0 0.0
"I Really Like The Video Positive Definite Matrices and Minima From Your" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 4992.0 0.0 0.0 0.0
"A great teacher ..." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 2123.0 0.0 0.0 0.0
"Isn't it crazy we still follow 15 years old lecture because its still best. What a legend G.Strang" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 6892.0 0.0 0.0 0.0
"This is a great course!" IycOPFmEQk8 "5. CF Pumping Lemma, Turing Machines" "MIT 18.404J Theory of Computation, Fall 2020" 10590.0 0.0 0.0 0.0
"holy cow?" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13182.0 0.0 0.0 0.0
"42:21 ""Euler never stop"" lol" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1180.0 0.0 0.0 0.0
"This man is definitely a legend. Much appreciated." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 10865.0 0.0 0.0 0.0
"Blackboard energy......." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2898.0 1.0 0.0 0.0
"@40:15 can anyone share the algebraic simplification of the resulting integral." l4NoMKEHQwM "11. Derived Distributions (ctd.); Covariance" "6.041 Probabilistic Systems Analysis and Applied Probability" 1555.0 0.0 1.0 0.0
"Intuitively, if X is a uniform distribution, why would Y=X^3 not be a uniform distribution? 32:10
Why is it , when cubed, there is more probability of getting numbers closer to 0?" H_k1w3cfny8 "10. Continuous Bayes' Rule; Derived Distributions" "6.041 Probabilistic Systems Analysis and Applied Probability" 6739.0 0.0 1.0 0.0
"great board...and chalk.
" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12967.0 1.0 0.0 0.0
"high respect for Professor Strang" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 13158.0 0.0 0.0 0.0
"Thanks for making this content available for everyone" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9689.0 0.0 0.0 0.0
"Ad hominems make your argument weaker. You seem to think the past did not affect their present. The past affects their present. As a group, they are disadvantaged. It was group policy from the gov't to treat them like cattle. Now the gov't believes otherwise. Fortunately, your point of view is not held by gov't. Identity groups may not be important to you but it is to gov't. That's why there are social programs in place since the Great Depression. Believe what you want. Many like me feel they" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2239.0 0.0 0.0 0.0
good dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 12939.0 0.0 0.0 0.0
"B is just the momentum :)" wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2798.0 0.0 0.0 0.0
"Thank you MIT. But how is he squaring the matrices when calculating the variance?  14:08" z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9164.0 0.0 1.0 0.0
"its fun truly just would continuously love  to  be engaged in a conversation" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13707.0 0.0 0.0 0.0
"Finally this course has been release in MIT OCW! Thank a lot!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3780.0 0.0 0.0 0.0
"I wish I knew phisics better :( For me that was just a set of magic rules." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6208.0 0.0 0.0 0.0
"MIT should really move on from chalk boards, not good for the profs health breathing in dust all day......" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7543.0 1.0 0.0 0.0
"LOL these people go to MIT?! and ask HS level question?!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7238.0 0.0 0.0 0.0
"So that any slow writers have time to finish copying it down for their notes." phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8790.0 0.0 0.0 0.0
"during lecture 8 there was exam going on, so no video." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12779.0 0.0 0.0 0.0
"12:11 for similar matrices" TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 390.0 0.0 0.0 0.0
"I can gurantee that if you watch it once, you will never forget. Literally, explanation is at awesome level with easy language.... Hats off Prof. Gilbert Strang❤️" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 5189.0 0.0 0.0 0.0
"Lecture starts at 13:20" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7295.0 0.0 0.0 0.0
"there are handheld calculators that invert matrices?!" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14759.0 0.0 0.0 0.0
"The host of 'who wants to be a millionaire' was Regis.

Hi caption reading comrades!" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 10138.0 0.0 0.0 0.0
"50:30 Anybody knows if it matters that the right angled triangle is in a different quadrant?
Thanks man!" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1337.0 0.0 1.0 0.0
"I followed every lecture, thanks Prof Strang, the course changed my view of Linear Algebra" rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5424.0 0.0 0.0 0.0
"Beautiful lecture. Thank you very much." MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2824.0 0.0 0.0 0.0
NB 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 7799.0 0.0 0.0 0.0
"This instructor is wonderful." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10576.0 0.0 0.0 0.0
"THANK YOU SIR!" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 8983.0 0.0 0.0 0.0
"Did he ever defined what a limit is ? where ?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3371.0 0.0 1.0 0.0
"I like turtles" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5698.0 0.0 0.0 0.0
"i love this man... i found a best teacher" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 13433.0 0.0 0.0 0.0
"Great professor as always at MIT.  However, I wonder if there is a mistake here for the deduction that he did (time: 13:28/46.03Min)...I did not get it.

Delta (U/V)=(U+DeltaU)/(V+DeltaV)-U/V" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4323.0 0.0 1.0 0.0
"https://youtu.be/XkY2DOUCWMU 
Better watch this video to visualize matrix multiplication." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13300.0 0.0 0.0 1.0
"Does anyone have the exam materials and the solution?" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3439.0 0.0 0.0 0.0
"Wish I went to MIT." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11957.0 0.0 0.0 0.0
"I don't even understand the title of the video" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 5300.0 0.0 0.0 0.0
"Yeah... question!" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12131.0 0.0 0.0 0.0
"Text book recommendations anyone ?" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 9035.0 0.0 0.0 0.0
"Prof. Gilbert Strang's videos had helped me during my M.Eng. study, I watched him once again in 2011-2014 during my PhD. Last year I got his new book, and today I am watching (again) he is teaching linear algebra for data analysis, signal processing and machine learning because I have to teach Fundamentals of AI for my undergrad students. Thank you so much Prof. Strang, you are my best online mentor in mathematics!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8298.0 0.0 0.0 0.0
"How is the nullspace of the 2nd matrix (-1,1)?" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 4874.0 0.0 1.0 0.0
"Great class! Thank you!  I have a question towards the end when we see that E(A) = I or Ainverse(A) = I.  Does this also mean that Ainverse = I/A ?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4214.0 0.0 1.0 0.0
"Such a great lecture! the best intermediate-level gold. Thanks.
Please dont fall for the parts where he forgot. He always tries to convey things that might not be obvious just from passive-reading." yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 8927.0 0.0 0.0 0.0
충성충성 FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 15690.0 0.0 0.0 0.0
"Amazing!  Thanks MIT and Professor." 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 2402.0 0.0 0.0 0.0
"I love the way this guy says ""way"" and ""when""" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 5793.0 0.0 0.0 0.0
"Really like the use of zoom!!" BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8525.0 0.0 0.0 0.0
"Good mathematics teachers are a gift from the gods." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 4145.0 0.0 0.0 0.0
"this is the least satisfying of the Strang lectures I've seen.  everything is so dumbed down until he gets into factoring the Fourier matrix and then all of the sudden doesn't really show that the factorization is correct.  Not even a rudimentary hand-waving." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 14883.0 0.0 0.0 0.0
"22:00 he says cubed that's ""(x-1)^3""" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 693.0 0.0 1.0 0.0
"Explanation of the relationship between the determinant of the Jacobian and the change of variables was handwavy at best! Would be nice to see a rigorous derivation of how these things work instead of accepting a magic formula..." UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3708.0 0.0 1.0 0.0
"I have a question here, for me a point in 3d is zero dimensional, but if some living entity is smaller than that point some microscopic living thing, for it the point will have some dimension, so, is it so that the vector spaces that i am studying, I can visualise in my existing space, if someone is there in some different space they will do some other vector space?The solution will remain same  in different spaces for a particular problem or example??" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 5498.0 0.0 1.0 0.0
"Unless you think of probability as belief in bayesian statistics, the whole framework makes no sense.
Statistics aids human epistemology, it's not a replacement for it, even a UMP test result can be rejected as a definite method of learning on other relevant grounds." bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 11126.0 0.0 0.0 0.0
"Sherman–Morrison formula 👌" XhSk_Lw2X_U "14. Low Rank Changes in A and Its Inverse" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8638.0 0.0 0.0 0.0
"Why do College Profs use such Large chalk???" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11819.0 1.0 0.0 0.0
"I think the teaching style in india is much better" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6067.0 0.0 0.0 0.0
"খুবই সুন্দর লাগলো..." rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15581.0 0.0 0.0 0.0
"in determining the range of of the area, the function depends on x...." YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13583.0 0.0 1.0 0.0
"He wears the same thing in every video that I've watched..." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4620.0 0.0 0.0 0.0
"What a great professor" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 11413.0 0.0 0.0 0.0
"Excellent presentation...Start watching 10 minutes in
...Bayesian starts 18 minute in" 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 3665.0 0.0 0.0 0.0
"A Sipser MIT course. :-) :-) :-)" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 2095.0 0.0 0.0 0.0
"properties of integrals" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14227.0 0.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8436.0 0.0 0.0 0.0
"39:02 What is that with the subs??" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 1090.0 0.0 0.0 0.0
"His gr8. ""Any questionzzz."" " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4752.0 0.0 0.0 0.0
"Love you sir" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7468.0 0.0 0.0 0.0
"Thank you!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9473.0 0.0 0.0 0.0
"Sneaky Freaky 💀 17:40 😂😂" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8725.0 0.0 0.0 0.0
"Actually he love maths so much that he wink to her again and again 👌🙏😅
Pls maths take his proposal .

Sry no offense 😅😎😎" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2235.0 0.0 0.0 0.0
"Expertise your engineering knowledge here" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 3705.0 0.0 0.0 0.0
"this guy was in a movie when he was a kid. just can't remember what movie he was in." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 14843.0 0.0 0.0 0.0
"25:15  ""Told you i was 'dyslectic'"" rather than dyslexic.  Does that mean he's lecturally challenged." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 773.0 0.0 0.0 0.0
"Quit the Row Picture, already.  😅" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8481.0 0.0 0.0 0.0
"I've watched and really enjoyed the previous lectures, but I have some doubts regarding this lecture.... what I have learnt from the book by J. Coley is totally opposite (interchanged) to what professor explained about Contour plot and Level curves......  Hoping for anyone's kind reply. Thank you." dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 6436.0 0.0 1.0 0.0
"The Bob Ross of maths :)" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 9957.0 0.0 0.0 0.0
"How will we define negative definate. Will it have everything negative like
1) All pivots are negative
2) All e-values negative ?" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 4905.0 0.0 1.0 0.0
"If anyone is confused at 23:50 (I was) have a look at slide #14 (pag. 17) in:
https://ocw.mit.edu/resources/res-18-010-a-2020-vision-of-linear-algebra-spring-2020/videos/MITRES_18_010S20_LA_Slides.pdf" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6494.0 0.0 0.0 0.0
"He likes Helena" mc1y8m9-hOM "22. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 4565.0 0.0 0.0 0.0
"Dr. Strang's Lectures are as entertaining as they are interesting. I enjoy this subject and look forward to learning it. Thank you, Dr. Strang!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 3512.0 0.0 0.0 0.0
"Sheldon Cooper?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8637.0 0.0 0.0 0.0
"that guy, Denis Auroux, is a genius in mathematics!" phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14630.0 0.0 0.0 0.0
"Great lecture." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 4287.0 0.0 0.0 0.0
"What does he mean by ""Pivot""?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11490.0 0.0 1.0 0.0
"Solving ❤️" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8820.0 0.0 0.0 0.0
"when linear algebra is a need to know....Prof Strang.....breakin' it down!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15209.0 0.0 0.0 0.0
"What are the exercises that I could practice so that it incorporates what I have learnt watching this video?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11468.0 0.0 0.0 1.0
"Well smart ass, then go a few lectures ahead." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11357.0 0.0 0.0 0.0
"to visualize quadratic function with its saddle point
https://www.youtube.com/watch?v=8aAU4r_pUUU&t=74s" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 14951.0 0.0 0.0 0.0
"39:30 ""That's OK, we only live so long, skip that proof"" LOL" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 1097.0 0.0 0.0 1.0
"hey Yuxuan Wang! congratulations for reaching here :)" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 13147.0 0.0 0.0 0.0
"why do you start with derivatives without going through  limits and continuity first ?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15308.0 0.0 1.0 0.0
"44:00 well that's an outstanding move" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 1225.0 0.0 0.0 0.0
"thank a lot" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14451.0 0.0 0.0 0.0
"Math ❤️" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7612.0 0.0 0.0 0.0
"@ Who else can't help but smile when the familiar formula for the volume of a sphere finally popped up?" ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1487.0 0.0 0.0 0.0
"MIT or UCLA for medicine? " UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7536.0 0.0 0.0 0.0
"Hopefully one day I get chance to touch his feet. So humble with so much knowledge." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4791.0 0.0 0.0 0.0
"26:42
Sir is explaining and he is not even caring!
Bad Attitude!" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 806.0 0.0 0.0 0.0
"Thanks a lot ""super"" Gilbert Strang.  All I know about linear algebra I know from your lectures!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9651.0 0.0 0.0 0.0
"How did it go?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4839.0 0.0 0.0 0.0
"i'm the 107.064 viewer" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13520.0 0.0 0.0 0.0
"I am confused with Thm2, the instructor said and explained like x is coarser than x' but since x' is contained in x and considering the definition of the partition, isn't his explain should be opposite while he is proving Thm2? so x contains x' and more I think" QeYUHA0UMVg "Lecture 21: The Riemann Integral of a Continuous Function" "MIT 18.100A Real Analysis, Fall 2020" 5074.0 0.0 1.0 0.0
"One important thing determinant says about a matrix is how much the volume/area/length is changing. Everything become much clearer with determinants when you learn this fact. There exist very good videos on Youtube about it, where you can see it in action." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 8079.0 0.0 0.0 1.0
MATGRRIXUE!! UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7494.0 0.0 0.0 0.0
"These lectures make me so regret that I was not fortunate enough to go to MIT and sit in this legend's classes." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10418.0 0.0 0.0 0.0
"Can please someone explain me 5:06? Don't get it :/" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3060.0 0.0 1.0 0.0
"@sanjaigupta 
I couldn't write the link, so I will send you by e-mail." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1998.0 0.0 0.0 0.0
"Thanks for iploading
" ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 9685.0 0.0 0.0 0.0
"we love you very much Gilbert Strang :)" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 15075.0 0.0 0.0 0.0
"nice course and teaching.
 hopefully can take next steps from here" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 14031.0 0.0 0.0 0.0
"Newton's method is so good that it takes only 26 steps to get x^2 - 5 root starting at 2 million" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7827.0 0.0 0.0 0.0
"Wow this man is a bomb👏🏽
Jesus is the Son of God. Believe in his death and resurrection then confess his lordship over your life. Love yall🙏♥️" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12043.0 0.0 0.0 0.0
"This is brilliant, go MIT!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10652.0 0.0 0.0 0.0
"28:50 -- The real answer to the question is that the negative there swaps the order of the vector columns. -a2 (b1c3-b3c1) = +a2 (b3c1-b1c3).

This is necessary because the way that the terms in the 3x3 matrix determinant are calculated actually requires you to horizontally scroll the matrix.

|a1 a2 a3|
|b1 b2 b3|  -> a1 (b2c3-b3c2)
|c1 c2 c3|

|a2 a3 a1|
|b2 b3 b1|  -> a2 (b3c1-b1c3)
|c2 c3 c1|

|a3 a1 a2|
|b3 b1 b2|  -> a2 (b1c2-b2c1)
|c3 c1 c2|

The reason why you have to horizontally scroll the matrix has to do with the noncommutativity of transformations. i.e. if you to rotate 90 degrees to the right and then rotate 90 degrees up; you'll be facing a completely different direction than if you rotated 90 degrees up and then 90 degrees to the right. Transformations have to be done in a very specific order: xyzxyz;  xy = -yx, zx = -xz, yz = -zy" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 845.0 0.0 1.0 0.0
"19:28 ... that was a lazy proof of why sin(theta) -> theta ...  when theta -> zero ... lazy lazy ..." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 560.0 0.0 1.0 0.0
"Amazing, this man gots his doctorate degree at 22 years when most of the people gets their undergrad. ""astonishing""" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2403.0 0.0 0.0 0.0
"Excellent professor" 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 3668.0 0.0 0.0 0.0
"If anybody fails with this guy as a teacher.. you should automatically be kicked out of school" wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 6493.0 0.0 0.0 0.0
"At 38:30, Strang says that det(Q)^2 = 1 means that det(Q) is 1 or -1...but that's not true if det(Q) is allowed to be complex. Twenty lectures into this course and I have to mentally question everything so far to see what does and doesn't apply to the complex numbers." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 2655.0 0.0 1.0 0.0
"Would love to see more from Alex Townsend. What a fantastic lecturer!" 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12011.0 0.0 0.0 0.0
"This professor is the platonic version of a professor" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10911.0 0.0 0.0 0.0
"lol at algebraic questions" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13821.0 0.0 0.0 0.0
"“Let’s talk about failure!” Excellent and nice!!!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15595.0 0.0 0.0 0.0
"For Wavelet, the transpose of w4 is shown in the video, or we can say we need to transpose w4(as shown in video) to get a orthogonal matrix" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3840.0 0.0 1.0 0.0
"First 4 minutes are a very poor introduction." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3813.0 0.0 0.0 0.0
"I don't understand hahahaha" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5340.0 0.0 0.0 0.0
"thank you very much" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14522.0 0.0 0.0 0.0
"Are the samples really independent? The 2 59s, they probably impacted." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 2527.0 0.0 1.0 0.0
"Can you guys please attach the PDF of the exam and it's solutions in the description. It would be great. ☺" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3118.0 0.0 0.0 0.0
cool 3eiio3Tw7UQ "19. Weak Law of Large Numbers" "6.041 Probabilistic Systems Analysis and Applied Probability" 12673.0 0.0 0.0 0.0
"30:38 YES!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 891.0 0.0 0.0 0.0
"Just finished a very important evaluation on Multivariable calculus...wow! I dedicate my fine grade to Denis Auroux...don't know how he does it...but his methods are really impactful!" sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7166.0 0.0 0.0 0.0
"It will be such honor to sit there to listen Mr Strang’s lectures" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7003.0 0.0 0.0 0.0
"2020 corona lockdown 2 months finished the course June 2nd, 2020" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 625.0 0.0 0.0 0.0
"what ages are the students in the class?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15118.0 0.0 0.0 0.0
"I'm Fayçal from Casablanca in Morocco and I do thank you so much for this courses, it makes me see matrices clearly :)" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6292.0 0.0 0.0 0.0
"I think there is one more assumption, that 'GB' and 'BG' are considered sequentially on the two children context. Otherwise, it should be 50% that the sibling is a girl." 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 6068.0 0.0 1.0 0.0
"@he2he Thank you man! That was a very good explanation :)" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 1863.0 0.0 0.0 0.0
"@LoquaciousApe , I get this and I learned it all as a freshman in highschool and as a sophmore now I understand this," PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1664.0 0.0 0.0 0.0
"When he said ""this is called a statistic"" it felt like that moment when they say the name of a movie in the movie." rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 11621.0 0.0 0.0 0.0
"It was nice when everyone was happy with dot products" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7000.0 0.0 0.0 0.0
"Yes. I actually am the dog and the kids too. All of them.
So. If I haven't seen you I supposed that it has to be because of matrice's elimination. 

*C'est clair*

*BIEN*" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12153.0 0.0 0.0 0.0
"I was so suprised when the rij(101) = rij(100). Beautiful." IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 6166.0 0.0 0.0 0.0
"Is video of 18.014 available？I hope to learn it after completing 18.01" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6888.0 0.0 1.0 0.0
"Watching this whole course has been a really impressive experience. Informative, clear, and relevant. I am still amazed by the clarity of Prof. Strang with subjects that run the risk of becoming extremely confusing or abstract if delivered in a more ""standard"" manner. Truly grateful to MIT OCW for making these high-quality contents available for everyone!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 11308.0 0.0 0.0 0.0
"just a small note 15:43) A_t*A is positive ""semi""-definite, in general. If A is non-singular(if all columns are independent), _then_ A_t*A is positive definite.
26:02) It can be solved by 'calculating' like u2 = 1/sigma2*A*v2, but the essence is that [the sigmas don't have to be positive, it's just that WE CHOOSE them to be positive].
[u2 / sigma2 / v2] - ANY one of them can have different sign. It's just our choice, like -p=q*r and p=-q*r and p=q*-r are all equivalent.
(of course the order of the columns and sigmas are our choice as well - that's how the sigmas are ordered like that)" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 13727.0 0.0 1.0 0.0
"Hey, did the guy make some mistakes, when he did the pivot numbers? I don't think the third pivot number should be 5, it should be -5 right?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4698.0 0.0 1.0 0.0
"Simply brilliant" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8663.0 0.0 0.0 0.0
"I think you're best in Linear Algebra Course and actually you live when you are teaching courses:d" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6085.0 0.0 0.0 0.0
"I'm mexican and I learned Differantial Calculus when I was 17. I took me a semester to complete the course and then I studied Integral Calculus. Both courses were in English.
" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6348.0 0.0 0.0 0.0
"Professor looks like sting." 4UJc0S8APm4 "23. Classical Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 8398.0 0.0 0.0 0.0
"omg jezz this is sooo basic to do at university we do this in high school in ireland!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14139.0 0.0 0.0 0.0
"@kevinbollers2 Nothing beats the good old blackboard as a teaching tool... especially for math" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1919.0 1.0 0.0 1.0
good JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 12938.0 0.0 0.0 0.0
"In 18.05, the camera movement was very nice. In 18.065, I think the camera person is not that professional." nrDkb2MAwSA "20. Definitions and Inequalities" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6590.0 1.0 0.0 0.0
"me: everything is clear and easy 
*start using miles and feets*
me: lost" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13936.0 0.0 0.0 0.0
"24:31 the guy's tee on the bottom right. A good MIT student." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 734.0 0.0 0.0 0.0
"To think the prof has to teach them how to calculate a determinant.  Smh." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11046.0 0.0 0.0 0.0
"rank=dimension of c(A)=2. how can c(A) be 2-dimensional. rectify me if i'm wrong. is it not a plane inside 3 dimension?" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 14245.0 0.0 1.0 0.0
"Wonder how they got into mit" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11979.0 0.0 0.0 0.0
"Matrices of linear transformations, isn't this part supposed to be in first courses ?" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7620.0 0.0 0.0 0.0
"44:00 covariance matrix" Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1224.0 0.0 1.0 0.0
"Thank you, MIT OCW, for great work you!  Thank you, guys, who leaves funny and helpful comments, from MIPT (Russia). It really helps to  improve and refresh knowledge. Our MIPT's course is built more on how to prove theorems. Maybe it's useful, but sometimes it happens that  students' skills to prove theorems and solve exercises are like two different areas without crossing." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9499.0 0.0 0.0 1.0
"Is MIT still using chalkboards ?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6752.0 1.0 0.0 0.0
2021-10-11 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 630.0 0.0 0.0 0.0
"Damn at the end when he said have a nice weekend I believed it for a second  but then realised it’s Monday today" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3292.0 0.0 0.0 0.0
"very very good & clear thanks very much MIT" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15043.0 0.0 0.0 0.0
"The fact that anyone anywhere can learn this is revolutionary, I think
Some impoverished Einstein now has a golden opportunity" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10098.0 0.0 0.0 0.0
"my question is, despite being the most prestigious technical university in the country, all they can afford is old school Black Boards!!!" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13999.0 1.0 0.0 0.0
great RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 12965.0 0.0 0.0 0.0
"Who can say why When the professor mentions Symmetric Matrices, the top left and bottom right digits don't equal? Is it necessary or irrelevant? 
And is it possible to explain what the represent linearly? " JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11727.0 0.0 1.0 1.0
"Thanks MIT & Professor Miller! This lecture helped me a lot with AP Calculus. I don't know what I would do without this lecture and the other lectures that you guys upload. :D " Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9604.0 0.0 0.0 0.0
"When I was in U the best fit line was calculated by noticing that if you add the deviations you might get even zeros if others are positive and others negative. So you can't just add naked deviations. So our teacher showed that if you take the absolute values and try that the derivation of the line is horrible mess. So next best way to get out of negative deviations is to square them and that was easy calculation. So, that was very illuminating excercise." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11608.0 0.0 0.0 0.0
"18:06 Why did he subtract 2 units?" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 528.0 0.0 1.0 0.0
"excellent Job Professor" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12817.0 0.0 0.0 0.0
"@t92hot But you know on the other hand in my first Mathematics semester at college we also first went through all the stuff we learned at school. However, like you wrote, it's the MIT and I would expect some knowledge about such basic things in advantage." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2032.0 0.0 0.0 0.0
"Sir looks like Creed from The Office. 
All in all great lectures" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 8699.0 0.0 0.0 0.0
"But is still good that you say that now so we don´t get too confused. Thank you.

And Thank you Gilbert Strang for this work!!!" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 2961.0 0.0 0.0 0.0
讲得好！ 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15659.0 0.0 0.0 0.0
"Finish in a week!. moving on to Topology, and optimization + graph theory ( not sure yet). LETS GO! I AM GOING TO IVY LEAGUE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!" rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 3800.0 0.0 0.0 0.0
"I don't know if anyone else has noticed this, but the gradual shift into abstract concepts is done flawlessly by Professor Strang. In the first few lectures, really up until the lectures on bases, all of the methods Professor Strang uses to teach the subjects were concrete examples; very little was done with abstract definitions and arbitrary matrices. Over the last few lectures, Prof. Strang has made a gradual shift into abstractness which let's the mode of this sort of thinking sink in. Now, in this lecture, nothing is concrete and no numbers are ever used (until the end) and it feels effortless to understand! This man is a genius when it comes to math education. Thanks so much MIT and Prof. Strang for the amazing experience!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5318.0 0.0 0.0 1.0
"just checking if Alex is still alive?" 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13730.0 0.0 0.0 0.0
"18:23 ""I'm ready for the kill"", amazing!" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 536.0 0.0 0.0 0.0
"Good Prof but brain wash message" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4121.0 0.0 0.0 0.0
"even the beauty gilbert strang cannot make me love that freaking algebra" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 12804.0 0.0 0.0 0.0
"Woah, it's so cool to see him teaching here 😮" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 11977.0 0.0 0.0 0.0
"What if we consider only rational numbers inside the square? In this case, the set is countable but individual probabilities are still zeroes." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 11507.0 0.0 1.0 0.0
🙏🙏🙏🙏 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 15742.0 0.0 0.0 0.0
"Gilbert Strang and Dennis Auroux are the best teachers I have learnt from and I haven't even attended their class physically, ever ! Thank's a ton MIT for developing a liking for mathematics in me." sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4015.0 0.0 0.0 0.0
"Thank you so much!  Enjoy your teaching!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9383.0 0.0 0.0 0.0
"Dear sir,
isn't the linear approximation formula the first two terms of the Taylor Expansion? Is Linear approximation like Taylor Series but for linear functions?" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3336.0 0.0 1.0 0.0
"Those chalk knocks like nails in the casket.
Or house." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10992.0 1.0 0.0 0.0
"He's a famous mathematician. Feeling privileged after watching his lectures." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 4625.0 0.0 0.0 0.0
"Ehhh, I get that these lectures are great for a lot of people and this man has a passion for math whose teaching has helped a lot of people, but I don't find these lectures are the best for learning the material as I was lead on to be. I find this lecture more theory based without too many examples showing you the step by step methods that others, most notably Professor Leonard, have done. That's understandable given format of the classes at MIT I guess but it would have been nice for me. Maybe that will change in his later lectures so I'll stay in for now." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3553.0 0.0 0.0 1.0
"Is the equation in 22:00 written with matrices M and M inverse switched?" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6812.0 0.0 1.0 0.0
"Is the distance matrix right?" 0Qws8BuK3RQ "34. Distance Matrices, Procrustes Problem" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6811.0 0.0 1.0 0.0
"sir you are a living legend! Cannot thank you enough." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 14311.0 0.0 0.0 0.0
"first time commenting but this is truly amazing" XhSk_Lw2X_U "14. Low Rank Changes in A and Its Inverse" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12872.0 0.0 0.0 0.0
"you're THE BEST wow thank you !" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 15522.0 0.0 0.0 0.0
"No thank you.I'm okay with Calculus" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 7894.0 0.0 0.0 0.0
"I wish I was taught calculus by this guy from the start!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6212.0 0.0 0.0 0.0
"Nice example." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 7841.0 0.0 0.0 0.0
"wat a messy chalkboard unacceptable!!!!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 15062.0 1.0 0.0 0.0
"Does anyone have a quick counterexample for why all rank 4 matricies don't form a subspace?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 3438.0 0.0 1.0 0.0
"@Voltar143 what a usa promoter!" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1756.0 0.0 0.0 0.0
"Really Enjoyed this lecture..helped me to understand double integration by perfect visualisation...thank you prof." YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8501.0 0.0 0.0 1.0
"@ligaluga26 Guck mal hier watch?v=4u0N9Srb3XY" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1930.0 0.0 0.0 0.0
"hello
" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13133.0 0.0 0.0 0.0
"why does nice have more likes than Awesome?" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 15311.0 0.0 0.0 0.0
"A MATH STUDENT IN INDIA PREPARING OF IITJEE WOULD KNOW SO MUCH MORE THAN ALL THESE IN HIGH SCHOOL ONLY" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2094.0 0.0 0.0 0.0
"Se vale lavar el pizarrón." RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 8607.0 1.0 0.0 0.0
"In Italy we don't have such beautiful chalks and erasers!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6613.0 1.0 0.0 0.0
great MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 12964.0 0.0 0.0 0.0
"Why use binomial theorem instead of Taylor expansion?

And professor said it is single variable calculus, but there may have many variables like x0,y0 to confuse peoples. But I think there is only one variable x, x0 is just one value of x." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11930.0 0.0 1.0 0.0
"very useful !!!!!!!!
" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 15039.0 0.0 0.0 0.0
"2 by 2? Easy 
3 by 3? WTF?
3 by 3 Column? WTF
HELP" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 608.0 0.0 1.0 0.0
"This lecture singularly helped me through the concepts on use of eigen values for capturing variability" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10826.0 0.0 0.0 0.0
"P(B/A) would be Sensitivity in Epidemiology. P(Bc/Ac) would be Specificity. This is a great lecture." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 8147.0 0.0 0.0 0.0
Se 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 8604.0 0.0 0.0 0.0
"Glad to see the classroom with students:)" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 4058.0 1.0 0.0 0.0
"""Be assured it works just the same way if you have 10,000 variables""" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 33.0 0.0 0.0 0.0
"Professor Dennis Auroux's #1 Fan" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8323.0 0.0 0.0 0.0
"This is really great and brilliant lecturer i never seen before. I like the methodology he is using and he knows how to engage his students.
I can see now how linear algebra is applied.
Thanks Gilbert Strang and MIT." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 10713.0 0.0 0.0 1.0
"Just based on the lectures until now:
we can’t just put a = between rank(A) and dimension of C(A) right? 
The number 2 may just „happens“ to be the same. 
We calculate the rank by finding the numbers of pivots with row elimination, which changes the column vectors and the eliminated column vectors are apparently not the linear combination of the original ones.
Maybe I will figure it out in lecture 10." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 7158.0 0.0 1.0 0.0
Witches'. ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11965.0 0.0 0.0 0.0
"Python code for the Markov chain n-step transition example: http://nbviewer.jupyter.org/github/YoungxHelsinki/jupyter-notebook-cheatsheet/blob/master/Markov%20chain%20n-step%20transition%20example.ipynb#" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 8466.0 0.0 0.0 0.0
"i think his a french as "" r"" is not well pronounced" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 13471.0 0.0 0.0 0.0
"block multiplication again." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12547.0 0.0 0.0 0.0
"Just finished whole single variable calculus, both prof. David Jerison and prof. Haynes Miller are amazing teachers, 
Thanks MIT OCW for making this possible. India, 2020" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7179.0 0.0 0.0 0.0
"It is nice to see someone who cleans the blackboard fully!!!" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6961.0 1.0 0.0 0.0
"This is an outstanding lecture on Eigenvalues and Eigenvectors. Eigenvalues and Eigenvectors are very important for solving linear systems especially in differential equations. MIT and DR. Strang thank you so much." k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10629.0 0.0 0.0 0.0
"yet ur watching...." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15489.0 0.0 0.0 0.0
"Slight slip at 53:02. The ratio is always greater than or equal to zero.
So set c to zero rather than minus infinity to always conclude H1.
At 1:01:40, on the other hand, we now have the difference of two logs
which isn't necessarily non-negative - it can range from minus
infinity to plus infinity." QXkOaifVfW4 "9. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 8721.0 0.0 1.0 0.0
"Awesome teacher..." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2771.0 0.0 0.0 0.0
"Why doesn't MIT use wet sponges to clean boards with?  >:(" mc1y8m9-hOM "22. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 11852.0 1.0 0.0 0.0
"6:15 COMO FUNCIONA EL CEREBRO HUMANO ...." 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 1381.0 0.0 0.0 0.0
"@blakescello If you use iPhone, then open a browser and go to wolframalpha and search for Limit[(1 + 1/n)^n, x -> Infinity] or just lim_(x->infinity) (1+1/n)^n." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1796.0 0.0 1.0 0.0
"How many blackboards do you want?
Dr Strang: Yes" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4883.0 1.0 0.0 0.0
"This guy is so cute" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 10543.0 0.0 0.0 0.0
"I feel so emotional at the end of the lecture!!! Long-live Prof. Auroux and MIT" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5398.0 0.0 0.0 0.0
"Amazing lecture professor, but I think someone ripped ass at 18:00. Can experts on the subject please verify for my sanity?" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2365.0 0.0 0.0 0.0
"Glad to see he's well!
Much better than the 240p quality of the original linear algebra videos." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4057.0 0.0 0.0 0.0
"not sure why MIT is so revered, this is almost verbatim what i had in my linalg class. i suppose the research is where its a bit different." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14083.0 0.0 0.0 0.0
"It's not that she found a numerical error, it was the power of her reasoning for it. I'm shook, whoever that girl is, she's clearly brilliant." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7062.0 0.0 0.0 0.0
"This lecture just brought my understanding of norms to a whole new level! Thank you so much Professor Strang!" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10816.0 0.0 0.0 0.0
"Which unıversıty" V3Wg_jrMSQY "Lecture 19: Differentiation Rules, Rolle's Theorem, and the Mean Value Theorem" "MIT 18.100A Real Analysis, Fall 2020" 11718.0 0.0 0.0 0.0
Finished. --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3812.0 0.0 0.0 0.0
"Нихера не понял, но лайк поставил)" Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15554.0 0.0 0.0 0.0
"@1:58 Did he just dis Gauss? Boy there's no telling what was natural in Gauss's mind" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1508.0 0.0 0.0 0.0
"@HunterDX77M It's actually not review. Its part of the material for calc 3." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1632.0 0.0 0.0 0.0
"Those paradoxes and the addressal of them: so good!" XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 10995.0 0.0 0.0 0.0
"Thank you so much, sir. From India." CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 9404.0 0.0 0.0 0.0
"will this be on the exam?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 15383.0 0.0 0.0 0.0
"@xo20202004 i also forgot to mention that you can also type in the name of the college eg. harvard, cambridge, StanfordUniversity, UCBerkeley, nptelhrd, calcommunitycontent  etc. (these are some that i have discovered with online courses being offered) in the search box and their channels or lectures would come up. from there you can check out what courses each individual schools are offering." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2070.0 0.0 0.0 0.0
"There seems to be a mistake in the explanation for why pairwise independence does not imply independence ...  at [36:30], event C should be that 'our tosses gave different results', rather than 'our tosses gave same results'.
After checking the book, and my suspicion is confirmed. See example 1.22 on page 39." 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 10382.0 0.0 1.0 0.0
"00:00 det(I) = 1
03:16 det(P) = 1 or -1
07:00 The determinant is linear in **each** row.  
11:34 2 equal rows => determinant = 0.  
14:34 det(A) = det(U).  
19:00 Row of 0s, determinant = 0.  
22:20 det(U) = product of pivots
28:30 det(A) = 0 <=> A is singular
37:40 det(AB) = det(A) * det(B)  
41:40 det(A^T) = det(A)
47:00 Odd / Even number of row exchanges" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 283.0 0.0 0.0 0.0
"I did this in my last year of high school !" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5262.0 0.0 0.0 0.0
"Excellet lecture. Many thanks professor Strang!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3695.0 0.0 0.0 0.0
"Thank you, karsonson. It makes sense to me now." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9520.0 0.0 0.0 0.0
FCP hwDRfkPSXng "Lecture 32: ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3720.0 0.0 0.0 0.0
"@LogicalFlawDetector He would, however, expect his physics teacher to teach him vectors which are used to represent Force, Displacement etc in physics. Dot Product is also highly useful in determining force distribution. More useful in engineering , perhaps, than physics, but there you have it." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1662.0 0.0 0.0 1.0
"Given that column space and null space of a transpose are perpendicular to each other, if p is a projection of b on A then shouldn't it be parallel to N(At)? How can it be perpendicular to N(At) as well? any help pls" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 4051.0 0.0 1.0 0.0
"""@35:53 Forget the word 'associative', but don't forget the law"". Love this." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 23.0 0.0 0.0 0.0
"You should include the case where the saddle point runs diagonally to the axes. Then you would have two critical points, neither being max or min." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12237.0 0.0 1.0 0.0
"If you guys find the determinant of the matrix, it shows Det = 1*(16-15) - 2*(8-6) + 3*(5-4) = 0. So the matrix is not linearly independent." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 6546.0 0.0 1.0 0.0
"I think the shape of the bowl will change when we add (x^T)b at 17:00 . Am I right???" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6065.0 0.0 1.0 0.0
"Thanks to Professor Strang and whole MIT team for providing one of the best content free of cost. I have completed the journey today." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9807.0 0.0 0.0 0.0
"This vedio has thousands of fundamentals in those 50 minutes!!!!! Amazing Proff." EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 10948.0 0.0 0.0 0.0
"The meat starts at 09:56 for those who don't want to waste their time.
21:50 I'm not sure if this is correct :p The probability of 0 assigned to each of these points would mean that there is _absolutely no chance_ I hit _any_ of them :P So I wouldn't be allowed to hit anywhere inside that square, and I'm also not allowed to hit outside of it, so I simply am not allowed to throw the dart at all :P What would be correct to say, I think, is that if the precision _approaches_ infinity, the probability _approaches_ 0, but it is not _exactly_ 0, just something arbitrarily close to it." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 10187.0 0.0 1.0 0.0
"He just saved my from the brim of breaking down trying to understand SVD! What he presented is so natural, so beautiful that I instantly catch them. Appreciate MIT open courseware also!" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4559.0 0.0 0.0 0.0
"Superb teacher!" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 8964.0 0.0 0.0 0.0
"is this calc 3?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13658.0 0.0 1.0 0.0
"You are so nice human being sir." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 12178.0 0.0 0.0 0.0
"damn i spent the entire explanation of gauss jordan wondering why it works but he wrapped it up so nicely in the end" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12710.0 0.0 0.0 0.0
"Ahhhhh, full of knowledge 😛" BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 2290.0 0.0 0.0 0.0
"Wait now i have a question supposed i got the eigenvalues if i used elimination and then i got the eigenvalues again. Would they be the same?" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 11257.0 0.0 1.0 0.0
"finished just now .thanks prof.denis and mit ocw and cameraman/woman.camera focus was amazing😍🥰😘.am gonna miss his board cleaning unless i forget everything" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12866.0 1.0 0.0 0.0
"Likex100! These lectures are simply amazing." wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 7365.0 0.0 0.0 0.0
"No offense to the prof, but the geometric proof was way too convoluted than needed.   

P.S. I've learned calculus before, and just revising the topics." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7881.0 0.0 0.0 0.0
"Thank you sir." u4qQ1oIQcW8 "Lecture 25: Power Series and the Weierstrass Approximation Theorem" "MIT 18.100A Real Analysis, Fall 2020" 9338.0 0.0 0.0 0.0
"this dude makes me happy aha" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14802.0 0.0 0.0 0.0
"23 yrs ago i've learnt linear algebra from Strang's book , thanks sir." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 707.0 0.0 0.0 0.0
"Thank you Professor, i am a medicine doctor. I just wanted to learn linear algebra out of curiosity. Even I, who had not dealt with mathematics for a long time, was able to understand the subject. Thank you very much indeed." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9229.0 0.0 0.0 0.0
nice 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14025.0 0.0 0.0 0.0
"39:45 Taylor Series" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1103.0 0.0 0.0 0.0
"Thanks so much for sharing those excellent courses!!!!! :)  I learned a lot from your open courseware!!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9788.0 0.0 0.0 0.0
"I know of no soft power more effective than these lectures. Thank you MIT for the generosity and commitment." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 5636.0 0.0 0.0 0.0
"I found this helpful for understanding around t=20
https://www.youtube.com/watch?v=0WDUWCtxM1U" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 5432.0 0.0 0.0 0.0
"where is prof jerison. buaaaa!!!!! buaaa!!!!!
" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15240.0 0.0 0.0 0.0
"your teaching is supper, sir, i never see before such knowledge any professor" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 15527.0 0.0 0.0 0.0
"MY WORD THAT DOME" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7557.0 0.0 0.0 0.0
"I think this is love
" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 6075.0 0.0 0.0 0.0
"Saving students from crappy Teachers since Nov 9, 2012... THANK YOU!!!
REPLY" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 8602.0 0.0 0.0 0.0
"Around 6:40 6:40
              6:40 6:40

he says 2 equations, with 4 *unknowns*? Does he mean 4 variables, x_1, x_2, x_3, x_4? Because x_1 and x_3 are in pivot columns and shouldn't be unknowns." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 2558.0 0.0 1.0 0.0
"44:43 Bayes' rule" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 1243.0 0.0 0.0 0.0
"this is awesome." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14855.0 0.0 0.0 0.0
42:00-43:30 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 1171.0 0.0 0.0 0.0
"8th dimensional plane inside a 9th dimensional space. If the values of the 8th and 9th columns are same than it would like a plane over a plane like an onion. I am confused." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 1428.0 0.0 1.0 0.0
"you'll find that with everything like this, it's like a new years resolution. People go ""I'm gonna learn linear algebra!"" then a week later they forget about it" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15521.0 0.0 0.0 0.0
"Thank you !  professor Strang" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9089.0 0.0 0.0 0.0
"14:38, shouldn't that (1,1,1) be in the left nullspace of (A - I) instead of left nullspace of A as demonstrated in the tape？" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 432.0 0.0 1.0 0.0
"@sbhdgr8 you substitute z=x^2 so the higher power ""quadratic"" equation can be written as a actual quadratic equation az^2+bz+c." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 2003.0 0.0 1.0 0.0
"Professor Strang, you're continuously amazing!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8389.0 0.0 0.0 0.0
"But how is this useful?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 2960.0 0.0 0.0 0.0
"Is this video incomplete?" ImHAGH_OEow "Lecture 20: Taylor's Theorem and the Definition of Riemann Sums" "MIT 18.100A Real Analysis, Fall 2020" 6886.0 0.0 0.0 0.0
"Thanks.  The MIT website provides pdfs of the prepared slides.  So the student can see a clear pdf side by side to the video on their computer. The pdf file can be downloaded.  Window placement can be side by side.  The State ID Numbers (IDs)are absent when I view the pdfs for this lecture.  The Professor John Tsitsiklis does refer to the IDs.  Some PDF readers including Adobe products can annotate with a text box the downloaded pdf.  You can add the same IDs fresh in your copy of the document.  The annotation can make the lecture easier to follow." HIMxdWDLEK8 "18. Markov Chains III" "6.041 Probabilistic Systems Analysis and Applied Probability" 9857.0 0.0 0.0 0.0
"Thank you Professor for an amazing lecture and MIT for publishing!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 9228.0 0.0 0.0 0.0
"Great interview! Thanks for all your lectures" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4235.0 0.0 0.0 0.0
"At 24:20 when he says that the multiplier goes directly into L, he means the negative right? If you keep a track of the operation on the left side, it inverts while bringing it to the right side." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 2619.0 0.0 1.0 0.0
"Did he say toin coss instead of coin toss LOL" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3379.0 0.0 0.0 0.0
"Shouldn't students at MIT already know this?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8648.0 0.0 0.0 0.0
"I was worrying about how tough and dense this lecture was, then the rest of the comments were reassuring! It all came clear in that final step too." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6177.0 0.0 0.0 0.0
"Of course it's going to be easy for a high schooler to understand this. It's the third lecture... People in that classroom only have high school math behind them." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7996.0 0.0 0.0 0.0
"The summary is brief and billiant!, Ax=b, cool!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 10294.0 0.0 0.0 0.0
"I want to self teach calculus 3 in a month, is it possible?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6142.0 0.0 0.0 0.0
"Thank you!!!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9485.0 0.0 0.0 0.0
"Correction of error from previous lecture 0:43
Introduction to the four fundamental subspaces
(column space, null space, row space, left null space) 4:20
Basis and dimension of each fundamental subspace 11:44
Basis and dimension of the column space 12:50
Dimension of the row space (it is the rank) 14:41
Basis and dimension of the null space 17:05
Dimension of the left null space (m - rank) 19:41
Basis of the row space (nonzero rows in the rref) 21:08
Basis of the left null space 29:48
Review of the four fundamental subspaces 42:09
A new vector space of all 3 by 3 matrices 42:32" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3221.0 0.0 0.0 0.0
"Chalk ❤️" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3138.0 0.0 0.0 0.0
LEGEND 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7225.0 0.0 0.0 0.0
"Gil flips his shit ... ~45:00" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 4007.0 0.0 0.0 0.0
"God bless you." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4090.0 0.0 0.0 0.0
"Ive watched all lectures in 18.06 and it's a shock to me how old Srang has grown. I pray that we can keep him forever. Please god, never take him from us." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7106.0 0.0 0.0 0.0
"My guy be spittin'straight facts right there 👉" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7758.0 0.0 0.0 0.0
"@yamborghini3 2:40, girl on the left." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2074.0 0.0 0.0 0.0
"I should be going to MIT" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5963.0 0.0 0.0 0.0
"This is quite possibly the best lecture, and certainly the best explanation of how the formula for combinations is derived from the formula for permutations, that I've ever seen." 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 10709.0 0.0 0.0 0.0
"I think khanacademy did a better video =) just my opinion, this video is helpful also =)" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6033.0 0.0 0.0 0.0
"Thanks Mit" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 9625.0 0.0 0.0 0.0
"if only in schools we could get that clarity of concept :'(" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13536.0 0.0 0.0 0.0
"BEAUTIFUL 板书 ，neat！" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2800.0 1.0 0.0 0.0
"very good but so slow ..." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 15003.0 0.0 0.0 0.0
"You are MIT and still using chalkboards?!!!" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 12162.0 1.0 0.0 0.0
"When in our short lives would when ever use this-or even need to know it--just multiply numbers, divide them, add them subtract them and know how to figure out a percent-other than that the rest is all just bullcrap and worthless. It's mind games with no everyday use whatsoever. he's a nice guy and i expect from the comments he's good-but it's just mine games with no common use in our everyday lives." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11629.0 0.0 0.0 0.0
"Amazing lecture" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 2363.0 0.0 0.0 0.0
"God bless you sir. I see in this video professor Strang has injured his left hand. Yet he taught the class. I don’t know if any of the other viewers noticed that." sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4084.0 0.0 0.0 0.0
"The term universe is very and increasingly overused. Everything has to be clearly defined and understood. Outer “space” is not to be referred to as SPACE. Gravity, as it has been written, is an interaction. It is fundamental. The term inertia is now redefined as “inertia/inertial resistance”. BALANCED inertia/INERTIAL RESISTANCE is fundamental. Einstein never nearly understood physics/physical experience. Here are the facts.

PRECISELY WHY AND HOW THE BALANCED, TOP DOWN, COMMON SENSE, SIMPLE, EXTENSIVE, AND CLEAR MATHEMATICAL UNIFICATION OF PHYSICS/PHYSICAL EXPERIENCE IS PROVEN BY (AND CONSISTENT WITH) F=MA AND E=MC2:

The following also CLEARLY explains why the rotation of WHAT IS THE MOON matches it's revolution.

c squared represents a dimension of SPACE on balance WITH the fact that the stars AND PLANETS are POINTS in the night sky. Indeed, the sky is blue; AND what is THE EARTH/ground is ALSO BLUE (on balance) !! Consider what is the speed of light (c) ON BALANCE. A PHOTON may be placed at the center of what is THE SUN (as A POINT, of course), AS the reduction of SPACE is offset by (or BALANCED with) the speed of light (c) (ON BALANCE); AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/energy is (CLEARLY AND necessarily) proven to be gravity (ON/IN BALANCE).

General Relativity is directly taken from Special Relativity. E=mc2 is taken directly from F=ma. CLEARLY, gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites (ON BALANCE); as the stars AND PLANETS are POINTS in the night sky. Consider TIME (AND time dilation) ON BALANCE. I have exposed Einstein. Beautiful.

Note: Consider what is THE EYE ON BALANCE. Think carefully about the black “space” AS WELL. Great. It ALL CLEARLY makes perfect sense, as BALANCE AND completeness go hand in hand. THE EYE represents a two dimensional surface OR SPACE (ON BALANCE) that is consistent with F=ma AND E=mc2. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN/ON BALANCE. Consider what is necessarily, CLEARLY, logically, and by definition the MIDDLE DISTANCE in/of SPACE ON/IN BALANCE. GREAT !!! Think about what is true/real QUANTUM GRAVITY !!! Great.

Consider what is THE SUN. The sky is blue, and THE EARTH/ground is ALSO BLUE. Again, the stars AND PLANETS are POINTS in the night sky. GREAT. E=mc2 IS F=ma. This explains the fourth dimension AND the term c4 from Einstein's field equations. BALANCED inertia/INERTIAL RESISTANCE is fundamental.

The gravitational “field” is E=mc2 as F=ma. Consider what is THE EARTH/ground ON BALANCE. The stars AND PLANETS are POINTS in the night sky. Consider TIME (AND time dilation) on balance. Consider what is THE SUN ON BALANCE. I have explained why the rotation of WHAT IS THE MOON matches it's revolution. The sky is blue, and THE EARTH/ground is ALSO BLUE. Carefully consider what is THE EYE ON BALANCE. Consider what is the balanced MIDDLE DISTANCE in/of SPACE. E=mc2 IS F=ma ON BALANCE. That's the answer. ELECTROMAGNETISM/energy is CLEARLY and necessarily proven to be gravity (ON/IN BALANCE).

Get a good LOOK at what are the fully illuminated (AND setting) Moon AND the orange AND setting Sun. Consider what is the blue sky ON BALANCE. Lava is orange, and it is even blood red. THINK !!! SO, ON BALANCE, consider what are the tides !!! Excellent. E=mc2 IS F=ma. Accordingly, it ALL CLEARLY makes perfect sense; as BALANCE AND completeness go hand in hand. Again, the stars AND PLANETS are POINTS in the night sky. Consider what is THE SUN ON BALANCE. Think about what is the BALANCED MIDDLE DISTANCE in/of SPACE, AND consider what is the speed of light (c) ON BALANCE !!! GREAT !!! Consider TIME (AND time dilation) ON BALANCE !!! Wonderful. The sky is blue, AND THE EARTH is ALSO BLUE. The tides are CLEARLY and necessarily proven to be ELECTROMAGNETIC/gravitational ON/IN BALANCE, as E=mc2 IS F=ma (ON/IN BALANCE).

By Frank DiMeglio

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Frank DiMeglio

 · Just now" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 10297.0 0.0 0.0 0.0
"While discussing 4th way of matrix multiplication, gives subtle hints so that it'll strike you that matrix multiplication is actually about the inner product of the column vectors of the 2 matrices (a^T×b).

What an absolute legend." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11722.0 0.0 0.0 1.0
"Is it just me or did we learn this all in pre calc?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6780.0 0.0 0.0 0.0
"question, why does curl come out twice the rotational speed" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14238.0 0.0 1.0 0.0
"01:38 that girl in left corner of video having breakfast in classroom reminds me of elementary school" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 287.0 1.0 0.0 0.0
"great lecturer!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12991.0 0.0 0.0 0.0
"Why 140 dislikes" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11763.0 0.0 0.0 0.0
"Had to go on Khan academy to learn what this guy was teaching: all he had to do was say ""at this point, I am adding zero to this equation.""" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4412.0 0.0 0.0 0.0
"a legend, not less than a legend" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 12285.0 0.0 0.0 0.0
"live long and prosper" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13812.0 0.0 0.0 0.0
"Remember guys, believe in the law of cosines!!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8548.0 0.0 0.0 0.0
"At 30.29 he ask"" what is the dimension of S? "" How Dim(S) = 3 ?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 2635.0 0.0 1.0 0.0
"students are dumb in his class." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 14404.0 0.0 0.0 0.0
"26:20 shouldn't it be row * column? Column * row is not the right order?" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 799.0 0.0 1.0 0.0
"Do americans learn calculas in college? Because in India we learn this in high school" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3408.0 0.0 0.0 0.0
"well... professor is using ""distance"" so speed would be correct... if he said displacement then he should have used ""velocity""" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15096.0 0.0 1.0 0.0
"Great professors, great institution" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4329.0 0.0 0.0 0.0
"where is lec 17" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15234.0 0.0 0.0 0.0
"I was forwarding like crazy until I hear something and was thinking ""Damn not only the first minute without audio"". Just to realise my sound was mute" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 6153.0 0.0 0.0 0.0
"Interesting facts about normal matrices!" 1pFv7e9xtHo "31. Eigenvectors of Circulant Matrices: Fourier Matrix" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6728.0 0.0 0.0 0.0
"He teach me how to draw" WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4611.0 0.0 0.0 0.0
"When would any of this be used in life?" G3mAXHuoDSw "Lecture 4: The Open Mapping Theorem and the Closed Graph Theorem" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 11642.0 0.0 0.0 0.0
"U don't respect book....
U put it down" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11110.0 0.0 0.0 0.0
"Thanks to you we really start to  see what s going on in Algebra" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 9814.0 0.0 0.0 0.0
"it's snowing，how cute" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13699.0 0.0 0.0 0.0
"@ttttrigg3r Because he was friend with Ralph's little brother :-)" jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2050.0 0.0 0.0 0.0
"Sal from Khan Academy has a much more analytical and easier to follow proof for why lim sin(x)/x is 0." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8594.0 0.0 0.0 1.0
"Why lecture 2 has no audio.?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11897.0 0.0 0.0 0.0
"10:00 When I was in U in Helsinki, Finland in 80's in comparable lecture the same question about generilization to higher dimension was asked and our lecturer gave almosty exactly the same answer as in here but augumented it with this: ""One should invert a 100*100 matrix once in a lifetime to appriciate the fact that almost all multivariable mathematics can be reduced to two or three dimensions.""" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 339.0 0.0 0.0 0.0
"my 5 year old son can study it easy instruction" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13969.0 0.0 0.0 0.0
"Just amazing!" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 7156.0 0.0 0.0 0.0
"Thanks, merci beaucoup prof Strang, absolute brillant" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 9849.0 0.0 0.0 0.0
"Dear Professor, I saw most of your video. you teaching strategy is just awesome. you really know magic. you changed my life." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3332.0 0.0 0.0 0.0
"I cant wait til the fuckers thinking they smart cus they understand this get slapped in the face by the reality of proof based math, if you think this is as hard as it gets your in for a fun time." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5236.0 0.0 0.0 0.0
"This just makes me want to go to MIT that much more...." 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10778.0 0.0 0.0 0.0
"Kih kih, look in biginning!" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 7215.0 0.0 0.0 0.0
"One of the best explanations of determinants I've seen! Thanks MIT!" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8089.0 0.0 0.0 0.0
❤️❤️ MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 15612.0 0.0 0.0 0.0
"What came first? The differential or the Leibniz notation?" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11474.0 0.0 1.0 0.0
"Great professor, makes these concepts so much easier to understand" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 4327.0 0.0 0.0 0.0
"e, one of the most beautiful functions describing the nature should be presented in a way crystal clear and enjoyable by the audience, but shouldn't be this laborious. This is not typical of Prof Jerison." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12781.0 0.0 0.0 0.0
"26:04 What the heck is a transformation? What is he explaining here? Somebody, help!" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 792.0 0.0 1.0 0.0
"and the sidewalk chalk is a great idea. I sit in the second (out of 4) row in my calc 3 class and often can't tell what is being written on the green board. also green boards are a terrible idea. " dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 12374.0 1.0 0.0 0.0
"Just Finished 18.01.
Thank you Prof. David Jerison, Prof. Haynes Miller and MIT OCW!" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7149.0 0.0 0.0 0.0
"@32:40 - ""I don't care!""" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1539.0 0.0 0.0 0.0
"32:00 نقطة مثير للأهتمام" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 924.0 0.0 0.0 0.0
"Amazing Content , Thank You." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 2349.0 0.0 0.0 0.0
"Yeah, without proofs its strange but this guy is a brilliant prof. I love him. Good job!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12130.0 0.0 0.0 1.0
"Amazing pedagogy" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 2385.0 0.0 0.0 0.0
"my lecturer covered this topic within 10 powerpoint slides-.-" WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13986.0 0.0 0.0 0.0
"Gotta read that article on kissing so I can better understand statistics..." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 4172.0 0.0 0.0 0.0
"Is there any proof on the column vectors where the free variables lie are independent to each other so that one can say the dimension of the null pace of a m by n matrix A is n-r ¿" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6840.0 0.0 1.0 0.0
"this is the best way possible to describe the rank of a matrix! for so long I have struggled with this concept! And now it feels so rudimentary, so basic! Thank you professor strange for such a fantastic way of explaining things" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 14879.0 0.0 0.0 0.0
"11 students failed this class" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 357.0 0.0 0.0 0.0
"Finally!! I had been checking for it every day the last couple of weeks 👌👌👌" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3792.0 0.0 0.0 0.0
"thank you Professor Strang~ inspiring me so much in learning in linear algebra <3 <3 <3" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 14489.0 0.0 0.0 0.0
"Thank you so much" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 9340.0 0.0 0.0 0.0
"@Bubblewhip341   lol. MIT is not an Ivy league school (although it's still a top notch college)." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 1605.0 0.0 0.0 0.0
"what's the story with all the spam below" PnPIqh7Frlw "Lec 24: Simply connected regions; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15198.0 0.0 0.0 0.0
"Lol he fails to explain the ""binomial theorem"" so I had to look it up in the middle of the video." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7398.0 0.0 1.0 0.0
"does anyone know a good textbook to buy for this course?" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12764.0 0.0 0.0 0.0
"how a matrix can be symmetric and triangular at the same time? got lost in this lecture" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 13190.0 0.0 1.0 0.0
"You know why he writting so fast . If you think it is for style , Wrong . Because of video length ." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12220.0 0.0 0.0 0.0
"Absolutely well done and definitely keep it up!!! 👍👍👍👍👍" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 2212.0 0.0 0.0 0.0
23:12 QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 709.0 0.0 0.0 0.0
"Great lecture!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 4260.0 0.0 0.0 0.0
"it would be great if u stop thinking!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13688.0 0.0 0.0 0.0
"I Really Like The Video Linear and quadratic approximations From Your" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4987.0 0.0 0.0 0.0
"This Prof. must be French." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10461.0 0.0 0.0 0.0
"This is incredible!! Thank you so much! You can’t even imagine how much I appreciate this. I would really love to see more pure math content like topology and abstract algebra!!" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 10677.0 0.0 0.0 0.0
"@7:00 ish.. If I am understanding correctly, limiting distribution is not always Gaussian. There might be cases when CLT isn't valid such as when n is small. Are there any other cases? And how were the bounds defined for kiss example? If someone can explain, I would appreciate it." C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 1576.0 0.0 1.0 0.0
"Is there any one one who can help me which book or slides this course is based on? It would be very great, thank you." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 6835.0 0.0 0.0 0.0
"Column picture is my favorite 🤓💯👍" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3164.0 0.0 0.0 0.0
"24:27 the author explains that since 1-cos(theta) goes to 0 while theta goes to 0 and considers this a proof. This is not. Because theta goes to 0 also. This limit can't be proven geometrically, because both quantities are going to 0 and even if 1-cos(theta) is presumably much less then theta, it doesn't mean the ratio of them equals to 0, from this geometric construction. Maybe it is equal to 0.0000000000001. So, unfortunately the lim (1-cos(theta))/(theta) = 0 remains mathematically unproven. The prove can be derived from the first remarkable limit (sin(x)/x ---> 1) and fact that cos(x) = 1-2*sin(x/2)*sin(x/2). I leave the proof to the reader as a 2 minutes home work." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 733.0 0.0 1.0 0.0
"Brilliant!!!!! 😍" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2942.0 0.0 0.0 0.0
"u r comment is more random than chaos is." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14974.0 0.0 0.0 0.0
"How do we clone this guy!!??  He`s fantastic!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4850.0 0.0 0.0 0.0
"Love those sliding elevated MIT blackboards!" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7462.0 1.0 0.0 0.0
"43:10 ""please say it"" ahhahah" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 1198.0 0.0 0.0 0.0
"Every time he erases the chalkboard I sneeze :(" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3604.0 1.0 0.0 0.0
"42:15, 42:42,46:35" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 1176.0 0.0 0.0 0.0
"So thankful for this wonderful material! Thank you and congratulations for the commitment to human education!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 8789.0 0.0 0.0 0.0
"""I didn't GOT to MIT""

agreed" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 54.0 0.0 0.0 0.0
"IELTS Academy" BctaYoR9tOY "Lecture 18: The Adjoint of a Bounded Linear Operator on a Hilbert Space" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 6444.0 0.0 0.0 0.0
"Where can I get the slides used in the video?" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 11661.0 0.0 0.0 0.0
"What does it mean when the projection matrix is trying to be the identity matrix?" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 11492.0 0.0 1.0 0.0
"One thing I didn't understand. When he solved for A transpose ..2nd row becomes 0 because it's dependent on 1st row ..4th row also became 0 but it doesn't depend on any other row.. he said that row of 0's means that original row is a combination of other rows ..but 4th row is not a combination so why it became 0??? Please help if anyone knows the answer!" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 8108.0 0.0 1.0 0.0
"he's a magician" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 13121.0 0.0 0.0 0.0
"""Mit cheap black board"" 😂" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 88.0 1.0 0.0 0.0
"11:48 ""what the hell""... hahahahha" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 380.0 0.0 0.0 0.0
"Thank you." 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 9542.0 0.0 0.0 0.0
1:15:00 VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 591.0 0.0 0.0 0.0
"Unique and best explanation of derivation in youtube, love this!" lWW54ts9Ubo "24. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 11123.0 0.0 0.0 0.0
"I like the sound that the chalk makes on the board." PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5683.0 1.0 0.0 0.0
"Complete 😋
(BTW there're some errors in caption" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3179.0 0.0 0.0 0.0
"I LOVE YOU MAN" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 4930.0 0.0 0.0 0.0
"came here from 18.06 fall 2011 Singular value decomposition taught by Professor Strang" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12588.0 0.0 0.0 0.0
"can we diff tan inverse  using definition of differentiation " eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12635.0 0.0 1.0 0.0
"To be clear that I'm not missing something in the lecture, he assumes exp(lambda*t) is a solution to the matrix differential equation BEFORE he has explained what a matrix exponential is or shown how it might be derived, correct?

I'm asking because I want to make sure I'm not missing some section of the video.

I went back and watched parts of it multiple times and I think he is skipping around at some places in a way that makes it hard to follow, even if you're familiar with differential equations and the material up to this point.  I generally like his broad and conceptual approach but in this video I believe there were too many jumps from one line of thought to another.

Nonetheless, once I got past some of the excessive handwaviness, the overall approach to decoupling differential equations is excellent and I learned a lot." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 11026.0 0.0 1.0 0.0
"OK, we're executing a determinant formula here. lol!" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 7975.0 0.0 0.0 1.0
"the first lecture has 580k viewers, and lecture 23 has 30k viewers? Are those people really want to learn something?" 4UJc0S8APm4 "23. Classical Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 14691.0 0.0 0.0 0.0
"What a lovely teacher..." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 11425.0 0.0 0.0 0.0
"What is particular solution and the meaning of ""one one"" professor said at 34:30 ?" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 11521.0 0.0 1.0 0.0
"Not able to understand.. 😔" 0Qws8BuK3RQ "34. Distance Matrices, Procrustes Problem" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7915.0 0.0 0.0 0.0
"what happend at 07:35 . I heard beeep sound lol." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 15139.0 0.0 0.0 0.0
"Transpose([0 1 -2 1]) 
 is also nullspace....why didn't he include that??" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 11082.0 0.0 1.0 0.0
"""I'm sorry that's on tape"" Strang 2005" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 66.0 0.0 0.0 0.0
"Thank you, thank you a lot. I live in Spain and now I can studied Algebra thank to this videos." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9535.0 0.0 0.0 0.0
"for the proof of the limit of (1-cos(x))/x - > 0, why doesn't he just use the sin(x)/x limit he just used beforehand?  Seriously,  take the expression for: sin^2(x/2) is equivalent to (1/2)(1-cos(x)), multiply both sides of the identity by 2,  then bring in the x denominator, and divide top and bottom of left side by 2, giving: (sin(x/2))(sin(x/2)/(x/2)).  Limit of a product is product of limits = (0)(1) = 0?

I know the answer is to prove it geometrically,  however he could prove it with identities, and tell the student to look up a book if they required a more rigorous explanation - assuming that's not in an exam!

Note: I do really like these videos. " kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12890.0 0.0 1.0 0.0
"@aljoshabre The only requirements to go to college (or University in my case) is willingness and money, in this case, money is no concern. But the requirement to GRADUATE and CONTINUE in college is different. So they all deserve to go if they wanted." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1774.0 0.0 0.0 0.0
"really useful, thanks!!" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14257.0 0.0 0.0 0.0
"samurai jack too!" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14280.0 0.0 0.0 0.0
"It's real algebraist hours, my dudes." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 7066.0 0.0 0.0 0.0
"what is so funny about the board???? it wasn't funny the first time. And still isn't, considering its like de 10th lecture." 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15161.0 1.0 0.0 0.0
"thanks professor Strang!!!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14602.0 0.0 0.0 0.0
"If I don't get any point in a small region of topographic map of a mountain, it indicates there is no peak . Is this true ??" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 6464.0 0.0 1.0 0.0
"I love this course" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 5802.0 0.0 0.0 0.0
"its because he leaves al the' in math written"" proves to the book and get to the point and explains what he's doing where as most teachers  explain something by writing the prove down that no-one really understands" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13705.0 0.0 0.0 1.0
"Buena exposición, con una clara forma de comunicar la idea de un campo conservativo y las interpretaciones físicas del mismo." z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2953.0 0.0 0.0 0.0
"To anyone considering watching all 35 lectures, do it. Professor Auroux teaches better than anyone I've ever seen before. Everything is structured, thought out, and flows from one topic to the next so effortlessly that you'll be amazed you just sat through 50+ minutes of math." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11024.0 0.0 0.0 0.0
"Love OCW. Figured they would have something for this to self study" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 7431.0 0.0 0.0 0.0
"for anyone wondering how he turned the fibonaci sequence to a matrix @ 37:00 you are not alone , check this video out  https://www.youtube.com/watch?v=iVNoIwY0UV8" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 12881.0 0.0 1.0 0.0
"how is it different from the precious set of videos?" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13236.0 0.0 0.0 0.0
"WOW....
Awesome ...Professor is direct, to the point, simple and comprehensive at the same time in explaining the concepts...." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 11248.0 0.0 0.0 0.0
"how is he able compute the matrix result at 29:33 so quickly?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13235.0 0.0 1.0 0.0
"i hate when teachers be like : who does not know this: and then go and read about it. LOL" JTbZP0yt9qc "6. Maximum Likelihood Estimation (cont.) and the Method of Moments" "MIT 18.650 Statistics for Applications, Fall 2016" 13391.0 0.0 0.0 0.0
"He makes PCA way more complicated than it should be, wow..." WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 4582.0 0.0 0.0 0.0
"It is the best linear algebra lecture ever!!! But I do not get where the Identity matrix E31 comes from (at 16:47) ? Could anyone pls help me with this?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 6968.0 0.0 1.0 0.0
"This lecture is super easy to understand. Thank you for this legendary lecture, Michael.  
1. Parallelism(Union) shows branching in programming. 
2. Sequential process(Concatenation) shows just the process of programming itself. 
3. Star (*) means the loop in programming." oNsscmUwjMU "2. Nondeterminism, Closure Properties, Conversion of Regular Expressions to FA" "MIT 18.404J Theory of Computation, Fall 2020" 10812.0 0.0 0.0 1.0
"So much white patriarchy, microaggression, and racism in this video!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8781.0 0.0 0.0 0.0
"This single lecture is like the backbone of this subject.

Great revisioh" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 10928.0 0.0 0.0 0.0
"DR. Strang thank you and MIT for another great lecture on classics linear algebra topics." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 3278.0 0.0 0.0 0.0
"Thank you!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9467.0 0.0 0.0 0.0
"what a lecture." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15110.0 0.0 0.0 0.0
"Yufei Fucking Zhao? Omg this guy is a god." RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 12267.0 0.0 0.0 0.0
"limit of cos(x)-1/x^2" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13796.0 0.0 1.0 0.0
"Dterminants is my fav part of linear Algebra xD" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 3520.0 0.0 0.0 0.0
"great person" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12996.0 0.0 0.0 0.0
<3 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 1455.0 0.0 0.0 0.0
"Why? Why talk about matrix space?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 11943.0 0.0 0.0 0.0
"Best prob lect!" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 2872.0 0.0 0.0 0.0
"Can't wait for next Marvel's ""Doctor Strang in the Multi-Dimension of Madness""" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 3127.0 0.0 0.0 0.0
"yedin ömrümü cilbırt" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 15477.0 0.0 0.0 0.0
"@aadityakalsi Actually, there is.
-1, +2, -1" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 1764.0 0.0 0.0 0.0
"how come there are people dislike these lectures?" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 13205.0 0.0 0.0 0.0
"Differential Geometry, and yes even Geometric methods for Number Theory (potentially)" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3399.0 0.0 0.0 0.0
"dang! i am 13 and this is how school is going to be when i grow up." XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12719.0 0.0 0.0 0.0
"dam  such  fun  memories  loved calculous" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12704.0 0.0 0.0 0.0
"Wonderful lecture series Pro. Strang. Hats off. Explanation of the intuition is great, which lot of others can't." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11989.0 0.0 0.0 0.0
"I finally understood OLS in econometrics, now I can say I comprehend what I'm doing, instead of mindlessly applying formulas and rules. Thank you verry much Mr Strang." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 5409.0 0.0 0.0 0.0
"""frog leg"" 28:15 (:
" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 153.0 0.0 0.0 0.0
"dang i am in precal class, wanting to get a jump start on calculus, and none of this or lecture one made any sense, he kept talking about limits and derivitaves and even showed examples, but never explained how to get them that well, or even what they were....have the ppl in this class had previous exposure to this stuff?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12717.0 0.0 0.0 1.0
"okay this was extremely useful! 
revising for exam for discrete mathematics first year at the University of Bath, and  from 16:25 best way of thinking of fast fourier transforms and matrices that i have heard!! very simple, well explained, he's a great lecturer. " M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 14131.0 0.0 0.0 0.0
"The prof says A means B writes C" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10242.0 0.0 0.0 0.0
"Anyone from SRM , AP" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2494.0 0.0 0.0 0.0
"@hvutrong of course, i can't even begin to understand most of them and their complexities, i think they are useless unless you wana become some linear algebra lecturer." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 1874.0 0.0 0.0 0.0
"be thankful" rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 12514.0 0.0 0.0 0.0
"how many times has watching a lecture brought a smile to your face ? I was constantly smiling - every time he pointed out something that I hadn't thought of in the way he mentions it. Such an amazing teacher!" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 13246.0 0.0 0.0 0.0
Boardseption FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2905.0 0.0 0.0 0.0
"In the original example we treated used all of the identity elements (1,0;0,1) in the solution (x), but in the transpose we just reduce it to ""1"". Why?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 6679.0 0.0 1.0 0.0
"This lecture was made just fine for dft." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 10832.0 0.0 0.0 0.0
thankyou！ Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 14620.0 0.0 0.0 0.0
"Around 40:27. Does anybody know how to derive the result of reduction rate of m/M (the condition number)? Any tip or reference?" AeRwohPuUHQ "22. Gradient Descent: Downhill to a Minimum" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2556.0 0.0 1.0 0.0
"Amazing lecture!" YAo1sd4kuOQ "2. Forbidding a subgraph I: Mantel's theorem and Turán's theorem" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 2366.0 0.0 0.0 0.0
"Thank you professor Gilbert Strang." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 9309.0 0.0 0.0 0.0
"Erm, on their website where these videos are uploaded, it says they were recorded in the Fall of 1999. Yet in the youtube videos, they are from 2005. Which is the correct date? ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3575.0 0.0 0.0 0.0
"if you belive the law of cosine, its a proof of the dot product. If you belive in the dot product but not in the law of cosine, then its a proof of the law of cosine. But if you don't belive in neither of them like me, then its a bit harder..." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13551.0 0.0 0.0 0.0
"I love you.Edna..Typical Bosniak name..23:33" wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 5853.0 0.0 0.0 0.0
"linear algebra is so fun in Prof Gilbert Stang 's hand." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 13802.0 0.0 0.0 0.0
"Really understanding inv(A) = 1/det(A) * CT because of prof. Strangs explanation is an amazing thing; it just hit me, epiphany style. Just marvellous teaching." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 8533.0 0.0 0.0 1.0
"these are my favorite lessons" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 14769.0 0.0 0.0 0.0
"awesome video. thank you!" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 12494.0 0.0 0.0 0.0
"Love it!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7445.0 0.0 0.0 0.0
"23:29 loved it!!!" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 711.0 0.0 0.0 0.0
"This MIT probability video playlist changed my way of thinking towards probability.... ✌✌✌" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 10458.0 0.0 0.0 0.0
"He's a Hero." hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4623.0 0.0 0.0 0.0
"Thanks MIT" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9592.0 0.0 0.0 0.0
"sigh! ... i wish they could upload the remaining lectures ... i wish!!" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14299.0 0.0 0.0 0.0
"Before this lesson, I liked linear algebra.

Now I LOVE IT!!" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 2837.0 0.0 0.0 0.0
"this is kinda boring, I mean, if we're going to be engineers, there's no way we're gonna do exercises like this. It doesn't have any application." eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14864.0 0.0 0.0 0.0
"Audio channels fixed!" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 2740.0 0.0 0.0 0.0
"Partial fractions starts at 0:45 until 18:20, which is also important." aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8155.0 0.0 0.0 0.0
"Well explained.
Look forward to having more lectures from your side." WWZ_CeiRnIo "Lecture 22: Fundamental Theorem of Calculus, Integration by Parts, and Change of Variable Formula" "MIT 18.100A Real Analysis, Fall 2020" 11351.0 0.0 0.0 0.0
"shit, you prophet or something?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14291.0 0.0 0.0 0.0
"can anyone tell me that how R is rotated by 90 degree , is R a vector too ?? it is just a matrix right ? it would be great help if someone can help ...." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12615.0 0.0 1.0 0.0
"Pure math man
" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8463.0 0.0 0.0 0.0
"If you take this class my advice is first dont let this be your first stat class, you will be in trouble. This professor might be super clear if you already know what he is explaining but if you dont, he is a terrible professor. The only ones that do good are the ones that already took other courses. He knows his stuff of course, but he is not an efficient communicator, he cant clearly think in the student perspective, and his TAs are just like him too. You will be dazed and confused, just a fair warning.. Plus adding to the above he also makes several mistakes in what he writes, and has the annoying habit of speeding up and talking fast as the content gets more complicated, instead of doing the exact opposite like a professor should. Case in point, at 47:04 professor changes variables to x, should be y. Its a small detail right? But this in newly introduced concepts can cause confusion, and put this together with a fast pace, and you will be struggling a lot of things that are quite easy, but because his communication skills are lacking, the easy becomes confusing and difficult fast." TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 6556.0 0.0 0.0 0.0
"lets do some base 8 octal trigonometry for fun and double check our binary conversions then run a hexadecimal sequence for simple trig so we can fast track it as brain only math once hardwired in neural think the jump to quantum consciousness it only a spark away" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13784.0 0.0 0.0 0.0
"Thank you MIT for posting these excellent courses online! The professors are great! The lectures are very well done!" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 9146.0 0.0 0.0 0.0
"His closet consists of 7 version of the exact same outfit." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 4745.0 0.0 0.0 0.0
"I wish I were as good at *anything* as this guy is at teaching." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6214.0 0.0 0.0 0.0
"def fibonacci(n):
	l1 = (1 + 5 ** .5) / 2
	l2 = (1 - 5 ** .5) / 2
	return (
		0.4472135954999579 * l1 ** n
		- 0.4472135954999579 * l2 ** n
	)" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 12732.0 0.0 0.0 0.0
"why is Q times Q transpose   not equal to the identity if the matrix is not square ?" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 15326.0 0.0 1.0 0.0
"Thank you professor Strang for letting me see the beauty of math. Being a Chinese that sucks at math was really tough... your course save me. Lots of respect" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9316.0 0.0 0.0 0.0
"A good teacher - Understand easily :) I watched them when I was a student 2th" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2118.0 0.0 0.0 0.0
gf PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12918.0 0.0 0.0 0.0
"Seeing that class after taking 2 from ap calculus ab makes me sad" cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 8614.0 0.0 0.0 0.0
"I love his lectures. I don't know if they will help me in my work but it's still worth it." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 5742.0 0.0 0.0 0.0
"An Indian edition of this book is available only in India
http://www.wellesleypublishers.com/buy.html" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2427.0 0.0 0.0 0.0
"Question: around the 22:00 mark when he divides the second pivot point by two, why does that change not have to be subtracted from the previous row the same way multiples were being treated for the rest of the equation? Is it just because the other values in that column are already equal to 0?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 8479.0 0.0 1.0 0.0
"At 15:21, isn't the right hand side the derivative of a constant quantity (the magnitude of the vector r) and therefore always zero?" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2593.0 0.0 1.0 0.0
"the component of F opposite the direction T is what causes the pendulum to move, and the component of F opposite the direction of N is responsible for the tension, perhaps this is what he said but perhaps not" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14677.0 0.0 1.0 0.0
"Thank you very much both to MIT and Prof Denis Auroux" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9437.0 0.0 0.0 0.0
"Could the camera show the blackboard for a second? It's just stupid how he asks ''does this matrix have an inverse'' and you have to rewind and pause in order to see the matrix, it would be a bit much to ask one to remember everything he says when there is a lot of new information presented." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3242.0 1.0 0.0 0.0
"Thanks MIT." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9616.0 0.0 0.0 0.0
"The Frenchs love frogs" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9962.0 0.0 0.0 0.0
"after 9 years, it is immortal ,professor, it is immortal" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12307.0 0.0 0.0 0.0
"How is A(A^TA)^(-1)A^T a projection matrix?
Please help." Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 4864.0 0.0 1.0 0.0
"23:57 What a genius. I love this lessons." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 720.0 0.0 0.0 0.0
"@sententia8 omg! he really fucking said that. oh man, this guy..." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2007.0 0.0 0.0 0.0
这个老师讲的很好，有些学生似乎基础有点差 kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15664.0 0.0 0.0 0.0
"When professor Stang says that A = uV^T, I suspect that u is the pivot column and V^T is the pivot row. Am I right? But nonetheless, the lecture is fantastic as usual and these truly are a gift. Thanks a lot professor Strang and MIT." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 11630.0 0.0 1.0 0.0
"I WOULD LIKE TO THANK HIM FOR HIS CALCULS ON THE WEB." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5006.0 0.0 0.0 0.0
"OMG!!! Best way to understand least square!!!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7989.0 0.0 0.0 0.0
"At 24:54 he uses for the arc length of the ellipse the same formula we would for a circle... I think there's a constant missing there." XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2621.0 0.0 1.0 0.0
"21:25 Inverses" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 677.0 0.0 0.0 0.0
"@1aMattes Haahaa is ja ekelhaft :D" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1509.0 0.0 0.0 0.0
"Wonderful explanation for Buffon's needle problem. Thanks a lot." CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 11985.0 0.0 0.0 0.0
"yeah, why not, accent can be funny and also interessting" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15474.0 0.0 0.0 0.0
"This lecture is particularly fun. The students are way more reactive in particular.
""Or if it is too traumatic that you've blocked it out of your memory...""lolll" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10807.0 0.0 0.0 0.0
"he is a legend." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 13090.0 0.0 0.0 0.0
"Beware of his explanation of y= x².  There is a well-defined method of handling this situation where units are treated as mathematical objects.  If x represents some real number times centimeters, like 5cm, then x² = 25cm².  There is no other correct interpretation.  Therefore, y = 25cm², and is an area.  If, like mafl25 writes, he really means the square of the ""magnitude"", then he should realize that a number without a unit _has_ no magnitude—it's just a number.  Is 10 a big number?  Or is it a small number?  What is its magnitude?  If y is really the square of the ""coefficient"" of x, then he must isolate the coefficient by dividing x by cm.  That is, he should write y=(x/cm)² cm, or y=x²/cm.  If you then carry out the rest of the problem, treating units as mathematical constants, you will arrive at the correct solution with the correct units.  This is common practice in solving physics problems.  Always be strict and always get the right answer.  There is no paradox here." ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2890.0 0.0 1.0 1.0
"Sound is very low and 

Handwriting also not perfect visible." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 8861.0 1.0 0.0 0.0
"The more I watch these videos, the more I hate the cameraman" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10191.0 1.0 0.0 0.0
"Fantastic lecture, really appreciate MIT sharing the course lectures for free." rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3732.0 0.0 0.0 0.0
"I've never come across a more eloquent, immaculate and lucid introduction to random processes before. It's a blessing to have the opportunity to listen to your lecture, Prof. Tsitsiklis. :)" gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 6424.0 0.0 0.0 0.0
"Be nice guys. They're freshman just starting, after a long summer." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2812.0 0.0 0.0 0.0
"I can’t say   I will have to review and review from beginning to end many times. You are most clear in explanations." L3-WFKCW-tY "33. Neural Nets and the Learning Function" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5237.0 0.0 0.0 0.0
"Brilliant leacture" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2928.0 0.0 0.0 0.0
"this is awesome, i feel like a student in the class :)" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14854.0 0.0 0.0 0.0
"Well i have studied these at the Technion isreal instittute of technology its an easy subject" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11353.0 0.0 0.0 0.0
"why does P0P have a dot product of 0 with N but the vector P does not have a dot product of 0 with N if the normal vector is supposed to be perpendicular to every vector in the plane?" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15310.0 0.0 1.0 0.0
"Looking at the comment section, I feel pretty dumb for barely feeling any intuition in whatever Prof. Strang said." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7420.0 0.0 0.0 0.0
"There is no issue of rotification of the formula, it depends on understanding to explain it to those who are learners. If a person rotifies all formulae but unable to understand to explain it to the learners would not bring forward any results to educate them." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10372.0 0.0 0.0 0.0
"Finally a Real Analysis course. Thanks MIT." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 3764.0 0.0 0.0 0.0
"Where was the energy equation mentioned in previous lectures?" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11698.0 0.0 0.0 0.0
"at 29:57 wouldn't the center of gravity of the pmf be (n+1)/2 not n/2  because the numerical values start at 0, not 1, so there are n+1  numerical values of uniform frequency. the middle would be (n+1)/2 no?" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 12434.0 0.0 1.0 0.0
"my head is spinning....." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13984.0 0.0 0.0 0.0
"sigma 1 >= sigma 2" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14300.0 0.0 1.0 0.0
"at 20:35, why use the positive square roots instead of negative ones?" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 12423.0 0.0 1.0 0.0
"Oh dear God, I can't believe this awaits me in college. Well, time to break out the red bull." ZwpwmGP5ITM "Lec 34: Final review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8003.0 0.0 0.0 0.0
"Chalk slip at 32:02 I think 0 + x = x, not 0 + x = 0
This is the advantage of having an audience, because most people would have pointed this out I think. Edit: He caught it at about 42:00." mlPLLXHZ8_U "Lecture 4: The Characterization of the Real Numbers" "MIT 18.100A Real Analysis, Fall 2020" 3137.0 0.0 1.0 0.0
"26:35 ☺️" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 804.0 0.0 0.0 0.0
"extraordinary lecture still in 2020" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12835.0 0.0 0.0 0.0
"Am I only one realize that there is nobody in class?" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 2333.0 0.0 0.0 0.0
"a thumbs up a day, guarantee you an A" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 12292.0 0.0 0.0 0.0
"J'aimerai bien avoir la traduction en français pleaaaase :(:(" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7121.0 0.0 0.0 0.0
"39:53, “Gauss would quit but Jordan says keep going”, I laughed the shit out of it" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1106.0 0.0 0.0 0.0
"i just skipped to 5 mins but I noticed something. Why tell people to use a calculator when you can solve that for e. when you do y=(1+1/k)^k take log on both sides lny=kln(1+1/k) use l'hospitals to get k and go back to e to solve and you get e^k" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13407.0 0.0 1.0 0.0
"Knowledge with Humility! <3" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7222.0 0.0 0.0 0.0
"Is that French accent?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 6803.0 0.0 0.0 0.0
"@27:27 f''(ln(1+x)) is -1/(1+x) not -1/(1+x)^2. f''(0) is still -1. Correct me if I'm wrong!" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1523.0 0.0 1.0 0.0
29:48 FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 859.0 0.0 0.0 0.0
"37:20 Define H(x) := F(x) - G(x), then H(b) - H(a)/ b-a = H'(c) for at least one c in (a,b) by MVT. Since H'(x) = F'(x) - G'(x) and F'(x) = G'(x) we have H'(x) = 0 and therefore H(x) = constant, i.e. F(x) = G(x) + constant." Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1063.0 0.0 0.0 1.0
"Thank you professor Gilbert Strang and MiT for this absolutely fabulous series on linear algebra, for the benefit of students all over the world. This, for me,  is USA at its very best. Greetings from Trondheim , Norway." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 9308.0 0.0 0.0 0.0
"Thanks for posting this!" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9694.0 0.0 0.0 0.0
"Lecture 1: Dot Product
Lecture 2: Determinants
Lecture 3: Matrices
Lecture 4: Square Systems
Lecture 5: Parametric Equations
Lecture 6: Kepler's Second Law
Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds)
Lecture 8: Partial Derivatives
Lecture 9: Max-Min and Least Squares
Lecture 10: Second Derivative Test
Lecture 11: Chain Rule
Lecture 12: Gradient
Lecture 13: Lagrange Multipliers
Lecture 14: Non-Independent Variables
Lecture 15: Partial Differential Equations
Lecture 16: Double Integrals
Lecture 17: Polar Coordinates
Lecture 18: Change of Variables
Lecture 19: Vector Fields
Lecture 20: Path Independence
Lecture 21: Gradient Fields
Lecture 22: Green's Theorem
Lecture 23: Flux
Lecture 24: Simply Connected Regions
Lecture 25: Triple Integrals
Lecture 26: Spherical Coordinates
Lecture 27: Vector Fields in 3D
Lecture 28: Divergence Theorem
Lecture 29: Divergence Theorem (cont.)
Lecture 30: Line Integrals
Lecture 31: Stokes' Theorem
Lecture 32: Stokes' Theorem (cont.)
Lecture 33: Maxwell's Equations
Lecture 34: Final Review
Lecture 35: Final Review (cont.)" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 7271.0 0.0 0.0 0.0
"shorter version of this https://www.youtube.com/watch?v=m2MIpDrF7Es" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14293.0 0.0 0.0 0.0
"46:15 Holy shit! He gave a teaser to abstract algebra right there! I just finished abstract algebra and was just watching these lectures because... I don't need a reason, and I just noticed that now! Prof Strang is amazing. I am glad I can watch these lectures from anywhere and at anytime I want :)" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 1267.0 0.0 0.0 0.0
"great teacher I love you so much." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 13007.0 0.0 0.0 0.0
"@michalchik I hate everything to do with summations lol, one bad calc prof ruined my chances with summations lol" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1945.0 0.0 0.0 0.0
#safetyschool 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 203.0 0.0 0.0 0.0
"33:50 don't understand why theta get smaller and smaller, the origin go farther away?" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 968.0 0.0 1.0 0.0
"wow! Watching computational formula for determinant emerging out of the three basic rules of determinant is the most wonderful thing in this series." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 15426.0 0.0 0.0 0.0
"newtons method is beautiful. its such an efficient algorithm to use with so many applications. " sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14021.0 0.0 0.0 0.0
"It's an interesting lecture.... But at some points it is little confusing..... :-)" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7029.0 0.0 0.0 0.0
"@Abmaj7add2 In this perspective, look at the matrix by rows, every row corresponds to an edge. And the first three rows, if see it in the graph, make a loop." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1580.0 0.0 0.0 0.0
"And if I have no interest in becoming any of that I still have to learn it because less then 5 percent of the population will use it in there profession?" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2445.0 0.0 0.0 0.0
"Comman man's Justice League:- Batman, Superman, Wonderwoman, Aquaman

My Justice League:- Gilbert Strang, Walter Lewin, Ben Polak, Patrick JMT, Ben Lambert" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3173.0 0.0 0.0 0.0
"the power of the test shouldn't it be 95% ? 1-alpha ?" 4HRhg4eUiMo "8. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 14725.0 0.0 1.0 0.0
"at 41:20, why the rank 1 matrix has 2 zero eigenvalues?  because 3 - 1 = 2? does the professor mean that number of zero eigenvalues always equals to nullity of that matrix?" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12452.0 0.0 1.0 0.0
"Like his explanation of how a normal distribution can be constructed by adding direction (negations), width controls (sigma^2), and nomalizers (so that integral is 1). I always had trouble remembering the normal distribution, now I don't anymore." mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 7353.0 0.0 0.0 1.0
"""Statistics is about replacing expectations with averages. That is what all of statistics is about.""" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 112.0 0.0 0.0 0.0
"just watch any other videos, they quickly turn tough" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13744.0 0.0 0.0 0.0
"This lecture is great!" XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 10803.0 0.0 0.0 0.0
"I finally understand that lecture clearly.  That is beginning of Calculus 2 because fist half of semester covers entire Calculus 1.  I took Calculus 2 (MAT 205) at Gallaudet University but professor did not teach clearly and I failed course.  I re-took Calculus 2 with different professor and finally passed a course.  That is great lectures!!  Thanks, MIT!" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5407.0 0.0 0.0 0.0
"bu adam süper değil mi yahu" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 12563.0 0.0 0.0 0.0
"Great lecture 👌" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 4257.0 0.0 0.0 0.0
"Is it better to take this course straight away or finish 18.06 first? 
Thanks!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6779.0 0.0 1.0 0.0
"35:24 When you just want some love but no love is given to you." XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1009.0 0.0 0.0 0.0
"When we lump more than 1 state into a class, and find the probability of entering the lump or the time needed to reach that lump: how do we calculate the values for individual states within the lump?" HIMxdWDLEK8 "18. Markov Chains III" "6.041 Probabilistic Systems Analysis and Applied Probability" 11639.0 0.0 1.0 0.0
"Math surprises you everytime...🤔 Never thought that connections between rate of growth in system dynamics, fibonacci Series and diagnalization of an INDEPENDENT vectors will finally boil down INTO GOLDEN RATIO OF EIGENVALUES at END! 😳" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 7610.0 0.0 0.0 0.0
"i am from india and i studed this when i was school  in 11 class" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13330.0 0.0 0.0 0.0
"why is 2xo(yo) = 2?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15322.0 0.0 1.0 0.0
"""Statistics is about replacing expectations with averages.""" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 113.0 0.0 0.0 0.0
"i see how the students are so quite in college is that real? 
" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13455.0 0.0 0.0 0.0
"6 people dont have brains" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1372.0 0.0 0.0 0.0
"Amazing teacher and than some! " _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2394.0 0.0 0.0 0.0
"35:54: Like a boss. " 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1022.0 0.0 0.0 0.0
"... It's called vectors, you'll learn about them later. To add vectors you put them tip to tail and draw a vector from the tail of the first to the tip of the last. So in this case, when you put them tip to tail, it forms a rectangle. Then when you draw the ""resultant"" vector, it is the diagonal of the rectangle." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 260.0 0.0 0.0 1.0
"I'd love to know if MIT teaches tabular integration?  Probably not, because it's not a ""rigorous""  method." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6280.0 0.0 1.0 1.0
"“Take a breath and listen up!” - lecturer’s perspective starting vector spaces.  👍 I just love Gilbert Strang! I completely agree. I will tell that to my students tomorrow. 🙏" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 15597.0 0.0 0.0 0.0
"These ugly people come with their own inner limitation to what we call walk
..... They say blame not a man in his trail to the mountain
It's what he does in the community first and he finds itself at the mountain when everyone else could only guess what was taken.
They're too nasty for eternal feed..... Numeral matters are based the same
..... They don't get their on their own" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 10430.0 0.0 0.0 0.0
"Maths is not limited to formulas and algebra, it's about insights and thought process, and that makes it beautiful. Thanks Prof Gilbert Strang for wonderful lectures" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 7617.0 0.0 0.0 0.0
"Is L0 norm is not convex ????" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6749.0 0.0 1.0 0.0
"11:20 deserve a clap" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 370.0 0.0 0.0 0.0
"Dose anyone know in which lecture he talked about Jacobian or Hessian matrix" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3488.0 0.0 1.0 0.0
"You must first explain what are the applications of  linear algebra ...then students will get connected to the subject." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12230.0 0.0 0.0 1.0
"sorry to disappoint you but it's d(sigma) not dS. that MIT guy needs a reanimation." WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14379.0 0.0 1.0 0.0
"Thanks MIT.     :"""")" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9617.0 0.0 0.0 0.0
"For someone searching for Fisher information matrix, it starts roughly around 1:12:50 (continue to the next video), and the implication starts at 1:14:10" 0Va2dOLqUfM "5. Maximum Likelihood Estimation (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 3875.0 0.0 0.0 0.0
"Oh my god. It's like my whole life was a lie. And now I am discovering unicorns and dragons and magic exists!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8019.0 0.0 0.0 0.0
"Better than it's 18.06 counterpart" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2887.0 0.0 0.0 0.0
G.O.A.T!!!! 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 3965.0 0.0 0.0 0.0
"two guys at the front bench" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 14964.0 1.0 0.0 0.0
"I just found that the way Strang talks sounds a bit like David Lynch. Anyone agrees?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 3.0 0.0 0.0 0.0
"d/dx (1/v)=0. What’s he talking about?" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12702.0 0.0 1.0 0.0
"Great lecture. Thank you!" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 4293.0 0.0 0.0 0.0
"Yes but you should do Calc problems as well to get in down." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12137.0 0.0 0.0 0.0
"ha ha... Past Time of the Bernoulli's were to flip coins!! It made me laugh so loud!! Great humor sir!! :D :D" gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 13031.0 0.0 0.0 0.0
"Prof. Strang's style is amazing. He keeps you curios, suspended and involved the whole time." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8311.0 0.0 0.0 0.0
"I love the moment when the prof spotted the solution 3, 3, 4 and exclaimed “it works!”. Eureka!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5778.0 0.0 0.0 0.0
"Excellent way to introduce the concept of random process." gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 3683.0 0.0 0.0 0.0
"I love this man" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 5822.0 0.0 0.0 0.0
"This is amazing" jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 10611.0 0.0 0.0 0.0
"Probably the most coherent explanation of Euler's constant's fundamental tie to calculus." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8259.0 0.0 0.0 0.0
"45:37 
in the pyramid example  how do we know that the distances  from Q to the sides of the bases meet the heights of the triangles with the unknown point P? could it not be that the dont meet at a single point??" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1258.0 0.0 1.0 0.0
<3 VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 1458.0 0.0 0.0 0.0
"This lecture is not just for once, you probably come back to see and will find new things that you didn't get it before." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10806.0 0.0 0.0 0.0
"Holy crap this is a good lecture" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4778.0 0.0 0.0 0.0
"4a.m.
5th day of October
2021st year of the Common Era.

I've finished it.

Now, to 18.02 shall I go!" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1330.0 0.0 0.0 0.0
"I have really enjoyed Dr. Jerison's lectures. His sense of humor is wicked." R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5552.0 0.0 0.0 0.0
"The board has something interesting thing..." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 10022.0 1.0 0.0 0.0
"Simply just too good." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8669.0 0.0 0.0 0.0
"Thank you so much Gilber Strang for teaching the way you teach. It helped me so much in my studies at TUM in linear algebra. You did sth my prof would never be able to." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9346.0 0.0 0.0 0.0
"are those sidewalk chalks.....?" XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12400.0 1.0 0.0 0.0
"Very good" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 11172.0 0.0 0.0 0.0
"thank you very much <3" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14523.0 0.0 0.0 0.0
"एक्दम मस्त होत हे लेक्चर 👍☺️" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 15579.0 0.0 0.0 0.0
"At at 31:40 shouldn't that area be G(x) - G(a)?" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2710.0 0.0 1.0 0.0
"Prof. Denis Auroux and MIT thankyou!!!!" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8292.0 0.0 0.0 0.0
"I beg you MIT, please upload the rest of the Calculus lectures. One of the most fundemental classes for math and science and they have only about a third of it up. ;-()" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5165.0 0.0 0.0 0.0
"Ok guys don't complain about the difficulty of this section. You're gonna need some differential equation knowledge in order to fully understand this one, and the next one (FFT). E.g. solving a system of differential equation. Prof Strang did a fantastic job on that which I've never used a linear algebra point of view to understand system of differential equations and stabilities." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 8045.0 0.0 0.0 1.0
"11:00 There is a ghost on a board, in a right lower corner of it." WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 360.0 1.0 0.0 0.0
"People complaining about the cameraman dont know that the blackboard is more important to see? lol" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8166.0 1.0 0.0 0.0
"22 minutes in, still waiting for the hard part; that's the genius of Gilbert Strang." k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 691.0 0.0 0.0 0.0
"a 'couple' doesn't turn their heads right. only 1 person of the couple does it in the end. if there are n couples, there are 2n individuals who can go Left or Right. that's the amount you have to look at right?edit: retarded because both people do kiss in the same direction. bye" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 12277.0 0.0 1.0 0.0
"At 16:21 Why does function depends only on one direction if 4ac - b^2 = 0 ? Yes the term with y^2 is 0 but don't we have y in first term as well? (x + b/2a * y)^2" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2595.0 0.0 1.0 0.0
"Master in engineering here🇺🇸🇺🇸🇺🇸" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 7602.0 0.0 0.0 0.0
"And yeah, very quiet class O_O? " ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2454.0 1.0 0.0 0.0
"why he use that method for solve the equation?, why he didn't use gauss jordan method?" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15320.0 0.0 1.0 0.0
"Thanks for this one ! Was awaiting it for a long time :D" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 9734.0 0.0 0.0 0.0
"I love this guy's accent." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5807.0 0.0 0.0 0.0
"I would love to know the principle on how to construct the wacky (2-x^2)/(2(2x+1)) (Rudin's book used (2-x^2)/(x+2))." nbENJ-Ce7Nc "Lecture 3: Cantor's Remarkable Theorem and the Rationals' Lack of the Least Upper Bound Property" "MIT 18.100A Real Analysis, Fall 2020" 6266.0 0.0 1.0 0.0
"may not be important to go university. i love for ur lecture give me enjoyment" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 13925.0 0.0 0.0 0.0
"Prof is great. MIT is very good." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 8281.0 0.0 0.0 0.0
"19:00, 21:10, 22:50, 31:40" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 551.0 0.0 0.0 0.0
"Thank you, MIT OCW team! Thank you, Dr. Rodriguez! These videos will change a lot of people's lives. It's a great contribution to the education!" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 9498.0 0.0 0.0 0.0
"What are X_1, X_2....X_n? Is each X_i a single measurement, or a bunch of measurements (of let's say Penguin height)?


EDIT: Now that I think of it, a single measurement is also a subset of ""bunch of measurements""" 3eiio3Tw7UQ "19. Weak Law of Large Numbers" "6.041 Probabilistic Systems Analysis and Applied Probability" 11464.0 0.0 1.0 0.0
"lol, " FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13836.0 0.0 0.0 0.0
"Oh this guy! Recognise his voice. Fantastic lecturer." 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 8025.0 0.0 0.0 0.0
"Thanks sir 🙏🙏🙏🙏🙏🙏thanks🙏🙏🙏🙏🌹🌹🌹🌹🌹🙏🙏🙏🙏🌹🙏🙏🌹🙏" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9777.0 0.0 0.0 0.0
"Excellent job . I've never seen such an amazing calculus professor. Thanku so much for this wonderful series." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3647.0 0.0 0.0 0.0
"Thank you MIT, you guys are the best in spreading knowledge to human kind =)) This is epic!!! I feel like being a student of one of the top institute in the world without paying extremely high tuition!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9161.0 0.0 0.0 0.0
"What textbook does this class use?" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11554.0 0.0 0.0 0.0
"Why only  ""Invertible A"" at 6:06???" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11904.0 0.0 1.0 0.0
"Hmm... They have 1200 videos up already. They may not be terribly organized, but that's what the search bar is for." sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4775.0 0.0 0.0 0.0
"How did he get all the equations of xk, yk and fk at 45:35? Specifically, how did he get (b-1)/(b+1) and vice versa? I shifted the equation to make xk+1 and yk+1 the subjects of the equations but instead I got xk+1 = xk (1-2sk), where xk = x0 = b." AeRwohPuUHQ "22. Gradient Descent: Downhill to a Minimum" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4834.0 0.0 1.0 0.0
"Love him. But always the same pants(nothing wrong with them). And the desk?, so ugly" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 7440.0 1.0 0.0 0.0
"@inuyashalivesbaby 

I'm not judging. Lol.

I'm just saying quite plainly that those boards aren't a very impressive feature." dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 1890.0 1.0 0.0 0.0
"Gradient Descent
 https://towardsdatascience.com/gradient-descent-algorithm-and-its-variants-10f652806a3" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4181.0 0.0 0.0 0.0
"Professor Strang : Thank you once again !!!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8342.0 0.0 0.0 0.0
"My favourite US mathematicians are Gil and the late, great Eli Stein from Princeton.  Lovely people and great mathematical communicators. When doing proofs Eli used to say things  like: ""Morally this has to be right!""  For a small homage to Gil on SVD go here: https://gotohaggstrom.com/Singular%20Value%20Decomposition%20worked%20numerical%20examples.pdf" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7751.0 0.0 0.0 0.0
"Thumbs up if you have a final coming up and you are watching this.
" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 11001.0 0.0 0.0 0.0
"Is he disabled or why is he using this retarded bike all time?" TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 6770.0 1.0 0.0 0.0
"Is this course usefull for machine learning ?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 6864.0 0.0 0.0 0.0
"Too much talk and not enough example. He doesn't not go through one single basic example to help understanding the subject. He just repeats what is said on intorduction to probablity by Dimitri Berteskas. Just read the book is just as good as watching this video. Unless u know the subject very well, I would not recommend watching the video" 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 11068.0 0.0 0.0 1.0
"hey!my left ear can be smarter too!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13151.0 0.0 0.0 0.0
"rich people." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14267.0 0.0 0.0 0.0
"Denis is the best teacher I have ever seen!" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3351.0 0.0 0.0 0.0
"I can't believe I'm watching this for entertainment at my own will. He's probably the greatest math teacher I've ever had" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5204.0 0.0 0.0 0.0
"Is sad for me to see how much i could learn some years ago if i have acces to his class." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6801.0 0.0 0.0 0.0
"He looks great considering the lectures were from 1876." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4566.0 0.0 0.0 0.0
"""Always ready for questions.""
I've watched every one of these lectures and I don't think anyone has ever asked a single question.  Kind of odd." HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 26.0 0.0 0.0 0.0
"Thank youpi stand up spiritual get up Opéras CréďèÔ CoolœuR FrèdéØ opening" asjAc90L8rE "12. Time Complexity" "MIT 18.404J Theory of Computation, Fall 2020" 9567.0 0.0 0.0 0.0
"How many hours per day? I would like to finish all these in a week. " 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4884.0 0.0 0.0 0.0
"OMG, best ever explanation of maximum likelihood estimator!" rLlZpnT02ZU "4. Parametric Inference (cont.) and Maximum Likelihood Estimation" "MIT 18.650 Statistics for Applications, Fall 2016" 7990.0 0.0 0.0 0.0
"He is really easy to understand...if you've ever heard someone talk with a foreign accent before, you could tell his accent is very understandable. Plus, he's a great teacher, get used to it." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4533.0 0.0 0.0 0.0
"Such a cute Professor, going back and forth, a dilemma of continuing doing use cases or discovering the formula. 🐼" XhSk_Lw2X_U "14. Low Rank Changes in A and Its Inverse" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8923.0 0.0 0.0 0.0
"It's just easy that's why you like this 1 perhaps others may be Better than this but you are not worth enough to understand that difficulties 😏" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7055.0 0.0 0.0 0.0
"where can i access the slides?" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 15227.0 0.0 0.0 0.0
"Thanks sir
Jesus is the Son of God. Believe in his death and resurrection then confess his lordship over your life. Love yall🙏♥️" 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9776.0 0.0 0.0 0.0
"this got a whole lot less interesting as soon as we started talking about current and physics" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14806.0 0.0 0.0 0.0
"I wish I had a professor like him" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6197.0 0.0 0.0 0.0
"¿Que mierda dicen?" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 15537.0 0.0 0.0 0.0
"Too many who comment here seem to think this too fundamental for a great technical school like MIT.  The sad truth is that most high schools do an atrocious job of teaching Calculus.  So bad, in fact, that a growing number of universities now virtually insist that the subject be retaken under a competent instructor.  Poor preparation in mathematics tends to feed upon itself, for in mathematics, virtually everything depends upon the thorough mastery of that which came before.  Shall we now pretend that our secondary education in the USA is not the worst in the industrialized world?  Shall we forget that our secondary school educators, with rare exception, are among the most incompetent of those who own college degrees?  And yet, we somehow are willing to trust the instruction of this important topic to these institutions without reservation!  Further, I would not hesitate to suggest that only someone who staggered  through though Calculus in a mechanical, inartful way would fail to appreciate a fine presentation such as this." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11065.0 0.0 0.0 0.0
"I like this video. I think it's great that I don't have to pay to learn calculus" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5695.0 0.0 0.0 0.0
"Can anyone please tell me where do I get the problem sets??" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3042.0 0.0 1.0 0.0
"Gilbert Strang a legend" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 4013.0 0.0 0.0 0.0
"Oh man, these probabilistic proofs are so ****ing beautiful.....are they intrinsically equivalent to some kind of counting?" hDwkKrWqdZE "3. Forbidding a subgraph II: complete bipartite subgraph" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 8013.0 0.0 0.0 0.0
10:30. z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 349.0 0.0 0.0 0.0
"This lecture plus 3blue1brown's videos are getting these concepts to stick for me. Thank you Prof. Strang!!!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10824.0 0.0 0.0 0.0
"I love these lectures!!! Now I'll be able to get ahead in my highschool math!!
THANK YOU MIT!!!!!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5796.0 0.0 0.0 0.0
"Im happy to see how healthy his mind is, its impressive how body deteriorates but mind can last forever if well kept." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6570.0 0.0 0.0 0.0
"His clothes reminded me of Walter Lewin, lol!" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4746.0 0.0 0.0 0.0
"note: row*matrix=row, (abc)(3*3)=a(row1)+b(row2)+c(row3), matrix*column=column, (3*3)(abc)=a(col1)+b(col2)+c(col3)
(a11 to a33)(3*3)=({(a11,a12,a13)(3*3)}, {...}, {...})=({a11(row1)+a12(row2)+a13(row3)}, {...}, {...}), we can represent elimination by Matrices." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14085.0 0.0 0.0 1.0
"39:45 not that serious paradox if (constant with) correct dimensions were used, e.g.: 'y = x^2 (1/m)' or 'y = c x^2' with 'c = 1/m' (from 'c = m / m^2')) (see https://www.mathcha.io/editor/7rrGpc0WSLdHDxZdJHGXxY0Gun6zLQQSq2wd3 )" ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1104.0 0.0 1.0 0.0
"Thank you so much Dr.Gilbert,
I am a 12 year old boy in the middle east with a special interest for math, and your teaching methods are quite clear even for a person of my age, with a brief background in differentials, derivatives, and other relatively basic things in pre-calculus (hoping to understand integrals by the end of the next 2 months!!)
Once again, Thank you soooo much, I cannot express how happy I am to finally find an amazing mathematical-based professor!!!!

P.S. I would also recommend Dr.Eddie Woo and Dr.Edward Burger for any more math!!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 9344.0 0.0 0.0 1.0
"the teacher also must tell the students that are a little lost what is the meaning of their answer for instance at 5 feet the water is raising 1/2pi he could show that the volumen of water is 2 per minute which means also that at a higher point the raising of water will be even less. this sort of explanations will make the students to understand better all these answers." sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14743.0 0.0 0.0 1.0
"49:36 did he flip someone off?" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1309.0 0.0 0.0 0.0
"where is the online homework ?" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15243.0 0.0 0.0 0.0
"😒  indian teachers are much better.....
....
..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15736.0 0.0 0.0 0.0
"Gilbert Strang is extremely likeable." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4021.0 0.0 0.0 0.0
"The best linear algebra teacher in the world now is going to  teach us how to apply this concepts in real world problems . I can't thank enough MIT OCW and professor Strang for this." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10001.0 0.0 0.0 1.0
"It was an accident. He ended up correcting it later." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6995.0 0.0 0.0 0.0
"I love the sound of chalk on a chalkboard.. he has great handwriting" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5784.0 1.0 0.0 0.0
"man the students in this lecture are either slow or dont like to shout out answers on camera lol" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 13900.0 1.0 0.0 0.0
"Great lecture. One of my favorite professors." ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 4291.0 0.0 0.0 0.0
"Love Prof.Strang so much!!!really excellent lecture!!!!" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7432.0 0.0 0.0 0.0
"I got confused when he says length of vector with magnitude of vector ..
I guess magnitude is only valid to find the length of one vector only..
Because I guess it cannot do dot product with other vector to find it's length/magnitude..
So we need to find it using pythogoras theorem..i.e find the hypotenuse..
The problem is simpler if you have more than one vector..
Just do the dot product and you get the length" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5445.0 0.0 1.0 0.0
Good J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 4108.0 0.0 0.0 0.0
"I have fallen for Dr. Strang. He is actually Dr. Strange. 💗 I don't know how he gives me some feeling through these videos. Only kudos....👏." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 5525.0 0.0 0.0 0.0
"Thanks so much Prof Auroux and MIT, clear explanations and for free! May god bless this university" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9784.0 0.0 0.0 0.0
"why was everyone clapping" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15374.0 0.0 0.0 0.0
"Don't complain whiners. There are TWO whole courses after this one that teach JUST applied linear algebra. 

1. Computational Science and Engineering I
2. Mathematical Methods for Engineers II

You can also read the book - Introduction to Linear Algebra, AND another entire book just for advanced applications - Computational Science and Engineering, both by Prof. Strang." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 3471.0 0.0 0.0 0.0
"at 32:40...the professor says...oh god, come out correctly!  and a moment later, aha, thank you, God.  haha..." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 12440.0 0.0 0.0 0.0
"was watching some gaming vids, fell asleep with autoplay on and woke up to this" N-_XmLanPYg "11. Recursion Theorem and Logic" "MIT 18.404J Theory of Computation, Fall 2020" 15059.0 0.0 0.0 0.0
"That guy who is always capturing the photo" wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9889.0 0.0 0.0 0.0
"Great series, sadly spoiled by bad camera zooms :(" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4331.0 1.0 0.0 0.0
"i just spent 8 hours looking at this videos and now that i check the problems from my school i am on the start again just wasted 8h...how can USA and EU have such different uses and concepts of matrix it suks donkey balls
" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13408.0 0.0 0.0 0.0
"It is too easy ,in fact !" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6970.0 0.0 0.0 0.0
"Yeah! I understand vector calculus clearly! Good job, teacher!" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12124.0 0.0 0.0 0.0
"Thanks to MIT for sharing the knowledge for free!" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9803.0 0.0 0.0 0.0
"Thanks, thanks, Thanks!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9851.0 0.0 0.0 0.0
"The best teacher ever. I really admire the act of MIT. Like in a phrase in its website: ""Unlocking Knowledge, Empowering Minds.""" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10009.0 0.0 0.0 0.0
"It's funny how the professor just throws these AMAZING examples as if they are nothing. :P 
42:26 ""That's actually relatively easy to do given all of the power that we have in our hands.""" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7042.0 0.0 0.0 1.0
"what a great professor" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 15107.0 0.0 0.0 0.0
"If 4ac - b^2 = 0, then the y^2 component disappears. However, you still have the x and y inside the first term, which you square. I don't get how it's degenerate. What if W = x^2 + 2xy + y^2? 4ac = 4, and b^2 = 4, so 4ac - b^2 = 0. However, it doesn't have a degenerate critical point." 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6460.0 0.0 1.0 0.0
"That feeling, when you find every thing you need in a MIT course. Much respect  Prof." 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 9885.0 0.0 0.0 0.0
"Thank you so much MIT and Professor Strang!" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 9351.0 0.0 0.0 0.0
"this guy is french right??" sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14826.0 0.0 0.0 0.0
"First lecture of the series that I've slightly struggled with :( I understand the second derivative test, and how to carry it out, but in the specific quadratic function example, why does a ""difference of two squares"" imply a saddle point? I see how a sum of two squares implies a local min or max depending on the value of a, but confused about how the algebra leads to the conclusion that we have a saddle. Also not quite clear on the degenerate case and why 4ac - b^2 = 0 implies degeneracy. Need to do some further reading on this before moving on methinks... " 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3816.0 0.0 1.0 0.0
"lol you're quite dense" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13835.0 0.0 0.0 0.0
"43:42 MCMC" bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 1217.0 0.0 0.0 0.0
"I thought of learning linear algebra during lockdown." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 6091.0 0.0 0.0 0.0
"One of my fav!!!" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8081.0 0.0 0.0 0.0
"didn't know that Jimmy Dore taught stats . . ." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 12745.0 0.0 0.0 0.0
"Thankyou prof." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9869.0 0.0 0.0 0.0
"Great lectures on linear algebra!" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4304.0 0.0 0.0 0.0
"I have lost myself for the last 10 minutes lol" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 5536.0 0.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8422.0 0.0 0.0 0.0
"@thejugglenaut91   again, exactitude is never reached.  I rest my case." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2041.0 0.0 0.0 0.0
"12:16 Conditional Probability" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 393.0 0.0 1.0 0.0
"Such a great course" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 8926.0 0.0 0.0 0.0
"This guy is a modern day genius." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 10519.0 0.0 0.0 0.0
"Thanks Dr Strang. Really Enjoyed the lectures" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9586.0 0.0 0.0 0.0
"Finally, thank you professor J.T" rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 3794.0 0.0 0.0 0.0
"From the bottom of my heart I want to thank MIT and the professors for creating such beautiful and elegant videos. They are hands down the only reason I understand this topic because my professor unfortunately can explain it as clearly as you guys have presented it or at least the way he presents the lecture isn’t my style." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3932.0 0.0 0.0 0.0
"I remember writing a comment ""I am 9th grade and these lectures are awesome"". But now when I am in a university and completed a calculus course, my opinion changed from awesome to good." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5950.0 0.0 0.0 0.0
"great teacher (Y) very friendly" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13005.0 0.0 0.0 0.0
"Shouldn't the last pivet be -5" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8652.0 0.0 1.0 0.0
"So have most Americans.  Not everyone in MIT is a math major." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8767.0 0.0 0.0 0.0
"30 minutes into the lecture and he is already talking about unions. the left has seized academia firmly in it's grip" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 879.0 0.0 0.0 0.0
"We do that in high school in French --'
But good teacher btw" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11320.0 0.0 0.0 0.0
"33:00
CROSS PRODUCT" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 949.0 0.0 0.0 0.0
"Is it only me or do others who know calculus feel that the students are asking questions just for you sake of asking and there is no genuine doubt as such" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6794.0 0.0 0.0 0.0
"Monica joke is just awesome!!" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 7689.0 0.0 0.0 0.0
"No jodas!!" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7874.0 0.0 0.0 0.0
"How can I calculate volumen of a solid of revolution generated by a curve turned aroun an inclined line?" TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4807.0 0.0 1.0 0.0
"That first lecture had hundreds of thousands of views. This one has less than 100,000 still. Let's see how many views there will be in lecture 30 lol" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9886.0 0.0 0.0 0.0
"This is how teaching should be, and it´s the only way that it works, going from example and observation, in order to understand what happens, and then go into abstraction. Not going from presenting abstraction and applying it to an example." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10676.0 0.0 0.0 1.0
"We love you Sir ❤🧡💛. Stay Safe." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11327.0 0.0 0.0 0.0
"This guy is some kind of magician of mathematics 😮" ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10544.0 0.0 0.0 0.0
"Maan, this person is just a cool dude mathematician" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7558.0 0.0 0.0 0.0
"Currently a sophomore in high school. I've heard a lot about calculus over the years and about just how powerful and beautiful it is. About 20 minutes in is when that rang so true for me." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3266.0 0.0 0.0 0.0
"there is some math humor at minute 32:46. 
I never knew about ""the column picture"" (which is very good) until I met this course." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14765.0 0.0 0.0 1.0
"Haha, I guess I'm challenging that demographic then since I'm a student using this as a supplement to my class XD" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4414.0 0.0 0.0 0.0
"Thank you MIT. Please consider uploading more lecture series in abstract mathematics (e.g. real analysis, complex analysis, abstract algebra, differential geometry, topology, ...) It will be of great help to us!" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 9169.0 0.0 0.0 0.0
"After watching this lecture, all I can say is how truly amazed I am. What a great video! Except for the fact that I couldn't understand one word he was saying( currently taking Tech Math at HS). I mean the camera was on point, his writing was nice, and the students were quite polite. Superb! MIT you surely do not disappoint :D" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2267.0 1.0 0.0 0.0
"Thanks so much. Notice much more white hair than the videos in 2008:((" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9792.0 0.0 0.0 0.0
"Why would the lack of pivot make the corresponding variable free?" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 11936.0 0.0 1.0 0.0
"I didn't know Bob Barker taught linear algebra." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5272.0 0.0 0.0 0.0
"One thing that I cannot figure out if somebody can help me. The projection is supposed to be A times that x hat. but when we solve, he does A^TAx = A^Tb. But that is not p, p would be A times all of that, wouldn't it?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 8111.0 0.0 1.0 0.0
"The ending of a great semestre, thank you professor Gilbert, because of you, I started to like Algebra and I'm sure I can do the course, keep up the great work!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 10089.0 0.0 0.0 0.0
"کثرت گرایی نفی هیچ دینی نیست 
تنها قوانین مذهبی را فردی می کند انهم با نقد علم بر فلسفه ها و ممانعت از تحکم شریعت بر زندگی انسانها ،
نکته اینجاست قوانین عرفی را ارج می نهد(وقوانین عرفی چیست غیر از تلقین ارزش)" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15577.0 0.0 0.0 0.0
"Can't help thinking: If Jimmy Stewart taught linear algebra.  Excellent lectures." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 3124.0 0.0 0.0 0.0
"Let’s talk about failure! Brilliant 😀🙏👍🏾 Pre-Calculus 1 and 2 totally confused what this man has fixed in my head after 40 years!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7343.0 0.0 0.0 0.0
"This class/course seems to be so organized and planned. Just pissed that I'm studying at a PBL institution right now where its just madness and chaos." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 10483.0 0.0 0.0 0.0
"Damn!
he draw the lines accurately like a ruler..." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3300.0 0.0 0.0 0.0
"LOL the king example is hilarious " 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 7237.0 0.0 0.0 0.0
"Ha! Tell everyone you use to boast about your intelligence on YouTube when you receive the Fields Metal." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4410.0 0.0 0.0 0.0
"So, ""estimate"" is the same thing with ""expectation""?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8804.0 0.0 1.0 0.0
"This lecture is basically a Physics lecture" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10797.0 0.0 0.0 0.0
"Thanks elotoff to MIT OCW;for interesant information;and to the Teacher" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 9679.0 0.0 0.0 0.0
"This is guy is so good in computation than concept explanation " seO7-TwXH_I "Lec 30: Line integrals in space, curl, exactness... | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10670.0 0.0 0.0 0.0
"51:37 wrong explanation? (it is surjective but not bijective?)" N28g_YBXY8Y "9. Reducibility" "MIT 18.404J Theory of Computation, Fall 2020" 1343.0 0.0 1.0 0.0
"What u just left at the end of the class was totally shocking me!!" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 11564.0 0.0 0.0 0.0
"I'm just wondering whether 67.5 is correct. I may be missing something, but as far as I run my R code, it says 73.866. Did I miss something ?
Below is my code and results.

--
(base) demo@ubuntu:~/SelfStudy/MIT-OCSW/18.650-Fundamental-of-Statistics$ ./1_1hour12mins.R 
[1] 73.86667
[1] 73.86667
(base) demo@ubuntu:~/SelfStudy/MIT-OCSW/18.650-Fundamental-of-Statistics$ cat 1_1hour12mins.R 
#! /usr/bin/env Rscript

x <- c(65,41,70,90,58,82,76,78,59,59,84,89,134,51,72)
result.mean <- mean(x)
print (result.mean) 
print (mean(x)) 
--" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 6343.0 0.0 1.0 0.0
"19:30 Reduced row echelon form(RREF)" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 562.0 0.0 0.0 0.0
"Several Questions:

1.  What is calculus?
2.  Does multi-variable calculus exist?
3.  Should calculus be re-written and given a field?
4.  Then should it only stick with the subject?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8634.0 0.0 0.0 0.0
"Did i miss anything,or did he actually prove quotient rule?" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3380.0 0.0 1.0 0.0
"He is." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4555.0 0.0 0.0 0.0
"Thank you Sir." 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 9237.0 0.0 0.0 0.0
"24:34 Asian Conspiracy Corona Virus 2009 2019" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 737.0 0.0 0.0 0.0
"No, in Zenon's Paradox there is convergence. In this case there is not." wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7902.0 0.0 1.0 0.0
"For anyone who may be confused in the first part of this video, it helps to keep in mind that he is talking specifically about a function with a tangent plane z=0 at the origin. Also keep in mind what the graphs of x^2 - y^2 and x^2 + y^2 look like!" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3857.0 0.0 0.0 0.0
"@XxBrian88xX I agree.  I have watched this series up to this point and though I can't say that he is not trying or is incorrect...nevertheless his treatment of the material is just too pedantic and never addresses the real issues.  This is especially apparent when he tries to answer questions from the students he seems to skirt the real stumbling blocks.  Combined with his twitchy mannerisms makes it hard to follow.  It's instruction like this that turned me off of math throughout my schooling." -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1758.0 0.0 0.0 1.0
"1:12:57 
Some serious mental arithmetic going on there xD  😂😂" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 585.0 0.0 0.0 0.0
"i really don't know who still goes to school?:-)
we have everything on the internet :-)
thank you, mit guys!" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 13452.0 0.0 0.0 0.0
"very useful and helpful i'd say
thanks MIT." 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15040.0 0.0 0.0 0.0
"Prof. Strang is such a good professor! Good pace and he explains it in a very clear and easy to understand way. Thank you so much!!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 8307.0 0.0 0.0 0.0
"can someone explain the proof again at the end? howd he get f'(x0).0?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12622.0 0.0 1.0 0.0
"I like it when Mr G.S. ask ""everybody with it ?""" sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5676.0 0.0 0.0 0.0
"These lectures are very creative.  I think he does a great job!" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10414.0 0.0 0.0 0.0
"Anthony Fantano covering math, I'm so happy." EBdgFFf54U0 "Lecture 14: Basic Hilbert Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 2464.0 0.0 0.0 0.0
"nice proof better than my maths prof
" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 14050.0 0.0 0.0 0.0
"It's funny that this video (lec 7) has vastly fewer views than both lecture 6 and  8. But if the title of this video was PCA instead of Eckart-Young it would easily be the most viewed video in the series.

That's why kids, do the entire course instead of just watching 15 minutes of popular concepts." Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7043.0 0.0 0.0 0.0
" " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1.0 0.0 0.0 0.0
"@mschahzad i think the cameraman usually falls asleep. maybe he's a professional who doesnt understand a word of maths, so he gets annoyed and takes small naps" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1954.0 1.0 0.0 0.0
"One thing to rule them all
One thing to find them
One thing to bring them all
And in a matrix bind them" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8113.0 0.0 0.0 0.0
"Whew. Not easy. So the gradient vector is perpendicular to the level curves, so can be drawn on the contour plot of the function, NOT the graph of the function itself (?)...took me a while to realise this, so my thinking was at cross purposes with what he was saying. Also this business of ""velocity vectors"" and the vector r I found a bit confusing...think I've got the concept of a directional derivative though. Need to do some more reading on this..." 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 11704.0 0.0 0.0 0.0
"@LAnonHubbard You don't really need to know about differential equations to understand this lecture. Just watch lessons 1 to 20 as well ;-). Takes you only 15h :-D." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 1654.0 0.0 0.0 0.0
"Did MIT clone Joe Blitzstein?" TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 3365.0 0.0 0.0 0.0
"Hello, i love lineer algebra so much! i want to be an good and hayirli engineer in future. thanks!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4665.0 0.0 0.0 0.0
"The David Attenborough of Mathematics" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9960.0 0.0 0.0 0.0
"OMG 😮 still going strong" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7986.0 0.0 0.0 0.0
"what is a relation in 3 d?????" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 15149.0 0.0 1.0 0.0
"Amazing stuff" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2393.0 0.0 0.0 0.0
"Great video! Just one question. At the very end when talking about Variances. I know he said it is two lines of algebra, but how did he get from the sum of [(distance from the mean) * p(X)] to E[X^2] - [E(X)]^2 ??" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 4354.0 0.0 1.0 0.0
"loving this Gilbert guy! his 6 lectures has taught me more than 2 months of linear algebra at Chalmers University did! thumbs up and thank you MIT!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 13890.0 0.0 0.0 0.0
"anyone wrote the topics he had cover?" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 12391.0 0.0 0.0 0.0
"Such a lovely human being." or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8935.0 0.0 0.0 0.0
"Great example and lecture pace. Thank you Dr. Tsitsiklis and @*****" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 4223.0 0.0 0.0 0.0
"Him is working with functions, a^x not is function when a<=0." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4736.0 0.0 1.0 0.0
"I wrote a proof explaining where the cosine went if anyone is interested. I've published on my github at https://github.com/darrenstarr/JupyterNotebooks/blob/master/Dot%20Product%20(law%20of%20cosines)%20Proof.ipynb" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6272.0 0.0 0.0 0.0
"Thank you Prof Strang!" L3-WFKCW-tY "33. Neural Nets and the Learning Function" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9182.0 0.0 0.0 0.0
"do not listen to this in stereo, i thought my left earbud fell out" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12754.0 0.0 0.0 0.0
特徵值，特徵向量 cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 15639.0 0.0 0.0 0.0
"The whole point is that something continuous, and smooth/analogue in nature requires a digital limit for its description and modelling.  I used the wrong word, ""plug in"".  I should not have used that terminology.  The fact of the matter is that from a floating point standpoint, you can only come as close as you would like to an exact answer, vis-a-vis, the limit, while never achieving exactitude from an emperical point of view." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10337.0 0.0 0.0 0.0
"Thank you Professor Strang for this amazing course! I spend around 2 months on it, taking notes, watching recitations, and solving those problems on the OCW website. It demonstrates the charm of maths, unique, inspiring, brilliant, makes me calm down and ignore all those annoying things in daily life, and just enjoy this journey!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9221.0 0.0 0.0 0.0
"Sorry sir but f =s not f" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8856.0 0.0 1.0 0.0
"Jesus Christ he's great at teaching.  I now understand the difference between spending $50,000 per year and $10,000 per year. At least they're paying for the tuition so I get to watch these videos for free." dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 7135.0 0.0 0.0 0.0
"EINSTEIN COULD. #LOL" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 3537.0 0.0 0.0 0.0
"LOL at the 35min mark, class cheers him for his sick erasing skills!" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7235.0 0.0 0.0 0.0
"Is this first year ?" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 6868.0 0.0 0.0 0.0
"This is a very fitting explanation for me, hwo has studied statistics, but some time ago. This really clarifies things." 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 10605.0 0.0 0.0 0.0
"3:08 how do you take (a_i - x) if a_i and x are not adjacent nodes?" cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1110.0 0.0 1.0 0.0
"This helped me a lot!" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 10573.0 0.0 0.0 0.0
"Camera man ....Follow Prof Strang!!!" ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2995.0 1.0 0.0 0.0
"It helps, also, if they have a unique personality, like this guy does.  I watched all these linear algebra videos and it was a pleasure watching this professor in action because it was entertaining.  No disrespect.  " FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6919.0 0.0 0.0 0.0
"What are  the prerequisites in order to take this course ?

I just passed out standard 10th , now i am in standard 11th. School has not started yet . Please guide.
Can i take this course ?
Please guide me 🙏" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 11461.0 0.0 0.0 0.0
"25:25 in 2007 when people were talking about the MBS crash" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 779.0 0.0 0.0 0.0
"I love that MIT still uses chalkboards." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5769.0 1.0 0.0 0.0
tangent=tangerine 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14438.0 0.0 0.0 0.0
21:45 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 682.0 0.0 0.0 0.0
太喜欢这个老师了，讲课讲的好生动呀~~~~ wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15621.0 0.0 0.0 0.0
"I Really Like The Video Differentials; chain rule From Your" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4941.0 0.0 0.0 0.0
"He just blew my mind with his explanation of Markov's Inequality." 3eiio3Tw7UQ "19. Weak Law of Large Numbers" "6.041 Probabilistic Systems Analysis and Applied Probability" 4556.0 0.0 0.0 0.0
"Nice lecture... Sir which source book you are using?" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 7851.0 0.0 1.0 0.0
"I LOVE it" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 4932.0 0.0 0.0 0.0
"this prof. is just perfect. I wish he taught me...!!
" 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 14912.0 0.0 0.0 0.0
"very nice explanation!!!!!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15029.0 0.0 0.0 0.0
"do directional derivatives only work in 3 dimensions?" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 12749.0 0.0 1.0 0.0
"Why am I watching this? I'm not even single." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11774.0 0.0 0.0 0.0
"35:32 ""ok you are easily amused"" 😂 lolz" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1013.0 0.0 0.0 0.0
"When he solves for the area of the triangle, why does he say it doesn't matter what X0 and Y0 are? Does he just mean that all values of f(x) = 1/x will result in the area of the triangle of the tangent line to be 2?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11625.0 0.0 1.0 0.0
"Did this in 8th grade lol @ mit students" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3386.0 0.0 0.0 0.0
"nice inspiration" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14038.0 0.0 0.0 0.0
"blackboard/whiteboard so much better than powerpoint!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12546.0 1.0 0.0 0.0
"19:52 A mistake here. A line through origin can be orthogonal to a whole plane." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 568.0 0.0 1.0 0.0
"Worth watching. My distance to Clinton is now three :D" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 12002.0 0.0 0.0 0.0
"Excellent Prof. I get the none english speaking chinese and indian professors in public shcool; Here is another reason why some things in life cost more!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 3632.0 0.0 0.0 0.0
"It is an excellent guidance" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6935.0 0.0 0.0 0.0
"is there a simple way to download all the lecs of this topic ?" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13650.0 0.0 0.0 0.0
"i did not get the 23:52" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 13355.0 0.0 1.0 0.0
"43:18 loll..... God I love this class. You definitely don't get to see this in Indian Universities." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1201.0 0.0 0.0 0.0
"This stuff is pretty good, but i dont see wats so special, we pretty much learn the same stuff with possibly better lecturers, in this at least, down here in sa" ZwpwmGP5ITM "Lec 34: Final review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10930.0 0.0 0.0 0.0
"Thank you Gilbert Strang !!!" 0Qws8BuK3RQ "34. Distance Matrices, Procrustes Problem" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9110.0 0.0 0.0 0.0
"This man is literally my favorite professor! His course on linear algebra saved me. I had really, really, low self-esteem and didn’t think much of myself, and somehow, he made me appreciate math again. I watched the first video in his series because I was looking for a cheap win, but his way of taking time to make us truly see the bigger picture really got through to me. No one in my family could get through to me but him, through his lectures. Thank you sir! You’re a real one ☝🏽🙌🏽❤️✨🤓🥳🎊 the og Superman" nvXRJIBOREc "Lecture 21: Minimizing a Function Step by Step" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10869.0 0.0 0.0 0.0
"Putz esse exemplo ai da area sobre a curva foi mt bom" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8465.0 0.0 0.0 0.0
"dat handwriting" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12724.0 0.0 0.0 0.0
"Is (1U0)* actually supposed to be {{1}U{0}}* ?  I might be wrong but we defined the union operation on languages which are sets. 1 and 0 do not appear to be set. This is min 40. Thanks in advance." 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 6743.0 0.0 1.0 0.0
"Will the first part of this lecture be added as a separate video or will this video be replaced?" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 11947.0 0.0 0.0 0.0
"List of lectures (for some reason, lecture 10 doesn't exist so I re-ordered the numbering, which is why there's actually only 23 videos)

Lecture 1: Part 1 - Intro to Statistics
Lecture 2: Part 2 - Intro to Statistics
Lecture 3: Parametric Inference
Lecture 4: Parametric Inference and Likelihood of Estimation
Lecture 5: Maximum of Likelihood Estimation
Lecture 6: Maximum Likelihood of Estimation and Methods of Moments
Lecture 7: Part 1 - Parametric Hypothesis Testing
Lecture 8: Part 2 - Parametric Hypothesis Testing
Lecture 9: Part 3 - Parametric Hypothesis Testing
Lecture 10: Parametric Hypothesis Testing and Testing Goodness of Fit
Lecture 11: Testing Goodness of Fit
Lecture 12: Part 1 - Regression
Lecture 14: Part 2 - Regression
Lecture 15: Part 3 - Regression
Lesson 16: Part 1 - Bayesian Statistics
Lesson 17: Part 2 - Bayesian Statistics
Lesson 18: Part 1 - Principal Component Analysis
Lesson 19: Part 2 - Principal Component Analysis
Lesson 20: Part 1 - Generalized Linear Models
Lesson 21: Part 2 - Generalized Linear Models
Lesson 22: Part 3 - Generalized Linear Models
Lesson 23: Part 4 - Generalized Linear Models


Good luck with your studies~" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7384.0 0.0 0.0 0.0
"wow..so clean now..thanks.." 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15437.0 0.0 0.0 0.0
"This lecture is such a jumbled mess.
At @13:20 the prof. defines the mystery base e such that d/dx (e^x) = e^x.
At @21:34 the prof. states that e is the base of the logarithm. (e is Euler's number)
How does he equate the e at @13:20 with the e at @21:34? He assumes that they are the same just because he has used the same letter in both places. There is not explanation as to why the logarithm base 'e' is the same as the mystery base 'e' defined earlier." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10810.0 0.0 1.0 0.0
41:30 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1153.0 0.0 0.0 0.0
"40:30 نقطة جدا جدا جدا مهمة" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1128.0 0.0 0.0 0.0
"Good lecturer." 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 4141.0 0.0 0.0 0.0
"This is why people applied MIT" 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10775.0 0.0 0.0 0.0
"what about what was written behind the boards?" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15115.0 1.0 0.0 0.0
"Prof. Strang is amazing but you should skip this lecture if you are NOT familiar with differential equations. It is too fast paced, and avoids multiple non-distinct eigenvalues. I didn't find the book section very helpful as well. 
The good thing is skipping this ""applications"" lecture doesn't affect the series. I would recommend Edwards-Penney differential equations Chapter 5 if you really want to understand what is going on and where these equations are coming from (i.e. the link between eigenvectors, exponential matrices and different equations). 
You can look at ocw 18.03 section 4 as well, which will explain this at a reasonable pace.
or you can just leave thinking aside and put the following things into memory.
A system of differential equations has a solution in the eigenvectors and eigenvalues of A. Exponential of a matrix is a taylor series with scalar replaced by a matrix and follows the same derivative. For stability, real part of eigenvalues has to be negative." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 8306.0 0.0 0.0 0.0
"13.00  that idea  never came to me" tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 402.0 0.0 0.0 0.0
"The only reason I can see that you'd be opposed to this is perhaps if you think that American workers and businesses cannot keep up? Or just threatened and xenophobic of non-Americans? Well, if rising standards serves as a motivation, then American businesses have to step up their games and become better. Which is better for you.

It's not all about direct national interest. And as an international student who is not going to MIT, I greatly appreciate this gesture (which doesn't cost them much)." Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10214.0 0.0 0.0 0.0
"thank you sir." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 14508.0 0.0 0.0 0.0
"I mean I know this is MIT but if at 9:40 he would just do factoring without skipping steps, it would be much clearer for everyone and he wouldn't have to go over everything to make sure people understood." 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5870.0 0.0 0.0 1.0
"This is the best introduction to markov chains ever!!!!!!" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 10737.0 0.0 0.0 0.0
"Like like like 👍👍👍👍" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7359.0 0.0 0.0 0.0
"At the last proof (A'A is invertible), why is he allowed to multiply both sides by a row vector? Shouldn't that change the solution set?

For example, suppose [x1 x2 x3 x4]' = 0. Then x = 0 vector. But if I multiply both sides by [1 -1 0 0], then [1 1 0 0]' becomes a solution. Should I assume that this operation can only add solutions, so the proof is still valid (since after the operation, only 0 is in the nullspace)?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 2730.0 0.0 1.0 0.0
"i wish they didnt move the cameras so much, i want to look at the blackboard, i don't mind if the professor is not in frame." k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13504.0 1.0 0.0 0.0
"I am not entirely sure if this is correct ( plz say if I am not), but I’m also pretty sure U, sigma, and v-transpose can also be called LDL-transpose or also LDU for L is lower D diagonal and U for upper" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5123.0 0.0 0.0 0.0
"after lec4, it feels like passing the right and clean side of the notebook" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 12309.0 0.0 0.0 0.0
"Something about Frobenius Profesor" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8842.0 0.0 0.0 0.0
"Can't believe I made it to the last lecture. Thank you professor Strang." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 3122.0 0.0 0.0 0.0
"am i the only one who thinks it odd to introduce derivatives before limits?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12340.0 0.0 1.0 0.0
"lol thats stupid that they are teaching those easy stuff in MIT.they must know all those easy shit from highscool" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13832.0 0.0 0.0 0.0
"I'm currently reading Calculus by Dr. Strang. One of the best books on the subject I have ever come across." NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6318.0 0.0 0.0 0.0
"Thank you Professor Strang for the great course, and MIT for making it accessible for us. This is such a great opportunity for those of us who want to learn more than what is offered at our high schools." Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 9220.0 0.0 0.0 0.0
"Warning: The difficulty rose exponentially in this lecture >.<" 4LYom0ekars "4. Forbidding a subgraph III: algebraic constructions" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 11268.0 0.0 0.0 0.0
"I am very happy to why the fuck is this full of bots in space and curl. Thank you, it really helps" seO7-TwXH_I "Lec 30: Line integrals in space, curl, exactness... | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5151.0 0.0 0.0 0.0
"i just had one of those OOOOOOOOh moments" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13406.0 0.0 0.0 0.0
"it would be better if the professor has provided a proof for the fundamental theory of calculus rather then just stating it and then providing examples." 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13687.0 0.0 0.0 1.0
"Great lecture! Thanks professor and MIT." 0Va2dOLqUfM "5. Maximum Likelihood Estimation (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 4271.0 0.0 0.0 0.0
"DR. Strang, thank you once again for another fantastic lecture on Matrices A(t) Depending on t. Using calculus to find dlamba/dt  is another great work of art by the grandfather of linear algebra." z3SmljnD_nQ "15. Matrices A(t) Depending on t, Derivative = dA/dt" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3288.0 0.0 0.0 1.0
"Knowledge for free. Thanks MIT, thanks youtube, thanks internet." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7221.0 0.0 0.0 0.0
"The joke at the end was likely very effective in making students interested and curious about the topic. What a genius!" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 10146.0 0.0 0.0 1.0
"Spinning in or spinning out? This is the question." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 8869.0 0.0 0.0 0.0
"I completed the course. Thank you, professor, so much." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5242.0 0.0 0.0 0.0
"27:16 can someone explain to me abit more about the height ""r"" ?" zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 817.0 0.0 1.0 0.0
"i think this lecture changed my life ...i now see education in a morer good perspection...by the way am from south africa ..stellenbosch university" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 13482.0 0.0 0.0 0.0
"Audio channels fixed!" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 2739.0 0.0 0.0 0.0
"47:33 b0ss music plays........." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1283.0 0.0 0.0 0.0
"You make teachers in my university look like trash" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 12224.0 0.0 0.0 0.0
"the pseudoinverse is denoted A+.  Prof. Strang said pseudoinverses wouldn't be on the final exam.  Therefore there were no A+'s on the final.  :/ ..." Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 14733.0 0.0 0.0 0.0
"How did sir prove that column rank = row rank by just decomposing the matrix into CR? Thanks" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4841.0 0.0 1.0 0.0
"THE BEST IN THE GAME!!! THE BEST IN THE GAME!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8993.0 0.0 0.0 0.0
"Wonderful lesson, beautiful teachings, Prof. Thanks!" rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 11990.0 0.0 0.0 0.0
"Professor Strang, I would like to humbly thank you for sharing this invaluable knowledge with all of us. And of course, thank you MIT for uploading such amazing content. I spent the last 2.5 months watching all the videos, preparing all 10 problem sets, 3 quizzes, and the final exam. I even uploaded my solutions here - https://github.com/alivay/mit_1806_linear_algebra in latex and pdf formats." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 8380.0 0.0 0.0 0.0
"More functional analysis courses please!! more advanced functional analysis courses! perhaps even non-linear functional analysis :D" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 7693.0 0.0 0.0 0.0
"This is the way mathematics should be taught explaining every logical step. Sadly it's lightyears away from the way it's usually taught." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10757.0 0.0 0.0 1.0
👍👍👍👍👍 QXkOaifVfW4 "9. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 15708.0 0.0 0.0 0.0
"My multivariable calculus class in Spain was at least 2 times harder than this, the entire carreer was 5 years long and it was FREE. People without resources even get extra money for transport etc.. of course this is already being fucked up because of your uncontrolled capitalism generated crisis, I used to think about MIT as something big and smart but it isn't.. the lectures are the same, even easier than in many other places.. you live indebted selling yout entire lives for nothing.. " YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7775.0 0.0 0.0 0.0
"auroux ftw." 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12482.0 0.0 0.0 0.0
"Prof. Strang. Thank you sir!!!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 8315.0 0.0 0.0 0.0
"Never learned determinants like this, always just given the formula and the applications. Very enlightening." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 7816.0 0.0 0.0 1.0
"buders daha iyi" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12564.0 0.0 0.0 0.0
"My Monica distance is too small 😂😭 Professor Strang comin’ at us with all that humor towards the end was fun 🧡🙌🏽✨" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 7734.0 0.0 0.0 0.0
"I think in the last mct, we also need assumption that f be nonnegative on E, because otherwise its integral over E is not defined since it is not in L+(E). It may be measurable and also nonnegative ae but I don’t see why it has to be nonnegative on all of E." ZWzCHjN3_3s "Lecture 11: The Lebesgue Integral of a Nonnegative Function and Convergence Theorems" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 6024.0 0.0 1.0 0.0
"Thanks sir" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9771.0 0.0 0.0 0.0
"Can someone explain the difference between two approaches of solving the least square problem 1) using Transpose(A)*A*x = Transpose(A) * b,  or 2) Using QR decomposition, i.e. R * A = Transpose(Q) * b" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 3072.0 0.0 1.0 0.0
"thank you a lot for such a great explanation" H_k1w3cfny8 "10. Continuous Bayes' Rule; Derived Distributions" "6.041 Probabilistic Systems Analysis and Applied Probability" 14491.0 0.0 0.0 0.0
"what is the professor showing on 1:28 when he's asking the students - ""physics, ha ?"" ))" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15168.0 0.0 0.0 0.0
"What an unusual way to say secant" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11460.0 0.0 0.0 0.0
"I can't breathe normally while listening to his lecture :)
 Anyway Prof. John Tsitsiklis has really helped me clear those important concepts." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 5208.0 0.0 0.0 0.0
"how can we relate raws in calculating the dimension of the column space" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 13203.0 0.0 1.0 0.0
"my lecturer is so smart he thought us all these 35 lectures in one lecture am i the only one who knows such Jenious" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 13987.0 0.0 0.0 0.0
"Thank You, Prof Strang." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 9057.0 0.0 0.0 0.0
"Both Questions at  25:25 were pretty stupid. They asked for solution of algebraic technics in Calculus Class." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2911.0 0.0 0.0 0.0
"Professor, I bow to u. May be someday i will be this deft a teacher in what I do. Thank you" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 8404.0 0.0 0.0 0.0
"thank you" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14464.0 0.0 0.0 0.0
"Great lecture!
13:22 and then on paper: ""P(A | B) undefined if P(B) = 0""
But what if B contains two points and A contains one of them?
P(B) = P(A) = 0, but I would like to say that P(A | B) = 1/2
What do you think about it?" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 4262.0 0.0 1.0 0.0
"life saver" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13787.0 0.0 0.0 0.0
"Εξαιρετικη δουλεια Κε Τσιτσικλη." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 15544.0 0.0 0.0 0.0
"34:00 If rank(A) = 3, then U*x = 0 has only trivial solution. But A*(-1, -1, 1)^T = 0. So rank(A) is not equal to 3." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 975.0 0.0 1.0 0.0
"I really hate to see any rewriting over partially cleaned blackboard, but our professor seems not to care" ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5918.0 1.0 0.0 0.0
"Thus authors of such texts VIOLATE their OWN rules in the early chapters of the text.  I understand why they do so, but they almost always do so somewhat high-handedly, with NO EXPLANATION of the pedagogical philosophy behind their ABUSE OF NOTATION.  Instructors who use this abused notation in class seem to be surprised that some students get confused by it.  These students are in some cases exactly the students who are being most attentive to detail, which is a necessary mathematical skill.  " 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 11003.0 0.0 0.0 0.0
"I just wanted to say to those of you who don't want to blindly accept this determinant malarky, get Serge Lang's Intro to Linear Algebra & do the First Chapter - focusing on the dot product especially! then you can rederive the cross product by using the dot product & ignore all of the nonsense like 
i x j = k
j x i = - k
with no motivation.

Do the Lang chapter then " 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5628.0 0.0 0.0 1.0
"At 18.07 why is d/dx b^x = d/dx f(kx) = k f'(kx) ? Thanks" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2598.0 0.0 1.0 0.0
"@RazackTheBuilder Thank you. I'm not very good at math." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1707.0 0.0 0.0 0.0
"40:41 why is that 7 and not -7?? did he flip the signs for both numbers on the first row of the inverse matrix?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1134.0 0.0 1.0 0.0
"Can someone please explain how did he get 100^2 and not 100 x 2 (multiply+substract) operations at 33:22?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 3087.0 0.0 1.0 0.0
"""Ok, so let's talk about geometry, that should calm you down""

Lmao" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 96.0 0.0 0.0 0.0
"5:10 There is a town in Finland and quite near Helsinki which swedish name is Alberga and we finn mathematicians always call is Algebra." HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1358.0 0.0 0.0 0.0
"This is also a very nice video on fisher information https://www.youtube.com/watch?v=pneluWj-U-o more intuitive but also quite interesting!" JTbZP0yt9qc "6. Maximum Likelihood Estimation (cont.) and the Method of Moments" "MIT 18.650 Statistics for Applications, Fall 2016" 10610.0 0.0 0.0 0.0
"where is lecture 8...." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15238.0 0.0 0.0 0.0
"yeah but they are not horizontal, as in f'=0. " twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15465.0 0.0 1.0 0.0
"Where is lecture 8 ?" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11685.0 0.0 0.0 0.0
"larual creek in fairfeild Ca" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 13756.0 0.0 0.0 0.0
"Ok let's move to space😂" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8046.0 0.0 0.0 0.0
"What the heck is wrong with this class. Are they even MIT students" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11557.0 0.0 0.0 0.0
"I just think, ""Why aren't they clapping?""" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 5621.0 0.0 0.0 0.0
"I always took the power rule for granted, but that was a mistake" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5048.0 0.0 0.0 0.0
"i am in love with gilbert <3
student of Electrical Engineering finding his lectures THE BEST!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 13333.0 0.0 0.0 0.0
"Too close. Moves too frequently." 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11061.0 0.0 0.0 0.0
"hmm, attrachon" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13176.0 0.0 0.0 0.0
"This man knows to make discussion about probability fun!" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 10876.0 0.0 0.0 0.0
"Denis rules. Top class." tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3352.0 0.0 0.0 0.0
"34:33 dat dramatic close-up though xD" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 983.0 1.0 0.0 0.0
"SUPER LOGIC" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 8586.0 0.0 0.0 0.0
"My head was hurting in class just a few minutes ago. I couldn't get it and some one was saying ""Oh easy so easy:"" Why couldn't I see it? Then I search the topic. This video is the best! I kept thinking that my prof didn't explain anything! Or maybe I need something like this.Thanks for the easy to understand explanation. You just made my day, May Allah bless the person filming the video and MIT. Thanks. You just saved me. I thought I might fail the exam. Thanks a lot!!!" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7759.0 0.0 0.0 1.0
"I couldn't watch this past 30:43. The ginormous spider on the blackboard I found very scary." 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5252.0 1.0 0.0 0.0
"8:10 Did he say ""probability for astrologists""? I guess it was a joke the audience did not get?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 1416.0 0.0 0.0 0.0
"A country that makes scientific knowledge public will always always be an oasis and an example to be followed." cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2106.0 0.0 0.0 0.0
"When I first started engineering school I had a great math professor. He would come completely unglued if u ever said ""minus 3"", it is ""negative 3""." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11603.0 0.0 0.0 0.0
"Never knew all these things are connected so beautifully ! Thanks prof. 🙏" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7815.0 0.0 0.0 0.0
"Et voila, Done.
First course which I completed." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 3578.0 0.0 0.0 0.0
"Why does C need to be invertible here @30:45 ? For (CD)x=0, if Dx=0 (ie null space of D) automatically CDx=0 as well." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 11835.0 0.0 1.0 0.0
"this is pure gold" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 14869.0 0.0 0.0 0.0
"Feels like 3b1b's video was inspired by this lecture!" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3749.0 0.0 0.0 0.0
"I have a trivial doubt,  23:38 professor says x1 = (b1.c11)/detA
But won't x1 = b1.(c11 + c21 + c31 +.....cn1)/detA by definition transpose(C) b = x.detA" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 5513.0 0.0 1.0 0.0
"sorry shoudk read

10x -1x = 9.999999... -.999999999
9x = 9" zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14378.0 0.0 1.0 0.0
"For those of us who are newcomers in ML, it's most enlightening to know that unlike ""pure optimization"" that aims to find the most exact minimum possible, ML aims instead to be ""close enough"" to the minimum in order to train the ML engine, if you get "" too close"" to the minimum an over-fit  of your training data might occur. Thank you so much for the clarification" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3906.0 0.0 0.0 0.0
"No it's kind of a review of high school calculus and few things are added to it. It's essentially calculus 1. " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7873.0 0.0 0.0 0.0
"Great course!" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4218.0 0.0 0.0 0.0
"21:00 I don´t understand that graphic. Is the graphic of a joint distribution? So, why the prof says that the distribution of the two random variables is a square? Does the function fx,y=1 has a height in the ""Z"" axis whose volume integrals to one?... HELP, PLEASE!" H_k1w3cfny8 "10. Continuous Bayes' Rule; Derived Distributions" "6.041 Probabilistic Systems Analysis and Applied Probability" 668.0 0.0 1.0 0.0
"If a point is the intersection of two lines, and a line is the intersection of two planes, then is a plane the intersection of two 3-dimensional spaces?  That doesn't make any sense, but it almost seems like it would be true if you kept following the initial logic." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6488.0 0.0 1.0 0.0
"what is prof name ? i see that he have more information about this chapiter or calculus in general ?" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15159.0 0.0 0.0 0.0
"When I was young I studied these topics at high school and again at the first year of the degree in physics 16 years ago. Now I’m rather surprised in be interested and in spending time to watch these valuable lectures on linear algebra, above all because I have nothing to do with them in my current life. But concepts are here so clearly explained that they turn me on the pleasure to remember how I was, that time puzzled, and how you can catch up comprehension of things after so many years." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11609.0 0.0 0.0 0.0
"how can I like a video twice?" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13194.0 0.0 0.0 0.0
"Great class! Ty MIT for open education!" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 4215.0 0.0 0.0 0.0
"MIT is the GOAT" smIcuRZybsA "Lecture 15: The Continuity of Sine and Cosine and the Many Discontinuities of Dirichlet's Function" "MIT 18.100A Real Analysis, Fall 2020" 7532.0 0.0 0.0 0.0
"*pulls into the garage" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 246.0 0.0 0.0 0.0
"why is it called ""integral""? what does this word mean literally?" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15332.0 0.0 1.0 0.0
"How could R be raised to a decimal number?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4830.0 0.0 1.0 0.0
"haha the second derivative test is just the determinant for a 2x2 hessian matrix, linear algebra FTW" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13044.0 0.0 0.0 0.0
39:38 Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1101.0 0.0 0.0 0.0
"wow... So I learned these stuff in 2nd grade of high school...so Harvard, here I come!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15434.0 0.0 0.0 0.0
"Timestamps and Summary of Lecture 2: Bounded Linear Operators

0:00 - Review of Banach Spaces 
In the previous lecture, we started with vector spaces (algebraic structures defined over a field, closed by operations of addition & scaling). We examined normed vector spaces, i.e. those with a notion of ""size"". Norms naturally give rise to metrics, furnishing an analytic context. Those normed vector spaces that are complete (every Cauchy sequence converges) with respect to the metric induced by their norm, are called Banach spaces -- central objects of study in functional analysis.

1:13 - Summability: 
Definition: A series is summable if its sequence of partial sums converges. It is absolutely summable if the series of its norms (nonnegative numbers) converges, which is stronger than regular summability. Useful theorem: a space is Banach if and only if the converse holds. 

19:05 - Operators and Linear Functionals. 
Linear operators (or linear maps) between vector spaces are described here as the analog of matrices; there is a correspondence between linear maps of finite-dimensional vector spaces and matrices that represent these transformations on a given basis. Functionals are linear operators from a vector space to its base field.

19:56 - Example of a Linear Operator: 
Consider a continuous map from the unit square to the complex numbers that takes in a function in C([0, 1]) and ""convolves it"" by integrating its product with the aforementioned map over the compact interval [0, 1]. This is linear by the usual properties of integration. 

23:16 - Linear operators in full generality from V -> W. 
A linear operator between two vector spaces satisfies additivity and scalar homogeneity. As algebraic structures, vector spaces are essentially characterized by their closure under addition and scalar multiplication from a base field. The carrying-over of these properties from V to W indicates that linear operators are the ""correct"" structure-preserving maps to study between vector spaces (abstractly, K-linear maps are the morphisms in the category of vector spaces over K). 

26:30 - Continuous Linear Operators
We describe a linear operator as continuous if it preserves convergent sequences. Equivalently, we can formulate continuity in a topological manner: inverse images of open sets under continuous maps remain open. This is important to distinguish in the infinite-dimensional case -- all norms on finite-dimensional vector spaces are equivalent, hence all operators between f.d. spaces are continuous, but this need not hold for Banach spaces (as we've seen, spaces like C([0, 1]) are infinite-dimensional). Unlike general or f.d. vector spaces, Banach spaces express nontrivial analytic information: to study them appropriately, we must restrict to a suitable class of continuous linear maps that do convey this data. 

30:06 - Continuity and Boundedness
Theorem: a linear operator between normed vector spaces is continuous if and only if it is bounded. Informally, knowing that an operator between normed vector spaces ""maps arbitrarily close points to arbitrarily close points"" tells us the same information that it ""maps bounded subsets to bounded subsets"". It turns out that it's enough to show this criterion for continuity at a single point, e.g., the zero vector.  

44:10 -  Example of a Bounded Operator
Interpreting the earlier example as a continuous linear operator from C([0, 1]) -> C([0, 1]), it is clearly continuous when acting on continuous functions. Regarding it as a map between normed vector spaces (in fact, Banach spaces) allows us to view it as a bounded operator, specifically under the supremum norm as discussed in the prior lecture. 

49:30 - The Space B(V, W) 
Given two normed vector spaces V and W, we define B(V, W) to consist of all bounded (eq. continuous) linear functionals V -> W. Define on it the operator norm, which returns the maximal norm of a vector in the image of a given bounded linear operator; by linearity we don't lose any information by normalizing & considering the supremum over the images of just unit vectors. This is checked to satisfy the norm axioms, turning B(V, W) into a normed vector space in its own right. 

58:44 - If W is Banach, so is B(V, W) 
Strengthening the previous observation that B(V, W) is a normed vector space, if we assume that W is Banach (V need only be an NVS) then B(V, W) itself becomes a Banach space. Completeness follows from the initial lemma that a space is Banach when a series is absolutely summable if and only if it is summable. 

1:21:08 - The (Continuous) Dual Space
For any normed vector space V, define its continuous/topological dual space V' to consist of all bounded linear functionals from V to its base field K. (i.e. B(V, K) with the above notation). These are always Banach - for the l^p sequence spaces, examples include (l^1)' = l^∞, but (l^∞)' is not l^1 (not symmetric!). In general (l^p)' = l^q, where 1/p + 1/q = 1 (conjugate exponents); l^2 is special since it is self-dual. Note: for finite-dimensional vector spaces, V' coincides with the usual (algebraic) dual space of all linear functionals V -> K because continuity is immediate. However, it is strictly a subspace of the algebraic dual in infinite dimension, since one can always construct discontinuous linear functionals on infinite-dimensional vector spaces." 78vN4sO7FVU "Lecture 2: Bounded Linear Operators" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 11017.0 0.0 0.0 0.0
"this guy is amazing!" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14817.0 0.0 0.0 0.0
"so it seems like the professor emphasized the importance of the eigenvalue here, that's nice. but is the eigenvector of any importance? what's a good example of eigenvectors?" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 14337.0 0.0 1.0 0.0
"23:00 I’m not following— where is the identity matrix?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 708.0 0.0 1.0 0.0
"Was is die text book? Vielen Dank." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 11272.0 0.0 0.0 0.0
"26:09 I doubt the statement that v must be in the row space." rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 796.0 0.0 1.0 0.0
"I love it when math gets graphic." 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 5760.0 0.0 0.0 1.0
"compared to 18.06 these lectures demand much more involvement of the viewer in terms of pausing and thinking about things which professor Strang is saying and once you start doing that this course would feel if not more but as beautiful as than 18.065.
Someone coming from 18.06 might feel a bit unhappy but trust me this is amazing just keep going." d32WV1rKoVk "12. Computing Eigenvalues and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12665.0 0.0 0.0 0.0
"Thanks so much from Thailand. I have learned a lot from you." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9790.0 0.0 0.0 0.0
"Professor Strang thank you for a straight forward  lecture on Gradient Descent: Downhill to a Minimum and its relationship with convex function. The examples are important for deep understanding of this topic in numerical linear algebra." AeRwohPuUHQ "22. Gradient Descent: Downhill to a Minimum" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8364.0 0.0 0.0 1.0
"just good for the future" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 13735.0 0.0 0.0 0.0
"For a second, I'm always surprised that people don't clap at the end of the lecture..." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 3846.0 0.0 0.0 0.0
"Thank you, Prof. Strang, for creating 18.01A and helping me get through freshman year with your avuncular style.  I can't thank you enough." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9511.0 0.0 0.0 0.0
"Ax is not same as ABx" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2795.0 0.0 1.0 0.0
"Very nice! :)" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 11217.0 0.0 0.0 0.0
"Whenever I make money I will donate!" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11651.0 0.0 0.0 0.0
"Can anyone explain how ""length of the linearly independent list ≤ length of spanning list""?
TY in advance." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3020.0 0.0 1.0 0.0
hahaha 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13050.0 0.0 0.0 0.0
"this inspires me for a small contribution to MIT OCW" rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 14848.0 0.0 0.0 0.0
"at 18:20, shouldn't it be   d/dx b^x = k * M (2^k)  at x=0?
If I apply the chain rule,    d/dx 2^kx  =  k * 2^kx * M (2^k)" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12418.0 0.0 1.0 0.0
"I hate it too,but i forcefully learnt it and it seems interesting!" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5480.0 0.0 0.0 0.0
"@kvasir40 Well if he is a s good as your English is i bet your right" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1927.0 0.0 0.0 0.0
"What did Professor mean by a pivot ?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11478.0 0.0 1.0 0.0
"45:10 Waste of blackboard energy." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1249.0 1.0 0.0 0.0
"Prof. Strang telling an empty room not to ""all speak at once"" at 19:07 gives me life." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 8310.0 0.0 0.0 0.0
"@fuckooo I don't know for sure, I relied on the comment I read back then. All this fuss about me trying to make a joke... :P" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1842.0 0.0 0.0 0.0
"this is the most excellent math leasson i have learned, impressive and fantastic!" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 14884.0 0.0 0.0 0.0
"What a good teacher
I can only dream of such a good teacher to my studies ..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11409.0 0.0 0.0 0.0
"I’m not imaginary!" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 7114.0 0.0 0.0 0.0
"I'm just a bit confused, but which one is an elimination matrix and which one is an elementary metrix?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6337.0 0.0 1.0 0.0
"...... i'm having math's exam tomorrow and i Optimistic that i can get a good mark after watching this ... this guy is knows how explain and justify !!!!!!!" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 263.0 0.0 0.0 0.0
"nghe di nghe lai van thay hay :D qua tuyet." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14023.0 0.0 0.0 0.0
"Thanks professor strang. Your lectures are amazing." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 9767.0 0.0 0.0 0.0
"i bet your a failure" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13345.0 0.0 0.0 0.0
"Well, that's the definition of critical point. If the rate of change wasn't zero, it'd mean the function would still change there. In extreme points, the function stops changind (increasing or decreasing), so the rate of change is 0." 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11369.0 0.0 0.0 0.0
"anyone can fix the subtitles?" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 12382.0 0.0 0.0 0.0
👍👍👍👍👍👍👍👍👍👍👍 QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15714.0 0.0 0.0 0.0
"You are amazing. Thank you so much!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12168.0 0.0 0.0 0.0
"Wow the video quality is awesome 
and lecture of Professor Gilbert Strang is the best" AeRwohPuUHQ "22. Gradient Descent: Downhill to a Minimum" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12036.0 0.0 0.0 0.0
"I love you so much. Thank you." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 5851.0 0.0 0.0 0.0
"How to find next date for earthquake ??so we know quantum physics easily found this situation
🕉🕉🕉🕉🕉" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 4899.0 0.0 0.0 0.0
"k = 1 / M(2) ; for b = e => b = 2^k => e = 2 ^ 1/M(2); for b = e and k = 1/M(2) => ln (e) = ln (2 ^ 1/ M(2)) => 1 = 1/M(2) x ln (2)
 => ----------------------------------------------------------------------------M(2) = ln (2) or M(a) = ln (a)------------------------------------------------------------------------------

d (2^x)/ dx = 2^x . M(2) => 2^x . ln(2) ; for any x.

In general rule: d (a^x)/ dx = a^x . M(a) => a^x . ln(a)" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13748.0 0.0 0.0 0.0
"Can someone explain how to calculate the y-intercept? If you replace y0 with 1/x and plug x = 0, wouldn't you get a division by zero error?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3071.0 0.0 1.0 0.0
"we can get free lecture from MIT?? WOW!!!!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15074.0 0.0 0.0 0.0
"Hmm.. as of 13/06/2015, This lecture has about 36E3 views; while lecture 1 has about 1.46E6 views. This assuming those that watch the quiz reviews are serious learners. Then you guys are about 2.5% (36E3/1.46E6). Congratulations, you guys are the course elite. (Of course life isn't a zero sum game so it doesn't matter elite or not). However A+ on self discipline." HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 4774.0 0.0 0.0 0.0
"Thanks MIT and Prof. Jerison!" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9608.0 0.0 0.0 0.0
"I don't know if there is already a comment on this, but I think there is a mistake in 34:24, because the derivative of tag^-1(x) is the derivative of cot x, that's to say, cosec^2(x), not 1 + x^2, that is the derivative of arctag x" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5320.0 0.0 1.0 0.0
"37:44 ... *I think he's done something wrong but I'm not going to say anything until 38:55* :P

(Just in case people get confused at this point)

In any case, a great informative video." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1072.0 0.0 1.0 0.0
"fantastic !" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 12845.0 0.0 0.0 0.0
"This guy's great : ) thanks mit" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10567.0 0.0 0.0 0.0
"At 40:40 why is P(X>1) = (1-p) ? Are we using total probability concept here?" -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 2659.0 0.0 1.0 1.0
"never seen liner equations ever and I am 15 and this guy explains it so perfectly" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 14019.0 0.0 0.0 0.0
"Question: If A is poorly conditioned, I thought QR decomposition was computationally unstable as well.  Why would we do this with a poorly conditioned matrix?" Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8478.0 0.0 1.0 0.0
"The probability is the probability of DETECTION not existence or state, the measurement problem is that we can only measure in one dimension of space and one of time in any quantised single act of measurement and the wave function NEVER collapses, it is always converted from distribution in time (wavelength) to distribution in space and vice versa. I have solved everything but as always people given accolades for incorrect ideas find it hard facing the truth that reverses those accolades. The Theory of Everything has been completed." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 10233.0 0.0 0.0 0.0
"fantastic cameo from mr. death" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 12846.0 0.0 0.0 0.0
"Cramer's rule? more like cram...ming for that test that I'm 100% not prepared for in the slightest amirightohgodpleasehelpme" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 3258.0 0.0 0.0 0.0
"this guy is fantastic!" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14825.0 0.0 0.0 0.0
"you could download the video from the course website and then play it from your hard drive. " ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15501.0 0.0 0.0 0.0
"Can anyone tell me where to practice the concepts he is teaching from?" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 3048.0 0.0 0.0 0.0
"I watch this video whenever I feel like giving up on Linear Algebra. Listening to him gives me encouragement to learn Math not for grades, but to understand what actually math means. Hats off to this legend." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6180.0 0.0 0.0 0.0
"thank you!!!!! so in love with this class :)" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14531.0 0.0 0.0 0.0
"this is masterpiece from educational perspective" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14867.0 0.0 0.0 0.0
"Most math teachers can't teach this well but have more attitude than this guy.
Respect" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7700.0 0.0 0.0 0.0
"I can't see, professor can you please write bigger on the blackboard?" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 5220.0 1.0 0.0 0.0
"The king's sibling problem at the end is thought provoking. Thank you" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 10151.0 0.0 0.0 0.0
"""Pi is about 3 and a little more, e is about 2 and a little more""
24:30
that's more badass than anything else 😂" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 100.0 0.0 0.0 0.0
"Thank you so much for the beautiful ideas behind the circulant matrices. Geometric ideas help me to understand the concepts easily, thank you." 1pFv7e9xtHo "31. Eigenvectors of Circulant Matrices: Fourier Matrix" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9371.0 0.0 0.0 1.0
"Just explained why we switch the order when taking transpose of matrices multiples together… amazing tiny connections" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7163.0 0.0 0.0 0.0
"at 13:30 my mind was blown." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12413.0 0.0 0.0 0.0
"Im in high shcool and this just Fucked my Mind...." ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6572.0 0.0 0.0 0.0
"Thanks a lot for this video, and by the way, for all the others as well. 5 Stars" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9661.0 0.0 0.0 0.0
"Actually, if you do a midpoint Riemann sum, you end up with a better approximation then a trapezoid rule. Left end and right end Riemann sums are just silly." jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2236.0 0.0 0.0 0.0
"Lecture 1: Dot Product
Lecture 2: Determinants
Lecture 3: Matrices
Lecture 4: Square Systems
Lecture 5: Parametric Equations
Lecture 6: Kepler's Second Law
Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds)
Lecture 8: Partial Derivatives
Lecture 9: Max-Min and Least Squares
Lecture 10: Second Derivative Test
Lecture 11: Chain Rule
Lecture 12: Gradient
Lecture 13: Lagrange Multipliers
Lecture 14: Non-Independent Variables
Lecture 15: Partial Differential Equations
Lecture 16: Double Integrals
Lecture 17: Polar Coordinates
Lecture 18: Change of Variables
Lecture 19: Vector Fields
Lecture 20: Path Independence
Lecture 21: Gradient Fields
Lecture 22: Green's Theorem
Lecture 23: Flux
Lecture 24: Simply Connected Regions
Lecture 25: Triple Integrals
Lecture 26: Spherical Coordinates
Lecture 27: Vector Fields in 3D
Lecture 28: Divergence Theorem
Lecture 29: Divergence Theorem (cont.)
Lecture 30: Line Integrals
Lecture 31: Stokes' Theorem
Lecture 32: Stokes' Theorem (cont.)
Lecture 33: Maxwell's Equations
Lecture 34: Final Review
Lecture 35: Final Review (cont.)" sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7279.0 0.0 0.0 0.0
"Thank you so much for this lecture series!" nvXRJIBOREc "Lecture 21: Minimizing a Function Step by Step" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9373.0 0.0 0.0 0.0
今天全部学习完了。非常好！感谢老师和MIT！ --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15616.0 0.0 0.0 0.0
"Must have missed something here. In one quadrant of a circle of radius 1 we get an area of pi/8. That would give the area of the circle to be pi/2?" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7726.0 0.0 1.0 0.0
"Thanks MIT, winning hearts and minds." RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 9615.0 0.0 0.0 0.0
"This lecture is amazing. Pro.Strang gives an intuitive perspective Fourier Series, and how it is related to orthogonal vector. I know Fourier transform pretty well but now have a deep understanding of that." lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 10794.0 0.0 0.0 1.0
"Outstanding Gill!  I studied LA 40 years ago, but it was a mere 2 dimensional projection of the many dimensions you present.  I bought your book and donated all my other LA texts.  You're an excellent instructor." TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 8140.0 0.0 0.0 0.0
"Why can't we solve 4 equations with 3 unknowns again? Considering people are still watching this in 2k18" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 11799.0 0.0 1.0 0.0
"Regards from 2004 particle physics batch" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8546.0 0.0 0.0 0.0
"haha that prof is jokes... but im very surprised at how elementary this course is compared to the equivelant course at university of toronto" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13043.0 0.0 0.0 0.0
"@sbhdgr8  No. He's trying to write the second order differential equation as a system of first order linear equations, or basically you are just substituting y'=some variable, basically just manipulating the expressions so the 2nd order equation is ""transformed"" into equations of first order. The matirx of coeffiecients represents the coefficients of the ""transformed"" resulting system of 1ST order linear equations. It is the same idea as substitution in quadratic equations like ax^4+bx^2+c, and " IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 2002.0 0.0 0.0 0.0
"This guy is really good. Wish my professor could articulate the material like this!" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 10541.0 0.0 0.0 0.0
"The permutation definition of determinants gave me so much strife, but Strang makes it crystal clear. What a legend." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 10224.0 0.0 0.0 1.0
"What level of probability is this course?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 11550.0 0.0 0.0 0.0
"Professor Strang, thank you for another classic selections and topics which include Saddle Points, Maximum Principle, Probability, Variance and Expected Values." 2K7CvGnebO0 "19. Saddle Points Continued, Maxmin Principle" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8385.0 0.0 0.0 0.0
"Thank you MIT, thank you Prof Strang." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9159.0 0.0 0.0 0.0
"Excellent. Thank you." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3694.0 0.0 0.0 0.0
"any one know where this lecture
please tell me" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12378.0 0.0 0.0 0.0
"@gorgolyt  they are all spelled correctly because this is youtube and i dont proof read my messages to accommadate for some douche with 8th grade argumentative techniques" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1856.0 0.0 0.0 0.0
"@JFwarrior What did you expect exactly? That's the heaven which every student seeks." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1643.0 0.0 0.0 0.0
"How come this video lecture has 29 dislikes?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4825.0 0.0 0.0 0.0
"Thank you Dr. Strang. I graduated from high school functionally illiterate in math. In my journey to teach myself math you have become a great mentor." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 9103.0 0.0 0.0 0.0
"No se entiende ni madres" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7890.0 0.0 0.0 0.0
"He wears the same shirt and same pants every lecture." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 4619.0 0.0 0.0 0.0
"I have a question. At 33 minutes, where did the negative of the x/Xo^2 go when he added the 1/Xo to the other side?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5508.0 0.0 1.0 0.0
"Love his way of teaching and how clearly he connects the physical meaning of what he is teaching." 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7443.0 0.0 0.0 0.0
"Helo,
Can anyone help me, how to learn Calculus in Linear fashion? From very basic i mean. 
Thank you very much, it’ll be a great help." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4669.0 0.0 1.0 0.0
"37:00 Mind blown" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 1052.0 0.0 0.0 0.0
"32:22 :D" WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 928.0 0.0 0.0 0.0
"The last function f(x1,x2,x3)>=0 can be proved by creating squares." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 10154.0 0.0 0.0 0.0
"Hi:

Only one thing, What´s your degree?" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4734.0 0.0 0.0 0.0
"Mr Strang makes me feel, in the first time of my life, that linear algebra is interesting!" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7710.0 0.0 0.0 0.0
"salam thanks" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14274.0 0.0 0.0 0.0
"I literally want to cry after watching this. Thank you so much for saving my ass." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 5708.0 0.0 0.0 0.0
"I Really Like The Video Final review From Your" ZwpwmGP5ITM "Lec 34: Final review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4946.0 0.0 0.0 0.0
"wow i envy ppl who can understand this stuff! " kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15417.0 0.0 0.0 0.0
"And this is useful to your average person how?" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2451.0 0.0 0.0 0.0
"Awesome, thanks a lot for this wonderful lesson 💗" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 2785.0 0.0 0.0 0.0
"Super poor photographer, this is not a movie, please leave the camera to the blackboard, students need time to digest, instead of continuing to give the teacher close-up. The teacher worked hard and the whole course was broken by the photographer." z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8958.0 1.0 0.0 0.0
"Is this course helpful for someone who is looking to get into Data science?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 6863.0 0.0 0.0 0.0
"This man teaches so clear thus finally I understand Matrics" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10879.0 0.0 0.0 0.0
"Great Course! Thank you MIT!" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4197.0 0.0 0.0 0.0
"At 33:11 it should be A(x_0)=3*[(2*V)^(2/3)]" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2649.0 0.0 1.0 0.0
"We love you, Pro Strang." z3SmljnD_nQ "15. Matrices A(t) Depending on t, Derivative = dA/dt" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11328.0 0.0 0.0 0.0
"I Really Like The Video Indeterminate forms L'Hospital's rule From Your" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4977.0 0.0 0.0 0.0
"My Linear Algebra course at Brandeis in 1968 left me totally confused; it was unintelligible. I wish I had had  Gilbert Strang as an instructor." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7732.0 0.0 0.0 0.0
"me: ""So....What?  Can you explain it again?""
him: ""Which part?""
me: ""All of it""
him: ""MIT OCW...Okay, so next...""" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 13935.0 0.0 0.0 0.0
"Wow, people have to take lectures for this? How stupid are you?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12072.0 0.0 0.0 0.0
"he is awesome!!
" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 13095.0 0.0 0.0 0.0
"I think after he went through the elimination process he should have summarized the rules of row operations (the algorithm) for programming purposes. Of course, in numerical analysis courses later, identifying the most efficient algorithm is a major task." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6006.0 0.0 0.0 1.0
"I wonder where is Lecture 8......" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6249.0 0.0 0.0 0.0
"@kotofu In 3D, you need z-axis. The slices could not work without a 3D visualization. In my understanding, that's why he used the z-axis... which is the vertical when you talk 3D." zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1923.0 0.0 0.0 1.0
"2:00 dang I should go to MIT" TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 864.0 0.0 0.0 0.0
"20:28 when you're about to say ""Oh f***!"" and you remember the camera is rolling! Haha gotta love Prof. Strang." lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 654.0 1.0 0.0 0.0
"elegantly explained, Prof!   respect" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 12793.0 0.0 0.0 0.0
"i love this teacher may  GOD  please him with long long life and good health" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13435.0 0.0 0.0 0.0
"stretching HAHAHH" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14402.0 0.0 0.0 0.0
"When we get linear equations, Ax=b, where A is an n  x n matrix, and x and b are column vectors with n components, we can see b as the linear combination of column vectors of A and components of x is equals to b. That is,

column 1 of A * 1st component of x 
+ column 2 of A * 2nd component of x ... 
+ column n of A * nth component of x. 

This view is new for me. Thank you, Prof. Strang." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11638.0 0.0 0.0 0.0
"48:00 Gosh, polar coordinates. I had it in uni and I never understood it, but that is so easy! Dr. Auroux is great in explaining!" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1288.0 0.0 0.0 1.0
"i think from now on in these lecture series my 10th grade level math just wont cut it :D Good part is that its summer and at the end of it i AM gonna know multivariable calculus, failure is not an option!:)
Awesome series, and professor." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13468.0 0.0 0.0 0.0
"Thanks MIT and professor ...." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9609.0 0.0 0.0 0.0
"Why u_0 can be written as a linear combination of eigenvector of A? 29:55" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 11929.0 0.0 1.0 0.0
"I don´t understand what people is talking about, I found this video just like others, I mean, It wasn´t slow at all, actually, I really really enjoyed it!!!

Thank you MIT and Professor David Jerison" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5375.0 0.0 0.0 0.0
"Lecture 1: Dot Product
Lecture 2: Determinants
Lecture 3: Matrices
Lecture 4: Square Systems
Lecture 5: Parametric Equations
Lecture 6: Kepler's Second Law
Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds)
Lecture 8: Partial Derivatives
Lecture 9: Max-Min and Least Squares
Lecture 10: Second Derivative Test
Lecture 11: Chain Rule
Lecture 12: Gradient
Lecture 13: Lagrange Multipliers
Lecture 14: Non-Independent Variables
Lecture 15: Partial Differential Equations
Lecture 16: Double Integrals
Lecture 17: Polar Coordinates
Lecture 18: Change of Variables
Lecture 19: Vector Fields
Lecture 20: Path Independence
Lecture 21: Gradient Fields
Lecture 22: Green's Theorem
Lecture 23: Flux
Lecture 24: Simply Connected Regions
Lecture 25: Triple Integrals
Lecture 26: Spherical Coordinates
Lecture 27: Vector Fields in 3D
Lecture 28: Divergence Theorem
Lecture 29: Divergence Theorem (cont.)
Lecture 30: Line Integrals
Lecture 31: Stokes' Theorem
Lecture 32: Stokes' Theorem (cont.)
Lecture 33: Maxwell's Equations
Lecture 34: Final Review
Lecture 35: Final Review (cont.)" seO7-TwXH_I "Lec 30: Line integrals in space, curl, exactness... | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7278.0 0.0 0.0 0.0
"There is a MISTAKE on the formula of the minute 32:31. It must be S(Λ^100)c in order to work as it is supposed. However it is an excellent lecture, thanks a lot. :)" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 10361.0 0.0 1.0 0.0
"starting from professor devid jerison`s lecture to girls who volunteer ,everything is amazing" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14396.0 0.0 0.0 0.0
awesome! Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12495.0 0.0 0.0 0.0
"if you are a random person like i am, which has nothing to do with anything of the information given in this video, like i am (i am a chef in a restaurant) you think to yourself, WTF IS HE TALKING ABOUT!!? and i watched this 10 fucking minutes ...." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13547.0 0.0 0.0 0.0
"Without the need of guessing, I use the cross product method and then I equate like-terms to like-coefficients followed by solving the very simple simultaneous equation - that is for coefficients of x^1,  (A + B) = 4 eqn(1) and for coefficients of x^0; (2A - B) = -1 eqn(2), therefore B = 4 - A by eqn (1), sub into eqn (2) to get A = 1 and hence B = 4 -1 = 3, Q.E.D." HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11974.0 0.0 0.0 0.0
"With his lecture, I could sit in my desk all day and study. Math is so great." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 11967.0 0.0 0.0 0.0
"Expecting to see Dr. Strang lecturing at age 106." k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3703.0 0.0 0.0 0.0
"jan 11? so did you approve?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13720.0 0.0 0.0 0.0
"I'm a math major, and my uni only offers theoretical CS as a unit to CS majors (or you'd have to do enough to earn a CS minor at least), which sucks because this really interests me, but I don't care much for the engineering/code-monkey stuff. Thanks for uploading this, I'm gonna follow these closely for sure!" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 6298.0 0.0 0.0 0.0
"i not understand - but it So hard.. i'll learen it soon :P~ lol" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13446.0 0.0 0.0 0.0
"@BYMYSYD yeah i got how X - Xo became zero but i don't get how the term multiplied with X - Xo became f'(x)" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1599.0 0.0 1.0 0.0
"anyone know where i can get solutions for this course on the mit ocw website?" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12386.0 0.0 0.0 0.0
"All these videos previously had a delay between the audio and video. These are reuploads, and that's why there's so few views" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 2312.0 0.0 0.0 0.0
"public school cannot effort teacher like that. his salary is probably more then high school teacher lol. " ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14228.0 0.0 0.0 0.0
"Why is Prof. Strang so successful at teaching? It's not just that his explanations are clear and reasonable. His personal style has a lot to do with it. He comes across as unpretentious and as someone who is doing this journey with you." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11865.0 0.0 0.0 1.0
"I think this lecture is a nice sip of randomized linear algebra for fresh people like me, but the notations are confusing (a lot of sum w/o specifying which variable to sum over) and I think the bit at 28:50 is incorrect (is professor confusing estimator of AB and the expectation of the estimator?). But the high level goal is clear, which is nice. I did some search online and I think the lecture notes at https://arxiv.org/abs/1608.04481 are helpful." z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6076.0 0.0 1.0 1.0
"Actually better than his textbook :)" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2234.0 0.0 0.0 0.0
"Cheaters on quiz!!!" 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 3144.0 0.0 0.0 0.0
"he gives you the right vision of mathematical concepts. and that's important for problem solving." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 13079.0 0.0 0.0 0.0
"It is a simple thing" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6928.0 0.0 0.0 0.0
"For a clearer images of the chalkboard contents, check out their OCW Scholar page for each lecture.

Here's the one for this lecture:
https://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/2.-partial-derivatives/part-c-lagrange-multipliers-and-constrained-differentials/session-42-constrained-differentials/" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3841.0 0.0 0.0 0.0
"This lesson is so great! Thank you so much!!!" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 10840.0 0.0 0.0 0.0
"This with the theory of relativity is moonshine..IIS has a clock and has been circling it for more than 10 years. No one has yet reported that cosmonauts have another time.
If you transmit one frequency f1 with an apparatus that has speed v, then that frequency will change to f2. That is a fact and the rest is Zionism.
If you want the receiver to receive f1 then you have to change f1 to the appropriate frequency." eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10978.0 0.0 0.0 0.0
"I Really Like The Video Determinant Formulas and Cofactors.From Your" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 4939.0 0.0 0.0 0.0
"I wish we had teachers like him in India." YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6235.0 0.0 0.0 0.0
"In 12:32, just LOL. That kid cant read" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6588.0 0.0 0.0 0.0
"I thought ""discrete"" and ""continuous"" random variables were statements about their domains instead of codomains." 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 6086.0 0.0 1.0 0.0
"47:25 drawing an eye 101" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 1282.0 0.0 0.0 0.0
"like what?" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13794.0 0.0 0.0 0.0
"God bless you!" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4086.0 0.0 0.0 0.0
"Not necessarily." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7927.0 0.0 0.0 0.0
"i will tell you why u understand everthing here..This professor is great and the other thing is..This lecture wont be explained in 10 minutes like here in Germany. Of course u understand fucking nothing if you explain such important things in 10 minutes and then begin with new stuff." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 13495.0 0.0 0.0 0.0
"Is there any prerequisite required?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6839.0 0.0 0.0 0.0
"At the end, the area is given in terms of the angle theta. I'm assuming this is in radians. Three questions:

1) What units is the solution in? Meters^2?
2) I assume you cannot simply change between radians and degrees, as that would cause the calculated area to be off by a factor of 180/pi?
3) If that is true, why not? What is special about radians that makes the solution specific to radians?" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2728.0 0.0 1.0 0.0
охуеноооо! J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 15560.0 0.0 0.0 0.0
"Oh geez. What happened to the MIT student body? Universities are just politically correct money making evolutionarily illogical units subject to corruption at this point" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8005.0 0.0 0.0 0.0
"Note: Transpose(a)*(b-xa) is the dot product expressed in matrix multiply notation.

Confused me for a moment." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7936.0 0.0 0.0 0.0
❤️❤️❤️❤️❤️ AeRwohPuUHQ "22. Gradient Descent: Downhill to a Minimum" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15613.0 0.0 0.0 0.0
"What an incredible human being--gentle, wise, and -- of course -- very smart! What a gift to the world!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11457.0 0.0 0.0 0.0
"It’s ok to put khoo lol" phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7100.0 0.0 0.0 0.0
"i only understood pdf" Tx7zzD4aeiA "20. Central Limit Theorem" "6.041 Probabilistic Systems Analysis and Applied Probability" 13449.0 0.0 0.0 0.0
"just in-case anyone was wondering the program he used to generate those parabola is 3D-XplorMath its a really fun program relatively easy to use its even how i generated my display picture :)" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 13739.0 0.0 0.0 0.0
"I just messed up in the odd odd, odd even part, whatever the rest is wonderful. Thanks to Prof. Strang from India." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 5611.0 0.0 1.0 0.0
"Good day. Is there a certain textbook recommending?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 4126.0 0.0 0.0 0.0
"Don't underestimate Gauß, his mental ability was exceptional." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3476.0 0.0 0.0 0.0
"Brilliant teacher. A person who can impart love for the subject he teaches" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 2935.0 0.0 0.0 0.0
"I have just try the quiz on the mit ocw. Before doing the quiz I supposed it was an easy course. Now I think I was wrong: although the calculation is simple, and the problem are not difficult, one needs to be very clear about the basic concepts taught in the lectures.

The quiz: https://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/ax-b-and-the-four-subspaces/exam-1/MIT18_06SCF11_ex1.pdf" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 5534.0 0.0 0.0 0.0
"Clear and straight to the point!!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3152.0 0.0 0.0 0.0
"Lmao the students, man. What part of 'I know this can be done without calculus but it's just to illustrate the general method' do they not understand? That girl at around 19 minutes into the video doesn't get the point" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7392.0 0.0 0.0 0.0
"Shouldn't the five be a negative 5...?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8651.0 0.0 1.0 0.0
"From where you people practice? Professor Strang's book?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3940.0 0.0 0.0 0.0
"9:24 so glad for this clarification, was confusing me while reading a different textbook that didn't quite cover that detail. P(X = x) huh?" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 1440.0 0.0 0.0 0.0
"First video series ive watched without getting bored (as for educative videos), this teacher rocks, all hail Mr. old genius guy. Perfectly understandable, my respect to him." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3822.0 0.0 0.0 0.0
"THANKS A LOT !!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8987.0 0.0 0.0 0.0
"In love with course outline" Tx7zzD4aeiA "20. Central Limit Theorem" "6.041 Probabilistic Systems Analysis and Applied Probability" 6640.0 0.0 0.0 0.0
"Thank you MIT, very cool!" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9160.0 0.0 0.0 0.0
"After seeing this video I wonder why people endure 100s of thousands of dollars worth of student loans in the us to get into a place where they teach the same stuff taught in indian high schools lmaoooooooooooo!" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2254.0 0.0 0.0 0.0
"More like dilbert space! Am I right?!" EBdgFFf54U0 "Lecture 14: Basic Hilbert Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 7694.0 0.0 0.0 0.0
"nice explaination, very usefull thank a lot" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 14033.0 0.0 0.0 0.0
"Completed 8 videos, watching 9th, 26 more to go!" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 3181.0 0.0 0.0 0.0
"Did this guy really trick these students into learning how to do a proof by contradiction, randomly, half way through? :P" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3385.0 0.0 0.0 1.0
"it is weird that in this series there is no such advertisement like others. that helped a lot in focusing in the lecture" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13677.0 0.0 0.0 0.0
"Anyone else see a face in the brackets at 30:22?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2490.0 0.0 0.0 0.0
"I finished this lecture on Sep. 16, 2022, at 22:35pm. Thank you Prof. Strang, the last month (Aug. 7 - Sep. 16) was so wonderful, memorable." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5422.0 0.0 0.0 0.0
"I dont get the part 18:4. Why does b=e all of sudden ? Can someone please explain it to me ?" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5365.0 0.0 1.0 0.0
"Thank you Universe for sending this happy man to the Earth." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9241.0 0.0 0.0 0.0
"Nice lecture, but you should also add the lecture contents in the description so that people don't have to go through the entire lecture to find out whether it's relevant to their course or not." EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 7847.0 0.0 0.0 0.0
"Df is decreasing when -2<x<∞, isn't it? for f(x)= x+1/x+2" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3362.0 0.0 1.0 0.0
Awesome! YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2780.0 0.0 0.0 0.0
"He is a greatt teacher💕" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4501.0 0.0 0.0 0.0
"why the applause?" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 15364.0 0.0 0.0 0.0
"I can't wait till anybody post that he is 12 and do this trivial thing just in school. -.-" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5228.0 0.0 0.0 0.0
"I was expecting claps at 11:10" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6151.0 0.0 0.0 0.0
"Thank you so much" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9341.0 0.0 0.0 0.0
"ths course is for the 1st year of university right  ?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14935.0 0.0 0.0 0.0
"what is Convext? like that ....hahah" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15148.0 0.0 1.0 0.0
"May God bless you, Professor Strang !" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7628.0 0.0 0.0 0.0
"16:02 is it in N(A-I) instead of N(A)?" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 467.0 0.0 1.0 0.0
"Beautifully delivered lectures. The content is well structured and easy to review." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 2827.0 0.0 0.0 0.0
"Vary good" tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11152.0 0.0 0.0 0.0
"26:10

I have a question about the cost of elimination.
Ax=b

For an nxn matrix A
For the 1st pivot, instead of 100^2, shouldn’t it cost 100*99?
2nd pivot, instead of 99^2, shouldn’t it cost 99*98?
3rd pivot, instead of 98^2, shouldn’t it cost 98*87?

So, instead of n^2+(n-1)^2+(n-2)^2+...., shouldn’t it be n(n-1)+(n-1)(n-2)+(n-2)(n-3)+.... instead?


Also, how did he get n^2 for the matrix b?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 797.0 0.0 1.0 0.0
"For the subspace in r4 with all the components of a vector adding up to zero, how is that a subspace? What if I had the vector with components [-4,-6,7,3], those add up to zero but if I were to add up any member than this wouldn't be a subspace." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 3897.0 0.0 1.0 0.0
"People who received this professor's lecture are bloody luck. These concepts and ideas were thrown in front of many high school, IB and undergrad students including me and they were expected to make sense out of them just by formula sheets and example questions. It is nice to see conceptual and even intuitive explanation of them." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8173.0 0.0 0.0 1.0
"handsome old boy" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 13058.0 0.0 0.0 0.0
"What a fantastic professor :) :)" sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11405.0 0.0 0.0 0.0
"I can't buy the book, how much will I miss due to that??" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5209.0 0.0 0.0 0.0
"Can anyone explain further why appending the 1s to the triangle matrix at the end shifts the triangle back to the origin? Also, if possible a little elaboration on why the cofactors columns equal 0 when multiplied by a different row number fro it's column number?" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 3019.0 0.0 1.0 1.0
"It's ironic how they still use chalkboards." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7053.0 1.0 0.0 0.0
"Why does my university not allow for students to record the lectures? It is so good to have those at home in video format. You can re-watch them and rewind time anytime you missed something because you weren't paying attention. Mighty helpful." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 11842.0 0.0 0.0 1.0
"24:40 what kind of coser is that?" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 749.0 0.0 0.0 0.0
"About calculating the power of a test (1:13:00 ->), isn't the most conservative choice for theta 3.49? I mean, when the true theta equals 3.49, the power becomes 5 % (with 5 % significance level). This is because the sampling distributions of Xn_bar (standardized) under theta_0 (3.5) and theta_1 (3.49) are basically equal.

Using this logic, the power of a test would always be equal to the significance level. Obviously, there's a flaw in my logic, but where? Prof. Rigollet says that we should look at the worst possible case (1:13:28). In my humble opinion, the worst possible case is when the difference between theta_0 and theta_1 is miniscule.

EDIT:

Ok, so Prof. Rigollet basically answers my question in the next lecture (8. at 13.45 ->). If theta_1 is defined on a set Theta_1, then the power is the value where it is minimized within this set. What I didn't get at first, or got overly confused about, is that in real life I choose my theta_1 basically as my best guess. This way, in general it won't always be equal to the significance level. If I let theta_1 be such that it can be the 'next door neighbor' to my theta_0, then the power will be equal to the significance level." phbw9r1iUDI "7. Parametric Hypothesis Testing" "MIT 18.650 Statistics for Applications, Fall 2016" 2195.0 0.0 1.0 0.0
"Thank you so much Prof.
Greetings from Jordan ^_^ " nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9356.0 0.0 0.0 0.0
"Show how barometer works and found its limits" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8657.0 0.0 0.0 0.0
"Absolutely wonderful series of lectures. Thanks a zillion to Prof Strang and OCW for making this available. These are absolutely priceless!" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 2223.0 0.0 0.0 0.0
"thanks to camera man and mit who put his time in making this lecture" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14609.0 1.0 0.0 0.0
"Best of bests" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 2870.0 0.0 0.0 0.0
"Thank you." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9549.0 0.0 0.0 0.0
"BEST TEACHER IN THE WORLD" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2802.0 0.0 0.0 0.0
"Isnt there a mistake @ 46:24 ? Shouldn’t the position 8,1 of matrix A contain a8,1 and not a1,8? Same for position 8,2, shouldn’t it contain a8,2 instead of a2,8? And same for position 1,2? Great lecture thanks!" 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 6902.0 0.0 1.0 0.0
"Yeah, I am taking it. YEAHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12125.0 0.0 0.0 0.0
Υο. PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15550.0 0.0 0.0 0.0
"The number of positive pivots may not equal the number of positive eigenvalues. Take the matrix [1,0;-1,0] for example: without row exchange ,it reduces to [1,0;0,0], but with row exchange it reduces to [-1,0;0,0]. Odd number of row exchanges will change the sign of determinant and therefore change the number of negative eigenvalues. Assume that there is no row exchange and no multiplication of a row by a (negative) scalar, then the result holds." UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 10208.0 0.0 1.0 0.0
"haha he gave those kids the ""i hate you and i am about to kill you... oh crap im being filmed"" look" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13038.0 0.0 0.0 0.0
"I'm looking to learn calculus and coming to the end of this video, it seems I'm missing lots of information.
What previous math categories should I learn to continue on with calculus?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6347.0 0.0 1.0 0.0
"So what if he forgot it? My teacher forgets a lot of formulae, he's still a beast at integrating though." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8801.0 0.0 0.0 0.0
"Thank you so much, best explanations and always interesting to follow" feb9j65Iz4w "24. Linear Programming and Two-Person Games" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9399.0 0.0 0.0 0.0
"watch this at 1.25x speed." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 15064.0 0.0 0.0 0.0
"at 6:07 he writes E2 is approx the square of E1 . But Shouldn't it be E1 is approx the square of E2?" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12467.0 0.0 1.0 0.0
"in 25:11 there was a student doing faces" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13575.0 0.0 0.0 0.0
"This is basic AutoCad.  I can do this all day." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10647.0 0.0 0.0 0.0
"I have a question about the last integral. About that last part. Can we manipulate the answer by log rules i.e. subtract ln2 from the answer as it's a constant and then write a new constant?" CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5497.0 0.0 1.0 0.0
"In the last bit, there lies the fact the alternating group A_n could be viewed as being a normal subgroup of index 2 in the corresponding permutation group S_n. Algebra is a fun topic." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 6671.0 0.0 0.0 0.0
"...because they're goobers, probably a freshman class." tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 268.0 0.0 0.0 0.0
"Denis Auroux: Fastest board eraser east of the Mississippi" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3350.0 0.0 0.0 0.0
"I am glad he got a bite on his cookie" os_XGBNPllM "Lecture 8: The Squeeze Theorem and Operations Involving Convergent Sequences" "MIT 18.100A Real Analysis, Fall 2020" 5094.0 0.0 0.0 0.0
"I dont understand why the cost is n^2 to make zero first column. A single operationg is multiplication and subtraction ,therefore i need to multiply first row with some constant and substract it from 2nd to get zero. It takes 1 operation to make (21) zero so 99 or 100 operation in total to make first column zero except pivot. Help me out here please" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 5369.0 0.0 1.0 0.0
"Thank god I'm majoring in accounting; the hardest math we have is just a little bit of partial differentiation that a five year old could do" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9064.0 0.0 0.0 0.0
"So, what's the point? ;-)" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8811.0 0.0 0.0 0.0
"Crazy, we estimate the probability of the mind. Bad that I don't already know the language. More homework if too much free time is a good way to progress. I like it. Means we should know where to put our mind to. There never should be too much. There is always more. Thanks..." bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3260.0 0.0 0.0 0.0
"@turkeyburgerfries me too" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2052.0 0.0 0.0 0.0
"The lecture is compressed into the matrices. This is so coooool!!!!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10161.0 0.0 0.0 0.0
"Yo, that Monica comment is GOATED! Had me dying from laughter. Gilbert Strang: Gentleman,  Mathematician,  Comedian. What a renaissance man." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 12158.0 0.0 0.0 0.0
"thanks! great lecture!" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14611.0 0.0 0.0 0.0
"Fantastic Lecture. Loved it..  Thanks a lot :)" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3725.0 0.0 0.0 0.0
"I'm not sure, if (1,1,2) (2,2,5) (3,3,8) are independent.
I mean, if we ignore the third component, (1,1) (2,2) and (3,3) are obviously NOT independent. They lie on the same line.
Now when we add the third component, the only thing that changes, is the Z-coordinate.
Those 3 vectors span a 2-Dimensional subspace in R^3 through (1,1), and are thus dependent." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 6360.0 0.0 1.0 0.0
"this cameraman is horrible" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14796.0 1.0 0.0 0.0
"all respect!king of algebra!!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 12325.0 0.0 0.0 0.0
"Can someone please tell me why he's a good teacher even though he stutters and is disorganized???
What do you see in him??" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3095.0 0.0 0.0 0.0
"What a lovely way of teaching." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11426.0 0.0 0.0 0.0
"It would be really good if this video series were continued..." -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7009.0 0.0 0.0 0.0
"Thank you so much MIT !!! I love all of your videos. However, I was really confused by all of the completing the square stuff and complicated inequalities and the like. After doing a bit of thinking, I realized there is no need to do all of that. You can simply look at the cross sections in the x and y directions respectively at the critical point and see if they are min or maxes. If they are both min, then its a min, if both max its a max, if one max and one min, then its a saddle. Lots of love for you, xxxx." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9347.0 0.0 0.0 1.0
"24:42 ""In general, what is BJ ?""  hahahahah Love this guy" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 751.0 0.0 1.0 0.0
"prolly this is the first lecture series with so many comments at its 15th lecture." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14223.0 0.0 0.0 0.0
"Starts at 9:56" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 8888.0 0.0 0.0 0.0
"20,000 views...2 comments....interesting..." ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 617.0 0.0 0.0 0.0
"The chalkkkkkkkkkkkkkk" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10041.0 1.0 0.0 0.0
"Thank you Professor Strang" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9212.0 0.0 0.0 0.0
"Holy ****. The algebra explanation is so much more undersandable for me than the geometric one." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4777.0 0.0 0.0 1.0
"is this a lecture for idiots or what? for the past two lectures he said like one or two major points and he is just keep repeating them..." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13657.0 0.0 0.0 0.0
Beautiful！ QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2828.0 0.0 0.0 0.0
"Amazing and intuitive material, keep these coming." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 2353.0 0.0 0.0 0.0
"Very Good but you would think MIT could afford better chalkboard erasers." 0Va2dOLqUfM "5. Maximum Likelihood Estimation (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 11156.0 1.0 0.0 0.0
"People diving into machine learning starting from here." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8167.0 0.0 0.0 0.0
"Clerly dependent -v1 + 2v = v3. But he straigts that out next time.  It is not so importent in this lecture." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 3158.0 0.0 1.0 0.0
"love you sir really love you" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 13886.0 0.0 0.0 0.0
"Matrix multiplication by four methods:
1. Cij: (ith row of A).(jth column of B)
2. Columns of C are a combination of columns  A. The columns of B tell how they are linearly combined.
3. Rows of C are a combination rows of B. The rows of A tell how they are linearly combined.
4. Sum of [(column of A).(row of B)]" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7621.0 0.0 0.0 1.0
"Lovely bit of explanation at 24:19. A great teacher." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7486.0 0.0 0.0 0.0
"Thanks for making probability easy  for us...u r really a good teacher.
..no doubt." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 9687.0 0.0 0.0 0.0
"these exam problems he's going over are so easy" PnPIqh7Frlw "Lec 24: Simply connected regions; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14772.0 0.0 0.0 0.0
"Why do all the videos start from the middle of the lecture, rather than the beginning? Can this please be fixed somehow? :( It starts off the bat & we spend like 15 mins trying to understand what the professor is discussing." rLlZpnT02ZU "4. Parametric Inference (cont.) and Maximum Likelihood Estimation" "MIT 18.650 Statistics for Applications, Fall 2016" 11822.0 0.0 0.0 0.0
"21:19 When your sneaky single-variable calculus prof sneakily does a multivariable calculus problem." zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 676.0 0.0 0.0 0.0
"any to recommend me?" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 12380.0 0.0 0.0 0.0
"I nod my head to the screen like listening to rock music, while I am not." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 5889.0 0.0 0.0 0.0
"Strang is so funny" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 8910.0 0.0 0.0 0.0
"""Biased"" is the word that u were looking for :)" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 35.0 0.0 0.0 0.0
"His lectures are in an endless loop. He comes back to the statements that he has said earlier in the lecture." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 4759.0 0.0 0.0 0.0
"Oh cool. I've never computer the nullspace of the row space before. Initially, I thought of computer the nullspace of the columnspace of the transpose, but the method he provides - calculating E - is so easy, once you've already done all the work computing the other subspaces." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 8001.0 0.0 0.0 1.0
"Did we ever prove that if the set of eigenvalues are distinct, the set of eigenvectors are linearly independent? I ask because at ~ 32:00 taking u_o = c1*x1 + c2*x2 + ... + cn*xn requires the eigenvectors to form a basis for an n-dimensional vector space (i.e. span the column space of an invertible matrix). It feels right but I have no solid background for how to think about it" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 3388.0 0.0 1.0 1.0
"I was trying to understand this for 3 years , THANK YOU PROFESSOR !" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6171.0 0.0 0.0 0.0
"Second-rate universities: Buys the most expensive hi-tech educational tools to provide ""high"" quality learning.
MIT: Buys ""just"" blackboard and chalk but hires the best and smartest professors." hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8611.0 1.0 0.0 0.0
"Thank you MIT and Prof. Jerison. Words, cannot express my gratitude." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9136.0 0.0 0.0 0.0
"I just spent 10 minutes going back and reviewing why the -1 appeared in that second row at 9:00 smh." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5618.0 0.0 1.0 0.0
"Professor Strang thank you for another well plan lecture on Structure of Neural Nets for Deep and Machine Learning. Learning is a life long process." sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8365.0 0.0 0.0 0.0
"This lecture was SOOOOOOO well done. Bravo." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10829.0 0.0 0.0 0.0
38:02 ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1074.0 0.0 0.0 0.0
"I'm still confused about independent vectors. how is [112],[225] independent? 
2(1)-2 =0. So, we do get a 0 using some linear combination, right?" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 6380.0 0.0 1.0 0.0
"After viewing the 3blue1brown video on Duality, I am just seeing xT*A*x as the results of applying a linear transformation to a vector x and then projecting that new vector back onto x; if the vectors still point ""in the same direction"" i.e. the projection is positive, then A is positive definite" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 2261.0 0.0 0.0 0.0
"Isn't the ""convolution"" covered in this lecture actually correlation? Real convolution involves a reflection across the y-axis right? So the numbers would be inverted first, then multiplied. As seen here https://en.wikipedia.org/wiki/Convolution" p-bXJIa7QVI "Lecture 30: Completing a Rank-One Matrix, Circulants!" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6895.0 0.0 1.0 0.0
"lol, that is so true" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 13840.0 0.0 0.0 0.0
"37:56 can use the wallis formula" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1073.0 0.0 0.0 0.0
"This is very cryptic, especially without the first part." C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 10763.0 0.0 0.0 0.0
"I connected the properties of a determinant (1-7) to the volume of a box. 
Now, can anyone please explain the connection of properties 8,9,10 to the volume of the box?" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 5246.0 0.0 1.0 0.0
"Thanks for your amazing course, professor Gilbert Strang! I really enjoy it." or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9743.0 0.0 0.0 0.0
36:02 TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 1027.0 0.0 0.0 0.0
"*Note:  Lecture 8 is Exam 1, so no video was recorded. View the complete course at: http://ocw.mit.edu/18-01F06." BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 236.0 0.0 0.0 0.0
"An Indian edition of this book is available only in India
http://www.wellesleypublishers.com/buy.html" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2417.0 0.0 0.0 0.0
"Why is the intersection of null space and row space, only the zero vector? Why can it not be a vector such that V times Vtranspose is 0?" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 11888.0 0.0 1.0 0.0
"Thank you very much, sir. I am watching lectures and enjoying them. I have benefited from you because we do not have a teacher  in Yemen because of the war situation, so you became my teacher" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9456.0 0.0 0.0 0.0
"absolutely a brilliant example for how to apply eigenvalues to real world problem" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 12302.0 0.0 0.0 1.0
"I wish my college tutor could watch this. So he won't fuck any more young brains." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 6227.0 0.0 0.0 0.0
"Maybe this helps someone: https://notebooks.azure.com/menziess/libraries/Python-Linear-Algebra" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 7641.0 0.0 0.0 0.0
"Very good, I am refreshing up all" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11189.0 0.0 0.0 0.0
"great course...was waiting for it for a long time!! :)" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12970.0 0.0 0.0 0.0
"I love Taylor expansions too, but It's really got a dreadful derivation. If I really want to get it, I am going to have to delete my facebook account, youtube account, sell my laptop and everything else I have except study tools and lock myself up with a month's supply bread and butter and isolate myself from everyone for a whole month's break if I am going to master this understanding. Doesn't seem realistic for many of us, but,idk, I might try it. Otherwise, mastery will take a verylong time. " 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5725.0 0.0 0.0 0.0
"thanks prof jerison and prof muller!
i found these lectures 10 years too late but thank you for giving me the much needed sense of purpose during this self-isolation period.

just finished 18.01 final exam. 
off to 18.02!!!

 -5/5/2020-
(that's 5/5/2020 for the Americans)" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14597.0 0.0 0.0 0.0
"Where is the lecture 8?" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11692.0 0.0 0.0 0.0
"Bravo perfect" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 2915.0 0.0 0.0 0.0
"so much humility and grace that he is working so hard even in his mid-80s... May God continue to bless you and your family." t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14340.0 0.0 0.0 0.0
"Why is that

 dw/dx=2ax+by

and 

d²w/dxdy=b

and not

d²w/dxdy=2a+b" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11884.0 0.0 1.0 0.0
"I didn't quite understand the area of the triangle to 1/2 question yet. Can someone please explain how it is so?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 5276.0 0.0 1.0 0.0
"I am an asian and i completely lost at 5 minutes at the end of lecture" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5064.0 0.0 0.0 0.0
"or rather, the room mic is sent to the left headphone while his lapel mic is sent to the right headphone." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 14160.0 1.0 0.0 0.0
"God I love him." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 4068.0 0.0 0.0 0.0
"Views are less than 100k already." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 11236.0 0.0 0.0 0.0
"and wtf you guys at MIT get tutors if you need help and by the sounds of it there are more than one?! jezz were lucky to get 1 tutorial a week with 1 assignment a week and 3 lectures a week per math module lol thats the max for a math module and its a lot more difficult :(" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12376.0 0.0 0.0 0.0
"Like if you spotted that error in lec 9 itself and were wondering for hours about it" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7356.0 0.0 1.0 0.0
"that cameraman job tho" phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14626.0 1.0 0.0 0.0
"Dear Gilbert Strang!! I wish to kiss your hands, your sacred hands as you are my Guru of Matrix Algebra. You explain so well. your way of teaching is miraculous." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 3321.0 0.0 0.0 0.0
"I had an incredibly difficult professor, Alex Freire at University of Tennessee, and your material helped me a ton back then. With the bar that guy set I learned a TON that semester. Thanks for your help in getting me through that class." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5463.0 0.0 0.0 0.0
"What a wonderful teacher.  Thanks a bunch." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11440.0 0.0 0.0 0.0
"31 years old curse is quite interesting." 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 902.0 0.0 0.0 0.0
"wtf this fella just said see ya next monday after thanksgiving and it is actually this weekend for me o.O" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 15447.0 0.0 0.0 0.0
"wow, this professor just get rid of all my confusions about the formula of Gram-Schmidt" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 15430.0 0.0 0.0 0.0
"I graduated in IT and Computer science a few years ago, and now when I see MIT courses online I am really impressed with the quality of it." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5451.0 0.0 0.0 0.0
"single integral - area
double integral - volume" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14307.0 0.0 0.0 0.0
"this is awesome." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 14856.0 0.0 0.0 0.0
"An awesome lecture indeed! Studied elementary differential equations at University 40 years ago. About two weeks of lectures to present the same materail. Linear algebra clarifies the process very well. The  information relayed here conveys the cumulative effort of my lifetime  study and concentration..as a hobby....yet some students will soak this up  in minutes...work problems for a couple of weeks and have it down.....Awesome!!!!" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 2436.0 0.0 0.0 1.0
"Blessing for mathematicians" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 2902.0 0.0 0.0 0.0
"Thanks Prof.Tsitsiklis for the amazing course." rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 9637.0 0.0 0.0 0.0
"So, Inflection points are not necessarily critical points. Am I right?" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8806.0 0.0 1.0 0.0
"My classmate and I independent studied Calc BC...we were told to learn trig substitutions, spent 2-3 weeks on them, then found out they weren't on the AP exam -.- *sigh* trig substitutions screws everyone over." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7741.0 0.0 0.0 1.0
"wow, this is the most basic in my country for secondary schools! we did this in Cambridge's o'levels examination a month ago....." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15428.0 0.0 0.0 0.0
"30:25 , It only means they are uncorrelated rather than independent." lWW54ts9Ubo "24. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 886.0 0.0 1.0 0.0
"God damn he must have showed how to compute determinant atleast 7 times... But he actually answers questions. That's quite good for a prof" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4092.0 0.0 0.0 1.0
"Great lecturer with good handwriting!" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4299.0 0.0 0.0 0.0
"I feel so sad. I feel like tat I almost touch my bound." hDwkKrWqdZE "3. Forbidding a subgraph II: complete bipartite subgraph" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 5401.0 0.0 0.0 0.0
"Thank you, Prof. Gilbert Strang and MIT." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9509.0 0.0 0.0 0.0
"v=vot + 1/2at^2" ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14990.0 0.0 0.0 0.0
"Astonishing lecture... !" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2578.0 0.0 0.0 0.0
"@45:00 . How does the professor conclude that variance is 1 if the random variable is divided by standard deviation?" mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 1561.0 0.0 1.0 0.0
"""Lec 1"".... this is the first lecture, which of course covers the basics. go deeper." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 76.0 0.0 0.0 0.0
"@xkeikoxsanxdesu Yip...true that but, when it comes to maths, science and technology MIT is best, the website is web.mit.edu" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2065.0 0.0 0.0 0.0
"what a nice proof at 35.27!  we had to proof it algebraically in analysis 1 for EECS, took me and my friends about 5 hours haha. this way its a lot more intuitive - what a great lecturer he is. Thanks!" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 15112.0 0.0 0.0 0.0
"I really enjoy learning in his pace." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5912.0 0.0 0.0 0.0
"at 17:10 what a noob that child is" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12417.0 0.0 0.0 0.0
"This mainly about definitions and the intricacies of proving what seems to be obvious but is not. Extremely fine attack." OHiu2F18dFA "Lecture 7: Sigma Algebras" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 10843.0 0.0 0.0 0.0
"Were all the following spam responses generated by some MIT genius? " BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 11380.0 0.0 0.0 0.0
"my uni should just play this video in class tbh" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 14008.0 0.0 0.0 0.0
"This works for me. Thanks " srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 10979.0 0.0 0.0 0.0
"Huge thanks to Prof Strang and MIT!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 4915.0 0.0 0.0 0.0
"haha XD
laughed my ass off till the end :p" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 13037.0 0.0 0.0 0.0
"Professor laughed 2 times. First time when a student said Cantor went crazy and second time when a student wrote cannabalism for feeding TM into TM" 3PzuSPQPEU4 "8. Undecidability" "MIT 18.404J Theory of Computation, Fall 2020" 8396.0 0.0 0.0 0.0
"This lecture is pretty insane." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10809.0 0.0 0.0 0.0
"omg I can't believe how people like this course... he is so random & disorganized and pretty much talks his thoughts out. it's hard to follow the logic... some important concepts were covered too fast and non-important talks were so abundant ..." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 14135.0 0.0 0.0 0.0
"ok i still need to ,land my missile on that asteroid you have not yet seen but hurry we must perfect all math to run scenarios so exciting ,no detail is unimportant , the hardwire the final chip to the launchpad mbefore t=0" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14126.0 0.0 0.0 0.0
"Was the Law of Cosines originally derived from the vector proof he showed, or was the vector proof [a dot b = ||a||*||b||*cos(angle)] derived from the Law of Cosines?
Or were they both derived from something else [originally]?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11277.0 0.0 1.0 0.0
"I love you, professor. it's so important that you're doing this.  it's an absolutely right thing to do. I remember completely different professors and completely corrupted faculty in Russia." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 5852.0 0.0 0.0 0.0
"thanks professor Strang, you don't know how helpful this is for many of us!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14603.0 0.0 0.0 0.0
"students are dumb in his class." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 14404.0 0.0 0.0 0.0
"We never could know what we learn in YouTube or Bilibili. Thanks MIT , Peking University and other universities those could really bring knowledge to me." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11330.0 0.0 0.0 0.0
"I don't know why but I feel kinda sad knowing that this course is over." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5322.0 0.0 0.0 0.0
"Has this video been remastered with AI techniques?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 4436.0 0.0 0.0 0.0
"This saved my life" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 10917.0 0.0 0.0 0.0
"A is singular -> eigenvectors are in null space.

31:43A에 I를 더해도 eigen vector은 그대로" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 2128.0 0.0 1.0 0.0
"Thanks for sharing these wounder class.
However it really drove me mad, cause the Professor doesn't clean the blackboard very well." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9700.0 1.0 0.0 0.0
"Thank you, MIT. I hope this can help out clarify some parts, i.e., the norm of magnitude space and the linear independent space, that I sometimes confuse at. As long as I can clearly understand the context about definitions well, I can correct what I mistake at. God bless you always." uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 9504.0 0.0 0.0 0.0
"Isn't AP Calculus equivalent to this course?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6890.0 0.0 0.0 0.0
"What is the text book of this course?" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 11537.0 0.0 0.0 0.0
"https://youtu.be/or6C4yBk_SY  : ""Orthogonal matrices are the queens, and symmetric matrices are the kings.. """ or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13305.0 0.0 0.0 0.0
"Matrix x" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7624.0 0.0 0.0 0.0
"I couldn't find the rest of the course. Where can I find the rest of the course?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 5251.0 0.0 0.0 0.0
"The dot product of orthogonal vectors equals zero. All of a sudden it clicked when I remembered my conclusion as to what a dot product actually was, that is, ""what amount of one vector goes in the direction of another."" Basically, if vectors are orthogonal, then no amount of one will go in the direction of the other. Like how a tree casts no shadow at noon." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10079.0 0.0 0.0 0.0
"Just binged 11 of these lectures in one day... should I rethink my life choices?" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7159.0 0.0 0.0 0.0
"Why there are no students sit there?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11923.0 1.0 0.0 0.0
"Took me some time but the whole Ascrewedup example is really neat for seeing why the off diagonals are 0" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 11072.0 0.0 0.0 1.0
"I Really Like The Video From Your Lecture 29: Partial fractions" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4957.0 0.0 0.0 0.0
"You have to love MIT! Thank you! :)" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12214.0 0.0 0.0 0.0
"Today I finished this course with respect to Linear Algebra. Although I had finished a linear algebra course in my university, frankly I realized that what I knew about matrix and four subspaces are not sufficient (and some of them are wrong). I really appreciate to professor Strang for his amazing lecture, not only concentrated on the algebric aspect, but also the ""matrix"" facet and the applications. I really enjoyed this lecture, and I will recommend this course to my friends who wants to learn about linear algebra. Thank you So MUCH!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 11050.0 0.0 0.0 1.0
"It is high time that all your theories on magnetism,electrical energy conversions theories and superconductive theories have to be reevaluated as we are being watched by Alien Flying Saucers and there is a possibiity that we may be controlled by them in future.
Refer Cheiro's Book on ""World Predictions ""
Sankaravelayudhan Nandakumar." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 6948.0 0.0 0.0 0.0
"Dude Im so gonna fail this course 😭" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 3522.0 0.0 0.0 0.0
"derivatives ? I'm in a my first year in university and in France we did that 2 years ago in high school " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12736.0 0.0 0.0 0.0
"man that was tragic..." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 13899.0 0.0 0.0 0.0
35:17 UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 1003.0 0.0 0.0 0.0
"""we only live so long, we just skip that proof"" -- Prof. Strang 2009 
(and I low-key wish this was the case for all math tests )" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 190.0 0.0 0.0 1.0
"14:58 نقطة مهمة جاد بالنسبة لي" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 440.0 0.0 0.0 0.0
"why is A-lamda I singular at 19:00?" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 15323.0 0.0 1.0 0.0
"Why joint density was not divided by f(x) to get posterior probability?" XtNXQJkgkhI "22. Bayesian Statistical Inference II" "6.041 Probabilistic Systems Analysis and Applied Probability" 11896.0 0.0 1.0 0.0
"Alongside this course, check out this too..           https://www.youtube.com/playlist?list=PL21BCE50ABFF029F1            This is a homework help content by MIT TAs for this course...     its really helpful....." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2320.0 0.0 0.0 1.0
"Loved the part when he said 'OK'" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7480.0 0.0 0.0 0.0
"why we always consider a level surface to prove that gradient is perpendicular to tangent vector to the surface...  what if the particle moves on a surface which doesn't has a  constant value throughout  its domain of definition" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 15375.0 0.0 1.0 0.0
"“I won, but it didn’t pay off!”  😂" sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15590.0 0.0 0.0 0.0
"How come at 12:44 the sum of S and U is all 3×3 matrices?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 4820.0 0.0 1.0 0.0
"@HikariOfTheAzureSky
Google says France, yes." tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1631.0 0.0 0.0 0.0
"thank you very much for these videos! these approximations make so much sense, it's like the sine wave is locally a quadratic curve at the crests and trough. what a light bulb moment for me!" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14524.0 0.0 0.0 0.0
"After you derive the product rule, you can easily prove the quotient rule by considering the derivative of the product f(x) * ( 1 / f(x) )" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2269.0 0.0 0.0 0.0
"You have to stand for all the bad jokes 😂" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 12215.0 0.0 0.0 0.0
"Please prove the facts." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 8210.0 0.0 0.0 0.0
"wow, beautiful, now i see why it oscillates" wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15427.0 0.0 0.0 0.0
"at  37:15 ,why P(A∩B∩C)=1/4 isnt supposed to be 1/8 as each one of event have a probability of 1/2" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 12408.0 0.0 1.0 0.0
"Without that lecture gallery and blackboards, it doesn't feel like MIT." cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 11973.0 1.0 0.0 0.0
"What a great set of lectures, thanks for putting these up." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 11416.0 0.0 0.0 0.0
"humans will start machine learning here" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 13316.0 0.0 0.0 0.0
"think of in linear equations: 4y+z-2(2y-2z) = 2-(6x2)  but that doesn't mean you have to change the original equation 2y-2z = 6  to  4y-4z = 12 because it's the same thing." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14788.0 0.0 0.0 0.0
"What a boss. " 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11396.0 0.0 0.0 0.0
"Lecture 26 is Professor Strang’s best performance so far.

In lecture 25, in front of students, he screwed up his proof showing real symmetric matrices have real eigenvalues.  Got confused and had to refer to his notes.  In this lecture, in front of no students, he gives a tour de force performance.

Hope there no students in his remaining lectures, because his cyberspace audience is orders of magnitude larger than his MIT audience.
" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 7287.0 1.0 0.0 0.0
"Prof John's lecture on Poissan PMF is available at: https://youtu.be/eTLa9GDID8A" jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 8267.0 0.0 0.0 0.0
"It was an awesome video,
But does anyone think sir looks like Elon🧐?" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 6996.0 0.0 0.0 0.0
"I'm not drinking! I'm serious, do you remeber ""your profile picture is a little dirty"" the strange thing is that i founded across internet again! just by chance!! Do you want it cold or hot, the drink i mean?" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 6352.0 0.0 0.0 0.0
"Is that a joke? If so, you're freaking funny." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6804.0 0.0 0.0 0.0
"Five Minutes of the ""GRAPHS"" is in lecture 11. Just follow lecture 11 from 39:30." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3827.0 0.0 0.0 0.0
"Wish you very best health Prof Strang, You're really good teacher" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11964.0 0.0 0.0 0.0
"*Differential
" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 233.0 0.0 0.0 0.0
"What's the difference between Bayes' theorem and conditional probability?" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 11578.0 0.0 1.0 0.0
"Good lecture, but I think the geometric intepretation of SVD is its motivation. We should use SVD as  a tool to understand general linear transformation" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4134.0 0.0 0.0 1.0
"Does anyone know where the notes are?" Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3445.0 0.0 0.0 0.0
"Thanks, Dr. Strang" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 9840.0 0.0 0.0 0.0
"I really like the post-processing of video that enhance all those handwriting." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5927.0 0.0 0.0 0.0
"I didn't understand anything" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 5278.0 0.0 0.0 0.0
"am i the first to comment here？ thank you Gilbert Strang !!! i really love your courses" 0Qws8BuK3RQ "34. Distance Matrices, Procrustes Problem" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12338.0 0.0 0.0 0.0
"I love learning the proofs of ideas I took for granted or only intuited vaguely" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5762.0 0.0 0.0 1.0
"Excelente colega, bien explicado" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3624.0 0.0 0.0 0.0
"excellent Teacher." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12818.0 0.0 0.0 0.0
"I LOVE THIS!
" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4929.0 0.0 0.0 0.0
"this is blowing up my mind wtf is happening lolol" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14858.0 0.0 0.0 0.0
"Who the heck disliked this ....those foolish mortals" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 11753.0 0.0 0.0 0.0
"Professor Strang is really enjoying teaching, I am so appreciate that I could learn from him! I like the way  he teaches so much!" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 8353.0 0.0 0.0 0.0
"Thanks for MIT OCW" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 9680.0 0.0 0.0 0.0
"They still use chalkboards?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10444.0 1.0 0.0 0.0
"I agree with you.. I mean I think he means the first one it makes sense better to me :/ " 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 5026.0 0.0 0.0 0.0
"Nothing but love <3" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7942.0 0.0 0.0 0.0
"Good lecture, but I feel it only just starts getting into the heart of PCA before it ends. I don't see a continuation of the the discussion in subsequent lectures, so I'm wondering if I'm missing something." Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4133.0 0.0 0.0 0.0
"So I managed to make it through the first lesson. Now, you lost me." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8731.0 0.0 0.0 0.0
"how could Bx = [1 0 1]' ??????????" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 13207.0 0.0 1.0 0.0
"im doing distance learning and this guy is saving my ass.
you cant imagine how hard is to learn calculus 2 from a book ! (or BAD book).

Its easier for me to hear this french talking in english than to read the book which is written in my mother tongue (spanish), so figure it out !

thanks dude !" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 13567.0 0.0 0.0 0.0
"수학이 여러가지 수학인데 결과가 다르게 나옵니다. 글로벌 뉴딜. 뉴딜의 결과를 뽑아보면 굉장히 나쁜 결과가 나올 겁니다." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 15680.0 0.0 0.0 0.0
"Why do we say that for a NTM decider, all branches halt on all inputs?
By ""branches halt"" do we include the possibility of one of the branches having an accepting state and hence all the other branches halt when we find that accepting state? (Since if the NTM finds an accepting state it halts)." 1VhnDdQsELo "14. P and NP, SAT, Poly-Time Reducibility" "MIT 18.404J Theory of Computation, Fall 2020" 11832.0 0.0 1.0 0.0
"Loved the lecture but when we assume that the weight is settled we balance the forces.
Balancing horizontal forces gives us Tcosa1=Tcosa2
Same T because we can't have tow tensions in one string or the string breaks.
Which gives angle a1=a2" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7479.0 0.0 1.0 0.0
"The breakdown of the decimal representation of Real numbers was genius. Thanks!

It also calls my attention that in a world-class University like MIT, lectures are still given in such a traditional fashion." PnDtMfyZSIE "Lecture 6: The Uncountability of the Real Numbers" "MIT 18.100A Real Analysis, Fall 2020" 10024.0 0.0 0.0 0.0
"Hi, can anyone explain why 10:20 sigma_1 and sigma_2 greater than 0? Thanks!" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 4725.0 0.0 1.0 0.0
"Got any Americans who know calculus?  Paul Revered" tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4168.0 0.0 0.0 0.0
"15:34 he sound like omega from gta 4 when he says protogalaxy" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 453.0 0.0 0.0 0.0
"So ver nicely done. Thankyou Professor" d32WV1rKoVk "12. Computing Eigenvalues and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8799.0 0.0 0.0 0.0
"nice.

expecting a decision tomorrow :)" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14058.0 0.0 0.0 0.0
"Oh my god, the revision for the connection between what we learned is sooooooooo helpful for me to see the full picture!" sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8018.0 0.0 0.0 0.0
"All respect!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2306.0 0.0 0.0 0.0
"You sir, are like master Yoda for so many of us! Wishing you many, MANY years in good health, so we can tap into your passion and wisdom. Thank you!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12240.0 0.0 0.0 0.0
"An Indian edition of this book is available only in India
http://www.wellesleypublishers.com/buy.html" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 2423.0 0.0 0.0 0.0
"Never think in public...." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7821.0 0.0 0.0 0.0
"I love the motivation he gives for the problem." 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5779.0 0.0 0.0 0.0
"Could anyone please help me with this? At about 15'30'', the professor says ""vertically simple"". Does he mean that the sides of  the solid is vertical (all equal to the height)? So the graph of the top is the same as the graph of the bottom? Thank you very much!" wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 3226.0 0.0 1.0 0.0
"For anyone confused by the block matrix explanation --- the I and F and blocks of zeros --- hang in there until lecture 8 where it all becomes clearer. And yes, F may be interspersed with the I, and, contrary to the top rated answer on Stack Exchange, this cannot be remedied with permutation matrices. Basically it's just a visual cue that allows you to pluck out the relevant numbers." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 3853.0 0.0 0.0 0.0
thanks srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 14547.0 0.0 0.0 0.0
"Fuck this is hard" 4UJc0S8APm4 "23. Classical Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 3943.0 0.0 0.0 0.0
"thank you Gilbert Sir" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 14477.0 0.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8430.0 0.0 0.0 0.0
"In the end why does he say that matrix converts 5th order differential equation to 1st order differential equation! there are higher orders in the L.H.S..." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 6662.0 0.0 1.0 0.0
"He is so precious. Bless his heart." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4538.0 0.0 0.0 0.0
"C'est du niveau de lycee.. Interessant mais le niveau parait bien bas a l'entree.." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2980.0 0.0 0.0 0.0
"Maths is strong. Problem with you is you follow some proven previous laws. Unless you break open those and see through...much gold is beyond. Live close to nature. It will teach you new maths, prodect and reality. Mit should travel with naturure for new definitions. I like it but." EBdgFFf54U0 "Lecture 14: Basic Hilbert Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 7618.0 0.0 0.0 0.0
"Love the lisp.
""There'th a third thubthpathe""
Thanks for the videos!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 7454.0 0.0 0.0 0.0
"Fantastic weather outside.
Snow!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3738.0 0.0 0.0 0.0
"How many of you here because of the 2020 coronavirus quarantine. I hope someone sees this comment in 10 years and remembers that once the society had functionally stopped." hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4887.0 0.0 0.0 0.0
"20:36 Great" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 660.0 0.0 0.0 0.0
"The thing I love about math, is that it is totally independent of the world. Although mathematics does have applicaitons in many aspects of reality, it doesnt necessarily say anything about it. So math in itself is really formless, and a playground for people to tinker around in. Where everyone can enjoy and express new ideas." aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10300.0 0.0 0.0 0.0
"Definitely you!" BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 3342.0 0.0 0.0 0.0
"Dude your awesome! haha i like learning maths this way idk why better than all teachers and coaches ive come across 
Tip for students learning maths online:
watch n learn all MIT-ocw  Maths lectures
watch n learn all khanacademy maths videos(there too many but still)

and ull be like king of mathematics lmao!
" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3526.0 0.0 0.0 0.0
"At 43:32, shouldn't Professor Strang have put *infinite* as opposed to *1* solutions to Ax = b. When r = m = n, all n (or m) - dimensional vectors can be obtained from linear combinations of A's columns because the column space is also n-dimensional." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 2672.0 0.0 1.0 0.0
"Are these really MIT math lecture? I think they are just some middle school math course. The teacher cannot go to any more details, but the students still have those stupid questions!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2534.0 0.0 0.0 0.0
"Amazing lecture! It will be better to learn this course with the textbook also by Strang. The videos provide big pictures and kind of whet your appetite for reading the book. The book gives detailed explanation and just satisfies your curiosity." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 2368.0 0.0 0.0 1.0
"great lecture .i am so grateful to prof.gilbert" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12978.0 0.0 0.0 0.0
"One day Lord Kelvin asked his students: what is a mathematician? Then he wrote on the blackboard the integral from minus infinity to plus infinity of e^-x^2 and added: a mathematician is the one who writes next to this integral the square root of pi without even thinking about it!" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8075.0 0.0 0.0 0.0
"Thank god you saved my life. Its mysterious how people could understand this kind of things without internet and youtube!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9066.0 0.0 0.0 0.0
"But Again. When is the average person going to find this useful or use it in the real world themselves? Should I really waste days and days of my short life so I can learn how to help a truck driver calculate the traffic flow at certain times of day? Why should I be forced to learn this and if I don't,I cant graduate?" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2955.0 0.0 0.0 0.0
"27:00 matirx A multiply orthogonal matrix, the norm of A doesn’t change" Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 813.0 0.0 1.0 0.0
"Great guy, these materials are very informative and provide a great insight" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4230.0 0.0 0.0 0.0
"it awesome. 
thank u prof" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 13671.0 0.0 0.0 0.0
"Completed this course. A great resource for anybody looking to gain a better understanding of probability and statistics. Professor Tsitsiklis is a great lecturer and thank you to him and MIT for bringing such a series to life." rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 3184.0 0.0 0.0 0.0
"RFS Israel *" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8487.0 0.0 0.0 0.0
"I really like that the instructors at MIT spend the time to write the topic on the board which reinforces the point of their discussion. And they all have good penmanship which allows the student to concentrate on what he is saying, not trying to interpret the writing. I also like they're using blackboards and chalk which show up nicely in the videos. When my school changed to whiteboards there were times when reflections obscured the writing and some of those markers had a distracting smell." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5925.0 1.0 0.0 0.0
👍👍👍👍👍👍👍👍👍👍 MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 15713.0 0.0 0.0 0.0
"Grant Sanderson ""3Blue1Brown"" has a great series on Linear Algebra (2016)
https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4185.0 0.0 0.0 0.0
"I believe in god now" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 5169.0 0.0 0.0 0.0
"Why do you assume everyone taking multivariable calculus already took linear algebra? In example, I've learned single variable calculus on my own, now I'm learning this and although I've known what a matrix is for a long time I've never actually learned how to perform operations or them or how to use them. And linear algebra I'm going to take in university after holidays are over." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11834.0 0.0 0.0 0.0
"In 41:23 he says that it's actually enough to look only at the terms of the form X to the k-th - why is it enough?" JTbZP0yt9qc "6. Maximum Likelihood Estimation (cont.) and the Method of Moments" "MIT 18.650 Statistics for Applications, Fall 2016" 6604.0 0.0 1.0 0.0
"I""ve watched the 18.06 from lecture 1 to this section, suddently realized that all contents were in Prof. Strang's brain and he didn't utilize any auxiliary materials/tools to control the rhythm, so amazing... Thank you Sir for your great teaching!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 6273.0 0.0 0.0 0.0
"Unrelated: What is the use of dislike button in comment section?" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 11127.0 0.0 0.0 0.0
"beauty of calculus, thank you, MITopencourse" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12524.0 0.0 0.0 0.0
"This guy needs Walter Lewin's chalk to draw those dotted lines" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10556.0 1.0 0.0 0.0
"34:00 but what if b = pi * i, it is wrong but that means, that i is less than 0 but why is it like that" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 976.0 0.0 1.0 0.0
"Determinant is the first chapter in some textbooks, which makes students lost in linear algebra.
Dr. Glibert made everything easy to understand, thank you!" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 3361.0 0.0 0.0 0.0
"dont mind me but why is A^TA symmetriiiiiiic" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12774.0 0.0 1.0 0.0
"i am gonna get cancer because of the cameraman. how hard is it to just shoot all the boards in a wide angle instead of zooming in on Strang's face. check the camera skills at 51:40" nvXRJIBOREc "Lecture 21: Minimizing a Function Step by Step" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13331.0 1.0 0.0 0.0
"If I knew why your messages keep coming in, I would try to make them coherent." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6470.0 0.0 0.0 0.0
"God i was so consfused on what he was talking about in the lecture one, everything seemed so pointless. But now everything makes so much sence" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4095.0 0.0 0.0 0.0
"thanks , even i thought so " 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 14548.0 0.0 0.0 0.0
"Amazing class. Thanks MIT and Prof. Strang for your generosity." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 2356.0 0.0 0.0 0.0
"amount of views in this lecture series is exponentially distributed" l4NoMKEHQwM "11. Derived Distributions (ctd.); Covariance" "6.041 Probabilistic Systems Analysis and Applied Probability" 12361.0 0.0 0.0 0.0
"Do you still use chalk and black boards in america?? We stopped using them in England when I was about 8 (i'm now 18). Seems a bit pre-historic. Has you're lecturer never heard of powerpoint? or even just a white board?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3423.0 1.0 0.0 0.0
"@13Septem13    ...uni ?? I went over to Australia and that was the only place i've ever heard that term. Are you form Australia? Just wondering if Australia is the only one who has the term ' uni '. " nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1497.0 0.0 0.0 0.0
"@5:57 - looks like class rooms at MIT have ledges to jump off from if you don't understand anything :-)" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 1570.0 1.0 0.0 0.0
"The funny thing is, I'm also doing a general relativity series and got to covectors. I understand what they are computationally, but couldn't ""visualize"" them, beyond the typical ""stacks"". Then I stumbled on the interpretation of covectors as linear maps, which served as a connection to linear algebra. I tried so many things to built a geometric interpretation all night but nothing formed in my head properly, so I was like, ""meh, I'm 80% done with Professor Strangs lectures, might as well do another one"". He led with x^H*A*x > 0 and for some reason, everything just started to click (x^H*A is an implicit map, so I have ideas about how to analyze things in my other GR class). Funny how his lecture was what I needed to get my head turning again. Thank you, and awesome lecture! ☺️🙌🏽 Stay safe during #COVID19" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 10117.0 0.0 0.0 0.0
"The best." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 10014.0 0.0 0.0 0.0
"everything is simple.." eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12808.0 0.0 0.0 0.0
"""forgive me for doing such a thing"" (looks at book)" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 152.0 0.0 0.0 0.0
"Interesante clase" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6722.0 0.0 0.0 0.0
"You are just amazing sir 🙏" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12173.0 0.0 0.0 0.0
"Can anybody solve a question asap ?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 3013.0 0.0 0.0 0.0
"this guy is a superman in mathematics" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 14814.0 0.0 0.0 0.0
"17:40 ""Murderers, cheaters-on-quizes, other stuff"" xD" 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 514.0 0.0 0.0 0.0
"This has been one my favorite lectures so far, for me really brought these concepts together beautifully for the first time." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 10570.0 0.0 0.0 0.0
"Anyone From MIT AOE?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 2481.0 0.0 0.0 0.0
"5 years of physics+4 years of phd in astrophysics and this man managed to give me a much clearer picture of algebra operations than what I got from all my professors.
Thank you so much for these lectures Proff. Strang!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1332.0 0.0 0.0 0.0
"Oh crap he just said what I just commented " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8002.0 0.0 0.0 0.0
"Thank you mit for your contribution. The thing that makes you better than harvard and princeton is that you allow other people who can't afford tuition to learn nearly as good as you students. That's what makes you the best university whether your teaching is the best or not. Thank you" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9298.0 0.0 0.0 0.0
"i dont know how but when ever i need he repeats it.thx mr Strang
" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 13368.0 0.0 0.0 0.0
"@AirlesMan 
True that. The best way I understand this is review. For Ex reading the chapter regarding vectors and 3 dimention math. Then you will be able to understand what the teacher is explaining. Personally I have a different way of learning and that is why I understand his clear lecture because of prior reviewing." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1581.0 0.0 0.0 0.0
"at 11:16 he says he can describe it without any coordinates , but he actually  uses theta(angle as a coordinate)" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12411.0 0.0 1.0 0.0
"I'm surprised he couldn't integrate sqrt(2-cos(t))." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6385.0 0.0 1.0 0.0
"So, I got a question:
e is perpendicular to both a1, a2 and thereby, all the vectors of that lie in their plane. 

So, the dot product should be taken between a1 or a2 and e. Instead, we take the dot products of transposes of a1, a2 and e. 
So, if a vector is perpendicular to another vector, does that imply that its transpose will also be perpendicular to it?" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 8805.0 0.0 1.0 0.0
"@hypnoticpoisons Because those are his reading glasses." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 1877.0 0.0 0.0 0.0
"@aylictal Absolutely not, I definitely encourage people asking questions, no matter how trivial it may seem. That's how we learn and understand things.
What I meant in my previous post was my surprise towards how a quality school would have admitted a student of this ability, who has problems manipulating fractions.  I just find it absurd, that's all." sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1787.0 0.0 0.0 0.0
"Thanks a lot!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 9667.0 0.0 0.0 0.0
"If this was during Fall 2007, why was it uploaded on Apr 14, 2009?" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6530.0 0.0 0.0 0.0
"Can you just stop walking while you are talking because the camera kept panning, it made me feel headache" bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3119.0 1.0 0.0 0.0
"In Linear Algebra, Professor Strang is God." UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 6615.0 0.0 0.0 0.0
"I think Prof. Strang really hates Mr. Schmidt ;)" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 6003.0 0.0 0.0 0.0
"The advantage of MIT is not that the classes are necessarily harder its that the quality of the student body is much greater." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9979.0 0.0 0.0 0.0
"@bud389 i am about to do that! :S" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 1807.0 0.0 0.0 0.0
Uzbekistan 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11145.0 0.0 0.0 0.0
"I  think that these kids need to take trigonometry before calculus!I can't believe that these are admitted to the MIT. Student is asking why the length is 1! God, if you dont know cos 0 =1. then good luck..." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7107.0 0.0 1.0 0.0
"These lectures are saving my bachelors in Engineering. Thanks MIT!" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10409.0 0.0 0.0 0.0
"Big thanks to help me pick up my lost memory of calculus, and ease my scary on this subject. math is beautiful." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2894.0 0.0 0.0 0.0
"Finished 18.02 on 16-06-2021. Thank you MIT OCW! Prof. Auroux's explanation and his amazing visual representations are going to stay with me for a very long time. His sense of humor makes everything interesting! <3 
Anmol, India" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3806.0 0.0 0.0 1.0
"MIT!! MIT!!
🇺🇸🏆👌🏼" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 7552.0 0.0 0.0 0.0
"This is a solid lecture that covers Circulant Matrix, Cyclic Convolution, and Eigenvectors. These are deep topics that help improves my understanding of Numerical Linear Algebra. Thanks to MIT and and grand dragon of linear algebra for another well explained lecture." p-bXJIa7QVI "Lecture 30: Completing a Rank-One Matrix, Circulants!" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10603.0 0.0 0.0 0.0
"Excellent lecture.  Different way to look at the Normal RV." mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 3658.0 0.0 0.0 0.0
"In pahhTiculAIR" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6651.0 0.0 0.0 0.0
"Thank you so much" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9342.0 0.0 0.0 0.0
"Statistics are about knowing the distribution of the entire poppulation given the distribution of one dataset" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8891.0 0.0 0.0 0.0
"@Shmling STOP WISHING AND DO SOMTHING ABOUT IT" BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1726.0 0.0 0.0 0.0
"Really enjoying this series! Thank you professor Strang and MIT. This is absolute service to humanity!" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 8511.0 0.0 0.0 0.0
"""please come out right"". ""oh yes!"" ""thank you god"" 😂" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 169.0 0.0 0.0 0.0
"Keep on producing videos like this! They are helping a lot!" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7209.0 0.0 0.0 0.0
"Hey OCW team,
Where is the 13th lecture? Was it not recorded?" bBESL68iX6s "Lecture 14: Limits of Functions in Terms of Sequences and Continuity" "MIT 18.100A Real Analysis, Fall 2020" 4690.0 0.0 0.0 0.0
"But is the life of a light bulb actually modeled by the memoryless Poisson process?  I would think the past takes it's toll on the filament." XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 2962.0 0.0 1.0 0.0
"if you are attracted to heavy mathematical physics all these theorems and techniques are absolutely necessary. Fluid dynamics done in tensors makes this look easy." phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13548.0 0.0 0.0 0.0
"processing fast" sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14209.0 0.0 0.0 0.0
"Love this man! Long live Prof. Strang" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7460.0 0.0 0.0 0.0
"HOW Is this calculus, it seems more like linear algebra" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4408.0 0.0 0.0 0.0
"@allenrobinson2012 Okay, truth: Some of my friends were chosen (as freshmen) for internships in big european chem labs over european juniors and/or seniors, because the companies recognize how damn impressive this college is.  They were paid by the company to go halfway around the world and work for them for one summer, chosen instead of people that lived down the street and were equally smart, simply because they came from MIT.  That's the truth." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1776.0 0.0 0.0 0.0
"Even tho I can follow the steps, it's very very very difficult for me not to have the concepts leave my brain the moment I don't concentrate very very hard on this for hours. That's incredibly frustrating. I get it, but if I don't think about it for a couple days, I no longer will. And if you ask me to explain it, I cannot. But if you go thru it, I follow it. And yet I feel I've been bamboozled. And yet computers work, so I know it is true." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3586.0 0.0 0.0 0.0
"Amazing Professor we have here." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 2352.0 0.0 0.0 0.0
"Professor Jerison is a joy to watch and listen to. He's really efficient, dare I say scarily efficient. I love the explanation of the derivative of y = arctan x with the right triangle and y as the angle." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8330.0 0.0 0.0 1.0
"Thank you Liam Neeson" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 9116.0 0.0 0.0 0.0
"I literally want to applaud after every lecture. If my linear algebra prof could communicate ideas this well, everyone in the course would definitely get an A." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 5707.0 0.0 0.0 0.0
"Bite of cookie" os_XGBNPllM "Lecture 8: The Squeeze Theorem and Operations Involving Convergent Sequences" "MIT 18.100A Real Analysis, Fall 2020" 2895.0 0.0 0.0 0.0
"I highly disagree with the resolution of the ""notation problem"" at 19'13"". The problem is well stressed, but ill solved, if a cat ought to be called a cat! 

A little ""mess"" indeed is runing around there, in the lecture notation, and confusion is rising with paradox from a rather different cause than the one stressed out, if RIGOUR is to be called RIGOUR!

The little ""mess"" that is at the core of these confusions is simply that, through the change of variables, though 
f(x,y) = x+y = 2u+v = g(u,v), 
which are NUMERICAL EQUALITIES and which are NUMERICALY true, nevertheless the functions f and g ARE NOT the same since
f : (x,y) --> f(x,y)=x+y, 
and 
g : (u,v) --> g(u,v) = 2u+v, 
WHICH IS equivalently written (since variables are ""DUMMY VARIABLES"") 
g : (x,y) --> g(x,y) = 2x+y.

From this rigourous functional (or algorithmical) way of looking at it,  it's obvious that f and g are DIFFERENT algorithms, that is DIFFERENT functions!

With things clarified this way, all confusions, danger, paradox... simply vanish : 
(df/dx)y = 1, 
and 
(dg/du)v=2 
No more pb!...

More over, be now clearly aware that we can write, with absolute rigour : 
(dg/du)v = (dg/dx)y, 
BUT ONLY IF YOU READ THIS IDENTITY IN THE PROPER WAY ONE SHOULD READ IT, THAT IS THROUGH ""FUNCTIONS SPIRIT"", AND NOT ""number spirit"". Why that? Because variables in these expressions, ARE AND MUST BE LOOKED AT, AS ""DUMMY VARIABLES""! 

More precisely, what both of these expressions (dg/du)v or (dg/dx)y, trully mean, is simply and unambiguously : DIRIVE WITH RESPECT TO THE FIRST VARIABLE (OF THE ORDERED PAIR, OF THE CROSS PRODUCT OF SETS), KEEPING THE SECOND ""VARIABLE"" CONSTANT. 
Therefore we could equivalently have written (dg/dk)@  (or any crazy other ""names"" of variables), if we had defined the function ""in such CHART"", labeled (k,@),  by :
g : (k , @) --> 2k+@

THIS is the only way of puting things trully clearly and rigourously, without ever giving rise to any notation confusion or paradox! Simply by calling a function a function, and NOT ""a cat a dog"", messing around with words and concepts, through rather ""physicist"" lasy notations wich turns sometime to prove to be ""bad"" habits. 

It's in fact a CHAIN RULE MISTAKE that is arising when one misleadingly identify f with g. If one realy wants to differentiate with respect to the same variable, x for instance, keeping y constant, it is possible! But to perform that without any mess and mistake, one SHOULD NOT naively compare  (df/dx)y=1 with (dg/du)/v=2, wich are clearly DIFFERENT (and nothing wrong about it!). But instead, one SHOULD think ""functionaly"" instead of ""numericaly""! That means one has to compute clearly the ""CHAINED FUNCTION"" G, which is different from g, but which is related to g by the Change of Variable. 

We thus express, first the change of variable in the PROPER WAY! That is, as the following FUNCTION :
C : (x,y) --> C(x,y) = (u,v) = (x, y - x)
We thus recall that the FUNCTION g is defined as the following algorithm :
g : (@,#) --> 2@ +#,
or equivalently (since what any function trully IS, IS it's defining ALGORITHM!), but more conveniently (for our CHAINING FUNCTIONS GOAL)  :
g : (u,v) --> g(u,v) = 2u+v

These two FUNCTION are now wisely CHAINED to build the FUNCTION G defined as follow :
G(x,y) = g(u,v) = g( (u,v) ) = g(C(x,y)) = (goC)( (x,y) ) = (goC)(x,y)
We now clearly see what is this FUNCTION G : THE CHAINED FUNCTION OF g and C :
G = goC

The central ""o"" meaning the CHAINING (COMPOSITION) OPERATION ON FUNCTIONAL SPACE, defined, in general, for any two function A : E--> F, and B : F --> G, very simply as :
BoA : E --> G , x --> BoA(x) = B(A(x))
Which could thus, aternatively be named ""THE BOA RULE"" instead of the usual ""fog"" and ""gof"" of ""FUNCTION CHAINING""... (joke!)

In our exemple we then get, finaly, since u=x and v=y-x :
G(x,y) = (goC)(x,y)  = g(C(x,y)) = g( (u,v) ) =  g(u,v) = g(x, y-x) = 2x + (y-x) = x +y
SO WE ""DISCOVER"" THAT for all x and all y, we have :
G(x,y) = f(x,y)
That means FUNCTIONAL EQUALITY :
G=f

So what have we done? Turning around? Yes, in a sens, because we have INSISTED in differentiating g with respect to x, IN A NUMERICAL SENS, instead of doing it in a FUNCTIONAL PROPER WAY that is, differentiating with respect to its FIRST variable in the ALGORITHM 
g : (@,#) --> g(@,#) = 2@ + #
Thus, in this NUMERICAL SENS, x is no longer a DUMMY VARIABLE, but a ""NUMBER ATTACHED TO f""! The physicist would call it a ""physical observable"". This way of looking at things makes it complicate and cand lead to confusions if one doesn't clearly understand the CHAIN FUNCTION KEY AND THE IN FACT THE MANIFOLD CHARTS MAPPING (THUS CHANGE OF CHARTS TRANSFORMATIONS, often differentiable for a regular manifold) laying under all this...  

We thus have, in a sens, ""turned around"", leading to G=f! But doing so we nevertheless HAVE CLEARLY WRITEN THINGS IN CHAIN FUNCTION PROPER WAY, that reveal to be EXTREMELY USEFULL in higher and more abstract DIFFERENTIAL GEOMETRY, where crucial concepts of COVERING and UNIVERSAL COVERING, TANGENT SPACE, GROUP, LIE ALGEBRA, LIE DERIVATIVE, COVARIANT DERIVATIVE, CONNEXIONS, DIFFERENTIAL FORMS,..for instance, are usefully springing, needing CHAINING FUNCTION PROCESS to be clearly understood and mastered!

Finally, often, this abuse of notation which misleadingly sets f=g, will be handled without damage by the ""human computer"", with some habits and agility. BUT only in rather easy area. On the contrary it will lead to catastrophic confusions, misconceptions, darmatically false results and chear non sens interpretations, in more suttle area...alike, not for naming them, general relativity, riemanian differential geomedry, condensed matter, plasma, etc...

CHAINING FUNCTION OPERATION is one of the most simple, but important one in all mathematics! It's the building block of nested structures, one inside the others alike Pandora box, BUT ""BOXES"" THAT REVEAL FASCINATING STRUCTURES ALIKE GROUP, ALGEBRA, CLIFFORD,...TOPOS... : 
Points
Functions, from points to points
Functional (or Operator), from functions to functions, 
etc...
All included IN...CATEGORY Groetendick SPIRIT...deap!" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5576.0 0.0 1.0 0.0
"The profession of teaching is being loved from all over the world as one of the most important profession of all time!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 10243.0 0.0 0.0 0.0
"@xxjash100xx If you liked this Calculus stuff you might also like this number pattern. Check it out! ""Speed maths- Multiplying without multiplying"". Click on my username and check the vid. Cheers." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2072.0 0.0 0.0 0.0
"sooooo what was x? lol" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14370.0 0.0 1.0 0.0
"@gunghojoeno 

Thats not what he's proofing though.  He's showing the sin(x)/x = 1, not 0." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1860.0 0.0 1.0 0.0
"A*S=S*Lambda (Using the linear combination view (Ax1=b1 column part) of Matrix Multiplication), That is Brilliant and Clear! Thanks!" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 2172.0 0.0 0.0 1.0
"This is an absolutely brilliant introduction to the theory of Probability. Many high school textbooks define probability as a frequency of possible outcomes to the total outcomes and get into counting problems. Students would quickly lose interest while solving myriad counting problems involving cards, dies, etc. and never see the bigger picture of probability. Here the professor instead choose to give a broader theoretical context behind the probability in the first lecture. Think what he did. He clearly defined his objective as to give a math framework to uncertainty faced in any field and started to systematically define the terms and rules. To begin with, we could call any uncertain activity that we are interested in, as an experiment and in that experiment, we could define a relevant sample space (he gives examples of irrelevant sample space to stress the importance of defining relevant ss) and then a probability law which quantifies our believes about how the outcomes in the sample space might occur. He stresses on this fact that probability law can be anything and need not be an empirical frequency which we usually observe. Probability of heads in a toss need not be 1/2 or probability of getting any one of the value when a six-sided die is rolled need not be 1/6. We assume them to be 1/2 or 1/6 because we empirically observe it and also logically it makes sense to assign those values when you know that the coin or the dice is not at all biased in any way. But some dices or coins due to their deformities   could favor certain outcomes and need not have equal fairness to all outcomes. This is such a revelation and not many realise this. He deals with uniform probability - finite sample space separately to make this point more clear. Also, the formulation of events that we are interested as subsets of possible outcomes and using pictures to find the probabilities of those events is absolutely beautiful.  He lays down the fundamental axioms and uses them wonderfully to derive the intuitive idea that probability of an event or a subset is nothing but the sum of probabilities of outcomes which are part of that event or subset. When we look at an event this way and also deal with uniform probability law (prob of each outcome is 1/N), we get probability of event as n/N where the formulation comes from  sum of n 1/Ns rather than dumbly solving counting problems for numerator containing possible outcomes of event and denominator containing all outcomes. This way of thinking helps one to understand and use probability theory beyond counting problems. Similarly, equivalence of probability to the areas while dealing with continuous distribution makes lot of sense and problem boils down to finding out the areas that our events occupy." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 10622.0 0.0 0.0 0.0
"27:28 I don't understand why they are considered projection matrices. Projection matrices from my limited understanding satisfy P=P^n, where n is any real integer. Projection matrices project a vector onto a certain subspace. Back in lecture 15, he derived P = A (A^T A)^-1 A^T. In the context of this lecture, A is an orthogonal matrix. Since A^T = A^-1 , P = A A^T. Does he therefore mean that q q^T are projection matrices in this sense?" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 819.0 0.0 1.0 0.0
"Completely confused by 10:57. Can somebody explain what's the difference between union and his sum ""+""?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 3187.0 0.0 1.0 0.0
"I love his blinking single eye, literally. this man is great." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 5738.0 0.0 0.0 0.0
"I can't believe the students start packing their stuff, slamming desks around, etc. at 48:30 before he's even done talking. So rude. They've just received a lecture by a brilliant mathematician, yet they have no respect!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5206.0 0.0 0.0 0.0
"not one person has a question in any of these?  wtf" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 14080.0 0.0 0.0 0.0
"Why is L half not a good norm? Why the P is restricted to be >= 1 instead of just p >0?" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11864.0 0.0 1.0 0.0
"thanks a lot <3" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14567.0 0.0 0.0 0.0
"The best professor.. ever!! 😊👍🏼" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10007.0 0.0 0.0 0.0
"Wrong? He's awesome, he has the best explanations! You should see my teachers :o" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 12097.0 0.0 0.0 0.0
"16:00 the fourth way is the best by far" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 466.0 0.0 0.0 0.0
"@tim888222 Do you have any idea how many grammatical errors there are in that one paragraph?" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2045.0 0.0 0.0 0.0
"Hey I actually got all this :D. I only have grade 10.5 math and want to continue  my math studies... one day I'll get there. So inspirational" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4687.0 0.0 0.0 0.0
"In finding the perpendicular vector why the subtraction why not project (dot) then cross?" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 6633.0 0.0 1.0 0.0
"Thank you...Greetings from Peru" sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9565.0 0.0 0.0 0.0
"I want to bring my past self from 1988 to the YouTube era." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6136.0 0.0 0.0 0.0
"this was hard" JBIz7UadY5M "14. Regression (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 14922.0 0.0 0.0 0.0
"Thanks a lot for the best math classes" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9658.0 0.0 0.0 0.0
"Today I have completed the course; actually, I cannot be more proud to take this course and understand linear Algebra more than Any course that my uni gave me. Reckon that I am doing my masters in CS, and this basically is the key to everything since my uni bachelors failed to offer me reasonable mathematics courses.
I was never good at any major of mathematics, but right now, I feel I can rock any exam with the highest grade and enjoy studying for it. If there is a way to thank Dr Strang via email or something, tell me." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 11051.0 0.0 0.0 0.0
"The formula at the end is given as exercise in A first course in Probability by SM Ross. This Is really based on Combinatorics. The formula is based on combinations i.e. nCr or n combinations of r things at a time." sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10114.0 0.0 0.0 1.0
"That black board paint on the walls sure does go a long way in these modern times!  That is a great idea if I ever get to teach again with all these budget cut backs!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9878.0 1.0 0.0 0.0
"Why does this have so many dislikes?" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11850.0 0.0 0.0 0.0
"Very helpful to future students! Great work! Thank you!" oNsscmUwjMU "2. Nondeterminism, Closure Properties, Conversion of Regular Expressions to FA" "MIT 18.404J Theory of Computation, Fall 2020" 11196.0 0.0 0.0 0.0
"29:35 The vectors are not independent. 2*[2,2,5]-[1,1,2] = [3,3,8]." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 856.0 0.0 1.0 0.0
"Mr. Jerison is super." jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7714.0 0.0 0.0 0.0
"thank for the person who asked for the 2nd row in min 8:55" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14455.0 0.0 1.0 0.0
"5:03: big snow!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1355.0 0.0 0.0 0.0
"This makes me want to applaud.  I watched his summary lecture that reiewed this course and I damn near clapped in my home.  I should buy his book - I bought another one that's working fine, but didn't emphasize the row space column space null space left null space fundamental theorem of linear algebra picture that this course develops." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10846.0 0.0 0.0 1.0
"Wonderful teaching" AeRwohPuUHQ "22. Gradient Descent: Downhill to a Minimum" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11993.0 0.0 0.0 0.0
"What a good prof. At my school I have all sorts of questions but my prof doesn't take them. I wouldn't even need to ask in this class," 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 11408.0 0.0 0.0 0.0
"I also want to point out something that most people would forget: the cameraman is very professional, always got the timing correct. It's really not a trivial work! The cameraman has to listen thoroughout the lecture and keep focusing on the right thing. A big thank you to the camera man as well!" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5038.0 1.0 0.0 0.0
"wish you a very long and healthy life, Professor Strang." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 15386.0 0.0 0.0 0.0
"Where can we find 18.06 from Alex Townsend? I would love to see more lectures from him, such a rich explanation" 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11667.0 0.0 0.0 0.0
"51:19 it is not straightforward to me why the BW theorem is correct given the previous theorem." Xn8wL2ItzZw "Lecture 9: Limsup, Liminf, and the Bolzano-Weierstrass Theorem" "MIT 18.100A Real Analysis, Fall 2020" 1342.0 0.0 1.0 0.0
"I just love Prof. Gilbert Strang. One of the best teachers humanity has to offer. To all those who haven't watched this playlist - This is the best way this subject can be taught." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 5609.0 0.0 0.0 0.0
"how come in the first example of the sphere F.nhat = a and not 1/a and in the second example H.nhat = z^2/a instead of az^2" phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13204.0 0.0 1.0 0.0
"you put them in there(the right angel notation which aide in comprehension and even more so for the visually impaired ) but not in the book fig 1.2 a quote from the forth objection   the omission of (what seem to be ) irrelevancies that give rise to contentions ,least the reader argue (self debate)over (perceived to be by the writer )inessential and so be prevented from perceiving what is important  ,  the space is there to define the object not the other way around , if a line is infinite  its space is so limited to the object/s with in it ,if not the space reflects its limits i.e its  dimensionality    its called ambiguity  , of course not there trained monkeys your tossing peanuts to" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15513.0 0.0 0.0 0.0
"Theres only 3 kinds of mathematicians: those who know how to count and those who don't." wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 10392.0 0.0 0.0 0.0
👍🏼 ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15700.0 0.0 0.0 0.0
"What's the probability of someone entering the wrong lecture theatre at 28:37 ?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 11584.0 0.0 1.0 0.0
"For z = z0 + a(x-x0) + b(y-y0),
wouldn't that mean:
-1(z-z0) + a(x-x0) + b(y-y0) = 0
so from lecture 4 the normal vector for any f(x,y) tangent plane is <-1, a, b> ?
I'm missing something about the -1 I'm sure" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3916.0 0.0 1.0 0.0
"excelente !!!!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 12809.0 0.0 0.0 0.0
"colombia exploded because a welder slacked on an o ring u idiot dont fuck up facts. columbia exploded causee of power point lol wow u are smart" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12661.0 0.0 0.0 0.0
"He is one of the worse teachers.  He needs to do better job of preping for the lecture or he just stop teaching." yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 4529.0 0.0 0.0 0.0
"I'd like to say, this video is the best I've ever seen. The instructor's mind is very clear so that he can relate all critical notions together and depicts vivid images for us in brief." JTbZP0yt9qc "6. Maximum Likelihood Estimation (cont.) and the Method of Moments" "MIT 18.650 Statistics for Applications, Fall 2016" 6279.0 0.0 0.0 1.0
"thank you MIT" a1ZCeFpeW0o "20. Principal Component Analysis (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 14478.0 0.0 0.0 0.0
"It’s been a journey Professor Strang. It’s quite sad that this has come to an end, but what a beautiful way to come full circle." Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 7098.0 0.0 0.0 0.0
"Anyone failing after the doc's lectures for a semester should be arrested and banished to Siberia" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2493.0 0.0 0.0 0.0
"1 + w + w^2 + ...  + w^{n-1} = (1 - w^n )/ ( 1 - w )" 1pFv7e9xtHo "31. Eigenvectors of Circulant Matrices: Fourier Matrix" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 313.0 0.0 0.0 0.0
"The mistake starts at 11:26. The right hand side is (1 2 2), not (1 2 3). But he later uses the (1 2 2) for all other calculations, so not a big deal." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 10190.0 0.0 1.0 0.0
"horrible camera work" Xn8wL2ItzZw "Lecture 9: Limsup, Liminf, and the Bolzano-Weierstrass Theorem" "MIT 18.100A Real Analysis, Fall 2020" 13187.0 1.0 0.0 0.0
"oh i'm still in highschool and i can understand and apply everything he's taught!
I was wondering why he was taking his glasses off all the time" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 14107.0 1.0 0.0 0.0
"There are just few people all the way getting there , glad I did it also" PnPIqh7Frlw "Lec 24: Simply connected regions; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10349.0 0.0 0.0 0.0
"25:20
Not every one at MIT is a nerd!!" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 776.0 0.0 0.0 0.0
"Thanks ,,,," PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9582.0 0.0 0.0 0.0
"Now I am wondering that all those students are 11 years older than me




2020 ( During Lockdown)" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7948.0 0.0 0.0 0.0
"I actually found this lecture hard to follow. I've taken Single Variable Calc and the Probability course from MIT on EDX, and found those teachers' rhythm much easier to follow. Here it feels like the professor is jumping from one train of thought to another , making it difficult to follow." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5015.0 0.0 0.0 0.0
"18:26 isn’t N1 with ab not only in q3/q4 but also in q1?" oNsscmUwjMU "2. Nondeterminism, Closure Properties, Conversion of Regular Expressions to FA" "MIT 18.404J Theory of Computation, Fall 2020" 539.0 0.0 1.0 0.0
"Hello! Does anybody know any other lecturers like Dr. Strang with such passion in fields like convex optimization, detection estimation or probability theory?" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4662.0 0.0 0.0 0.0
"@AnimeBelover they can afford best chalks in the world. these chalks consist about 28% of calcium this why these chalks very tough and u can draw long straight lines. and if someone have trouble with teeth it can be eaten as well. but before u need smash chalks or scrape off whiteboard and mix it with some limon- or other acid. without acid you wont consume calcium. they called also eatable chalks." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1586.0 1.0 0.0 0.0
"i'm tunisian estudent, " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13521.0 0.0 0.0 0.0
"Thank you, MIT for making this publicly available and for free. 
Thanks, Youtube for storing and serving the content." RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 9500.0 0.0 0.0 0.0
"got another way of slightly less clumsy integrating to pi/8
cos^4(t)=cos^2(t) - cos^2(t) sin^2(t)=cos^2(t)-1/4 sin^2(2t)

double angle formulae again, original integrand becomes
3/8+1/2 cos(2t) +1/8 cos(4t)

happy integrating" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12957.0 0.0 1.0 0.0
"Are elimination and elementary matrices the same? Some books mention elementary matrices and others don't, so I wanted to know!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2523.0 0.0 1.0 0.0
"8:55 Min why does he want to avoid A to be singular? don´t quite understand...the only reason i see (in hindsight), is that the step, he does at 12:30 Min (rewriting LU with a diagonal matrix in the middle) wouldn´t be unique. But i assume, there must be another reason." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 1427.0 0.0 1.0 0.0
excellent sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12815.0 0.0 0.0 0.0
"Does undergraduates in the us only learn about calculus  when the reach university at 18, in the uk we learn't about it a 15 " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3466.0 0.0 0.0 0.0
"Thank you prof I'm writing a exam tomorrow morning" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9300.0 0.0 0.0 0.0
"ngl, good video, but thumbnail creeeeeeep" P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 14024.0 0.0 0.0 0.0
"when i hear eigenvalue, I think of Häagen-Dazs®" HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 15207.0 0.0 0.0 0.0
"I have so much difficulty coping with my Linear Models subject. Thank you prof for this! You're a blessing. Continue uploading your lectures. You are a great help to us!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5556.0 0.0 0.0 0.0
"Fine lecture, amazing offering, PLUS, in the scuffs, dusts, and blears of the chalkboard panels, a poetry in black I haven't seen since Ad Reinhardt!" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 3798.0 1.0 0.0 0.0
"Nice tie. :)" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 7858.0 0.0 0.0 0.0
"43:20 Why students are laughing?" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1203.0 0.0 0.0 0.0
"why is |e^(6it)|=1?" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 15351.0 0.0 1.0 0.0
Immortal Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6585.0 0.0 0.0 0.0
"I am shocked at 40:48, why isn't there any students at the lecture hall?" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 5137.0 0.0 0.0 0.0
"I dont understand why individuals dont always make the sample space explicit. That way, a nonconditional probability is conditional on the given sample space. It shows that probability is dependant on sample space and there can be varying specification of it." -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 5368.0 0.0 0.0 0.0
"So nice and educative sir" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 8782.0 0.0 0.0 0.0
"@jazzyb1030 that would be great, the problem is  how..:D" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 1899.0 0.0 1.0 0.0
"This is really a good video, it helps a lot for my entrance exam. Thank you so much!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10711.0 0.0 0.0 0.0
"Parlez-vous français?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8154.0 0.0 0.0 0.0
"i have finished 18.06 and i thought that i wont see professor gilbert and the infinite black black board together in  a video again 
pretty happy :D" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13395.0 1.0 0.0 0.0
"Any subspace must contain vector (0,0,0), otherwise, if you do w*0 the answer would not belong to the subspace.

If the plane doesn't go through the origin, it's not a subspace." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 2474.0 0.0 1.0 0.0
Inspiring VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 6715.0 0.0 0.0 0.0
Amazing… 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 2411.0 0.0 0.0 0.0
"Great additional material to help with clarifying my studies." CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4212.0 0.0 0.0 0.0
"Finally finished the whole 18.01 playlist. 
Thank you Prof. Jerison and Prof. Muller. I have finally understood the essence of single variable calculus which I could not for several years. Now in my 4th year of engineering, I can finally appreciate the beauty of calculus. Thank you very much. 🙏🙏🙏

02/01/2023, India" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3771.0 0.0 0.0 0.0
"That is why MIT is called the ""Mecca of Engineering"". Brilliant !!!!!!!!!" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 9901.0 0.0 0.0 0.0
"I believe there is an issue on 18.01sc (on the MIT OCW website): One of the recitation videos asks us to be aware of representing functions as series before it is introduced." wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5173.0 0.0 1.0 1.0
"Actually, very few people use iPods today 20190124" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2238.0 0.0 0.0 0.0
"The natural log is just a massive piece of junk 🤣" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10199.0 0.0 0.0 0.0
"He is my guru" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4526.0 0.0 0.0 0.0
"Can someone help me? Around 30:0 to 33:33 I don’t understand that multiplication. To me it doesn’t look the A matrix is equal to the transposed matrix times the identity matrix. One time zero is zero. Not one. (From top row of second column)" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3084.0 0.0 1.0 0.0
"How do we get the picture (triangle) in the stick-breaking example which is later used to get the limits of the integral" CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 4853.0 0.0 1.0 0.0
"Is it sufficient to follow along with this video playlist and do the problems on the OCW website or should one work through the textbook alongside? 
I'm a third year engineering student in europe (mechatronics engineering), but my school doesn't go heavy on theory and only teaches bachelor's students the bare minimum of linear algebra." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6797.0 0.0 0.0 0.0
"35:25  Piecewise linear conferences... multiple dimensional dry humor!" sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1012.0 0.0 0.0 0.0
"@ 50:18

Now I see, guess I made the same mistake. It is -1." aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1481.0 0.0 1.0 0.0
"The first lecture is simple even for 2* speed. Youtube needs an option for 4* speed with subtitles, so that we can skip simple things and learn more in less time." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10108.0 0.0 0.0 0.0
"EA= R; the EAR rule" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3534.0 0.0 0.0 0.0
"I have a small doubt, what if we assume that population parameter itself is a random variable, not a constant in frequentist sense, can quadratic risk still be decomposed into Bias and Variance like this?" rLlZpnT02ZU "4. Parametric Inference (cont.) and Maximum Likelihood Estimation" "MIT 18.650 Statistics for Applications, Fall 2016" 5512.0 0.0 1.0 0.0
"Thanks sir" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 9772.0 0.0 0.0 0.0
"Wizard of LA" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 11975.0 0.0 0.0 0.0
35:00 ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 992.0 0.0 0.0 0.0
"I'm honestly so glad these lectures are posted" 4MgN6uxd4i4 "7. Decision Problems for Automata and Grammars" "MIT 18.404J Theory of Computation, Fall 2020" 6328.0 0.0 0.0 0.0
"I Really Like The Video From Your Line integrals in space, curl, exactness and potentials" seO7-TwXH_I "Lec 30: Line integrals in space, curl, exactness... | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4961.0 0.0 0.0 0.0
"46:47 ""It's a very popular model for modeling people who are drunk"" lol" ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 1276.0 0.0 0.0 0.0
"pointless no talent teacher." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14197.0 0.0 0.0 0.0
"I am missing a reference to the population when explaining expected mean and expected variance. Then you sample the population for a sample mean and/or a sample variance." nrDkb2MAwSA "20. Definitions and Inequalities" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5118.0 0.0 1.0 1.0
"I chose number 8. Why would it be 7 instead of 8? 7 and 8 have the same probability to attain?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 5238.0 0.0 1.0 0.0
"Thank you MIT, and can you PLEASE post the names of these wonderful professors so we can thank them by name too?? I go to a small community college and our instructors are wonderful.... but.. not quite like this :)  These videos make me feel smart again when I was starting to ask myself ""what's wrong with my brain??""" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9156.0 0.0 0.0 0.0
"While in high school (in India), I used to hate matrices, determinants, and vectors. They taught it like they were just a bunch of mindless, random calculations. Prof. Strang gives meaning to all of them and linear algebra has suddenly become wayyyy more interesting!" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 11723.0 0.0 0.0 0.0
"@shinyralle all he wants is, that you get a better view for that what he wants you to see. that why he writes it that way" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 2011.0 0.0 0.0 0.0
rubbish FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14269.0 0.0 0.0 0.0
"here you go down to problem set and find which tasks were given to each lecture:
https://ocw.mit.edu/courses/18-01-single-variable-calculus-fall-2006/pages/assignments/


and here you find the homework with solutions(as a bonus there are supplementary notes):
https://math.mit.edu/~jorloff/suppnotes/suppnotes01-01a/index-01A.html" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13142.0 0.0 0.0 0.0
"At the run time 38:20, regarding the third possibility of SUB SPACES of R^2, zero vector only.
If we add any vector other than zero vector to the zero vector, wouldn't the vector be shifted to another position rather than staying at zero vector position i.e. won't it jumps out of specified vector space?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 2731.0 0.0 1.0 0.0
"i think at 44:58 it should be 1/4 + 1/4 = 1/2 not 1/2 +1/2 =1" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 13467.0 0.0 1.0 0.0
"I'm guessing this was a re-do lecture, probably due to some recording malfunction when they first recorded it. It would be odd to have a packed room for lecture 4 and then have no one show up to lecture 5, haha." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 6325.0 1.0 0.0 0.0
"Not gonna lie, the last video I saw of him was from 2015. I fought he was dead. so good to see him again" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7923.0 0.0 0.0 0.0
"'if i had a prof like him' statement in my head" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 211.0 0.0 0.0 0.0
"thank you prof. Strang. you are brilliant!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 14505.0 0.0 0.0 0.0
"At min 26:00 by double differentiate f(0) it comes 51/8 and it's much faster to put zero in e^x and x" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2717.0 0.0 1.0 0.0
"13:31 Flat Earth confirmed!" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 419.0 0.0 0.0 0.0
"@Mydyingbride It's good to know that you know how to copy and paste Google search results.

I can't believe you are trying to gain an ""I'm so smart"" off of YouTube. Fucking sad." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1689.0 0.0 0.0 0.0
"I'm disappointed he didn't write down Euler's Identity in the end :(" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6319.0 0.0 0.0 0.0
"9:13 i've never realized that! awesome!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1438.0 0.0 0.0 0.0
"Just finished single variable course 18/05/19 thanks a lot MIT, someday I'm going to donate money for this incredible resource thay you give us.. carry on with this quality at education!" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7169.0 0.0 0.0 0.0
"Such a legendary professor. He rocks! :)" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 8934.0 0.0 0.0 0.0
"mit still uses chalkboards. while my shitty hs has marker boards and smart boards. parady?" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 13954.0 1.0 0.0 0.0
"|det|,absolute value" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15531.0 0.0 0.0 0.0
"wish i could become a MIT student one day." BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15384.0 0.0 0.0 0.0
"Can anyone explain why he leaves out the abs() sign when saying integrating u'/u to get ln(u)
>> Shouldn't it be ln|u| ?" CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3033.0 0.0 1.0 0.0
"very good teacher, very helpful video" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 15011.0 0.0 0.0 0.0
"Crystal clear see through.Excellent." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3264.0 0.0 0.0 0.0
"Proof of Markov Inequality: 
https://en.wikipedia.org/wiki/Markov%27s_inequality#Proof_in_the_language_of_probability_theory" nrDkb2MAwSA "20. Definitions and Inequalities" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8416.0 0.0 0.0 0.0
"Given one of the children became a king, we know it's a boy. So, now there are 4 possibilities.
1. Male, King
2. Female, King
3. King, Male
4. King, Female

(First born first)

In this, it's safe to assume '1' didn't happen, as in that case the king wouldn't be the king. So, we got three possibilities with 2 of them having a female sibling. Thus probability is = 2/3.

Doesn't this make more sense?" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 4050.0 0.0 1.0 0.0
"this is mind-blowing
i don't fully understand it
but i know it's mind-blowing" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14868.0 0.0 0.0 0.0
"procedury ai tygłupku zostały zbudowane na krzywych fundamentach.ai" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 14207.0 0.0 0.0 0.0
"The only question I'm now left with is what the hell is ""a real New England weekend""." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 10213.0 0.0 0.0 0.0
"I remember when the 4 color was a lived controversy." G3mAXHuoDSw "Lecture 4: The Open Mapping Theorem and the Closed Graph Theorem" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 5949.0 0.0 0.0 0.0
"Where is the class 10 video?" a66tfLdr6oY "11. Parametric Hypothesis Testing (cont.) and Testing Goodness of Fit" "MIT 18.650 Statistics for Applications, Fall 2016" 11690.0 0.0 0.0 0.0
"With lectures this good I can watch this instead of Netflix. I have one professor who also hold phenomenal lectures and lectures this good bring me as much joy or even more than playing a good video game or watching a good show. It is interesting and entertaining and it blows my mind. Truly a fantastic job! Thank you professor Strang!" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 11968.0 0.0 0.0 0.0
"@vex123 How the guy manages to expose concepts. Now... if you value the education as a function of it's price (that seems to be the usual criteria for americans), you're not being educated, you're being sold a product. This is why american science of today has to graze its intelectual power from escaped minds from the former soviet union, china, and india: you simply can't produce good scientists, just good salesmans. Aside from very honorable examples, american science has been made by foreigns" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2060.0 0.0 0.0 0.0
"His name is Gilbert Strang, mathematician." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4761.0 0.0 0.0 0.0
"Where does n^2 - n come from and how is it obtained? Is it just the initial nuber of hats mutliplied by th remaining number after 1 is correctly selected?" EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 11678.0 0.0 1.0 0.0
"In case of normal distribution you say that when sigma smaller then that parabola will narrower but if we take sigma getter than 1 then opposite situation happened. Please explain it." mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 6628.0 0.0 1.0 0.0
"Can the determinants that compute the triangle(not including origin) be generailized to n dimension? I look around internet but found nothing related." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 3106.0 0.0 1.0 0.0
"What combination should we take? Why not the right combination what the hell🤣" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11476.0 0.0 0.0 0.0
"Hey MIT, you guys rock for putting up such exquisite material online for free. I will definitely be making a small donation for such a great cause.  " j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 4689.0 0.0 0.0 0.0
"you are really a good teacher.  When u teach Math it's like  flawless.  I am truly inspired sir" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 15495.0 0.0 0.0 0.0
"Thank you" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 9087.0 0.0 0.0 0.0
Touching！ t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11079.0 0.0 0.0 0.0
"at 31.40 can I also say that a matrix is invertible only if linear combination of its columns can create vectors which are linearly independent." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12437.0 0.0 1.0 0.0
"Micro printing" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7664.0 0.0 0.0 0.0
"Gave me some insight, Thanks. I liked the part about how u^TSu is the variance of the X's along the u direction. Good to know for an alternative viewpoint to Singular value decomposition as a PCA." WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 3989.0 0.0 0.0 0.0
"just wow" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 13746.0 0.0 0.0 0.0
"Finally! We start with a clean board." lWW54ts9Ubo "24. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 3790.0 1.0 0.0 0.0
"Dude the professor is freaking awesome.i have fallen in love with maths cause of him" ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3524.0 0.0 0.0 0.0
"note: there are 5 ways to think of matrix multiplication.
1. cij=Sum[aik*bkj,{k,1,n}]
2. (Matrix*column=column), Columns of C are combination of columns of A.
3. (row*Matrix=row), Rows of C are combination of rows of B.
4. AB=sum of (columns of A)(rows of B).
5. We can cut matrix into blocks." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14086.0 0.0 0.0 0.0
"Love it. Thanks MIT!" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7448.0 0.0 0.0 0.0
"26:59 I'm sorry, I don't get this. w takes both positive and negative values. How does that lead to saddle point?" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 810.0 0.0 1.0 0.0
"HOW IS THIS FREEE!!" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 4407.0 0.0 0.0 0.0
"9:11 ""I can assign anything that I like for X2 and X4...""

So, what's stopping us from choosing the free variables as X2 and X3? Because, it seems clear from the equations that they can be assigned any value arbitrarily.

Somebody!" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 1436.0 0.0 0.0 0.0
"How come he considered a hyperbola that passed by (x=0) and (y=0) simultaneously ???
at 46:55 ." UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4823.0 0.0 1.0 0.0
"his 7 looks like a 1 and thats really confusing :D
But as always great lecture!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13159.0 0.0 0.0 0.0
"I love this guy." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 5810.0 0.0 0.0 0.0
"I'm back! 🤓" wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6308.0 0.0 0.0 0.0
"i still do not understand how it works , F and I definitely can have different shapes ? This part is not clear from the video." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 13460.0 0.0 1.0 0.0
"More than twenty years after college, I stumbled upon the gem that is MIT 18.06 taught by Professor Strang. Watching him giving the lectures on the subject really changed my understanding of and perspective on some of the basic concepts of linear algebra. I would like to imagine Professor Strange as the great mentor I never had the luck to have in real life, and I am so lucky to finally find him on the Internet through MIT OCW. Thank you sir!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7695.0 0.0 0.0 0.0
"This video is amazing! AMAZING! All the principles fit reality so nicely! LONG LIVE MATRICES." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 10952.0 0.0 0.0 0.0
"how the heck are those people mit students?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13249.0 0.0 0.0 0.0
"He is excellent, indeed. His ability to explain simply is great" gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 4511.0 0.0 0.0 0.0
"I have taken several Probability and Random Proceses at different stages in my academic background career as well as many Advanced Stochastic Processes in many Electrical Engineering fields [Control Systems, DSP; Communication Systems, Radars, Electromagnetics, Machine Learning, DSP....].  It is really a pleasure to attend virtually to the lectures of Professor John Tsitsiklis.  He makes probability a wonderful experience !!!  Pd. I have a question for him that makes me think:  Normally advanced  sophisticated radar systems have PROBABILITY OF FALSE ALARM in the order of 10^-6 to 10^-10. Though his probability decision tree for the DETECTION of a plane is a wonderful really great and pretty neat  example for the derivation of conditional probabilities, why did You use only a probability of false alarm [PFA] of 0.10?  Isn´t it too high for advanced state of the art Radar Systems receivers Rx?" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 5560.0 0.0 1.0 1.0
"This is another excellent video on transposes, permutations and vector spaces. This is the real part of linear algebra." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 10633.0 0.0 0.0 0.0
"I suppose that’s why MIT is not for every student and why it is difficult and costly to get into. This course review requires a special level of mastery of the material, which assumes a great deal of understanding and problem practice throughout the course. When a matrix is not square and doesn’t have a unique solution (independent rows or columns) all kinds of scenarios could happen. Adding to that, whether the matrix is orthogonal, orthonormal, symmetric, positive or semi definite, as well as others involving Eigenvectors, values, pivots and determinants. I suppose that the best way to wrap all that information around the head is to start with some simple 2 by 2 or 3 by 3 matrix and experiment with all different scenarios using a good software package to spit out the output and see how the theory works. I am using scientific notebook." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5983.0 0.0 0.0 1.0
"This video should be included in every teacher preparation/training/professional development program ... and learn the lessons and apply them." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 10960.0 0.0 0.0 0.0
"Language of column space , OMGGG <3" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 7248.0 0.0 0.0 0.0
"In case you , like me, are wondering what this video is exactly - He's doing a recap of the first 12 lectures. This is NOT him going through the solutions of a quiz that the students sat. Rather, it's him reviewing the material so far before the students have the quiz." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 6629.0 0.0 0.0 0.0
"He explained it actually. Tangent plane is horizontal meaning that there is no lower or higher value than f(x,y) other than the intersection point of the tangent plane and the function. 
" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4481.0 0.0 0.0 0.0
"No students today :{" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 7892.0 0.0 0.0 0.0
"It should actually be f'(kx) = k*f '(kx)
It's the chain rule." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6986.0 0.0 1.0 1.0
"Conan's voice" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3191.0 0.0 0.0 0.0
"Why at 16:45, (6*2 ) - 2 = -10 instead of just 10?
I guess I learned this another way" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11792.0 0.0 1.0 0.0
"29:10 Here's the paper covering the proof for anyone wondering:- https://www.cse.iitk.ac.in/users/manindra/algebra/primality_v6.pdf" 1VhnDdQsELo "14. P and NP, SAT, Poly-Time Reducibility" "MIT 18.404J Theory of Computation, Fall 2020" 851.0 0.0 0.0 0.0
"Thank you really" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 9328.0 0.0 0.0 0.0
"An Indian edition of this book is available only in India
http://www.wellesleypublishers.com/buy.html" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2421.0 0.0 0.0 0.0
"You must be really special..." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12229.0 0.0 0.0 0.0
"Saddle Points: sometimes you gotta get up to get down." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 8589.0 0.0 0.0 0.0
"good for me." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12944.0 0.0 0.0 0.0
"this is very nice video about the conspectus of vector  add, multiply & how would to draw the vector in space(x,y,z)

" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14887.0 0.0 0.0 0.0
"why are we representing mu(k) vector as the combination of eigen vectors in the problem of Fibonacci sequence?" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 15287.0 0.0 1.0 0.0
"Thank you for this opportunity to learn such a valuable material" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 9283.0 0.0 0.0 0.0
底下并没有学生，然而讲的仍然非常好 nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 15626.0 0.0 0.0 0.0
"Whoa, did I miss something here?
At 42:11, he set dA/dx = 0. How did he get that? Can someone explain? Thank you :)" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11760.0 0.0 1.0 1.0
"Quality at its extreme !!! Respect professor strang !!! Hats off to you !!!" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 8469.0 0.0 0.0 0.0
"I found a mistake in a problemset of open courseware page of Calculus. How do I report it?
Mistake is in the problem 1A-4 b.
https://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/1.-differentiation/part-b-implicit-differentiation-and-inverse-functions/problem-set-2/MIT18_01SC_pset1prb.pdf" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5428.0 0.0 0.0 0.0
"if you find this lecture challenging, it might be because you forget some basic linear algebra. Don't be discouraged by the somewhat trivial algebraic calculation. the Prof does a very good job in explaining the intuition and statistical foundation for doing PCA. PCA is so commonly used in psychology studies, yet no one in the my Psy department seem to have a clue where PCA is coming from." WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 13554.0 0.0 0.0 1.0
"MIT can't figure out how to apply a filter to the audio to remove the hiss?" TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 7512.0 0.0 0.0 0.0
"The phenomenon he mentioned in the first 5 minutes is a very interesting psychological question. Is it about the sequential effects of decision making? Anyone knows the field? Please feel free to share some papers. Thank you." NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10227.0 0.0 0.0 0.0
"I Really Like The Video Transposes, Permutations, Spaces R^n From Your" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4999.0 0.0 0.0 0.0
"pretty interesting to hear in min 25 about ""fat tails in finance and the morgage scandal"". This was recorded in Fall 2007, and 15 years later we're still feeling the effects of the 2008 economic crisis." MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14204.0 0.0 0.0 0.0
"I got confused when he said that the column space of two 3-D vectors will be a plane (The column space of two 2-D vectors was also a plane, so, there won't be any difference in any column space?). Isn't the linear combinations of two 3-D vectors supposed to fill out the entire 3-D plane?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 5444.0 0.0 1.0 0.0
"This class is concerning of the the product of two huge matrices A and B,  assuming in the simple case that  A is [a,b], and B is [cT,dT], and the algorithm is that we choose one column from A and one row from B. For instance, we might choose column a from A and row cT(c transpose) from B, and then we do out product of these two vectors to get a*cT, this will serve as a sampling to simulate (or one of our guesses) the real product AB. As we accumulate more and more of the samples, if we sum all of these out-products together, we will gradually approach the real answer AB. His calculation on the [a, 0], [b,0] business in the fist part is only tryting to capture on average how the algorithm is dealing with one  of the components A in the product AB." z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10474.0 0.0 0.0 0.0
"Why is he so gittery :(" z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11872.0 0.0 0.0 0.0
"Thanks much, this was really helpful " ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 9754.0 0.0 0.0 0.0
"Was it a burp at 48:48?" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 11273.0 0.0 0.0 0.0
"the best of the best" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 14667.0 0.0 0.0 0.0
"I want to meet this amazing teacher and tell him how much I value this video. My stats teacher is really bad!" P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 6140.0 0.0 0.0 0.0
"@Shmling not all people in mit are smart. " BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1727.0 0.0 0.0 0.0
"Thanks  a lot. A great  work you have  done  sir." 8IxHMVf3jcA "Lecture 16: Fejer’s Theorem and Convergence of Fourier Series" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 9579.0 0.0 0.0 0.0
"this professor has really nice handwriting lol" BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14913.0 0.0 0.0 0.0
"İys timmy tim" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 15539.0 0.0 0.0 0.0
"I have a doubt regarding choosing the values for the free variables. Why do we choose only values like 0 or 1? If we choose another value like 2 or 10, the solutions change. So what about those solutions?" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 5488.0 0.0 1.0 0.0
"The jokes near the end: Hilarious." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 10147.0 0.0 0.0 0.0
"Wow this guy is an incredible teacher. Constantly states why things are important. Has a sense of humor. Builds up logic so that things flow vs. a spattering of random facts. 💯" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 12038.0 0.0 0.0 1.0
"all hail to open courses" cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12321.0 0.0 0.0 0.0
"Thats interesting. Tell me more." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9950.0 0.0 0.0 0.0
"that is greatness - shows a different level of clarity...." 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 14633.0 0.0 0.0 0.0
"I am taking linear algebra class at my own college. It's a top 20 university, but the professor totally messes stuff up! He didn't even emphasize the closure of linear combination when he introduced vector space! I thought linear algebra is super hard but I realized it's actually not after I watched this video! " JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 5146.0 0.0 0.0 0.0
"i have never been so lost in my entire life....." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 13397.0 0.0 0.0 0.0
"for cycloid the proof was given in terms of angle,later it was told that at radius =1 and speed=unity, angle may be replaces with time.thus r vector of cycloid was arrived at in terms of t.
also using this r in terms of t, speed was calculated as  sqrt(2-2cost).
my question is when  relation in terms of t was arrived at by using speed =unity,why it is coming as sqrt(2-2cost) ?" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12882.0 0.0 1.0 0.0
"I love this dude. I love his unique way of talking." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5803.0 0.0 0.0 0.0
"YEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEAAAAAHHHH!!
SO good! <3" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12108.0 0.0 0.0 0.0
"@paolabayybee1 College." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 1961.0 0.0 0.0 0.0
Great PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4193.0 0.0 0.0 0.0
"Why doesn't he use symbols for divergence and curls?" _CdoRiNSrqI "Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11853.0 0.0 0.0 0.0
"Am I mistaken or is he making several mistakes in the box problem? Such as A in terms of V, the value of A as x approaches 0,..." YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2332.0 0.0 1.0 0.0
"시대의 명강" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 15682.0 0.0 0.0 0.0
"God I love the Strang." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 4069.0 0.0 0.0 0.0
"I think about this in my sleep.............lmao." Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 6005.0 0.0 0.0 0.0
"Meraviglioso. I'd never seen such a quality in teaching. I am really amazed and full of respect." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 7656.0 0.0 0.0 0.0
"thx, now i know how is like a course in MIT.." IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 14937.0 0.0 0.0 0.0
"it would be great if we have video lecture for commutative algebra as well" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 13689.0 0.0 0.0 0.0
"@hiphoplanla knew* i think your should look at some lower level education videos." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1868.0 0.0 0.0 0.0
"15:02 interested information inside matrix - eigenvalues" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 447.0 0.0 0.0 0.0
"I agree. during the period i was introduced to calculus, i had no problem with the derivative, but did so with the integral, because it didnt seem very intuitive to me. it shocked me that knowing the area under a curve of a function only depended on two points. and teachers or textbooks didnt realy explain why that was. it seemed shocking to me at the time. but with further investigation i found out all the terms between canceled out, and that helped my thought so much." 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5033.0 0.0 0.0 1.0
"Months later, I'm doing the exact same thing." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7692.0 0.0 0.0 0.0
"I am not in the class but I still watched the first 13:20 minutes" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 5125.0 0.0 0.0 0.0
"I would love a board like this. My actual teachers write so fast and they just erase the whole thing before I have time to copy. (I write slow)" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6264.0 1.0 0.0 0.0
"So clear the explanation is that for a simple matrix (3X3) I can directly flush out the inverse matrix given the multiplier at each elimination step, without going thru matrix inverse and multiplication. 
Here is the process:
(1) Flip the sign of multiplier at each elimination step. 
(2) Directly add it in the L matrix in the same position (index) of L. 
In the example of 18:00, flip (-2) I get 2, then add 2 in position L[2,1]; flip (-5) I get 5, add 5 in position L[2,3]. So I got L.

BTW, another way to understand that L is better than E is that: 
(1) When producing E, there are interfered operations happening and thus a new (implicit) relationship between row1 and row3 is formed. As a result, a new entry (10) is appearing to reflect the newly created (implicit) relationship among row1 and row3, as shown at the position E[3, 1]. 
(2) When producing L, the operations are in the right order that there are no interfered operations thus no implicit relationships were generated. So we can just plug in the multiplier (the entry) directly to L, without worrying about missing any entries. 
(3) As a side note, the entry value tells about the multiplication, BUT more importantly, the index of each entry tells about he the relationship between rows. Eg. In matrix E32, the entry E[3, 2] = -5, it means the change coming from row2 to row3, with (-5) as the amount. Getting an explicit explanation on the role of entry indexes helps a lot to build some intuitive in a long run.

Thank you Dr. Strang. You are the hero of Linear Algebra!" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 8746.0 0.0 0.0 0.0
"Excellent lecture" wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3650.0 0.0 0.0 0.0
"when you realize that guy must have missed over 20 lectures in a class of only 24 lectures" mc1y8m9-hOM "22. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 15216.0 0.0 0.0 0.0
"Great lecture, and what I can commit is just 'like it' and 'comment'. 
Without any payment like other MIT students, This is huge opportunity.
Thanks for sharing this greatness with world. As we grateful, let's do study hard. :)" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4277.0 0.0 0.0 0.0
"There are so many moments when I wanted to give this video an extra LIKE! He's such a good teacher!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10356.0 0.0 0.0 0.0
"화이팅! 2020" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 15694.0 0.0 0.0 0.0
R QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8485.0 0.0 0.0 0.0
"Turns out I'm dumb." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11103.0 0.0 0.0 0.0
"can anyone explain to me what the dx in the indefinite integral stands for? Ive heard that it can be interpreted in different ways." -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12603.0 0.0 1.0 0.0
"A lot of examples in this video that show why the cameraman would be better if he/she could follow the subject matter - the camera is left showing the wrong part of the blackboard." TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 2136.0 1.0 0.0 1.0
"Thanks a lot prof Strang, the way you explained transposes is so clear. I can't thank you enough. " JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9662.0 0.0 0.0 0.0
"Thank u sir" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9075.0 0.0 0.0 0.0
"nao consigo assistir aos videos.
gosto muito de matematica mas de vido ao trabalho estou a assimilar pouco preciso de aulas virtual." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14012.0 0.0 0.0 0.0
"a very clear, no wishy washy lecture on Bayesian Statistical Inference" 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 12294.0 0.0 0.0 0.0
I=Lu MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 6443.0 0.0 0.0 0.0
"There is always a piece of chalk in his pants pocket" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10369.0 1.0 0.0 0.0
"2:46, guy next to white shirt ded lol" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 871.0 1.0 0.0 0.0
"Great lecture" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4245.0 0.0 0.0 0.0
"The only issue I have with Calculus currently is a fundamental one.  Basically, the entire premise relies on shaky ground...a limit.  This is an approximation.  In theory, you never achieve an exact answer, because you have to make an uncertain assumption that as you actually plug in zero, the exact answer is achieved.  This is the flaw of trying to describe a continuous space with descrete mathematics." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10212.0 0.0 0.0 0.0
"It helps a lot Polytechnique Montreal students, cuz we re using Gilbert Strang book translated and course" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 6918.0 0.0 0.0 0.0
"This lesson is so good. But I would suggest that he takes a short pause from time to time. It is tiring to listen continuously." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 10839.0 0.0 0.0 0.0
"42:28 pure beauty" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 1182.0 0.0 0.0 0.0
"At 5:38, what if b is not in column space nor perpendicular to column space?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 2692.0 0.0 1.0 0.0
"34:38 برهان مهم جدا" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 985.0 0.0 0.0 0.0
"His way of teaching is very engaging and intuitive. He kind of eases the viewers into the topic and makes them visualise bit by bit until he and the viewers both arrive at the same conclusion and understanding. To me that's art. Not too many professors or any kind of speakers for that matter are able to do that. One can also view his love and fascination for everything he teaches. It's just great. Thankyou for your lectures professor Strang. 👍👍👍" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4768.0 0.0 0.0 1.0
"I have a question, he said that if we rewrite the matrix as 
R = [ I  F
         0 0]
and if the nullspace is N = [ -F
                                                 I]

then RN = 0. But when you do the multiplication you get : -IF + FI, but I and F are matrices which means that FI and IF are not the same. So what's going on here?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 5505.0 0.0 1.0 0.0
"Wow!! What an amazing professor. I'm in the middle of his course on Linear Algebra, pursuing knowlegde to get a better base for studying Machine and Deep Learning in the near future. Guess I'll rush it a little bit, got very anxious to start this new one hahah sounds spetacular. Thank you MIT and Professor Strang <3 cheers from Brazil" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12057.0 0.0 0.0 0.0
"the joke about Hillary and Monica...Strang BASED" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 14703.0 0.0 0.0 0.0
" his name is John N. Tsitsiklis.
check how great this scientist by clicking mit.edu/~jnt/home.html
I am from yemen.I really just want to appreciate the knowledge he have and how much he gives. 
 I never heard someone like this miracle. I starting loving probability" mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 10.0 0.0 0.0 0.0
"I watched this once, taking all notes. Then watched it again (with break) without taking notes. Then I read my notes (after a break). The lecture's quite good! Btw for those that thought the second derivatives thing came out of left field, Du is the directional derivative operator, so you want Du( Du( f(x1,x2,...,xn) ) ), which gives the expressions for x^T*A*x for a connected f and A. This tells us that x^T*A*x is like a second order operation for the derivative of a function when A is the Hessian (matrix of second derivatives) of said function f(). This wasn't clear to me initially so I was kinda lost. Best!" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 6186.0 0.0 0.0 1.0
"5:14 how many rows must a man walk down.." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1360.0 0.0 0.0 0.0
"Ze Vectaire.... love it" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12272.0 0.0 0.0 0.0
"is it possible to post old tests, exams or assignments?  t'would be much appreciated." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 13640.0 0.0 0.0 0.0
"This is awesome" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10642.0 0.0 0.0 0.0
"fattar noll" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12852.0 0.0 0.0 0.0
"Second half start" 1VhnDdQsELo "14. P and NP, SAT, Poly-Time Reducibility" "MIT 18.404J Theory of Computation, Fall 2020" 8610.0 0.0 0.0 0.0
"This is another masterpiece by the grand dragon of mathematics DR. Gilbert Strang. I did not have any professor at the University of Maryland College Park in Mathematics and Electrical Engineering  in the 1990's that makes math and science easy to understand. This professor is incredible in every math lecture/video at MIT." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 10638.0 0.0 0.0 0.0
"man this guy is awesome. you can def integrate the function at @20:20 just use a Weierstrass substitution!!!!" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13902.0 0.0 0.0 0.0
"Give a lot of examples, very helpful,  still useful now" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4047.0 0.0 0.0 1.0
"Thanks very moch Teacher for your excelent informeison about the ecuecion’s linears." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 9815.0 0.0 0.0 0.0
"I Really Like The Video From Your Path independence and conservative fields." z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4967.0 0.0 0.0 0.0
"he is a legend" 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 13088.0 0.0 0.0 0.0
"What is meant by energy whe X^t S X multiplication is carried?" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11520.0 0.0 1.0 0.0
"Amazing!  The closing example is mind-boggling:  a concrete illustration of how probability applied to social sciences can be far trickier than simple coin-flipping or die throwing..." 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 2399.0 0.0 0.0 1.0
"at 4:45 he is drinking a coffee. Do we need a coffee for his lectures??" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 12462.0 0.0 0.0 0.0
"That's some tight chalkboard manuscript" 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9940.0 1.0 0.0 0.0
Thx. nrDkb2MAwSA "20. Definitions and Inequalities" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11011.0 0.0 0.0 0.0
"I didn't know teachers of STEM could speak in clear, logical English  (or any other natural language)." 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 5274.0 0.0 0.0 0.0
"Old people are really our pride" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8056.0 0.0 0.0 0.0
"i finish the course at Germany 06.11.2020 watch this in last 5 day with 1,5x speed. inspiring me alot, thank you Dr. Strang." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 13379.0 0.0 0.0 0.0
"nice lecture but i can always hear COS product rather than CROSS product..." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14043.0 0.0 1.0 0.0
"On 45:55 he says that any two linearly independent vectors would span the C(A). But these two linearly independent vectors should also be in C(A) he forgot to mention that i think. Because (1,0,0) and (0,1,0) are linearly independent but they do not span C(A). I listened carefully that part 3 times before writing this comment but maybe I missed it." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 8066.0 0.0 1.0 0.0
"kookoo transpose" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 13755.0 0.0 0.0 0.0
"The Einstein field equations state that the superpostion principle will not work on gravitational fields. So using the formulas at ~41min wouldn't take relativity into consideration :)" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9961.0 0.0 0.0 0.0
"I love when he erases the blackboard." WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5842.0 1.0 0.0 0.0
"If only my high school teacher explained this well." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6511.0 0.0 0.0 0.0
"At 42:17 why does multiplying each side by A^T change x?  In other words why isn't x equal to x_hat?" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2668.0 0.0 1.0 0.0
"@TaMoPerdidoMsMo math" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1737.0 0.0 0.0 0.0
"great video." TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 13016.0 0.0 0.0 0.0
"Could anybody explain me why the hight of each block is 1 in the pyramid trick?" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3224.0 0.0 1.0 0.0
"my english is not good enough but this guy teaches better than my teacher speaking my native language" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 13978.0 0.0 0.0 0.0
"I love mathematics, because I like  true reasoning, the problem seems to be the language, I told my friends that I saw more truth in 3dMax of Autodesk because its language is perfect, they use objects, transformation, parameters, functions... but all these words are always in the right place, here I have no problems understanding, geometry, algebra, arithmetic, the problem arises when different variables come into the ecuation and notations are not rigurous such as confusing a line with a plane" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5764.0 0.0 0.0 0.0
"integrating 'x^-1' ... produces Ln(x) ... obviously this is a unique function.  This lecture holds insights but I'm going to have to read up on integration more & more to appreciate this lesson.  Many of these lessons can not be grasped without prior study , in my opinion" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13613.0 0.0 0.0 0.0
"LOL at 38:55 MIT really ?" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7233.0 0.0 0.0 0.0
"Is he alive?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 6769.0 0.0 0.0 0.0
"Hi, when is the rest going to be uploaded?

THANK YOU MIT
I Passed Calc 1, now awaiting Calc 2 integration.

Best supplementary lesson." -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4730.0 0.0 0.0 0.0
"nice video" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14052.0 0.0 0.0 0.0
"Gilbert Strang is a FREAK" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 4017.0 0.0 0.0 0.0
"Thank you Dr. Tsitsiklis. This lecture is a masterpiece." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 9105.0 0.0 0.0 0.0
"Thanks mit for those lessons. I'm a hummble boy from a country área and now I have access to the BEST math lessons" 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9753.0 0.0 0.0 0.0
"sweet, did this like a term and a half ago in higshcool. aced the test for it too :D
gosh calculus is awesome!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14429.0 0.0 0.0 0.0
"MI freaking T!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7497.0 0.0 0.0 0.0
"@GreenAms Ah, I have to look over that again. Thanks for the reminder" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1625.0 0.0 0.0 0.0
"This guy is extremely thorough and the ""simplicity"" of the material is only a testament to his teaching ability. He's teaching vectors, and its not like ""mit vectors"" would be something different, special, or requiring genius to understand simply because the school has a prestigious reputation. If your school's reputation isn't as recognized as mit's your frustration should be directed towards the morons who can not appreciate anything other than what someone else tells them is the ""best.""" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10528.0 0.0 0.0 0.0
"8:44 Spotted a mistake, awards the student with an A in the course. lol." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1423.0 0.0 1.0 0.0
"Wow , feels nice to hear a statistics lecture from an MIT professor peeping from ceiling" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 12025.0 1.0 0.0 0.0
"listening to this on headphones; is there an issue with the audio?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 13810.0 0.0 0.0 0.0
"I'm just in 11th grade will I understand theses lectures?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6340.0 0.0 0.0 0.0
"In what year is this taught ? I'm unfamiliar with this way of listing lectures" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 6695.0 0.0 0.0 0.0
"awesome!! Greetings from Peru" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 12497.0 0.0 0.0 0.0
Cilindet tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3150.0 0.0 0.0 0.0
"@someonep93 How do you know?" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2021.0 0.0 0.0 0.0
"I Really Like The Video Lecture 16: Differential equations, separation of variables From Your" 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4983.0 0.0 0.0 0.0
"I stopped studying algebra 2 when I was in the 7th grade, and that meant I was in Mr. S class for 2 years" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 5974.0 0.0 0.0 0.0
"Poor Schmidt. Legacy ruined." 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 8228.0 0.0 0.0 0.0
"That was mathematics." MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9922.0 0.0 0.0 0.0
"Textbook problem13 . If e components of e=b−Ax  averages to zero, then so does (  A^T * A)^(−1)  * A^T  *  e.   Why?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 9037.0 0.0 1.0 0.0
"It is just fantastic !!!
Thank you !!!!" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 6953.0 0.0 0.0 0.0
"Great lessons," FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4314.0 0.0 0.0 0.0
"don't all speak at once :)))" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 12770.0 0.0 0.0 0.0
"@ 13:14, ""But, on the other hand, this formula here, I mean, you probably have a

right to expect some reason for why this works.""

My only wish is that ""teachers"" around the world understand and work with this principle!" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1467.0 0.0 1.0 0.0
"Full circle mate haha" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 3949.0 0.0 0.0 0.0
🐐 or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15698.0 0.0 0.0 0.0
"In france we do this at 16 years old !!! How old are they ?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6634.0 0.0 0.0 0.0
"this is really helpful, which makes me feel math is not so conceptual" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14872.0 0.0 0.0 0.0
Excellent!!!!!:) 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 3690.0 0.0 0.0 0.0
"Great lecture but itd be cool if the camera movenment is less. He writes reasonably clear and very neat. Great prof too" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 4250.0 1.0 0.0 0.0
"Thank you Camera man too !" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 9096.0 1.0 0.0 0.0
"This professor has always been able to clear my confusion on these higher level math courses." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10893.0 0.0 0.0 0.0
"Unfortunately I didn't get anything x(" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 11122.0 0.0 0.0 0.0
"I understand previous lessons very well but not this one" Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6120.0 0.0 0.0 0.0
"@44:25 2 (2 (2 (2 (2 (2 + 1) + 2) + 4) + 8) + 16) + 32 = 256 ， not 6×32 = 192" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 1560.0 0.0 1.0 0.0
"Love you MIT from India" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7463.0 0.0 0.0 0.0
"I am terrible at Math, but need to take statistics. I am a hard worker though. Any advice? Is it impossible to master for someone who isn't good at Math? :(" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 5147.0 0.0 0.0 0.0
"Love your content.. 😃" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7472.0 0.0 0.0 0.0
"einstein could do it :D :D :D aşsdkalskdaşlkasdka" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 12792.0 0.0 0.0 0.0
"Funny and very intuitive lecture" _CdoRiNSrqI "Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3958.0 0.0 0.0 0.0
"Thanks a lot to the camera guy ...amazing tracking" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9665.0 1.0 0.0 0.0
"I figure out why he looks different. He's not wearing a tie! Instead he's wearing a blazer" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5404.0 0.0 0.0 0.0
"Fuck statistics!!" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3942.0 0.0 0.0 0.0
"Hey people from the future that are watching this series just as me" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4694.0 0.0 0.0 0.0
"the professors rocks. what a stunning illustration. I wish i were present in his lecture" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14730.0 0.0 0.0 0.0
"take a shot every time he says ""I claim""" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14432.0 0.0 0.0 0.0
"19:38, that Rembrant reference though 😎😎" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 564.0 0.0 0.0 0.0
"@hellomate639 

Good for you and your university. :)" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 1864.0 0.0 0.0 0.0
"Professor Strang !!! You are my hero !! lots of hugs" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8334.0 0.0 0.0 0.0
"@GowanBray Well ok .... allmighty America :D.... we don't have money to finance research... i think it will take a bit to have Motor driven power Blackboard... :D Anyways a blackboard is a blackboard...the basic ones are fine.. all u need to know ...is what to write on them..and somebody that understands what is written ;)" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1624.0 1.0 0.0 0.0
"I may be stupid but, whats so different about him in teaching? I didnt understand my teacher when he taught this to us, and other things in Linear algebra too. And since everyone is praising this guy, I thought he teaches differently, but still I'm not understanding anything again, maybe Im just stupid and never will get LA." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5869.0 0.0 0.0 0.0
"Great lectures (19/20) but same remark than in lect5, there is great confusion between VECTOR SPACE and AFFINE SPACE, and in particular between the AFFINE ORIGINE (0,0,0) and the 0 VECTOR. The 0 vector is NO WHERE. He's NOT living in affine space. Actualy this aparent paradoxes can only be overcome by driling to the heart of the true definition of a vector space. For the 1-dim vector space, they are by serious definition an EQUIVALENT CLASS of infinitely many parrallel affine lines that fill the entire plane. Similarely a 2-dim vestor space is an equivalent class of infinitely many parallel affine planes that fill the entire 3-space R^3. The key word is thus, REPRESENTATION (Vorstellung in German). An affine line is a particular REPRESENTATION, a ""minister"" of a ""King"" which give the DIRECTION : the 1-dim VECTOR SPACE. Similarly an affine plane is a particular REPRESENTATION, a minister of a ""King&Queen"" which fix the TWO-DIRECTION : the 2-dim VECTOR SPACE" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 4302.0 0.0 1.0 0.0
"41:44... Clinton jokes" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 1161.0 0.0 0.0 0.0
"Lecture on higher order differential equations are available??????" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7294.0 0.0 1.0 0.0
"Why am I only finding this now?

This might be the difference between passing and failing 18.01 for the first time since I took it in 1972. 

Paul Bradford ‘76
(second time around!)" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11772.0 0.0 0.0 0.0
"excellent course, thank you professor" lWW54ts9Ubo "24. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 12819.0 0.0 0.0 0.0
"thank you :)) 
you are amazing " 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 14475.0 0.0 0.0 0.0
"Technically the set of all infinite binary strings maps to the any countably infinite set such as the integers or the rational numbers, but not the real numbers." gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 9024.0 0.0 1.0 0.0
"Good old days at cs university..." IycOPFmEQk8 "5. CF Pumping Lemma, Turing Machines" "MIT 18.404J Theory of Computation, Fall 2020" 4149.0 0.0 0.0 0.0
"His existence is a gift for seekers of knowledge!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4748.0 0.0 0.0 0.0
"thank Sir....!
I guess that not all MIT lecturers are great but I am very sure this guys is really amazing. I like him" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 14449.0 0.0 0.0 0.0
"Thank you MIT .. for these Quality content ❤️❤️ ,,, thanks a lot ❤️❤️❤️❤️ I can't describe my respect for you 🙏" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9126.0 0.0 0.0 0.0
"At 10:27 how are we calculating E21( elimination matrix)?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 2584.0 0.0 1.0 0.0
"Is he french?" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6772.0 0.0 0.0 0.0
"LOL ""for like, 48 different reasons, that determinant is zero. so this one is dead."" Heehee. Amazing video and series - thank you!! :)" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 7230.0 0.0 0.0 0.0
"50:30 lol" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 1338.0 0.0 0.0 0.0
"The Basis of Statistics & It's Technique
https://youtu.be/mC4cWH7SavY" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 9956.0 0.0 0.0 0.0
"everyone wonder why the professor didn't write ln y as ln |y|. my main language is not English but I watched the video four times to understand completely. very critical to sum up the part of the video's interval 14:30 - 19:00 . When is used the non-linear approximation, something should seem unnecessary for a short time.For example, If ve implement the y = 0 on the where equation beginning is dy/y the method won't be operated. professor said you will always face with these problem. if we consider all thing earlier, solution couldnt be reach ant useful information. the solution requires more information like y(0) = 3. Then the solution could be more considerable. I think professor wants to teach only solution approach at that part. This is my thought. if I am false please reply the true perspective of the solution." 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12807.0 0.0 1.0 0.0
"14:45: such as beautiful picture" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 438.0 0.0 0.0 0.0
"im a CSE student from india and litrally These videos are proving that Why MIT is best in the world...." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13562.0 0.0 0.0 0.0
"@Lemnirot u are right..but what if u look @ the two first rows? its also the same.." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 1659.0 0.0 1.0 0.0
"The problem shown in the video at 13:22 can't be found anywhere at http://ocw.mit.edu/18-02F07..." U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10238.0 0.0 0.0 0.0
"2:45
5:25 leaving out RHS
12:33

Cleaning up the 3-2 position" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 870.0 0.0 1.0 0.0
"MIT is the best.  thank you MIT !!!" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7534.0 0.0 0.0 0.0
"I dare him to prove the other letters in the alphabet as well. Him proving ""e"" is not enough. I want to see him prove 'f', 'g', 'h', and so on. That is the real test for a mathematician." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5255.0 0.0 0.0 0.0
"1.  Are students permitted to arrive late for lectures thereby disrupting the attention of other, more courteous students?  2.  Must every sentence start with ""so?""" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 321.0 0.0 0.0 0.0
"First to comment lol" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 3820.0 0.0 0.0 0.0
"Thankyou Professor." MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9866.0 0.0 0.0 0.0
"In other places, the DFT matrix has a minus in the exponential  (https://en.wikipedia.org/wiki/DFT_matrix). What am I missing here?" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 6650.0 0.0 1.0 0.0
"It's interesting that some professors still write a bunch of definitions and equations on a chalk board the way it has been done for well over 120 years.  A lot of that could be written out and provided to the students before class; this would permit the professor to spend more time answering questions and analyzing the information during class." uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 7051.0 1.0 0.0 0.0
"Dove chocolate is not smooth as silk. This lecture is. indeed" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 3491.0 0.0 0.0 0.0
"I love this man!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5826.0 0.0 0.0 0.0
"i watch 3 lectures of his every week.  This is amazing." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13491.0 0.0 0.0 0.0
"I thought Walter Lewin is awesome.Seeing this prof. I feel continuing.Awesome!!!!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6089.0 0.0 0.0 0.0
"Professor strang is master of teaching
He is an artist.
His way of teaching is a masterpiece.
Thank you Sir.
Respect, from India" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8401.0 0.0 0.0 0.0
"One awesome thing we can do is to skip certain parts if you knew / don't care about them. I wish I could do this in real life with real professors (lol)" ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 8073.0 0.0 0.0 0.0
"nvm lol you corrected it.... I hate the new youtube layout." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14094.0 0.0 0.0 0.0
"My greek professor should watch this. Thanks to this Professor Gilbert Strang!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 7757.0 0.0 0.0 0.0
6:22 srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 1382.0 0.0 0.0 0.0
"Amazing lecture. Thanks from Italy" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 2376.0 0.0 0.0 0.0
"how old is he!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 13247.0 0.0 0.0 0.0
"18:00 - have been fascinated by Dr. Jerison's lecture series, but at this particular moment the lead to the use of quadratic approx. is unclear to me." eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 525.0 0.0 1.0 0.0
"If I see the drawing of the vector field, how can I interpret it as he did with the example 8:48?" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6473.0 0.0 1.0 0.0
"Gonna remember 18.02 for a long time!! Will miss you professor!!!t this makes me sad" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4106.0 0.0 0.0 0.0
"Do maths/science/engineering students take this class or some other multivariable calculus course like 18.024?" WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3409.0 0.0 1.0 0.0
"Thank you so much! Professor Strang and MIT OpenCourseWare for making this happen! you are amazing! you made it possible for me to study Linear Algebra during the COVID Time. And this is one of the best Math I have ever taken in my life. I did not take Linear Algebra at college bc I did not like how it was taught. This course is the perfect one that I was waiting for. It's simple and beautiful, intuitive and reasonable! It explains all the logics behind these equations and formulas. It's the essence of it! I Thank you VERY MUCH!         -  LOVE!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9386.0 0.0 0.0 1.0
"thank you very much prof, very good lecture" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 14525.0 0.0 0.0 0.0
"In the 3X4 matrix example, shouldn't the dim Null(A transpose) be 4-2= 2 instead of 3-2=1?" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6656.0 0.0 1.0 0.0
"Why does everybody hates Taylor's Series.They are a live saver and allow you to do so much with a little work." dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 11837.0 0.0 0.0 0.0
"Why so much noice? no wonder why too few views compared to earlier lectures." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 11911.0 0.0 0.0 0.0
"Thank you SIR." hwDRfkPSXng "Lecture 32: ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9230.0 0.0 0.0 0.0
"🎉🎉🎉🎉🎉🎉🎉been waiting for this for a long time" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 15697.0 0.0 0.0 0.0
"Excellent lecturer with great style.  Jimmy Stewart teaches linear algebra." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3662.0 0.0 0.0 0.0
"what's the intuition behind 'Ax = b has no solution, however Transpose(A) Ax = Transpose(A) b has a solution'. 
I am having a hard time" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 15194.0 0.0 1.0 0.0
thanks sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14546.0 0.0 0.0 0.0
"professor Strang helped me for my entire linear course, thanks!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 14217.0 0.0 0.0 0.0
"老爷子万寿无疆！Gilbert is God!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15653.0 0.0 0.0 0.0
"Man, there is a LOT of coughing happening in the background. In 2021, if someone is coughing that much then clear the fucking room!" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 7586.0 1.0 0.0 0.0
"why this lecture is not being downloaded on Idm?
" aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15371.0 0.0 0.0 0.0
"the explanation starting at 25:10 helped me understand what a positive definite matrice is" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 14688.0 0.0 0.0 1.0
"Just my opinion -- If you want to appreciate these lectures, it is better to concurrently take a Physics 1 & 2 -- There are Prof. Walter Lewin's or Prof. Ramamurthy Sankar's full courses in YouTube. That way, it is very easy to connect the Work, Curl, Flux etc. more easily. This applies to Linear Algebra as well as the lectures are great to understand, but applications get a bit complicated.." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7189.0 0.0 0.0 0.0
"MIT has still got it. What a time to be alive that we can watch this for free" ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7521.0 0.0 0.0 0.0
"I had some trouble connecting the two pictures.  What helped me to understand the connection is rewrite the original equation as Ax = b = e + p.  That means we breaking down b into the error vector and its projection, p, onto A.  We find e1, e2, e3, which are the elements of the error vector, by solving for C and D such as e is in the null space of A transpose." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 5468.0 0.0 0.0 0.0
"this is awesome, Gilbert Strang you save me!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14853.0 0.0 0.0 0.0
"@Impresioniste , in your example r< m :)....the LHS of two equations are not independent." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 1641.0 0.0 1.0 0.0
"thank u sir! u r a true genius" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 14461.0 0.0 0.0 0.0
"Hello sir, can I copy paste your videos for teaching and learning purpose on YouTube? Have any copyright issues?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 4660.0 0.0 0.0 0.0
"I Really Like The Video Double integrals in polar coordinates; applications From Your" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4944.0 0.0 0.0 0.0
"@jxcess3891 ...or the cards have two sides?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1913.0 0.0 0.0 0.0
"Absolutely well done and definitely keep it up!!! 👍👍👍👍👍" feb9j65Iz4w "24. Linear Programming and Two-Person Games" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2214.0 0.0 0.0 0.0
"Gauss would quit, but Jordan says keep going." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3987.0 0.0 0.0 0.0
"Statistics is nothing else
1.deviation
2.mean
Equals, 
Understanding primes
Equals, 
The clay institute statement about riemann hypothesis:
1.The PNT determines the average distribution of the primes. 
2.The riemann hypothesis tells us about the deviation from the average. Average mens statistical mean or 0
Stochastic means 0
Statistis means 0.
Order means 1." 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 8893.0 0.0 0.0 0.0
"proofs are something you can look up in the text book or online. for me, they are also something I see in regular lecture. it's nice that the MIT videos are straight to the point." 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14226.0 0.0 0.0 0.0
"that -2 at 9:00 killed me :(" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14623.0 0.0 0.0 0.0
"45:40 gilbert strang equivalent of leaving a high five hanging" XhSk_Lw2X_U "14. Low Rank Changes in A and Its Inverse" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1259.0 0.0 0.0 0.0
"Oh no, 4:30 beware LGBTQ+!" sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8023.0 0.0 0.0 0.0
"I wish him the very best..." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6223.0 0.0 0.0 0.0
"Jordan Form in 31:10" TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 7142.0 0.0 0.0 0.0
"So abstract. Use examples to help students distinguish between different formulae. Lecturer is well intentioned and I blame the institutions for producing grads who can't apply the content they learn" 4UJc0S8APm4 "23. Classical Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 8738.0 0.0 0.0 1.0
"I'll add this to my watch later list, because I am going to need this when I do Mathematical Methods at UWA next year." dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 6285.0 0.0 0.0 0.0
"If anything stands out from these videos is the teachers humbleness - if this word exists.

They are modest and clear and respectful. And this is so rare these days.

Thank you, MIT!" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 6499.0 0.0 0.0 0.0
"Thank you." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 9539.0 0.0 0.0 0.0
"@fyckthissht Well, these are the non-science majors... ;)" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1844.0 0.0 0.0 0.0
"fking google can't even reply to comments. Anyway ppl may learn this shiet early on in other countries, but once we mature, Americans rush through this stuff really quickly. calc 1 to diff. equations in 2 years. There is a reason why US is the prime hub of innovation and it has a lot to do with our superior high education system." PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12874.0 0.0 0.0 0.0
"This guy is an absolute genius." mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 10522.0 0.0 0.0 0.0
"In u naught = c1x1 + c2x2 .... Cnxn what are X's the vectors of?" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 6693.0 0.0 1.0 0.0
"god i love that chalk " FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12931.0 1.0 0.0 0.0
"the guy who filmed these videos must by now be the best engineer of all times..." tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14697.0 0.0 0.0 0.0
"The discussions are clear and concise. Appreciate  it" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 10078.0 0.0 0.0 0.0
"Great now I have to watch all of these again." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4317.0 0.0 0.0 0.0
"thanks for the excellent explanation..." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14582.0 0.0 0.0 0.0
:) nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1448.0 0.0 0.0 0.0
excellent！ IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 12831.0 0.0 0.0 0.0
"where can i find the proof of procrustes problem?" 0Qws8BuK3RQ "34. Distance Matrices, Procrustes Problem" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15230.0 0.0 1.0 0.0
"nice papa :3" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14047.0 0.0 0.0 0.0
"Thanks for the details prof." l4NoMKEHQwM "11. Derived Distributions (ctd.); Covariance" "6.041 Probabilistic Systems Analysis and Applied Probability" 9710.0 0.0 0.0 0.0
"Thank you, Prof. Auroux and MIT! I learn it from lec 1 to the lec 32. 兴隆--2017.11.12" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9508.0 0.0 0.0 0.0
"Can MIT OCW please make short video lecture series complemented with interesting problems, so that it is easier and more effective to learn?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3008.0 0.0 0.0 0.0
"Since all eliminations must be done by computers for large matrices, intuitive approaches fail quickly. So, precise rigorous algorithms are the only practical way to do elimination. Gilbert Strang style defies the rigorous approach, and does it on purpose to breath life into the dull process of elimination." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 8678.0 0.0 0.0 1.0
"Literally ,the legend of linear algebra" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 7389.0 0.0 0.0 0.0
"This lecture needs to reach more people asap.
Total respect for the Professor!" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10821.0 0.0 0.0 0.0
rangle UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14243.0 0.0 0.0 0.0
"Great video!!! helped me alot in Embedded System for DSP course ... " JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4355.0 0.0 0.0 0.0
"very clear, many thanks" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14999.0 0.0 0.0 0.0
"Lovely and well-deserved applause!" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7485.0 0.0 0.0 0.0
"i feel honored to be able to listen to a MIT, math professor. I am trying to teach myself calculus this summer but his lecture is kinda advanced for me at this moment. lol." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13374.0 0.0 0.0 0.0
"What a disappointment after 18.06.... - I don't know what this course is for and what this lecture is aiming to achieve. I shall stop here after 13 lectures. Anyone familiar with courses covering the math that's related to machine learning? Not popular science basics - but deep dive?" z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11403.0 0.0 0.0 0.0
"I think Prof Jerison mixed up the Hare with the Tortoise in this one. The Hare is the one playing catchup, not the Tortoise (in the original, it was Archilles trying to catch up with the the Tortoise)." wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6000.0 0.0 1.0 0.0
"he is a good teacher.." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13086.0 0.0 0.0 0.0
"I have found some little mistake in those questions solutions which is about the area of enclosure.Ex1" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5527.0 0.0 1.0 0.0
"suppose that in all computer science universities around the world the lecturers teach like this. surely students will understand and be happy with mathematics" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 14425.0 0.0 0.0 0.0
"My Lord this man is so laborious to listen to" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7733.0 0.0 0.0 0.0
albegra? HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12320.0 0.0 0.0 0.0
"Professor, my gratitude 🙏🏼 from somewhere in the middle of nowhere in brasil. You are a treasure among humans. Thank you sir" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8405.0 0.0 0.0 0.0
"explanation is amazing" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 12833.0 0.0 0.0 0.0
"Hi, anyone know how did p=xa become p=ax. 

aTb/amag^2 a = aaT/amag^2 b ?" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4723.0 0.0 1.0 0.0
"At 24:29 a student asks a very elementary algebraic manipulation question, nothing beyond class 6 in India. Is this really MIT?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2620.0 0.0 0.0 0.0
"Pure gold. Amazing to hear that emphasis in LinAlg has been shifting until so recently (Jordan out of fashion, SVD to the forefront). Because of computational characteristics?" TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 8461.0 0.0 0.0 0.0
"I can't find lecture summary, anyone please help..." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5217.0 0.0 0.0 0.0
"What John Sheley did was beyond questioning the usefulness of Linear Algebra...he denounced the entire realm of academia. Little bit of a discrepancy there...

I don't think that his absurdly detrimental insinuations should be taken so lightly...

Burn him! He's conspiring with the devil! RABBLE RABBLE RABBLE" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11384.0 0.0 0.0 0.0
"@sponsoredwalk1 He does the exact same thing at 7:47. You surely passed out some seconds before this :)" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2025.0 0.0 0.0 0.0
"he's fabulous" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13122.0 0.0 0.0 0.0
"Thank you so much Pro Strang let me realized how beautiful mathematics can be!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9355.0 0.0 0.0 0.0
"He’s crazy smart" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4702.0 0.0 0.0 0.0
"Thanks professor strang, really useful!!" rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9766.0 0.0 0.0 0.0
"I really have learnt all of thesein high school but my teachers never explain it clearly but rather force me to remember the equations and do the problems. That ways of study left me lots of knowledge gaps. I should have realized it earlier. 😭😭😭" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5919.0 0.0 0.0 1.0
Wow Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12021.0 0.0 0.0 0.0
"Can someone explain to me the relationship between implicit differentiation and taking the total differential of a function? Is it that with implicit differentiation the function is set equal to a fixed point? THANKS!" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3073.0 0.0 1.0 0.0
"curve skething" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12699.0 0.0 0.0 0.0
"Can anyone tell me what's the age of the students taking this course and what are they studying? " FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3047.0 0.0 0.0 0.0
"Thank you Dr. Strang, it was your course that introduced me to algebra back in high school. - from University of Toronto, after quantum mechanics final exam" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9102.0 0.0 0.0 0.0
"Dear Professor Strang...  Please make many more interesting courses for the next 1000 years." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3331.0 0.0 0.0 0.0
"what is the text book for this course
" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15172.0 0.0 0.0 0.0
"Maza aa gaya bhai!" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 7643.0 0.0 0.0 0.0
👍👍👍👍👍👍👍👍👍 J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 15710.0 0.0 0.0 0.0
"Legend 🙏" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7321.0 0.0 0.0 0.0
"... only because he was born earlier... and died earlier .... )))))))))) I fond of his comments... This is how I call ""to make digits interesting to look at ..."" !!!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 262.0 0.0 0.0 0.0
"bro his rhos are so ugly" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12560.0 0.0 0.0 0.0
"Does it count as breaking the fourth wall that he talks about compression of this video?" 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 3456.0 0.0 0.0 0.0
"TBH, I did not like his method of teaching it's too abbreviated. It's like the student there were master hahaah maybe and maybe I am the problem. Good Luck." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8977.0 0.0 0.0 0.0
"False. kilowatt-hour *is* a unit of energy.

How about *you* use the metric system and learn what the units actually represent.

Nice fail, sir." jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3724.0 0.0 0.0 0.0
"@10243406 not actual idiots. i was actually responding to another person's comment. i was being somewhat exaggerated." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1494.0 0.0 0.0 0.0
"The thing I really like about these old timer Professors are the way they teach, he stops and ask questions as if he is also going through the problem he already knows everything but in the moment he is walking through us students and trying to look problems through our eyes, I would say this is the greatest method of teaching." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10301.0 0.0 0.0 1.0
"At 13:17-13:28 he wanted |U| = s, whoever did the lecture notes writeup for this class fixed it there.

I had to watch this lecture twice; the randomized probabilistic construction in the second half seems pretty sophisticated." 4LYom0ekars "4. Forbidding a subgraph III: algebraic constructions" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 2587.0 0.0 0.0 0.0
"he's really funny :)" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13124.0 0.0 0.0 0.0
"The course was extremely useful for me. Thanks a lot.
" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 10063.0 0.0 0.0 0.0
"thank you." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14534.0 0.0 0.0 0.0
"u just sumarized my 12 hours of studying in 50 mins" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 14973.0 0.0 0.0 0.0
"Every Software? That in't really true. Especially in Computer Science there are a lot of areas where you basically will never hear from Linear Algebra again.

But to question the usefulness of LinAlg is of course laughable. " FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3596.0 0.0 0.0 0.0
"I really appreciate this course and I hope complex analysis lectures will come out soon" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 5906.0 0.0 0.0 0.0
"Man... what´s this?? MIT??? This is the most basic Mathmatic Analysis you can find around here (PT) !! 1st derivative??!! That´s Pre-University work... Man, I hope, and I know you´re better than this... I envy you´re pratical appliance of things... that´s a plus, but the theory is WAAYYYY to easy to teach through a University degree!" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7591.0 0.0 0.0 0.0
"which book to refer for this course" l4NoMKEHQwM "11. Derived Distributions (ctd.); Covariance" "6.041 Probabilistic Systems Analysis and Applied Probability" 15250.0 0.0 0.0 0.0
"I don't get it :\" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5306.0 0.0 0.0 0.0
"@brco2003 because the point on the unit circle is given by (cos [angle] , sin [angle] ). Here, your angle is pi/4 . Which you probably know is square root of 2 over 2. But this is just simplified from 1 over the square root of 2, which is the point he has." z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1805.0 0.0 0.0 0.0
"Great video! I love this series. In this lecture, Dr. Strang briefly mentions that the cost of operations for the det(A) will be (n!) He also shows us how the cost of getting A into upper triangular form U will be (1/3)n^3. But from Lecture 2 we know that one way of finding det(A) is to get A into U and then simply find the product of all n pivots. So it seems like the cost for finding det(A) would just be a bit more than (1/3)n^3, perhaps (1/3)n^3 + n. I must be missing something here; any thoughts?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 4353.0 0.0 1.0 0.0
"His lecture on ""ways of looking at matrix multiplication"" changed my life." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4758.0 0.0 0.0 0.0
"Me before watching this lecture: ""Meh, elimination again. What possibly can I learn more about elimination? It's quite simple!""

Me after watching the lecture: ""That. Is. Just. Amazing! Never thought about Matrix Multiplication this way before. Permutation Matrix was a great example to show elimination steps in Matrix form, and not only he did swapping rows but went on and showed us how swapping columns can only be done with right multiplication! This is amazingly mind refreshing. One can really save their mind from Alzheimer by only watching Prof. Strang's lectures :'D""" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7645.0 0.0 0.0 1.0
"Ahh dont you love when the teacher says ""I am going to pick up this guy.."" and the camera just zooms in to the point you CANT SEE WHAT THE ""GUY"" IS!!! ahhhhhhh so good bravo bravo." C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 2285.0 1.0 0.0 0.0
"Just finished the whole 18.01 course. Thank you so much MIT for sharing such good educational resources for free!" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7171.0 0.0 0.0 0.0
"This man is a great teacher!" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10856.0 0.0 0.0 0.0
"@944Nima You need a minimum of precalc. Students usually don't skip multi calc (though they can) because very very few highschools teach mv calc, though they offer an advanced standing exam to skip it if you learned however you did." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1577.0 0.0 0.0 0.0
"49:14 friggin, this is why I hate math. Its too convenient how they make it so that they can get an answer. Maybe I am missing something.

multiplying and dividing(m&d) by 0 is illegal but limits cook up stuff by saying that we are not m&ding by 0 but by a very small ""non-zero number""(non-zero being the key and hence the savior in this step). Ok, that makes sense. 

But right in the very next step, he plugs x to be x0 to make the second thing(or term if you want to call it that) zero. Like in one scenario (x-x0) is not a zero, but in another it is? Why is that fair?

Now it makes sense if that final answer is only an approximation. Meaning that the whole limit actually is not zero, but is very closer to zero. But in the case, does it mean that entire calculus' premise is based on approximation? And that if someone asks me what is the derivative of some function, would I be answering only an approximation?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1305.0 0.0 1.0 0.0
"First video 1.2 M veiws
Second 402k" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3821.0 0.0 0.0 0.0
"i studied these things some 3 years ago and was pretty good at that. but never ever i have gone to such depths to understand these, this guy is a awesome." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13463.0 0.0 0.0 0.0
"Gratitude, respect and love to Prof. Strang  ❤️" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4188.0 0.0 0.0 0.0
"""lecture 1"". " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 163.0 0.0 0.0 0.0
"Thank you" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9080.0 0.0 0.0 0.0
"boner
" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12549.0 0.0 0.0 0.0
45:00 yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 1246.0 0.0 0.0 0.0
"is that why it says spring 2005?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13646.0 0.0 0.0 0.0
"Thank you Sir. This course was very much helpful for ML." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9240.0 0.0 0.0 0.0
"cs


can you imagine this guy teaching trigonometry" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12697.0 0.0 0.0 0.0
"anyone know how you would calculate the probability of x being greater than or equal to 1/2?" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12384.0 0.0 1.0 0.0
"Chalk ❤️" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3139.0 0.0 0.0 0.0
"Sir, you are the best. The way you think and ask questions during the lecture that really helps. I really enjoy your lecture and it really helped me to get my basics clear. I wish you a good health." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8716.0 0.0 0.0 0.0
"1-cosx just changes faster than x, when x -> 0, for example, how is the limit of n^2/n when n->0. Think about it." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 320.0 0.0 1.0 0.0
"Tested corona positive= 𝗣𝗔𝗡𝗜𝗞

After   33:15 = 𝗞𝗔𝗟𝗠" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 9033.0 0.0 0.0 0.0
"According to the course web site, lecture 8 is  the exam session, so I think there is no lecture 8." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2229.0 0.0 0.0 0.0
"I remember being a student and rushing out after class, as these students did. But now at the ripe age of 35, I see these students doing the same and I think ""HOW DARE THEY NOT STOP AND APPLAUD FOR SUCH A MASTERFUL PERFORMANCE""" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 5942.0 0.0 0.0 0.0
"oh damn I circled the wrong thing...lol" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14103.0 0.0 0.0 0.0
"Anyone watching from india ? 🤔" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2512.0 0.0 0.0 0.0
"Before the internet, we spent our days eating each others hair. Thanks, MIT and Professor Strang, for making these videos openly accessible. Learning online has really changed my life." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 2836.0 0.0 0.0 0.0
"This man is amazing. I used to only be able to compute derivatives and limits, but this man made me understand the why and how of it as well." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10861.0 0.0 0.0 0.0
"i am 7 yr old,,, this is VRY EASY HAHAHAH" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13326.0 0.0 0.0 0.0
"I've watched the first 6 videos without difficulty, but I'm confused by the definition and geometric meaning of different norms. Could anyone please tell me which textbook I should read to help me understand?  Thanks for your helping!" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6439.0 0.0 1.0 0.0
"He is really an excellent researcher, but not a good teacher. His explanation is going to make me crazy. I think for the newcomer these lectures are best:
https://www.youtube.com/watch?v=8OcoFcrLm0E" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4532.0 0.0 0.0 0.0
"the lecture is brilliant!" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14710.0 0.0 0.0 0.0
"it's good to see in 1.25x speed" -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 13695.0 0.0 0.0 0.0
"""I try not to lie too much to you... but I do succeed."" >:)" XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 64.0 0.0 0.0 0.0
"To whoever is developing the courses online - Could u edit the video, right where Prof Auroux explains how to find the x and y limits for the triple integral int(dV)?
I understood the z limits but I didn't understand the logic for the x and y limits. If he could add a snippet explaining the limits with a diagram of columns and slices like he did for the double integrals, it would be better.
Thanks in advance and GREAT VIDEOS (though u must be tired of getting that sort of comment by now!)" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11049.0 0.0 1.0 1.0
"Damn, this guy rocks 🎸" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 3307.0 0.0 0.0 0.0
"What are Vector spaces 1:05
Subspaces of R³ 2:33
Is the union of two subspaces a Subspace? 4:23
Column space 11:36
Features a Column space 14:46
How much smaller is the Column space? 15:48
Does every Ax = b have a solution for every b? 16:17
Which b's allow the system of equations solved 19:39
Null space 28:12
Understand what's the point of a Vector space 40:24" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 11463.0 0.0 1.0 0.0
"Absolutely great. If you have trouble getting this, maybe read a book first." WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 2205.0 0.0 0.0 0.0
"""your lecturer is not rembrandt"" HAHAHAH thanks for that" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 196.0 0.0 0.0 0.0
"As much as I may find him to be an excellent teacher, and easy to understand, I cannot rule out that he is more difficult to understand if one has learned english as a second language. Regardless, closed captioning (click the triangle in the bottom right and then click the ""cc"" button) should remove any problems, yes?" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2571.0 0.0 0.0 1.0
"This is so helpful, the whole series. My professor can't teach his way out of a paper bag. I finally understand all of this! These videos are how I am passing my math class! Thank you!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10721.0 0.0 0.0 1.0
"thats the problem with these programms! They have the better teachers not the better pupils!" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14655.0 0.0 0.0 0.0
"Thank you professor Strang💥..." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9320.0 0.0 0.0 0.0
"((e^-3)/Squ.root(2))=0.035 which is approx. not equal to 1-3.5*1 at 39.09" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 213.0 0.0 1.0 0.0
"19:50 why can't a line through the origin be orthogonal to a plane? It looks natural to me, that the z-axis is orthogonal to xy-plane" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 567.0 0.0 1.0 0.0
"It's unfortunate that I use this video to help me fall asleep" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7076.0 0.0 0.0 0.0
"Why don't they just use the ratio test to find the radius of convergence?" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11856.0 0.0 1.0 0.0
"like it like it like it !!!!!!!!!!!!!!!!" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13792.0 0.0 0.0 0.0
"""The natural log is the one that comes out naturally"". Well, yeah, naturally. :D" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 121.0 0.0 0.0 0.0
"I learned a lot from his classes" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5648.0 0.0 0.0 0.0
"This is where it gets really lit 🔥" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10774.0 0.0 0.0 0.0
"Was there an 8th lecture? I can't find it?" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11279.0 0.0 0.0 0.0
"how do you remember all those formulas? I am impressed." a1ZCeFpeW0o "20. Principal Component Analysis (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 13227.0 0.0 0.0 0.0
"@muslim86mus Look what it says right next to the partial differential equations part. If you were hoping for lectures on PDEs, then this isn't the place. This lecture is a review of the material in the relevant unit." ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1957.0 0.0 0.0 1.0
"Nice haircut professor" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 7845.0 0.0 0.0 0.0
"""can I show you the eigenvectors?"" like an mit prof needs permission, lol. I love this guy" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 148.0 0.0 0.0 0.0
"he looks so old than several years ago! I have got so many assists from him in linear algebra." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 13107.0 0.0 0.0 0.0
"If you don't understand professor explanation at 15:00 the angular velocity is 1 because v = wr and v is equal to r basically since r vector rotated 90 degree becomes v; so w = 1" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6542.0 0.0 0.0 1.0
"I hope the person controling the camera could have shown the 2 or 3 boards the professor were talking about, not just simply chasing the professor ....." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5594.0 1.0 0.0 0.0
"they make this stuff all seem so complicated in the way they teach it, its really simple stuff." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14785.0 0.0 0.0 0.0
"Marvellous explanations" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 7597.0 0.0 0.0 0.0
"https://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/ax-b-and-the-four-subspaces/factorization-into-a-lu/MIT18_06SCF11_Ses1.4sum.pdf lecture script here" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 13263.0 0.0 0.0 0.0
"Yeah you can tell how he says his R's he is French not even close to german." 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12123.0 0.0 0.0 0.0
"love this course" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 13882.0 0.0 0.0 0.0
"I  am learning so much more from these lectures than from any teacher I have ever had" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4918.0 0.0 0.0 0.0
"I really like the explanations of memorylessness." -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 5926.0 0.0 0.0 0.0
"It easy wth vietnamese students" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6915.0 0.0 0.0 0.0
"The world has  very few gem of a teacher like Dr.Prof Strang. Thanks for all the effort Prof Strang, I really cherished and appreciated all these 34 lectures." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 10339.0 0.0 0.0 0.0
"John Tsitsiklis is so great teacher!" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 7140.0 0.0 0.0 0.0
"better then an Indian accent" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12540.0 0.0 0.0 0.0
"Thanks again Dr Strang. For those of us coming from the ill posed problems world (a.k.a.Inverse Problems world)  this lecture is both gold and awesome. 
A million thanks" Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9673.0 0.0 0.0 0.0
"@j4ckjs Thanks for the reply. It's just a confusing definition and if you google a bit on orthogonality, you find many other definitions contradicting this one. I think he should have pointed it out more clearly, but at least now I will be cautious when it comes to this topic. I guess that's good enough..." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1895.0 0.0 0.0 0.0
"This guy is good!" nbENJ-Ce7Nc "Lecture 3: Cantor's Remarkable Theorem and the Rationals' Lack of the Least Upper Bound Property" "MIT 18.100A Real Analysis, Fall 2020" 10533.0 0.0 0.0 0.0
"@rmhism Who Takes Calculus In Seventh Grade ? 
Better Yet , Who *Teaches* It ?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1992.0 0.0 0.0 0.0
"Thanks so much for each lecture you provide us, I love your way of teaching. Wish that you live forever and enjoy teaching <3" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9786.0 0.0 0.0 0.0
"long live MIT" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13845.0 0.0 0.0 0.0
"Think of the gaussian distribution...if you think this is easy you might be on the higher end of the curve and the questions you think were easy were targeted towards the average student...but because MIT is so selective their a the average for your xyz college will be much lower than that of MIT's for example my honors math at brown was way more challenging in a way too" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10449.0 0.0 0.0 0.0
"Most of the people don't   know that,Statistics is a subject of Science.🇧🇩🇧🇩🇧🇩 But we can't think any sectors that, where Statistics aren’t use.Thanks a lot for your explanation." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7702.0 0.0 0.0 0.0
"I don't understand. It should be 3 not 5 .  2*1=2 . 2-(-2)=4 . 4-1 = 3 ?  

Can someone help ?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5358.0 0.0 1.0 0.0
"great lecture!" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12984.0 0.0 0.0 0.0
"chinese teachers like to do the things that proceed without predefined variables before glance at audience and small smile thinking take that pupils . don't ask me how to know that because i am a chinese teacher too" YAo1sd4kuOQ "2. Forbidding a subgraph I: Mantel's theorem and Turán's theorem" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 12653.0 0.0 0.0 0.0
"Good Job Professor" CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4112.0 0.0 0.0 0.0
"why are they laughing when the boards move?" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 15286.0 1.0 0.0 0.0
"“Forget the Associate name, not the law”, and, “I’ll let the author deal with that.”😉😉" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15586.0 0.0 0.0 0.0
"Most of the tuition pays for professors, the facility, other faculty, extracurricular programs, some programs don't get enough money. It's just like our government with taxes, they need more money to do the programs that are charitable. " YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7704.0 0.0 0.0 0.0
"My 💓 heart touching thanks to prof Gilbert Stang" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7798.0 0.0 0.0 0.0
+ cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 249.0 0.0 0.0 0.0
"This lecture along with the entire course and you yourself will always remain immortal Prof Strang. 
Thank you from almost the entire world who have benefitted from these golden amazing insightful flawless transitioned lectures. You are a mathematical genius. Hope you read this comment someday and realise you have the biggest Indian Fan." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10782.0 0.0 0.0 0.0
"why sigma 1 is the largest singular value ? Why it's position relate to largest or not ? I dont understand" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15358.0 0.0 1.0 0.0
"Such a beatiful mind... Thank you so much!!! <3" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 8922.0 0.0 0.0 0.0
"yeah this guy is great! 

great stuff... 
regards from australia!" WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15471.0 0.0 0.0 0.0
"Speaking of the plane intersection point, by extension, doesn't it mean a plane's an intersection of two 3-d spaces, and by further extension a 3-d space is an intersection of two 4-d spaces?" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8863.0 0.0 1.0 0.0
"At 5:49, I really liked the way of thinking dx, dy, dz as placeholders for putting values delta x, delta y, delta z in order to get tangent approximation for the function. The differential notation has been a fishy thing ever since I learned it but now it feels less so." 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2694.0 0.0 0.0 1.0
"this guy is an amazing lecturer. his videos have helped me out so much. i wish the camera man was a fraction as good as he is, though." seO7-TwXH_I "Lec 30: Line integrals in space, curl, exactness... | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14819.0 1.0 0.0 0.0
"Love it when prof. Strang says ""OKhay"". Gives me a strange sense of satisfaction!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7444.0 0.0 0.0 0.0
"Before you get into this lecture, better review Tylor series." nvXRJIBOREc "Lecture 21: Minimizing a Function Step by Step" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2838.0 0.0 0.0 0.0
"This lecture is particularly good." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10808.0 0.0 0.0 0.0
"@34:03 Dr. Strang can read minds too!" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 1541.0 0.0 0.0 0.0
"16:31 ""For any other rangle""?" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 479.0 0.0 1.0 0.0
"I always thought econometrics taugh with sums was confusing. I finally found an intuitive way to understand least squares. The minimization  of errors proof is cool, but the simplicity of your proof combining the left nullspace,is awesome; thank you once again professor Strang." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5043.0 0.0 0.0 1.0
"""Deep Cognition"" is written on the blackboard behind Prof. Strang." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 39.0 1.0 0.0 0.0
"I want to cry happy tears." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6137.0 0.0 0.0 0.0
"What a blackboard.....wow" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11394.0 1.0 0.0 0.0
"29:00 30:00 
Plz someone tell me why is he taking -1 when going from P.Q
Same for P.R?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 849.0 0.0 1.0 0.0
"I'm just here to for the sound of chalk striking chalkboard................." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6339.0 1.0 0.0 0.0
"He said he would cover differentiation for every single function. So can anyone tell me why I'm not seeing absolute values?" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4600.0 0.0 1.0 0.0
"I’m in highschool watching this and this is soo helpful. Thank you" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7112.0 0.0 0.0 0.0
"Thanks to MIT and professor Strang. Is 18.06 is prerequisite to this course or it will be covered in this course?" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9801.0 0.0 1.0 0.0
"How to see that the two errors in the two pictures are equal? That is e1 = b - p, e2 = y - c - xd?" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4901.0 0.0 1.0 0.0
"The law of cosine could be proved in several minutes, why he ask to believe in something instead of just give proof?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10158.0 0.0 1.0 0.0
10:45 --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 353.0 0.0 0.0 0.0
"52:15. ""I'm gonna be stop by either the time runs out or the board runs out."" Ha, Ha, Ha" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 1345.0 1.0 0.0 0.0
"43:00 - Summary" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 1193.0 0.0 0.0 0.0
"the angular speed of the wheel was set to 1. That is it completed on revolution in 2pi units of time. The speed we calculated was the linear speed of a point on the wheel." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14658.0 1.0 0.0 0.0
"Yes but how is this useful to most people? Sure some people will use this,and some will every day, but why does someone who works as a truck driver, or a waiter,or a factory worker etc,etc need to know this? This math is only useful to a handful of people/jobs.Why does everyone have to learn this when most people will never once use this in the real world? Also,why are you so mad? I'm asking a simple question. I just think we should be learning more important things." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12136.0 0.0 0.0 0.0
"Fun fact, not mentioned in the video:

If the matrix A is singular, then the process is losing information because two linearly independent vectors in the input space could be mapped to the same output vector, making them indistinguishable. When the professor discussed the matrix for ordinary differentiation of a polynomial function, notice that it was singular. This corresponds to the arbitrary constant of integration i.e. information will be lost, so you save it ahead of time via initial conditions so you can reconstruct the input vector.

Linear algebra is amazing for this kind of insight." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3951.0 0.0 0.0 0.0
"Can someone wipe the blackboard for him?" TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 3103.0 1.0 0.0 0.0
"how can i compute the probability of been at one point before other point, starting from any point. for exemple, been  in point 4 before the point 2 starting at any point?" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 13196.0 0.0 1.0 0.0
"@48:15 Why is sin y considered equal to x as sin is equal to perpendicular/hypotenuse which should be equal to <x/sqrt(1+x^2)>
Am i confused or right
<y = 1/(cos y) = 1/(sqrt(1 - sin^2 y)) = 1/(sqrt(1 - x ^ 2))>" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1566.0 0.0 1.0 0.0
"camera man is stupid" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12591.0 1.0 0.0 0.0
"LOVE  YOU SIRRRRRR................................................................." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7242.0 0.0 0.0 0.0
"(y) excellent doc" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 228.0 0.0 0.0 0.0
"Delta modulation is a way to do the video compression from one image to the next that the professor was discussing. It only encodes changes in a signal. Electrical engineer here who does signal processing, linear algebra is so essential for such a task. These videos are extremely helpful." 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 3343.0 0.0 0.0 0.0
"very organized lecture.thank you prof. Jerison" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15033.0 0.0 0.0 0.0
"wow you fucking serious? dude im female and an electrical engineer. This was my first class freshman year. I would love to see you take the classes I'm taking right now" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15425.0 0.0 0.0 0.0
致敬！ rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15655.0 0.0 0.0 0.0
"I really enjoy this lessons as they allow me to look at mathematics from a different angle. It's nice to see it in a slow paced way rather than studying it on a rush.
" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5913.0 0.0 0.0 0.0
"Thank you !!! I finally completed this course!
This is really a long journey, with more than 34 lectures. I appreciate the elegance of linear algebra during this journey and I will never forget it.
Thank you, Professor Strang. Thank you, MIT OCW." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9090.0 0.0 0.0 0.0
"Thank You !!! Prof. Strang" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9046.0 0.0 0.0 0.0
"@ucrclxl I think this statistics is true. Because I don't think students need to watch again lecture they already have live in uni for second time. I think these videos in major for self learners or those who want to refresh their mind. I am 25 myself and I am not a student." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2055.0 0.0 0.0 0.0
"can anyone provide me notes" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12612.0 0.0 0.0 0.0
"To all those saying that this is the best math instruction ever. I like this guy and find his explanations good and useful, but have had at least 4 professors that were better. I am very grateful for these videos, but don't think this is as good as it gets. this is just what competent math instruction looks like, not excellent math instruction. I hope you guys get to experience first hand really good instruction." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11021.0 0.0 0.0 0.0
18:19 yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 533.0 0.0 0.0 0.0
"thank you teacher" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 14520.0 0.0 0.0 0.0
"17:54 Considering Prof. Strang's art is teaching, he is undoubtedly one of the greatest in the world!" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 520.0 0.0 0.0 0.0
"check how great is this lecturer. I am just from YEMEN>...
mit.edu/~jnt/home.html" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 12651.0 0.0 0.0 0.0
"This course is excellent, so much needed in the modern world." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 10492.0 0.0 0.0 0.0
"i thought i've been taught linear algebra till i met this guy." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 13484.0 0.0 0.0 0.0
"thanks a lot" P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 14562.0 0.0 0.0 0.0
beautiful 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 12515.0 0.0 0.0 0.0
"It's been a pleasure, Professor Strang. Thank you." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 7032.0 0.0 0.0 0.0
"ello sir youre very smart" 3PzuSPQPEU4 "8. Undecidability" "MIT 18.404J Theory of Computation, Fall 2020" 12794.0 0.0 0.0 0.0
"Where did M(2) come from?" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11671.0 0.0 1.0 0.0
"Is he just  making this up?I have no idea what he is talking about,  or why he is talking about it" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 6773.0 0.0 0.0 0.0
"Amazing lesson ♥♥" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2380.0 0.0 0.0 0.0
"this guy is great!!!" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14828.0 0.0 0.0 0.0
"Integration using the Reduction Formula starts at 27:45" aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6720.0 0.0 0.0 0.0
"At 42:10, why is Zigma * used in simulating M, can't we just directly use A to do it?" TTArY7ojshU "6. TM Variants, Church-Turing Thesis" "MIT 18.404J Theory of Computation, Fall 2020" 2666.0 0.0 1.0 0.0
"Mind blowing!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7667.0 0.0 0.0 0.0
"@Ourologos The point of learning this in high school is to get a early start.  Calculus in high school is not the same as calculus in college (as I learned the hard way).  The work is harder, workload is harder, tests are 10x harder.  Teacher doesn't spend a whole lot of time on things you don't understand.  Don't understand it?  Go back to your room and read.
You learn some of this in high school so you won't get a F in college." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1698.0 0.0 0.0 0.0
"I won't understand people who disliked this videos. I haven't liked revisiting a topic, unless it is from Deep Learning. But this! This is a gem that I will revisit my entire life, any given day. 

Bored? Pick a topic from this series.
Depressed? Pick a topic from this series.
Need inspiration? Pick a topic from this series.
Time on your hands? Still need a hint?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 6239.0 0.0 0.0 0.0
"I can't explain in the words that how much your lectures have changed the way I study. I hope to see you one day and thank personally." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 5212.0 0.0 0.0 0.0
"This is the best lecture series of Linear algebra ❤️" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 10740.0 0.0 0.0 0.0
"As easy as abc" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 2570.0 0.0 0.0 0.0
"The geometric approach to calculus is so helpful in understanding all sorts of concepts. " YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10118.0 0.0 0.0 1.0
"The thing to remember the right hand rule was quite funny,and reminded me of the one I personally use: be A the axis and B tangent to the rotation that'd happen in A, then it'll work like a screw, going forward when clockwise and backward when counterclockwise..." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10303.0 0.0 0.0 1.0
"""the more theta hat moves with theta the more uncertainty it removes from theta's..."" wow" XtNXQJkgkhI "22. Bayesian Statistical Inference II" "6.041 Probabilistic Systems Analysis and Applied Probability" 178.0 0.0 0.0 0.0
"16:35 - why is it not intuitive that if P(A) = 0, then A is independent with any other event?
If the probability of it's raining on Mars is 0, then is it still 0 even if any other event happened." 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 480.0 0.0 1.0 0.0
"@submelon8 How is that necessary for education?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2030.0 0.0 0.0 0.0
"Thank you, Professor.  You are remarkable at what you do and being able to watch your lectures is an honor." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9517.0 0.0 0.0 0.0
"The students are pretty observant too and ask good questions.Well done ✅" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10286.0 0.0 0.0 0.0
"He looks like Richard Dawkins" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 4570.0 0.0 0.0 0.0
"At 1:01:55 on checkin 9.5, I'd like to give you guys a intuition on why it is true.
It's true because if you look at the definition of a T - recognizer, it says -:
1. Halts and accepts
2. Halts and rejects
3. Loops and rejects
Now,
Let A be T - recognizable and O be it's recognizer.
Suppose w is a string not in A.
Now, when you look  Ā and it's recognizer Ō( Ō is implemented using O, it does opposite of what O does) and pass w through it, it should accept w, but since you're implementing Ō with the help of O, it loops on w and rejects it.
Therefore it's not always possible for Ā to be recognizable if A is. Infact it's possible on a special condition, which is A must be a decidable language." N28g_YBXY8Y "9. Reducibility" "MIT 18.404J Theory of Computation, Fall 2020" 2601.0 0.0 0.0 0.0
"Can someone help me understand how the pseudoinverse conclusion at 37:52 is reached?" Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3080.0 0.0 1.0 0.0
"Followed all the way until the IRLS method... a bit too much for my brain capacity for now but will challenge sometime later" lWW54ts9Ubo "24. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 3833.0 0.0 0.0 0.0
"Could someone help me understand ""where does the 2 by 2 matrix inverse formula come from?"" 1:33 I don't think this formula was taught previously. In my memory, only the Gauss-jordan method were taught to get inverse of a matrix.Thank youuu!" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 3237.0 0.0 1.0 1.0
"Very thanks MIT for sharing such a knowledge" L3-WFKCW-tY "33. Neural Nets and the Learning Function" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11226.0 0.0 0.0 0.0
"As someone who has studied mathematics for 40 years and taught mathematics for 30 years, I can say that Professor Strang's wisdom and insight is amazing. Moreover, his ability to share this insight with enthusiasm (however quirky and geeky) is a gift to all of us. Thank you Sir. Bless all those dedicated to teaching." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2574.0 0.0 0.0 0.0
"@MrFatalist07 but you study derivatives, integrals and limits at 10th class with 16 age old???????" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1683.0 0.0 0.0 0.0
"Lecture 1: Dot Product
Lecture 2: Determinants
Lecture 3: Matrices
Lecture 4: Square Systems
Lecture 5: Parametric Equations
Lecture 6: Kepler's Second Law
Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds)
Lecture 8: Partial Derivatives
Lecture 9: Max-Min and Least Squares
Lecture 10: Second Derivative Test
Lecture 11: Chain Rule
Lecture 12: Gradient
Lecture 13: Lagrange Multipliers
Lecture 14: Non-Independent Variables
Lecture 15: Partial Differential Equations
Lecture 16: Double Integrals
Lecture 17: Polar Coordinates
Lecture 18: Change of Variables
Lecture 19: Vector Fields
Lecture 20: Path Independence
Lecture 21: Gradient Fields
Lecture 22: Green's Theorem
Lecture 23: Flux
Lecture 24: Simply Connected Regions
Lecture 25: Triple Integrals
Lecture 26: Spherical Coordinates
Lecture 27: Vector Fields in 3D
Lecture 28: Divergence Theorem
Lecture 29: Divergence Theorem (cont.)
Lecture 30: Line Integrals
Lecture 31: Stokes' Theorem
Lecture 32: Stokes' Theorem (cont.)
Lecture 33: Maxwell's Equations
Lecture 34: Final Review
Lecture 35: Final Review (cont.)

got tired of MITs site, hope you find use of this as well" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7269.0 0.0 0.0 0.0
"Thank you!! These lectures are so clarifying and ease to watch!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 9484.0 0.0 0.0 0.0
"You can get the slides if you go to the link in the description (and read the missing part in this video).
Excelent lecture,it took me 3 days to understand all the concepts exposed.
At 55:23 is not equal to alpha, is equal to (1- alpha) since that is the way he defined the q (you can see that in the slides)." C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 12190.0 0.0 1.0 1.0
"This is pure gold... such a fantastic Professor!! Thank you" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10708.0 0.0 0.0 0.0
"Very enjoyable lectures. Prof. Auroux is a great teacher." 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11169.0 0.0 0.0 0.0
"A stands for arya.
Arya stark
Arya stark of winterfelf" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2156.0 0.0 0.0 0.0
"Which chalks do you use MIT they are incredible" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11715.0 1.0 0.0 0.0
"about to cry of how beautiful this is" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12301.0 0.0 0.0 0.0
"to much teacher centered" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14946.0 0.0 0.0 0.0
"If my teachers would have asked , any questions 
I wouldn't have come here . 
excellent teacher !!" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6509.0 0.0 0.0 0.0
"The professor's face when people were coming in late pained me 😥" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10253.0 0.0 0.0 0.0
"21:53 How most textbooks use the term ""obvious.""" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 688.0 0.0 0.0 0.0
"Wow, zero dislikes as of now!!!!" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12082.0 0.0 0.0 0.0
"Could anyone explain why solving A_T A  x_hat = A_T b is equivalent to using calculus? Specially how does the least square error fit in the first method?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 3225.0 0.0 1.0 0.0
"LOL at taking a vote on the sum formula of sine" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7234.0 0.0 0.0 0.0
"Why is dim S = 6   ?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 11870.0 0.0 1.0 0.0
"Hawkings radiation compels us to go in for Blackhole as singularity becomes unsteady flow for a vaporisation in a way supports Einstein's refusal to accept Blackhole as singularity." lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 4455.0 0.0 0.0 0.0
"It's a pleasure to listen to you Sir !! I am studying at an IIT" XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 7022.0 0.0 0.0 0.0
Useful cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 11136.0 0.0 0.0 0.0
"@hypnoticpoisons Because e^(6it) = cos(6t)+i sin(6t), which always has a modulus of 1." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 1876.0 0.0 0.0 0.0
"thank a lot" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 14453.0 0.0 0.0 0.0
"Interesring the Math on MIT. Greattings from México" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6723.0 0.0 0.0 0.0
"Interesting observation of human behaviour that the first lecture in this series has >1mill views and now we are <100k" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6729.0 0.0 0.0 0.0
"Stats are like bikinis, what the reveal is very tantalizing but what they conceal is vital." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8896.0 0.0 0.0 0.0
"Excellent videos:) but in the end doesn't he say ""if you multiply u1,u2,u3 by this you get x1,x2,x3"" because on the transcript its switched." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3681.0 0.0 1.0 0.0
"Great lecture" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 4241.0 0.0 0.0 0.0
"38:35 pilot in class" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1082.0 1.0 0.0 0.0
"TILL NOW. In college senior year. I had never known that elementary transformations were just multiplying matrices on both sides of Ax = b 🤦🏻‍♂️" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8998.0 0.0 0.0 0.0
E VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3533.0 0.0 0.0 0.0
"Can I become pretty good at probability after attending all the lectures of this course?" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 3002.0 0.0 0.0 0.0
"By far the best explanation of chi squared distribution in the last two lectures I've seen anywhere. How come lecture 10 is not available?" QXkOaifVfW4 "9. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 2973.0 0.0 0.0 0.0
"@xboxMontagers that's what she said. . ." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2064.0 0.0 0.0 0.0
"I wish more people knew MIT did such a thing.
Thanks Professor Jerison and Muller. It's been an honour to learn from you.
India, 2022." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6226.0 0.0 0.0 0.0
"30:28 xD" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 888.0 0.0 0.0 0.0
"@35:45 when you do the row exchange, do you need to do the row exchange in the vector x solution ?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 1544.0 0.0 1.0 0.0
"*circuitous but not circular*" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 245.0 0.0 0.0 0.0
"Professor Strang mentions that U and V form bases for the four fundamental subspaces of A, but it's not clear to me how C(A) = C(Ur) and C(A') = C (Vr'). I know that U and V were determined by the eigenvectors of AA' and A'A, respectively, but how are these related to the column and row spaces of A?" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8359.0 0.0 1.0 1.0
"I wish I would have watched this videos back in my Engineering. No problem I will watch it now though I am 26 now." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6215.0 0.0 0.0 0.0
"@HD4WG This is Calc 2. Your argument is invalid. ocw (dot) mit (dot) edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1628.0 0.0 0.0 0.0
"For those of you who can properly understand this course, what basis courses have you taken? I'm a computer science major and I cannot quite follow the maths here." QXkOaifVfW4 "9. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 3908.0 0.0 0.0 0.0
"He is excited about questions. That's awesome.." eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4512.0 0.0 0.0 0.0
"The camera person was really defocused that day." TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 10034.0 1.0 0.0 0.0
"I only hope that when I move to MIT next month, I learn as much from lectures in person as I can from watching them on youtube. This was great, I've decided that learning more math is a good way to kill some time this summer =)" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5892.0 0.0 0.0 0.0
"but if the input nodes count in NN is lower than num. of  outputs then the forward mode changes to backprop from the other side, I mean if you compute Jacobians and use them in successive computations in the right order, is that so?" lZrIPRnoGQQ "27. Backpropagation: Find Partial Derivatives" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12571.0 0.0 1.0 0.0
"@3:43 from normal we can find equation of the plane" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1552.0 0.0 1.0 0.0
"what happened at 7:09???" 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15140.0 0.0 1.0 0.0
"An Indian edition of this book is available only in India
http://www.wellesleypublishers.com/buy.html" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 2431.0 0.0 0.0 0.0
"35:08 I think this will still work as long as f/g tends to a non-zero finite number. Is this correct?" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1000.0 0.0 1.0 0.0
"1 minute in and I'm bored fuck this..math is lame." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 316.0 0.0 0.0 0.0
"Even Gilbert Strang doesn't tell us where the determinant formula comes from... Really sad... Properties 1-3 are also deducible from that formula." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 3581.0 0.0 0.0 0.0
"If the line lies in the plane, then is their union a subspace" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 6522.0 0.0 1.0 0.0
"Thanks MIT " 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9602.0 0.0 0.0 0.0
♥♥♥♥♥♥♥♥♥ IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 15603.0 0.0 0.0 0.0
"I'm 1 year old and I learned that 2 years ago...hehehe! bastards" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6289.0 0.0 0.0 0.0
"I think for 2 and 3 way of matrix multiplication there should be change.Rows of C are combinations of rows of A and columns of C are combinations columns of B." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6009.0 0.0 0.0 0.0
"Thank you so much to professor Jerison and the MIT team for creating this whole course. I'm starting my journey in Calculus and it is way easier and more appealing because of you." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9381.0 0.0 0.0 0.0
"the derivative is linear thing blew my mind" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14682.0 0.0 0.0 0.0
"대박!!
" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 15674.0 0.0 0.0 0.0
"same content as my non ivy league university. in fact because the professor is so good here and i had to teach my self everything i would say it was harder." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14278.0 0.0 0.0 0.0
"The bit at 4:54 where b is replaced by Ax giving A(A^TA)ˉ¹ATAx, which then collapses to Ax is fantastic. It's so high-level and so simple to see." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 10019.0 0.0 0.0 0.0
"you guys betterate the video. cool" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 15504.0 0.0 0.0 0.0
"Could you please upload the notes to the new community section of mit" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3246.0 0.0 0.0 0.0
"My right ear learned a lot" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 7786.0 0.0 0.0 0.0
"why someone is interested to change columns?? it doesnt make sense to me." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15361.0 0.0 1.0 0.0
"since the rectangles are squared ( which proved by the professor about the reverse power rule but on squared - i think - ) ,thus if you raise to cube then the graph will be 3 dimensional, so if the higher the nth power the higher the dimensions??? i thought of it cause of how he relates the pyramid and the rectangles with the square 


edit: well.. ok he didnt relate it but thats how i think of it" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14306.0 0.0 1.0 0.0
"The G(n-1) function IS the integral of x^(n-1)*e^x." aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9963.0 0.0 0.0 0.0
"great lecture thanks again mit" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12982.0 0.0 0.0 0.0
"I'm upset to see all the likes, I always liked trig substitution. It preserves the domain, changes at the same rate, and breaks open radicals. It's pretty darn elegant and powerful too" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6395.0 0.0 0.0 0.0
"I think Strang leaves out a key point in the difference equation example, which is that the n unique eigenvectors form a basis for R^n, which is why u0 can be expressed as a linear combination of the eigenvectors." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 6004.0 0.0 1.0 0.0
"What do you mean you don't know how to integrate it??" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11483.0 0.0 1.0 0.0
"Who more felt hurt when saw him really old" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11749.0 0.0 0.0 0.0
"The legend! Thank you!" 1pFv7e9xtHo "31. Eigenvectors of Circulant Matrices: Fourier Matrix" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10175.0 0.0 0.0 0.0
"To check the vector field is conservative, compute the cul of the vector field and see if it  is zero .I think it is easier." seO7-TwXH_I "Lec 30: Line integrals in space, curl, exactness... | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11029.0 0.0 1.0 0.0
"Great prof! Wish I found this sooner, my mutivariable woes would've been dispelled" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4320.0 0.0 0.0 0.0
"9:00 “you get an A in the course now” i hope the student got an A" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1433.0 0.0 0.0 0.0
"Awesome video! Thank you!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2775.0 0.0 0.0 0.0
"Gauss-Jordan, a genius method!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3988.0 0.0 0.0 1.0
"Great lecture, thank you.  Will help me with my Stochastic Processes course" XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 4282.0 0.0 0.0 0.0
"The proof contents of the previous lecture and this lecture is breathtakingly amazing!" aVv9WXwW95w "18. PSPACE-Completeness" "MIT 18.404J Theory of Computation, Fall 2020" 10255.0 0.0 0.0 0.0
"Good time!" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 4157.0 0.0 0.0 0.0
"46:46 ""he had m=2, but we should yeah grow up and get m to be 5 dimensional""  lol this guy is so funny :)" sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1275.0 0.0 1.0 0.0
"Anyone who tries to attempt the double integeral by hand at 13:23. Remember when switching to polar coordinates dA is r drdθ and x=2+cosθ because r=1 and center of circle is at (2,0). Aso it's really weird at first since you try to calculate the area of a circle on shifted x and you think that the area of the circle remains the same since the radius is the same. You would think Α=πr^2 no matter what x is but no. The area of the circle depends on the center (x,y) because of the force field." tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2513.0 0.0 1.0 0.0
"""Somebody got it. It's i^ith power. let's not get hung up on that please.""
literally half a second later:
""i^ith oddly enough can be seen as a real number if you define the imaginary exponentiation, which is weird.""" 3PzuSPQPEU4 "8. Undecidability" "MIT 18.404J Theory of Computation, Fall 2020" 110.0 0.0 0.0 0.0
"How i find the homework of this course ?" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4863.0 0.0 0.0 0.0
"To him, beasts are little mice..conceptually and symbolically ..wau wau" sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11039.0 0.0 0.0 0.0
"i always forget how big an assumption iid is." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 13324.0 0.0 0.0 0.0
"The unsightly newsprint pivotally deserve because discovery additonally precede at a ill battle. abortive, nifty skill" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10308.0 0.0 0.0 0.0
"I appreciate the brief discussion of the philosophical implications of Bayes' rule at the end, it's very interesting to know." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 5159.0 0.0 0.0 0.0
"Why do we have to take the derivative of the area?
What does that mean in this case?" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11830.0 0.0 1.0 0.0
"The father of ""Maths..."" I like all your lectures very much!!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10103.0 0.0 0.0 0.0
"Best maths teacher ever in my life , respect sir. Love from India ♥️" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 2868.0 0.0 0.0 0.0
"Thank You Prof. Strang for making this available for free" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9052.0 0.0 0.0 0.0
"Can anyone explain the applause?" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3025.0 0.0 0.0 0.0
"Love MIT, I feel moore conected with them than my own university. You have a place in my hart!
" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7430.0 0.0 0.0 0.0
"Can someone please tell us why we are stuck using (*) at 26:32 to find the value of y? If I substitute 2 for x, y^2 will have 2 values, 0.73205 and -2.73205. We can discard -2.73205 as that t=will give imaginary values for y. Can someone please tell me where I am going wrong? 
Many thanks in advance." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3096.0 0.0 1.0 0.0
"25:25 Does Positive Definite and Projection Matrices require eigenvectors to be orthogonal? Thank you." HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 778.0 0.0 1.0 0.0
"Great lecture! Took me a moment to process r x v = constant. I have always thought of Kepler's 2nd as 'equal area in equal time' but that translates to 'proportional to time'" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4273.0 0.0 0.0 0.0
"1:24 crowded class" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 593.0 1.0 0.0 0.0
"Gil Strang is a legend. I learned so much from him even though I never set foot on MIT's campus. Glad to see him still active after all these years." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4006.0 0.0 0.0 0.0
"He basically can write with the eraser instead!" bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 4461.0 1.0 0.0 0.0
"Why slope is 2?" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11909.0 0.0 1.0 0.0
"i love how the end of this lecture just turns into a bill clinton roast" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 13427.0 0.0 0.0 0.0
"You are the god of Maths.Thank you for making such videos. Most maths teachers know maths but they dont know how to teach maths.You teach in such a way which could be understood by even a high school student.thanks a lot" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12182.0 0.0 0.0 0.0
"It seems that this course is a combination of what is usually separated into two courses typically named ""Calculus 1"" and ""Calculus 2"". Is that correct?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6983.0 0.0 1.0 0.0
"wow. im in 8th grade and i got this (well how to solve the first segment on vectors). and i was just looking at this video for kicks. and THOSE idiots got into MIT!!??" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15433.0 0.0 0.0 0.0
"fuck this course was long af, made it" rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 12904.0 0.0 0.0 0.0
"25:35 Ok boomer to Cramer." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 782.0 0.0 0.0 0.0
"Waait a sec, this is college mathematics in America? " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11256.0 0.0 0.0 0.0
"This is best Linear Algebra Course one can find on the internet" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10648.0 0.0 0.0 0.0
"i aspire to be his level in atleast one subject" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 13343.0 0.0 0.0 0.0
"35:17 The lovely sound of science" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 1005.0 0.0 0.0 0.0
"what's the program he's using for plotting the functions??" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 15195.0 0.0 1.0 0.0
"I love the trees and recursive nature of the multiplication rule" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 5787.0 0.0 0.0 0.0
"hahahahaha xD , hilareous lecture , <3" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 13055.0 0.0 0.0 0.0
"better to watch the Khan Academy statistics playlist before MIT18.650" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 12541.0 0.0 0.0 0.0
"@ 11:45 How is f-double prime of x(0) equals to c & not to zero ???" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1466.0 0.0 1.0 0.0
"So this is Independence Day." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 8794.0 0.0 0.0 0.0
"@27:12: Given full rank (r = n) and m<=n, does that implies r can be larger than m?" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 1521.0 0.0 1.0 0.0
"great lecture!" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12983.0 0.0 0.0 0.0
"Wait...why is a topic that requires L'Hôpital's Rule to prove...
...being used as a ""foundational"" principle?!

I'm all for --integrating-- incorporating transcendental functions early, but this is a bit absurd.
WHY?!?!?!?

*edit:* ""Integrating"" was a poor choice of descriptor (obviously)" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11265.0 0.0 1.0 0.0
"Taking a break from elden ring to learn something that will help me not die" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9013.0 0.0 0.0 0.0
"do i make sth wrong when i still dont have that at school with the age of 17?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12750.0 0.0 0.0 0.0
"Thanks Prof. Strang!!! This lecture is a work of art. I was doing some work on a DFT course and needed a comprehensive approach to DFT/IDFT, Best 50 minutes I have spent. Thanks for the tip on Hermitian and unitary matrices!!! " M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 9635.0 0.0 0.0 0.0
"Anyone know someone this good at explaining probability theory?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2503.0 0.0 0.0 0.0
"2019.10.29. 16:57" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 623.0 0.0 0.0 0.0
"I actually enjoyed the lectures by professor Miler much more than the lectures by professor Jerison." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5013.0 0.0 0.0 0.0
"Great lectures. By the way, the students are so easily amused.🤣🤣" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4309.0 0.0 0.0 0.0
"How I would wish to stay at MIT studying right now" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 4795.0 0.0 0.0 0.0
"The combination of lecture 14 and 15 are works of art, things of beauty. 

Thank you MIT. Thank you professor Strang." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10051.0 0.0 0.0 0.0
"I think his most exceptional ability is to understand the questions that people ask him. I don't think I have seen him misunderstand one question.  I have seen a lot of good lecturers, but not all of them are good at understanding the questions they are asked. Logically, he would be an even better lecture if he encouraged even more questions. I also like that he does not try and put on a show but gets to the point.  A weak point. i wish he would motivate his topics upfront with concrete examples" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6021.0 0.0 0.0 1.0
"can someone explain to me the hat problem? esp for the variance. thx so much!" EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 12623.0 0.0 1.0 0.0
"wow this lecture is really dense" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15424.0 0.0 0.0 0.0
"i think 19 people didn't understand this lecture =) 
Nice vid  btw " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13465.0 0.0 0.0 0.0
"Wow. I wish I had him when I was taking this stuff 10 yrs ago.Thank you Dr. whoever you are.Thanks MIT!
" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12087.0 0.0 0.0 0.0
"Has any encountered viewing problems with the video?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4432.0 0.0 0.0 0.0
"this is really neat :)" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14873.0 0.0 0.0 0.0
"That exchange with the student between 15-20 min was because Jerison wrote ""right hand limit"" but really meant ""the limit on the right hand side of the equation"". The student (and probably most of the other students) thought he meant ""the limit as x approaches a from the positive direction"", which is what people usually mean by ""right-hand limit""." PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9883.0 0.0 1.0 0.0
"Thank you for this beautiful lecture Sir!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9278.0 0.0 0.0 0.0
"I high-key thought it was hella cool when he added the two loops together on the picture, subsequently adding the two basis vectors for N(A)^T and creating a dependent vector. 
I was kind of expecting that to happen just theoretically, but to actually see it happen just blew my puny mind." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5575.0 0.0 0.0 1.0
CX 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 2984.0 0.0 0.0 0.0
"Why is this being taught at MIT, I feel as if you attend that school you should at least have a grasp on FTC. Great video though! Thanks MIT" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11894.0 0.0 0.0 0.0
"so what?..." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14350.0 0.0 0.0 0.0
"This is mind blowing. Great lecture." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 10690.0 0.0 0.0 0.0
"but the rest the lecture is pretty good!!" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12573.0 0.0 0.0 0.0
"He has a french name ""Denis Auroux"" and also a french accent so i guess he's certainly from france." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4488.0 0.0 0.0 0.0
"Love you sir. Hats off." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7471.0 0.0 0.0 0.0
"Ok, this is kinda weird, but I love the lady's speaking voice. It just sounds so... peaceful? calm?

idk but I feel relaxed somehow" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8049.0 0.0 0.0 0.0
"Thanks for the videos! Any lecture on econometrics?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 9724.0 0.0 0.0 0.0
"Randomness is a big rug under which we sweep everything that we don't understand; and we hope that, on an average, we've captured the effect of what's going on. Leap of faith: We don't know whether we are correct of doing this - Maybe we have made systematic biases by doing this." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8492.0 0.0 0.0 0.0
Thanks! hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9824.0 0.0 0.0 0.0
"i never go to school thanks to and get to have way better lecture thanks to mit and the professors there." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 13444.0 0.0 0.0 0.0
"Super high watching these, very relaxing and informative." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8956.0 0.0 0.0 0.0
"Lol, this is easy.
I'm going to Uni this year and was super nervous that I wasn't going to be able to manage the maths. I can sleep calmly now :)" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7406.0 0.0 0.0 0.0
"love him so much!!!!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13861.0 0.0 0.0 0.0
"Thank you sir,
Gr from Holland" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 9335.0 0.0 0.0 0.0
"Since 10:40 Professor changed the notation, right? I think he swaps the notation of g(.) and b(.)." lWW54ts9Ubo "24. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 8674.0 0.0 1.0 0.0
11:14 j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 367.0 0.0 0.0 0.0
"Wow. Nice explanations. Thank u MIT." 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 12093.0 0.0 0.0 0.0
"If Philippe speaks too quickly for you don't forget you can slow down the speed in the settings.  I found 0.75 worked for me." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 6482.0 0.0 0.0 0.0
"Prof Strang is a blessing to humanity!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 8271.0 0.0 0.0 0.0
"我是中国人 很感谢🙏" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 15634.0 0.0 0.0 0.0
"@Bilalz1987 
Yes thanks a lot Prof. Strang, I had the same problem than you , the more I tried to know the difference the more I got confused, but this video really made me undestand, thanks so much !" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 1601.0 0.0 0.0 0.0
"@kc8omg Hello it is not about what you use. It is about how you use it or what you do with it. Mr. White board there are many with one. You will be able to distinguish the difference. Indeed that is the choice of the Professor well you could choose to teach with what you feel is more appropriate." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1917.0 0.0 0.0 0.0
"The reason I went from hating math to loving math (especially linear algebra) is Gilbert Strang. What an incredible teacher." NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10271.0 0.0 0.0 0.0
"DR. Strang thank you for a powerful lecture on the Survey of Difficulties with Ax=b. In linear systems this equation is displayed in many technical books, with little or no thought about it's difficulties. From watching this lecture, the difficulties of this equation is explained in great detail." Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3280.0 0.0 0.0 1.0
"So he's saying we can email him our homework problems?" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8768.0 0.0 0.0 0.0
"Terrific, terrific lecture, esp his way of using linear combination / ""column picture"" to solve equations. I have never heard of it, but it is so much easier! " 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 9030.0 0.0 0.0 1.0
"WHAT A LEGEND" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11242.0 0.0 0.0 0.0
"Does anyone tell me the material URL used in this lecture?" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 3449.0 0.0 0.0 0.0
"(21:29) ""So, anytime I multiply cofactors by some numbers, I'm getting the determinant of *_something_* "" - Important point in this lecture!!   
And (14:16) also the same idea(""...determinant of *_some_* matrix..."")." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 218.0 0.0 0.0 0.0
"Made it here from Lec 1. Very satisfied" sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7559.0 0.0 0.0 0.0
"Thank you, so, so much!" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9534.0 0.0 0.0 0.0
"What if he realises I’m not registered for his class , I won’t be allowed to watch this video" mc1y8m9-hOM "22. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 11504.0 0.0 0.0 0.0
"that is very satisfying sounding chalk" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14636.0 0.0 0.0 0.0
"Very good!!!
" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 11188.0 0.0 0.0 0.0
"As an electronic engineer I absolutely loved this class, just amazing!" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2569.0 0.0 0.0 0.0
"that the most convoluted explanation for what ""e"" is. I now feel like i don't understand it." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14640.0 0.0 0.0 0.0
"Around 34:00 : what about the case there AC - B^2 > 0 but A = 0? I take it that is also a case where we have a local max, since -B^2 is always negative; i'm just sorta surprised no-one noticed the omission?" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2555.0 0.0 1.0 0.0
"String theory" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8914.0 0.0 0.0 0.0
Wow! 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12047.0 0.0 0.0 0.0
"Good luck! I was in your position once! I didn't get into MIT, but I was accepted into Stanford." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4144.0 0.0 0.0 0.0
"I am from India .
 American Maths is too easy...I am in Ninth and I have studied this chapter its to easy...The questions sir written on the board were to easy to calculate..😂😂😂" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5091.0 0.0 0.0 0.0
"@6:49 The fact that A^T * A and A * A^T have the same non-zero eigenvalues is blowing my mind right now. I guess this is intimately related to the fact that det(B) = det(B^T), since det is where we get the characteristic polynomial/egenvalues..." rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1574.0 0.0 1.0 1.0
"25:24 To prove AB and BA share the same eigenvalues, I think here the proof only proves the case when B is invertible. So this is not a general proof." k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 777.0 0.0 1.0 1.0
"Maybe it'll get harder later on?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7638.0 0.0 0.0 0.0
"Lecture 1: Dot Product
Lecture 2: Determinants
Lecture 3: Matrices
Lecture 4: Square Systems
Lecture 5: Parametric Equations
Lecture 6: Kepler's Second Law
Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds)
Lecture 8: Partial Derivatives
Lecture 9: Max-Min and Least Squares
Lecture 10: Second Derivative Test
Lecture 11: Chain Rule
Lecture 12: Gradient
Lecture 13: Lagrange Multipliers
Lecture 14: Non-Independent Variables
Lecture 15: Partial Differential Equations
Lecture 16: Double Integrals
Lecture 17: Polar Coordinates
Lecture 18: Change of Variables
Lecture 19: Vector Fields
Lecture 20: Path Independence
Lecture 21: Gradient Fields
Lecture 22: Green's Theorem
Lecture 23: Flux
Lecture 24: Simply Connected Regions
Lecture 25: Triple Integrals
Lecture 26: Spherical Coordinates
Lecture 27: Vector Fields in 3D
Lecture 28: Divergence Theorem
Lecture 29: Divergence Theorem (cont.)
Lecture 30: Line Integrals
Lecture 31: Stokes' Theorem
Lecture 32: Stokes' Theorem (cont.)
Lecture 33: Maxwell's Equations
Lecture 34: Final Review
Lecture 35: Final Review (cont.)" BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 7273.0 0.0 0.0 0.0
"how are we supposed to get into mit?" BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13192.0 0.0 0.0 0.0
"8 people got a F- in this class" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1407.0 0.0 0.0 0.0
"i'm confused, why are there so many students in this class? aren't most MIT students going in with a bunch of AP courses under their belt. surely, ap calculus is one of them ." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13513.0 0.0 0.0 0.0
"4:42 A multiply x, matrix A times vector x, how to look at that, think of the *rows* , combination of the vectors
8:56 column space of A,  C(A)
18:31 C: the basis of A's column space
20:00 the column rank of A
20:22  A= C times R,  factoring
23:49  column rank = row rank" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1323.0 0.0 0.0 0.0
"Thanks so much Prof Gilbert Strang, I wasn't understanding Determinant usage, and now I fully understand owing to the proprieties, which makes it so simple. you have just a gifted skill to teach so well and clear, before answering the questions, putting the shoes of a student, to think of a possible solution and applying what u have just teach, and applying to problem solving instead of mechanizing meaningless math rules." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 9785.0 0.0 0.0 1.0
"This lecture is closed under any other lectures!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 10799.0 0.0 0.0 0.0
"His explanations on the normally convolutedly explained Markov Inequality, Chebyshev's Inequality, heck, even convergence of limit, are spotless! Such a gem. Thank you MIT, thank you Prof.Tsitsiklis." 3eiio3Tw7UQ "19. Weak Law of Large Numbers" "6.041 Probabilistic Systems Analysis and Applied Probability" 4750.0 0.0 0.0 1.0
"Hi there,

I think MIT's answer was clear enough; their goals are not your goals. They work to educate ALL students - those that can and those that can't afford it.

I fail to see what this has to do with anybody's eaten flesh. And developing international academic standards helps to increase competition which is beneficial to the international body of knowledge. It increases global standards which leads to more motivation to you know, work hard, and stay relevant. It's good for mankind." Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4716.0 0.0 0.0 0.0
"great video, you're one of the best lecturers i've found on youtube!" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13015.0 0.0 0.0 0.0
"amazing person, a legend!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 12352.0 0.0 0.0 0.0
"Thanks for taking the time out to do this interview" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9705.0 0.0 0.0 0.0
"I found which one is pink!" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5434.0 0.0 0.0 0.0
"Is there some similar course for Functional analysis? Need it badly" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 6844.0 0.0 1.0 0.0
"He is the Morgan Freeman of mathematics...Respect🙏" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4546.0 0.0 0.0 0.0
"Great lectures, really enjoyable" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4307.0 0.0 0.0 0.0
"No idea what he was doing between 24:43 to 30:00" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7872.0 0.0 1.0 0.0
"A brilliant lecturer." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 2101.0 0.0 0.0 0.0
"at 48:42, what algebra is he talking about in order to obtain 1/3 as a result of the sum of all probabilities?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 12460.0 0.0 1.0 0.0
"16:30 the free variable, rank, and special solution amount relation" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 478.0 0.0 1.0 0.0
"Thank you Professor Denis Auroux and MIT. 
Just now completed the 18.02, (18 August, 2022).
Single variable calculus - Prof. David Jerison
Multivariable calculus - Prof. Denis Auroux.

Thanks again !" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9208.0 0.0 0.0 0.0
"""Ok, you are easily amused""


I know right?" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 98.0 0.0 0.0 0.0
"John Tsitsiklis is awesome !
Clear explanation, no philosophical mumbles. 
Plain old school scholar which I like very much !  Conveying idea via paper and pencil these days is rare and should be treasured !" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 7139.0 0.0 0.0 0.0
"It is human to make an error.
It takes a computer to screw things!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 6949.0 0.0 0.0 0.0
"Do you study maxwell's equations?" BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 3424.0 0.0 1.0 0.0
"@blackrobe2007 The third row in the matrix says that 0 = b3 - b2 - b1, so the values for b1, b2 and b3 must satisfy the result 0.
And the numbers 1, 5 and 6 for b1, b2 and b3 are good because they turn the equation 0 = b3 - b2 - b1 into 0 = 6 - 5 - 1, which is true.

There is an infinite number of other possible solutions as well --- for example, you could choose b1, b2 and b3 to be 50, 100 and 150, and in that case you would get 0 = 150 - 100 - 50, which is also true." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 1795.0 0.0 1.0 0.0
"Notes for future ref.)
(7:16) there are _some_ matrices that do _NOT_ have n-independent eigenvectors, but _most_ of the matrices we deal with do have n-independent eigenvectors.
(17:14) If all evalues are different, there _must_ be n-indep evectors. But if there are same evalues, it's possible _no_ n-indep evectors. (Identity matrix is an example of having the same evalues but still having n-indep evectors)
* Also, the position of Lambda and S should be changed(32:36). You'll see why by just thinking matrix multiplication, and it can also be viewed by knowing A^100=S*Lambda^100*S^-1 and u_0=S*c.
 Thus, it should be S*Lambda^100*c, and this also can be thought of as 'transformation' between the two different bases - one of the two is the set of the egenvectors of A.
* Also, (43:34) How prof. Strang could calculate that?? Actually that number _1.618033988749894..._ is called the 'golden ratio'.
* (8:15) Note that A and Lambda are 'similar'. (And, S and S_-1(S inverse) transforms the coordinates.. you know what I mean.. both A and Lambda can be though of as some ""transformation"" based on different basis.. and S(or S_-1) transforms the coord between those two world.)" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 7939.0 0.0 1.0 0.0
"Thanks so much, Professor Strang!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9791.0 0.0 0.0 0.0
"23:30  "".... including slightly more legit businesses like insurance"", lmao!" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 712.0 0.0 0.0 0.0
"I have never seen Professor Strang simplicity and humility to explain complex concepts in other person. I still remember a summer when I took an accelerated course at the University, I remember I was not able to understand even a word from the professor giving the course at that time, so, I remember went back home totally upset, and I saw the first Linear Algebra video of the Professor Strang, and I spent the whole week watching the full Linear Algebra course videos, and that summer, I approved Linear Algebra with a 9, completing the exam in record time, avoiding complex resolution steps explained by the current professor giving the course, and applying the simplicity Professor Strang transmitted on his lectures. And the most important thing was that I learnt a lot, everything was looking super clear for me at the time of reading the exercises in the exam. Absolutely brilliant, humble, and simple, as everything in life has to be. Thank you Professor!!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5540.0 0.0 0.0 0.0
"sure :)" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14426.0 0.0 0.0 0.0
"As a German I'm obliged to note that: ""Eigen"" is a German word and means ""own"" or ""selv""." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 2562.0 0.0 0.0 0.0
"Imagine this guy breaking bad .." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6584.0 0.0 0.0 0.0
"Man, I love professsor Strang, but his brain was not working very well during this lecture." lZrIPRnoGQQ "27. Backpropagation: Find Partial Derivatives" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7582.0 0.0 0.0 0.0
"5:43 close enough
HE KNOWS MEMEBASE! GASP!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1364.0 0.0 0.0 0.0
"looks  like right hnded rubixs alg" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13852.0 0.0 0.0 0.0
"There was nothing new that I had learned by watching this, although I did enjoy it very much. The only thing that I noticed about the section that pertains to the dot product that wasn't mentioned but I feel is just as significant is that it doesn't just check for orthogonality whether two vectors are perpendicular or not, but that it also tests if two vectors either coincide or are parallel! They are parallel or coincide when the dot product yields (-1). This is simply because theta will equal either +/- 180 degrees or +/- PI radians where cos(+/- 180) or cos(+/- PI)  yields (-1) because the cosine is an even function." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10384.0 0.0 0.0 0.0
lol xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13817.0 0.0 0.0 0.0
"just watching." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 13745.0 0.0 0.0 0.0
"10:41 you're a rock star" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 352.0 0.0 0.0 0.0
"Why delta v becomes 0 when delta x goes to 0?" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11804.0 0.0 1.0 0.0
"Lecture 1: Dot Product
Lecture 2: Determinants
Lecture 3: Matrices
Lecture 4: Square Systems
Lecture 5: Parametric Equations
Lecture 6: Kepler's Second Law
Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds)
Lecture 8: Partial Derivatives
Lecture 9: Max-Min and Least Squares
Lecture 10: Second Derivative Test
Lecture 11: Chain Rule
Lecture 12: Gradient
Lecture 13: Lagrange Multipliers
Lecture 14: Non-Independent Variables
Lecture 15: Partial Differential Equations
Lecture 16: Double Integrals
Lecture 17: Polar Coordinates
Lecture 18: Change of Variables
Lecture 19: Vector Fields
Lecture 20: Path Independence
Lecture 21: Gradient Fields and Curl Of Vector Fields
Lecture 22: Green's Theorem
Lecture 23: Flux
Lecture 24: Simply Connected Regions
Lecture 25: Triple Integrals
Lecture 26: Spherical Coordinates
Lecture 27: Vector Fields in 3D
Lecture 28: Divergence Theorem
Lecture 29: Divergence Theorem (cont.)
Lecture 30: Line Integrals
Lecture 31: Stokes' Theorem
Lecture 32: Stokes' Theorem (cont.)
Lecture 33: Maxwell's Equations
Lecture 34: Final Review
Lecture 35: Final Review (cont.)" _CdoRiNSrqI "Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7283.0 0.0 0.0 0.0
"I had horrible experiences with learning math in elementary school and since then, I've had a negative predisposition to it. This playlist is reversing that predisposition." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 5464.0 0.0 0.0 0.0
"By the chain rule, (d/dx) f(g) when g is a function of x is g' * f '(g).
In this case, the ""g"" is (kx) so you can get the answer by using the chain rule." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2976.0 0.0 0.0 0.0
"I wish there wasn't so much fn data but until we grow up a species we're going to have to learn this shit" 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 6228.0 0.0 0.0 0.0
"Lecture 1: Dot Product
Lecture 2: Determinants
Lecture 3: Matrices
Lecture 4: Square Systems
Lecture 5: Parametric Equations
Lecture 6: Kepler's Second Law
Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds)
Lecture 8: Partial Derivatives
Lecture 9: Max-Min and Least Squares
Lecture 10: Second Derivative Test
Lecture 11: Chain Rule
Lecture 12: Gradient
Lecture 13: Lagrange Multipliers
Lecture 14: Non-Independent Variables
Lecture 15: Partial Differential Equations
Lecture 16: Double Integrals
Lecture 17: Polar Coordinates
Lecture 18: Change of Variables
Lecture 19: Vector Fields
Lecture 20: Path Independence
Lecture 21: Gradient Fields
Lecture 22: Green's Theorem
Lecture 23: Flux
Lecture 24: Simply Connected Regions
Lecture 25: Triple Integrals
Lecture 26: Spherical Coordinates
Lecture 27: Vector Fields in 3D
Lecture 28: Divergence Theorem
Lecture 29: Divergence Theorem (cont.)
Lecture 30: Line Integrals
Lecture 31: Stokes' Theorem
Lecture 32: Stokes' Theorem (cont.)
Lecture 33: Maxwell's Equations
Lecture 34: Final Review
Lecture 35: Final Review (cont.)" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7280.0 0.0 0.0 0.0
Beaut 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2813.0 0.0 0.0 0.0
"Perhaps Gil Strang would have replaced Newton if he were his contemporary" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 8183.0 0.0 0.0 0.0
"Is all math solving?" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6757.0 0.0 0.0 0.0
"How the imaginary parts are taken care of in Fourier Basis for JPEG?" 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 4896.0 0.0 1.0 0.0
"These are too good. I spent days reading abstract definitions and formal explanations in books to understand concepts this professor explains so vividly and creatively with 10 seconds! Thank you!" _CdoRiNSrqI "Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10397.0 0.0 0.0 1.0
"When deriving the normal equation AT * A * x_bar = AT * b, I struggle to understand why I cannot simply divide both sides by AT, leaving me with A * x_bar = b, which is wrong. Solving for x_bar and plugging it back into p = A * x_bar just seems to circular of an argument. Can someone help me understand? :)" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 11612.0 0.0 1.0 0.0
"Is he talking about Galois or Abel?" d32WV1rKoVk "12. Computing Eigenvalues and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6775.0 0.0 1.0 0.0
"Actually, it's 'quod erat demonstrandum'" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2237.0 0.0 0.0 0.0
"21:12 In fact, if we normalize x1, x2, x3 to q1, q2, q3, then A = 0*q1*q1^T + c*q2*q2^T + 2*q3*q3^T (since q's are orthonormal). Any c, which is not necessarily real, can make A symmetric. ---can anyone help me check this statement? I havent found any comment discussing this yet." HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 675.0 0.0 1.0 0.0
"dang!! takes me back to me college days for my undergrad in EE" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12720.0 0.0 0.0 0.0
"Huwen= When" 3eiio3Tw7UQ "19. Weak Law of Large Numbers" "6.041 Probabilistic Systems Analysis and Applied Probability" 4916.0 0.0 0.0 0.0
"It's employed in all the physics that go into making pretty much any electronic device, including the one that you use to spread your stupidity. Without calculus, you'd be stupid AND lonely." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7037.0 0.0 0.0 0.0
"Can someone help me in f =cosxcoshy . We have to find gradient" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 3079.0 0.0 1.0 0.0
"46:19  Professor Strange lets his anger out on the class" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 1269.0 0.0 0.0 0.0
"I've yet to take Calculus, many people make it out to be the achilles heel of those who seek higher learning. I hope that's not the truth." jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6441.0 0.0 0.0 0.0
"If w is constant, how can its gradient vector point toward higher values?" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 6531.0 0.0 1.0 0.0
"This guy is good to a great extent but I like somebody like Eddie Woo who looks for feedback from students and has more of a personality.    He should occasionally take questions which he does not. Often times he is looking at the floor." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 10532.0 0.0 0.0 0.0
MATH 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7495.0 0.0 0.0 0.0
"I'm taking this course at IU using the book Dr. Strang wrote and this is extremely helpful" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6389.0 0.0 0.0 0.0
"minute 19:00 was very funny! such a sweet teacher, I wish I had a teacher like that! The best Linear Algebra Course in the history of men!" TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 13947.0 0.0 0.0 0.0
"toán học ứng dụng hiện đại." V3Wg_jrMSQY "Lecture 19: Differentiation Rules, Rolle's Theorem, and the Mean Value Theorem" "MIT 18.100A Real Analysis, Fall 2020" 14956.0 0.0 0.0 0.0
"I had linear algebra over 40 years ago, but this was the first time I'd seen it presented this way.  I've done fine in my engineering career, but this kind of thinking would have definitely made a few things easier." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5465.0 0.0 0.0 0.0
"Brilliant example. 30:55" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 2926.0 0.0 0.0 0.0
"On our faculty they didn't tell us anything about  3-diagonal. GREAT video and thx for the lecture." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 8069.0 0.0 0.0 0.0
"Very good prof" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11183.0 0.0 0.0 0.0
"why is phi limited from 0 to 180" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15338.0 0.0 1.0 0.0
"Wow, great professor! Thank you!" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 12069.0 0.0 0.0 0.0
"very interesting video thanks" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 15026.0 0.0 0.0 0.0
https://www.youtube.com/watch?v=HUThHJ6E3rY VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 13271.0 0.0 0.0 0.0
"Great lecture series!!" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4256.0 0.0 0.0 0.0
"Is anyone viewing this after 13yrs🙁" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6763.0 0.0 0.0 0.0
"Thank you, you are an excellent teacher and I learned, thank you" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9538.0 0.0 0.0 0.0
"lol, i think i see a FACE on 43:17 right next to the + sign!!" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13838.0 0.0 0.0 0.0
"Does anyone understand the symmetry thing he was talking about? Which equation did he stare at XD" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3450.0 0.0 1.0 0.0
"I also found [-2,2,-2,1] seems to produce a zero vector and it is not a multiple of the special solutions [-2,1,0,0] or [2,0,-2,1]. Can someone help me understand why [-2,2,-2,1]  also produces a solution? Is it because column #1 and column #2 are dependent?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 5035.0 0.0 1.0 0.0
"I think he made a mistake on A+B before 26:23 because I'm not quite sure but as what I saw, he formed a rectangle that has  length A and width B, however he said that A+B is the Diagonal of this rectangle, but theoretically speaking all diagonals of a rectangle is the square root of the sum of the squared length and squared width. right?and before the video hits 23:33 I see couple of students asking the question that I should have asked. But NO ONE IS PERFECT. so please be kind to him." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6014.0 0.0 1.0 0.0
"talking about splitting hairs, at 20:10 he states that the sample space is infinite. but he must be talking about impossibly small darts. all real objects are confined within the limits of plank space and plank increments. although the number is very large, there is actually a finite number of real spaces that a real dart could land on within that square. the plank units are what stops infinite regression within a limited area of space in actual real world applications. only in thought experiments can you have points that are smaller than plank units of size." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 14435.0 0.0 1.0 0.0
"Brilliant Job done here ...." IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 2925.0 0.0 0.0 0.0
"These lectures are awsome. Strang makes Linear Algebra seem so easy - completely oppisite of his ""colleagues"" at my university. I've stopped attending their lectures in favour of these. Thanks MIT (W. Gilbert Strang)!" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 10406.0 0.0 0.0 0.0
"39:03 where the A (1,1,1,0) comes from? help....." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 1092.0 0.0 1.0 0.0
"im  bored...onto Quantum Mechanics" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13559.0 0.0 0.0 0.0
"wait, why did delta F when finding the derivative of  f(1/x) become the inverse of the previous delta f? " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15052.0 0.0 1.0 0.0
DanceTroupe!!! wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3310.0 0.0 0.0 0.0
"Is this for beginners ?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6869.0 0.0 0.0 0.0
"is anyone solving assignment problems on their website?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13626.0 0.0 0.0 0.0
"I love the sound of chalk on the blackboard in the morning." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5785.0 1.0 0.0 0.0
"A question: for MLE of the multivariate case (for example, see slides on 57:45), does the expression of quadratic risk of \hat{\beta} implies that the quadratic risk goes to zero when n becomes large (i.e., more and more data)?" JBIz7UadY5M "14. Regression (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 2150.0 0.0 1.0 0.0
Awesome!!! Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2783.0 0.0 0.0 0.0
"Thank you Prof. G. S. and MIT, it's a wonderful journey" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9190.0 0.0 0.0 0.0
"I love watching Prof Strang suddenly have an epiphany. It's like he wants to jump up and shout ""Eureka!""" xaSL8yFgqig "Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5840.0 0.0 0.0 0.0
"use of so called super high tech class room with big screens is bullshit, stands no chance against the good old black boards" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14984.0 1.0 0.0 0.0
"how do we define vector?" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 13221.0 0.0 1.0 0.0
"i haven't finished high school and i've done this already.
I've done volumes (cylindrical shell method and cross sectional method (find volume of anyhing basically) , graphing (harder applications, manipulating graphs without being given a function), complex numbers, mechanics, polynomials, integration( harder applications i.e. integration by parts and reduction), Conics (i.e. Ellipses, rectangular hyperbola), mathematical induction, differential equations,Newtons method of approx. and cooling" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13400.0 0.0 0.0 0.0
"How are those variables “FREE”? Can someone explain" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 4804.0 0.0 1.0 0.0
"Can someone guide me to anova lectures please? please MIT reply or anyone 🙏" a66tfLdr6oY "11. Parametric Hypothesis Testing (cont.) and Testing Goodness of Fit" "MIT 18.650 Statistics for Applications, Fall 2016" 3078.0 0.0 0.0 0.0
"yeah and who makes those software another software?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 15463.0 0.0 0.0 0.0
"Thank you MIT and thank you professor John Tsitsiklis" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 9140.0 0.0 0.0 0.0
"How to work out that the base of the box must be square in problem at 19:50?" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4903.0 0.0 1.0 0.0
"This is night and day to my professor. So much simple insight I didn't glean like the simple fact: to swap columns, put the elementary matrix on the right. Wow. I didn't get this until now, I would always try to transpose in a roundabout way." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10695.0 0.0 0.0 0.0
"lol close up of rangle" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13824.0 1.0 0.0 0.0
"why are these videos plagued by bot comments." sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15285.0 0.0 0.0 0.0
"Wait why did delta v turn to zero ?" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11259.0 0.0 1.0 0.0
"I learned more about determinants within the first 5 minutes of this video than I did 
in my 3 hours of lectures on the topic so far." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 5652.0 0.0 0.0 0.0
"In the concluding ""review"" he reminds us that initial state vector u₀ must be decomposed into eigenvectors. However, he seems refused to say that the eigenvector will look like exponential function [1 λ λ² λ³ ] of eigenvalues λ, http://valjok.blogspot.com/2013/12/eigenvectors-of-recurrence-equations.html. In case you start evolving from y₀ !=1, instead of [y₀ y₁ y₂ y₃  …] = [1 λ λ² λ³], your recursive process evolves through the state variables [y₀ y₀λ y₀λ² y₀λ³ ]. Yet, y₀ is unimportant as long as eigenvector is concerned. Only eigenvalues λ are important. It is cool that [1 λ λ² λ³] is the exponential vector and since exponents must be the solutions of linear differential equations. I just do not understand how why does he explain how our recursion evolves u₀ → u₁ → … (the initial value problem) if our goal is to find all solutions, regardless of what are the boundary conditions." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 6661.0 0.0 1.0 0.0
"This is very good." 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 10764.0 0.0 0.0 0.0
"I think Prof. Strand made a little mistake in calculating the variance at 35:00, both terms should be further divided by an ""S""(the sample size), and the final variance should have 1/S in front. Besides, the variance of N IID variables should be 1/N of the indiviual IID variable." z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6001.0 0.0 1.0 0.0
"""blackboard extends to infinity..."" yeah, MIT does have infinitely long blackboard..." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 147.0 1.0 0.0 0.0
"Great lecture and professor!" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4249.0 0.0 0.0 0.0
"For the pumpkin example, at t=4 and h=0, why isn't the instantaneous velocity 0? Wouldn't v=-40m/s at t=~3.999999 or h=~0.000001 but at impact point v=0 since pumpkin transitions from -40m/s to 0m/s when it collides with the ground?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3895.0 0.0 1.0 0.0
"There is something I cannot understand when prove Alon-Boppana bound.
1:01:38
|V_i| w_i (w_{i-1} + (d-1)w_{i+1}) is bad for i=0 since the unique vertex v in V_0 does not have a predecessor. (It must be |V_0| w_0 d w_1.)
w_{-1} = (d-1)^{1/2} and |V_0| w_0 = 1 and |V_i| w_i^2 <= 1, so I think that this gap may not be negligible." Rlvwagd2BmY "12. Pseudorandom graphs II: second eigenvalue" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 10380.0 0.0 1.0 0.0
"Thank you Professor Strang for being such an inspirational teacher and thanks to the MIT for making this possible !" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9218.0 0.0 0.0 0.0
"Oh I cannot thank you enough!!! Thank you!!" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 7999.0 0.0 0.0 0.0
"Professor Strang thanks for showing different ways to  Solve Least Squares problems in linear algebra and statistics. Least Squares is used every day to fit data." ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8370.0 0.0 0.0 1.0
"""Mathematics is an Art""-Gilbert Strang" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 82.0 0.0 0.0 0.0
"Thank you! I'm learning good stuff for free." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9478.0 0.0 0.0 0.0
"Here's some more redundancy (ya' know, as an engineering safety factor):
You were wrong. You admitted it, so stop trying to fight. You failed. You lost.
Try again tomorrow." jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4678.0 0.0 0.0 0.0
"Last two minutes for Gram-Schmidt is really remarkable, 2 mins hardly time to see the heart of that mathematic machine." ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7251.0 0.0 0.0 0.0
"Did he get censored @ 7:21?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 3372.0 0.0 0.0 0.0
"How come e^[lim n->ග ln(1+1/n)^n] = e^1... well i thought it will be e^0 because (1+1/n)^n will be eventually reach 1 as n approach infinity and ln(1) is just 0 so i thought it must be e^0" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4822.0 0.0 1.0 0.0
"As a non-mathematically inclined person I found this lecture to be gripping." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2566.0 0.0 0.0 0.0
"Just watched christopher nolan  movie... Super lecture.." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 7203.0 0.0 0.0 0.0
"@alimunth yes, that is real.

" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1773.0 0.0 0.0 0.0
"Those blackboards..." UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10991.0 1.0 0.0 0.0
"hmm is  there a complementary book we must follow? I'm puzzled as I don't think we've introduced the elementary matrices in previous lectures, or Upper/lower matrices. I feel this is not beginner friendly." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 13174.0 0.0 1.0 1.0
网易公开课有没有正在翻译这门课？？？ j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 15648.0 0.0 0.0 0.0
"Most professors in Indian Universities would've happily retired by now because they never had passion like this man" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7707.0 0.0 0.0 0.0
"u guys are awsome
" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14972.0 0.0 0.0 0.0
"24:33 Coronavirus spotted" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 736.0 0.0 0.0 0.0
"Strang is a legend. He should get an ovation everytime!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 8905.0 0.0 0.0 0.0
"PLEASE DO NOT CODE A.I TO USE ALL THESE FREE INFORMATION ESPECIALLY MIT LECTURES ON YOUTUBE😭😭🤣I HOPE THE AVERAGE JOE TAKES NOTE AND START STUDYING ASAP" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 8152.0 0.0 0.0 0.0
"I don't know if if made my point, but if you see the other lectures you will understand better... in fact i just realize i made a mistake in the grammar at the end... next time i'll review before posting anything." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5319.0 0.0 0.0 0.0
"e-2 is correct. (-e+2e-0-2) = e-2 and the other calculations are correct" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12782.0 0.0 1.0 0.0
"40:01 how did he get the projection matrix? what is the a??" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1123.0 0.0 1.0 0.0
"Thank you, this is so helpful" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9537.0 0.0 0.0 0.0
"Finally a real analysis video lecture series from the OCW :'). Thank you" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 3766.0 0.0 0.0 0.0
"The example on 16:14, I think (-2)/(x+2)^3 the power to the 3 should be 4, since you use quotient rule solve the next derivative." twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10096.0 0.0 1.0 0.0
"Uve gotta love him!!!<3!!hehe!!!!!Very well explained lecture....." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11144.0 0.0 0.0 0.0
"What's with the weird comments here?" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11592.0 0.0 0.0 0.0
"I used to think Princeton's cal 3 is better but this guy is actually the best I've seen." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6129.0 0.0 0.0 0.0
Awesome VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 2751.0 0.0 0.0 0.0
"I would like to ask about the example with kepler's law.
Professor considers radius r as constant, but the object is moving around elliptical trajectory, so radius varies as function of theta. Have I missed something, or has he made an error?" BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6260.0 0.0 1.0 0.0
"It's like an enlightenment moment when he says, ""she said, it's got two identical rows""" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7057.0 0.0 0.0 0.0
"He is French isn't he?" phbw9r1iUDI "7. Parametric Hypothesis Testing" "MIT 18.650 Statistics for Applications, Fall 2016" 4495.0 0.0 0.0 0.0
"I am loving mathematics now... which makes life easier at NIT
" tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5115.0 0.0 0.0 0.0
"33:01 after watching the 3blue1brown serie and being on this video on this serie I'm a huge fan of columns, and find they make much more sense than rows.
If you want to understand the geometrical meaning of linear algebra I recommend everyone to watch the 3blue1brown playlist, everything you use on linear algebra has a geometrical equivalent, why matrices that have determinant equal to 0 doesn't have an inverse, how linear transformations (matrices) modify space, how the basis vectors generates the space, how the determinant of a linear transformation is the factor by which the area of something in that space changes, and so forth." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 950.0 0.0 0.0 1.0
"He reminds me of Jimmy Stewart.  Very unassuming.  Makes out as though he's figuring it out as he goes along, but of course he wrote the book.  Zen master at work!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4595.0 0.0 0.0 0.0
"This is an awesome lecture. I just had a little bit of confusion at the first of the lecture, when Prof. Strang was talking about the four ways to do Matrix Multiplication. How are they all connected? I couldn't get it very well, and there weren't examples on this particular point." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10626.0 0.0 1.0 0.0
"Feel like I'm watching an episode of Seinfeld with that laugh track, great set of lectures tho" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3748.0 0.0 0.0 0.0
"This real professor taught me a lecture that our ""fake professor"" couldn't teach for weeks. I hate to say that woman is a professor, it is just rudeness to this man. Thanks TEACHER." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10914.0 0.0 0.0 0.0
"This comment section is so surprisingly positive... almost makes me suspicious :,D" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 10484.0 0.0 0.0 0.0
"Such a great teacher you are Prof. Thank you so much for every moment you spent teaching..." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8933.0 0.0 0.0 0.0
"The best ever way to teach Jacobians, wow greatest of the great, Jacobians .......great, the professor explanation ...great" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9996.0 0.0 0.0 1.0
"sad. the formal definition of the saddle point isnt given...and where is the proof that the difference of two linear functions squared always yields a saddle?" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14272.0 0.0 1.0 1.0
"12:10 very good explanations on what a link function does" X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 388.0 0.0 0.0 1.0
"how is 4ac-b^2 a square term? and how is that in the third case if a<0 it is max and a>0 it is min" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13232.0 0.0 1.0 0.0
"Lecturers with dry humor are the best" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 7304.0 0.0 0.0 0.0
Lovely! 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 7488.0 0.0 0.0 0.0
"Such a great professor. Calc made simple." 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8932.0 0.0 0.0 0.0
"Perfect explanation， thanks" cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8177.0 0.0 0.0 0.0
"Prof, I have watch this through lec 1. I have to say, you are awesome. Thank you so much for teaching. I wish I could be your student in your class. So jealous the guys in class applause for your super erasing. " 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8286.0 0.0 0.0 0.0
"Arrr, finally I found a key to understand multivariables! My lecturer is just screwing it up! I couldn't understand it even I study by myself. Is worth a waste of 46 minutes on watching this recording!
" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 2560.0 0.0 0.0 0.0
"what book is he using?
" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15128.0 0.0 0.0 0.0
"I also love this series of lectures, but in this lecture I find that he does not explain perpendicular subspaces enough. The example with the blackboard and the floor is just confusing (to me and my colleagues at least), because obviously they form a right angle and thus are perpendicular. And obviously they are both subspaces. Which leads me to believe that the definition is wrong, which I'm sure it isn't." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5037.0 1.0 1.0 1.0
"This lecture and the one before are some of the hardest in the whole course. Stay the course, everyone." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 10783.0 0.0 0.0 0.0
"the lecturer somehow reminds me of harryson wells from the flash" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14711.0 0.0 0.0 0.0
"Amazing ending to an amazing series. Thank you MIT OpenCourseWare, thank you Professor David Jerison and thank you Professor Haynes Miller" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2359.0 0.0 0.0 0.0
"Eigenvalues ""The big stuff"".  Awesome!!!!" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 3556.0 0.0 0.0 0.0
"Finally taking my ""first adult analysis class""!" 78vN4sO7FVU "Lecture 2: Bounded Linear Operators" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 3777.0 0.0 0.0 0.0
"This lecture is amazing! Its amazing how well he communicates these concepts" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 10792.0 0.0 0.0 0.0
"@LeRoiZed no money?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1655.0 0.0 0.0 0.0
"do you mean d2/d^2x?" TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12759.0 0.0 1.0 0.0
"This professor's voice is like John Wayne." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 10912.0 0.0 0.0 0.0
"Very well explained. Really big fan of prof.John Tsitsiklis" EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 11233.0 0.0 0.0 0.0
"@TurdWolf1 I know. It's weird how these are already intelligent students that got in, yet they have professors that are millions time easier to comprehend and a lot more attentive of their students than at most other universities! Anyways i love these videos they sure do help a lot!" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1746.0 0.0 0.0 0.0
"One of the best online courses I have seen - he is such a good lecturer, so clear and concise." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8091.0 0.0 0.0 0.0
"is he french???tht accent sounds a bit french..." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13632.0 0.0 0.0 0.0
"yea that is actually a good point. thanks" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15461.0 0.0 0.0 0.0
"ILAS – The International Linear Algebra Society
https://ilasic.org/" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6446.0 0.0 0.0 0.0
"wowww...the perfect professor!!!!!! congratulations!!!!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15439.0 0.0 0.0 0.0
wow.Thanks. YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15438.0 0.0 0.0 0.0
"For the last example why did we not convert the matrix to reduced row form.....and then find the pivot column? Find converting column 2 and 4 are the free column......" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 3890.0 0.0 1.0 0.0
"In 38:30 , I didn't understand how elements inside B are equally likely if elements inside sample space are not. 
Even if B occurred, how elements of B become equally likely?" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 6602.0 0.0 1.0 0.0
"I believe that guy is troll. My advice is, next time you see something as stupid as that just laugh to yourself and play another of those excellent videos.
:-)" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5171.0 0.0 0.0 0.0
"These lectures should be stored properly so that whenever aliens do come, they can learn linear algebra the right way." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10420.0 0.0 0.0 0.0
"what is going on " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15154.0 0.0 0.0 0.0
"b turns out to be, right.  This guy is brilliant." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 12505.0 0.0 0.0 0.0
"@FmMan33 Scrap that after watching a little more the way he pronouncing words like ""Grow"" makes me assume French" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1621.0 0.0 0.0 0.0
"extremely helpful with building the basics and then moving forward" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 12837.0 0.0 0.0 0.0
"a weak man with the stronger brain.
new approach of learning ....😍😍" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12295.0 0.0 0.0 0.0
"A true gift to the world" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 2163.0 0.0 0.0 0.0
"Thm. A vector is orthogonal to itself if and only if it is the zero vector.
Proof. Backwards. Suppose there exists a vector x s.t. that is orthogonal to itself has a nonzero entry. Then xTx=summation xixi>=bi^2. Analog holds for negative bi. Which contradicts there existing a vector with nonzero entries which has a zero dot product.
Forward. Trivial.
Then Ax=0 If A has independent columns ie. is of full rank, then the only vector in the N(A)=[0].
Δ" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 10983.0 0.0 0.0 0.0
"can hardly hear with max volume..." X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 12616.0 1.0 0.0 0.0
"i like his pants tho" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13416.0 0.0 0.0 0.0
"Thank you Prof Strang! See you at lecture one again pretty soon xD" rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9183.0 0.0 0.0 0.0
"Let A and B be two events such that the occurrence of A implies occurrence of B, But notvice-versa, then the correct relation between P(A) and P(B) is?
a)P(A) < P(B)
b)P(B)≥P(A)
c)P(A) = P(B)
d)P(A)≥P(B)

Correct answer of this question ? Please tell" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 7331.0 0.0 1.0 0.0
"If you're actually being serious, you're seriously lacking insight, hahahahaha!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6561.0 0.0 0.0 0.0
"thank you" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14468.0 0.0 0.0 0.0
"S contains a bunch of numbers independent of t (the eigenvectors), so d/dt and S would commute." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 8577.0 0.0 1.0 0.0
"well thats true.... whats the wrong thing with that?" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15093.0 0.0 0.0 0.0
"He is great." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4518.0 0.0 0.0 0.0
"20:28 When you raise your hand but your professor pretends you are invisible." R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 653.0 0.0 0.0 0.0
"36:58 I studied matrix for 3 years ( 1 year in school and 2 years in university) and nobody told me that i can multiply a matrix in this simple way" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 1049.0 0.0 0.0 0.0
"Great video, finally I understand! :) thanks, MIT!!!" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 4358.0 0.0 0.0 0.0
"great class =)" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12968.0 0.0 0.0 0.0
"I'd just like to say thank you to Prof. Strang. The best prof I never had." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 6276.0 0.0 0.0 0.0
"Thank you Prof Gilbert." Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9180.0 0.0 0.0 0.0
"Thanks for MIT OCW and Prof.Auroux." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9681.0 0.0 0.0 0.0
"Oh man, 3 years since my last comment. Well, I think that is good, you finish it by 10th grade and you can move on to advanced stuff." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8012.0 0.0 0.0 0.0
"I completely understood in math terms the concept of wavefunction collapse by measurement (projection) after watching this brilliant lecture..." lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 5245.0 0.0 0.0 0.0
"no entendi ni madres, aqui en mexico nos enseñan puras estupideces para niño chiquito con retraso" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14067.0 0.0 0.0 0.0
"@anillatoo I had the opposite reaction. 7 was a fortunate choice (or maybe he really chose it on purpose). The point of the demonstration is the ideas behind Guass-Jordan. There's no reason to make the calculations messier than they need to be." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1783.0 0.0 0.0 1.0
"Now I have something to watch on the bus" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 7952.0 0.0 0.0 0.0
"why is iteration in newtons done..i cant understand the logic behind this" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15336.0 0.0 1.0 0.0
"EPFL student here, school is closed for a month because of Corona so came here lol" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3538.0 0.0 0.0 0.0
"27:02 I didn't like Cramer's rule since my school days, others did like it. It's so satisfying that he thinks the same about it." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 814.0 0.0 0.0 0.0
"Sir lec 8" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8698.0 0.0 0.0 0.0
"Why not just explain How the first mathematician who figured out the derivative of an exponential did it?" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11902.0 0.0 1.0 0.0
"c=a-b because it leads from where b is to a. numerically: b+c=b+a-b=a" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12582.0 0.0 0.0 0.0
"why not simply convert to the units needed before starting the calculations?" ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15354.0 0.0 1.0 0.0
"I am taking MBA, the statistics lessons is very useful. Thank you for sharing" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 5145.0 0.0 0.0 0.0
"is this graduate class or undergrad?" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13663.0 0.0 0.0 0.0
"He just transposed my brain!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4561.0 0.0 0.0 0.0
"polar coordinates 28:48" XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14198.0 0.0 0.0 0.0
"thats right, i live in in india and stay touched with these educational videos of america,its superb" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14653.0 0.0 0.0 0.0
"It's insane to think that this lecture was recorded 17 years ago. I just wonder where all of these brilliant students are now" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7049.0 0.0 0.0 0.0
"I went to a GOOD university and met some GOOD people, but I did not GOOD GOOD study, day day up. Watching these videos just because I missed my undergrad life so much" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6189.0 0.0 0.0 0.0
"If you're confused about his 'trick' or the idea in general...  /watch?v=BdO48p4DSWk" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 6562.0 0.0 0.0 0.0
"He is the master." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4550.0 0.0 0.0 0.0
"12:12 - well said, accurately diagnosed one of humans' 'weaknesses', sloppiness. It is the source of many societal problems." YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 392.0 0.0 0.0 0.0
"So happy to see Professor Strang still teaching beautifully. Even more happy that he’s mentioned Julia already in lecture 1. Thank you MIT for providing such up to date material." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8765.0 0.0 0.0 0.0
"21:55 My brain stopped working when he drew ℝ4 on 2 dim board! Woah!!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 689.0 1.0 0.0 0.0
"This actually makes sense now! Thank you!" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 10464.0 0.0 0.0 0.0
"A great lecture. At 38.58 he should have said Likelihood of observing the data given that the data is distributed according to parameters theta" bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 2121.0 0.0 1.0 0.0
"Have learnt whatever I know about  Linear Algebra mostly because of Gilbert Strang's lectures in OCW.
Thank you very much sir you have made understanding this corse the simplest.
🙏" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4447.0 0.0 0.0 0.0
"The camera needs work. :(" yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 10033.0 1.0 0.0 0.0
"My favorite was mathematical modeling - using calculus, physics, engineering, diff.eq., etc. to model physical systems. 
Very challenging and very interesting." jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7749.0 0.0 0.0 1.0
"can anyone provide me notes" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12609.0 0.0 0.0 0.0
"00:00 Hermitian Matrices
16:34 Fourier" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 280.0 0.0 0.0 0.0
真的是讲得好，虽然看英文视频有点儿费劲，但是值了 mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 15643.0 0.0 0.0 0.0
"Beautiful lecture, this one, and the entire series." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 2823.0 0.0 0.0 0.0
"my homework is to watch this lecture" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13985.0 0.0 0.0 0.0
"Professor Strang, thank you for explaining the Eigenvectors of Circulant Matrices ,Fourier Matrix and their impact on Machine Learning." 1pFv7e9xtHo "31. Eigenvectors of Circulant Matrices: Fourier Matrix" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8386.0 0.0 0.0 0.0
"dang just got his book introduction to computation and now i m watching his videos :) amazing video :)" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 12718.0 0.0 0.0 0.0
"I enjoyed this" TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 5382.0 0.0 0.0 0.0
"I think prof. Strang gave a much better explanation of the FFT algorithm in his other course - Mathematical methods for engineeers I" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 6037.0 0.0 0.0 0.0
"To get sound in both ears, on windows:

Go to start-> Search ""Turn on mono audio"" and click on it -> Turn mono audio on in the settings, and then turn it off after completing the video." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 11037.0 0.0 0.0 0.0
"slope ☃️🗻" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14320.0 0.0 0.0 0.0
"why arent they using white boards? and why are they still using black boards when green boards is better for the eyes." 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 15288.0 1.0 0.0 0.0
"No sound?" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 7891.0 0.0 0.0 0.0
"Superb clarity.world renowned professor of Mathematics.see how he acts on the stage one should inspire.I grace your heels." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8960.0 0.0 0.0 0.0
"Prof assumed all the variables are scalars so, while moving loss towards down hill or local minimum; how does loss function is guided to minimum without any directions (scalar property)" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8279.0 0.0 1.0 0.0
"Yeah this is what I've been waiting for. " BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 12122.0 0.0 0.0 0.0
"Soo the video is published in 2009 and I am wondering how advanced the boards are!!!" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8848.0 0.0 0.0 0.0
"I have no doubt his explanation is excellent, but as someone who was not taught by an excellent teacher prior to viewing this video, I was somewhat confused. Honestly, most of the students in this class appear to have already had linear algebra multiple times. Many of these conclusions they come to naturally require extensive underlying knowledge." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 5544.0 0.0 0.0 0.0
"Exam prep. lecture:
At 1:00, he cover subspaces of 3x3 matrices, call it M.
At 3:00, basis for M. At t = 15:00, basis for eigenspaces.
At 24:00, he covers rank 4 matrices. At 29:00, feasible exam problem.
At 39:00, graphs." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 3621.0 0.0 0.0 0.0
"Trzeci raz spośród 945 599 wyświetleń i za każdym razem fascynujący." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11099.0 0.0 0.0 0.0
"Thank you so much! My professor's lecture left me completely confused. I think I'd still be pretty lost without this lecture." HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9385.0 0.0 0.0 0.0
"Wow, I wish I watched this before spending 4 hours doing problems trying to figure this out." xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12063.0 0.0 0.0 0.0
"The lecturer looks like an old version of Nicholas Brody" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10168.0 0.0 0.0 0.0
"Those are some fat points." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10988.0 0.0 0.0 0.0
"A rugby ball has 2 out of three eigen values the same." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 2155.0 0.0 0.0 0.0
"Plank leanth printing" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8193.0 0.0 0.0 0.0
"Could someone provide me with the textbook for this course,  please?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 3240.0 0.0 0.0 0.0
"OCW is the Best!" -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 7970.0 0.0 0.0 0.0
"I came to comments section to see what doubts people have discussed. The only thin I see are funny jokes. LOL" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5184.0 0.0 0.0 0.0
"I love Prof. Strang and he is awesome. So, I will try to slow this lecture down. 
If you copy the following text into a mathjax friendly interface, you can read all the equations properly.


The basic knowledge we need from calculus is $\frac{d}{dt}$$e^{ax} = ae^{ax}$. Now we have two equations $$\frac{du_1}{dt} = -u_1+2u_2$$ $$\frac{du_1}{dt} = u_1-2u_2$$ I write these equations as $$\begin{matrix} u_1'\\u_2' \end{matrix} = \biggl[\begin{matrix} -1&2\\1&-2 \end{matrix}\biggr] \begin{matrix}u_1\\u_2\end{matrix}$$.

In matrix form, $U' = AU$. Now if I take $e^{\lambda t}k$ where 'k' is a vector as a solution, I get $\lambda e^{\lambda t}k = Ae^{\lambda t}k $, which is $Ak = \lambda k$. Hence lambda gives the power of the exponential in the solution which multiplies an eigenvector k. 

Part two (after minute 29): We already know that a complete set of eigenvectors will form a basis. So we can use eigenvector matrix to write any column vector. Then $u=Sv$; $\frac{du}{dt} = S\frac{dv}{dt} = ASv$, and $u(0) = Sv(0)$

Again from calculus, the solution of $\frac{dx}{dt} = ax$ is $x(t) = ae^{at}x(0)$. Now lets write this equation with a matrix $\Lambda$. For a vector 'v', $\frac{dv}{dt} = \Lambda v$, the solution is $v(t) =  e^{\Lambda t}v(0)$. For 'u', we just substitue the values, we get $$ u(t) = Sv(t) = S e^{\Lambda t} S^{-1}u(0) $$

We started from $U'=AU$. Now we know that if $U = e^{At}$ then it solves the equation. Hence, $e^{At}=S\Lambda e^{\Lambda t} S^{-1}$.

We also know that $e^x = 1+x+x^2/2+x^3/(3!)+....$. Now, let's replace 1 with $I$ and x with $At$ $$e^{At} = I+At+(At)^2/2+(At)^3/(3!)+....$$

Here (minute 40), I will slightly deviate from lecture here: 
$$e^{\Lambda t} = I+\Lambda t+(\Lambda t)^2/2+(\Lambda t)^3/(3!)+....$$

Substituting this in the equation for u(t), 
$$ u(t) = Sv(t) = S (I+\Lambda t+(\Lambda t)^2/2+(\Lambda t)^3/(3!)+....) S^{-1}u(0) $$
$$ u(t) = (I+S \Lambda S^{-1}t+S(\Lambda t)^2S^{-1}/2+S(\Lambda t)^3S^{-1}/(3!)S^{-1}+....) u(0) $$

Since $u(t) = e^{At}u(0)$, and A is $S^{-1}\Lambda S$, we have
$$e^{At} = I+At+(At)^2/2+(At)^3/(3!)+....$$

As before :)

Remember : A is diagonalizeable

(Edited based on the suggestion of Tony Jiang below)" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 5724.0 0.0 0.0 0.0
"Is there a video where he addresses the failures like he mentioned at 14:35" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6826.0 0.0 1.0 0.0
#DEE wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 200.0 0.0 0.0 0.0
"45:55 - shouldn't it be +2 (-2(-1) instead of -2?" aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1262.0 0.0 1.0 0.0
"im not sure these lectures are from 2005, they seem older" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 13569.0 0.0 0.0 0.0
"+Osman ÇALIŞIR All the lecture notes, exams with solutions and assignments are available on the MIT OpenCourseWare site at: http://ocw.mit.edu/18-01F06" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 254.0 0.0 0.0 0.0
"Thankyou for posting this, 10th grade is too slow." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9868.0 0.0 0.0 0.0
"wow. blackboards. it seems so archaic for MIT." MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15432.0 1.0 0.0 0.0
"A brand new view of the world" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2100.0 0.0 0.0 0.0
"Okay nerd" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 8052.0 0.0 0.0 0.0
"I was looking at some of these videos as recently I took all my college math classes. I was able to follow along but got a bit out of tract. Later, I noticed I have yet to take this class and will need it in university. 😂" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6159.0 0.0 0.0 0.0
"thk u sir.... awesome..." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14928.0 0.0 0.0 0.0
"Best maths teacher i have ever had !" sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2869.0 0.0 0.0 0.0
"17:31 bless him" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 511.0 0.0 0.0 0.0
"@IamJacksColon4 
So sill people are." 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 1640.0 0.0 0.0 0.0
"Can't wait to use this in real life!" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3131.0 0.0 0.0 0.0
"@beefstu20077 No, I am from Ukraine. English is not even my native language. Don't know why I use ""uni"". Probably heard somewhere before." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1788.0 0.0 0.0 0.0
"professor Alex Townsend, thank so much for a very theoretical background of  numerical linear algebra at MIT. DR. Gilbert Strang has created a powerful course in linear algebra." 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14216.0 0.0 0.0 0.0
"Thank you so much, professor...." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9403.0 0.0 0.0 0.0
"I dont know if there is any comment on this explanation, but I think there is a mistake in 09:15 > u’ shold be R X^r-1 and not just R > hence this should be the expression when you pass U to multply… R x^r ( x^r-1) / x^r / then you simplify and get R (x^r-1)" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5366.0 0.0 1.0 0.0
"Thanks MIT" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9598.0 0.0 0.0 0.0
"इ सब भी math रिसर्च मे लगा रहता है अब बर्लिन" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 15578.0 0.0 0.0 0.0
"Thanks a lot for this course. It helps me a lot. John Tsitsiklis is one of my idols now." rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 9660.0 0.0 0.0 0.0
"LIKE.....    ......❤️👍❤️. Wonderful, Good job. THANK YOU SO MUCH MY DEAR FRIEND. YOUR CHANNEL IS VERY NICE. I LOVE YOUR BLOGS TOO! I AM SO GLAD FOR YOUR SUPPORT TO MY CHANNEL. THANK YOU FOR TAKING THE TIME TO WATCH MY VIDEOS. YOU ARE A GREAT PERSON. STAY CONNECTED. BE SAFE FROM CORONA VIRUS AND PLEASE STAY HOME AND SAFE. I HOPE YOU HAVE A GREAT WEEKEND.👍👍👍❤️44" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7228.0 0.0 0.0 0.0
"@kevinkuei Yeah, i see your point, everybody got different taste. But imo the Professor explains everything very well, so if they are unsatisfied with this video because they didn't learn enough maybe they should consider taking another class." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1921.0 0.0 0.0 0.0
Wow:0 J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12094.0 0.0 0.0 0.0
"This guy is giving me such a good intuitive understanding of linear algebra, rather than just presenting seemingly semi-random algorithms without explanation." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 10530.0 0.0 0.0 1.0
"Can we find the solutions for the problem sets?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3110.0 0.0 1.0 0.0
"What is the reference book for this lecture series?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 11535.0 0.0 0.0 0.0
13:25 VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 416.0 0.0 0.0 0.0
"I really enjoyed this series of lectures just to refresh my memory. Thanks.But I am also surprised that A MIT professor of statistics can stump on such a simple task of deriving the Poisson PDF." jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 5915.0 0.0 1.0 0.0
"I was Told I Have  Hi Functioning Autism 


So I See The World Somewhat in A Different Way 

When I Was In Grade School I ask My First Grade Teacher What would Happen When A Meatball  Is Dropped Of A Tall Building Consisting  Of More Then   70  Floors Or Higher
As We Know We Can't  Take in To Practice The Above Actions Because Of 9/11. 

  Here is The Way I  Would Like To Do This.

 Take Meatballs  Cooed In A Oven And  Look At Them Under A Microscope And Then Drop Them Off The Building From The Roof  On To A Plate On The Ground Then Look At The Again 
Then Without Touching The Meat Balls Bring One Up To The Roof Of The Building. One In the Elevator And The Other In The  The Stirs Of the Building  I believe That The Meatball that is Dropped  Will Shrink Some What Because How The Laws Of Physics Grover en the Meatballs." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6148.0 0.0 0.0 0.0
"wth r u talking abt? :)" IfwfCe-JZaI "24. Structure of set addition IV: proof of Freiman's theorem" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 15450.0 0.0 0.0 0.0
"very cool." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 15000.0 0.0 0.0 0.0
"You are a great man." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 12163.0 0.0 0.0 0.0
"DR. Strang thank you for another classic lecture and selection of examples on Positive Definite and  Semidefinite Matrices." xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3281.0 0.0 0.0 1.0
"the coughing noise is freaking annoying!!  but this video is awesome." seO7-TwXH_I "Lec 30: Line integrals in space, curl, exactness... | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14680.0 0.0 0.0 0.0
"The dude in the left corner at 11:02 eating a sandwich clearly knows the entire course already." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10080.0 1.0 0.0 0.0
"Thank You." mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 9061.0 0.0 0.0 0.0
"I love the way he says parallelogram <3" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5792.0 0.0 0.0 0.0
"Best way to learn -> Understand and understand how precious education opportunity we all here get just by generous decision by MIT and prof Strang. We never pay any(even ads), we even can do repeat as much as we want and stop for a while to think or write." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 2881.0 0.0 0.0 0.0
"Need a lot of practice to write everything in capital wow . Well done lecture" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7811.0 0.0 0.0 0.0
"is it worth for iitjee exams. coz I care about clearing my concepts?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13641.0 0.0 0.0 0.0
"lec 8 missing ?" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13768.0 0.0 0.0 0.0
"Not all of them pay, most of them have scholarship..." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7917.0 0.0 0.0 0.0
"that's really called mathematics." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14648.0 0.0 0.0 0.0
"is there snowfall outside 
?" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13655.0 0.0 0.0 0.0
"Fantastic, excellent lecture thank you." k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3743.0 0.0 0.0 0.0
"At 50:23 if x - xo is not zero as we multiped it to the numerator and denominator why then we are taking f`(x).(x-xo) as zero" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2689.0 0.0 1.0 0.0
GOOD PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3973.0 0.0 0.0 0.0
"Thx MIT! I don't need to go to class anymore!" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11006.0 0.0 0.0 0.0
"I'm a second year calculus student, and I find these videos very helpful. thank you MIT, for making these awesome videos." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6301.0 0.0 0.0 0.0
"my only complaint is that he should've explained the notation he used for quantition .Because It's not as simple as it looks deltau stands for u(x+delta×)-u(x) and with the u which stands for u(x) those cancel out so there is the main equation for the derivatives without the explanation for not so sceptical students this could really go wrong I'm just saying" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13995.0 0.0 1.0 1.0
"Accent ❤️" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2225.0 0.0 0.0 0.0
"I don´t think ppl will respond to this as most of the comments are from years ago, but anyway. I didn´t understand the ""conversion factors"" when he got 40pi to be 125(1000) kcal. 


I´m studying for economics so it would be nice to learn some more science as well as calculus :)" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5374.0 0.0 1.0 0.0
"What about hyperbolic functions?" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11442.0 0.0 1.0 0.0
cool 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 12672.0 0.0 0.0 0.0
"MIT Opencourseware, I see a problem. When he explains about th general derivative formulas at the beginning, he writes (cu)'=cu'...but this multiplication of derivatives is I think supposed to be c'u+cu'..." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7510.0 0.0 1.0 0.0
"Thanks MIT open courseware." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9611.0 0.0 0.0 0.0
"Never saw this derivation of determinant before.  Needed a break at midpoint" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7819.0 0.0 0.0 0.0
"hey...
what course does 21.01 stand for??" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13152.0 0.0 0.0 0.0
"The best teacher teaching this material as far as I know. I wonder whether his books are as good as his lectures. May he still have a long and healthy life. :)" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 10010.0 0.0 0.0 0.0
"Squeeze theorem to find limits of triagonometric functions." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8874.0 0.0 0.0 0.0
"tbh I prefer blackboard or whiteboards in math classes. it makes it easier to take notes." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14440.0 1.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8435.0 0.0 0.0 0.0
"Wow , This is fabulous fabulous .." 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12023.0 0.0 0.0 0.0
"I'm in first year of information of systems, we are studying it now, it's awsome, I love calculation, I love make programs to solve problems :) I love it, Very nice!!! my dream is study at MIT D:" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6331.0 0.0 0.0 0.0
"This is the most intuitive and comprehensive calculus lecture I've seen. Thank you, MIT!" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10753.0 0.0 0.0 0.0
"He reminds of my Calc 1prof, a French girl." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4597.0 0.0 0.0 0.0
"the lecture and the teacher of my life!" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 14707.0 0.0 0.0 0.0
"its not that he thinks they are obvious but rather they are arithmetic steps that can be easily solved. 

For example ((2+3)+(5-2))^2=64 

Now, I skipped a few steps but Id rather jst tell you the answer because you already know how to get the answer Im giving you. " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13715.0 0.0 0.0 0.0
"Use to think part 5 is easier than the former parts, but now I think part 5 is the hardest of all lol" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11135.0 0.0 0.0 0.0
"it's like i can hear him when i study his book... He is just excelent..." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13697.0 0.0 0.0 0.0
"thanks MIT" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14553.0 0.0 0.0 0.0
thanks!!!!!!!!!!!!!!! 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14612.0 0.0 0.0 0.0
"Fuck what reality says, this IS my true Linear algebra professor. Thank you, prof. strang." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 3945.0 0.0 0.0 0.0
"From 9:10 was professor saying Putin in the subset????" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 3926.0 0.0 0.0 0.0
"Rather than maths, the other subject vedios donot have lyrics. I hope they will take necessary steps as early as possible." 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8494.0 0.0 0.0 0.0
"""it works, don't mess with it, it works"" Gilbert Strang.
But seriously though I will be forever grateful for these lectures. Thank you very fn much!!!!!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 162.0 0.0 0.0 0.0
"34:43 why ""directional second derivative"" would not give us a clue of whether it is a min or max? I thought it is a promising way. hmmm. " 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 986.0 0.0 1.0 0.0
"All hail Hamilton" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2295.0 0.0 0.0 0.0
"All matrices matter, no such thing as a good or a bad matrix :P" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 2300.0 0.0 0.0 0.0
"I find it interesting that there were ~278,000 views of the first lecture, but only ~90,000 views of this one... I wonder if MIT has that sort of drop-out rate ;-). " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5413.0 0.0 0.0 0.0
"respect from hungary. wish i have you in my university instead of prof. szegedi gabor" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 14264.0 0.0 0.0 0.0
"These courses are amazing, Thank you so much MIT OCW" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10400.0 0.0 0.0 0.0
"I can't imagine how much has he taught me. You are the best teacher in the world!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5219.0 0.0 0.0 0.0
"Totally useless......this shows that not everything that comes from MIT is useful" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 11078.0 0.0 0.0 0.0
"bit all over the place but that's the nature of trig" CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12542.0 0.0 0.0 0.0
"""it takes approximately forever"" lmfao" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 161.0 0.0 0.0 0.0
25:46 bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 786.0 0.0 0.0 0.0
"I have never been explained calculus in a clearer way. Excellent, absolutely excellent. As a math major with education minor, it is a priceless opportunity to watch these extremely skilled teachers. This is how teachers should be. This is how I'll strive to be. Thank you." hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5537.0 0.0 0.0 0.0
"Why does the US & UK not use the metric system?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11843.0 0.0 0.0 0.0
"The most important is the Students NOT the Stuff in the University or the Multimedia Sources.
The Most important thing to force students understand the concepts .
Thank you" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10196.0 0.0 0.0 0.0
"i love you gilbert" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 13437.0 0.0 0.0 0.0
"In this course, I still did not get why we are considering or learning column space or row space or matrix space, the aim of linear algebra was to solve Ax = b, how the column/row/matrix space come in the picture? 
Please explain." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 6689.0 0.0 1.0 1.0
"if you don't remember that please take an immediate remedy hahahhahaha valid tho" rLlZpnT02ZU "4. Parametric Inference (cont.) and Maximum Likelihood Estimation" "MIT 18.650 Statistics for Applications, Fall 2016" 13552.0 0.0 0.0 0.0
"Need advance level Math...not this" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7812.0 0.0 0.0 0.0
"Thank you for sharing this. Truly very informative." V3Wg_jrMSQY "Lecture 19: Differentiation Rules, Rolle's Theorem, and the Mean Value Theorem" "MIT 18.100A Real Analysis, Fall 2020" 9260.0 0.0 0.0 0.0
"Why is everyone coughing" seO7-TwXH_I "Lec 30: Line integrals in space, curl, exactness... | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11871.0 0.0 0.0 0.0
"Really good videos!! This series are helping me pretty much!! I'm from Brazil and I'm loving this videos!! " YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 8513.0 0.0 0.0 0.0
"“Did I just invent a negative one? Thanks! You get an A for the course.”  Awesome 😎" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15584.0 0.0 0.0 0.0
"@47:29 But where do we get the d vector in the formula for the G = X^T * X matrix?" L3-WFKCW-tY "33. Neural Nets and the Learning Function" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1565.0 0.0 1.0 0.0
"Go to mit ocw scholar site and check out the calculus 1 course,it has all the tests and solutions." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4063.0 0.0 0.0 0.0
"So brilliant." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8744.0 0.0 0.0 0.0
"OMG I studied this at uni, but I haven't used maths in a long time. I was trying to figure out how he got a 5. Took me 10 minutes to work out that 1 - - 4 = 5" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7982.0 0.0 0.0 0.0
"The best visualization on conditional continuous r.v. I've ever seen (even after I've already taken some courses on probability)." CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 10013.0 0.0 0.0 0.0
"cade os br`s? parece ate que sou o unico aqui" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12584.0 0.0 0.0 0.0
🖤 VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 15731.0 0.0 0.0 0.0
"I can't stand dislikes on stuff like this. That doesn't even make a statement when so few are towered by so many." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5221.0 0.0 0.0 0.0
"43:25 funny" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1207.0 0.0 0.0 0.0
"@PolskaUrban 

Well isn't math reality?

Like, vector fields are useful in describing electromagnetism and forces etc., which are real." z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1704.0 0.0 0.0 0.0
"He Using Simmons Book" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4457.0 0.0 0.0 0.0
"I am not an MIT student, but I study OpenCourseWare allowing me to further my education. Thank you for providing this material. Mr. Sipsen did a good job on these videos, I like how they are long and in-depth." 4MgN6uxd4i4 "7. Decision Problems for Automata and Grammars" "MIT 18.404J Theory of Computation, Fall 2020" 5121.0 0.0 0.0 0.0
"Thing that  he  said  eventually is so  nice  for  the  computer  engineers  to  understand  how  computational circuits  uses  FFT  in  order to increase efficiency 🥰🥰🥰  legend  Gilbert" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 10445.0 0.0 0.0 0.0
"One point I think he should have emphasized more is that concatenation with the empty language gives you the empty language.
Then it becomes obvious why no arrow is the same as the arrow with and the empty language." KAySmSEGc9U "3. Regular Pumping Lemma, Conversion of FA to Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 8104.0 0.0 1.0 0.0
"why can't covid lectures be like this?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 15292.0 0.0 0.0 0.0
"This is not difficult. I'd have assumed that MIT would have a more advanced treatment of this" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10698.0 0.0 0.0 0.0
"Enlightened !! Thanks Prof. Gilbert.." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3571.0 0.0 0.0 0.0
"42:40 every childbirth is basically a coin flip. yeah, right." 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 1185.0 0.0 0.0 0.0
"thank you..!!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14536.0 0.0 0.0 0.0
"we've used it without proving it but that's okay we only llive so long, let's skip that proof. :))" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 15081.0 0.0 0.0 0.0
"It took me some time to convince myself why As has two identical rows. The example only shows an example of 2x2 matrix, but the question of why is still there.  Someone helps explain this? 


I have a thought on this. We know that the reduced row echelon form of A has no more than 1 of ""1"" at each row and cols. If we multiply a row of A (let's say the 1st row) with a col of C^T (let's say 2nd col), we get 0 because each co-factor matrix in 2nd col of C^T (e.g. C21) always consist a zero vector. (C21 consists of zero vector of col  1 of A). Thus, their product is 0. 

Is it the right thought?" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 6992.0 0.0 1.0 0.0
"I agree.
> Just one small correction at 32:30: It should have been S * LAMBDA^100 * c instead of LAMBDA^100 * S * c." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 5028.0 0.0 1.0 0.0
"Thank you so much MIT for providing high quality courses like that OMG !

And i'm entering my math major next month, that's a GREAT TIMING😄" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 9353.0 0.0 0.0 0.0
"It is awesome! Thank you professor!" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 6937.0 0.0 0.0 0.0
"YAY FOR MORE CALC VIDEOS! 
I waited for so long lol :D" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12105.0 0.0 0.0 0.0
"The fact that he has to explain the last proof a few times to different people tells us something." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10099.0 0.0 0.0 0.0
"Thank you professor for all your efforts through the way of teaching us maths in an understandable and clear way!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9322.0 0.0 0.0 0.0
"I like his accent...." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5662.0 0.0 0.0 0.0
"Lot of rhetorical questions indeed ." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7427.0 0.0 0.0 0.0
"This man is a master expositor" l4NoMKEHQwM "11. Derived Distributions (ctd.); Covariance" "6.041 Probabilistic Systems Analysis and Applied Probability" 10859.0 0.0 0.0 0.0
"dam so much chalk in every stroke..interesting." BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 12705.0 1.0 0.0 0.0
"Small point - in the last proof, the theorem is for c >= -1, but we only proved for c >= 1. It's trivial to prove, but still worth noting, I think." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 8723.0 0.0 1.0 0.0
"""The Professor"": who makes sure that students do not miss even the tiniest detail of any concept." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 115.0 0.0 0.0 0.0
"41:40 ""gauss-given order"" LOL" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1157.0 0.0 0.0 0.0
"That was an outstanding explanation.....👌👌" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9921.0 0.0 0.0 0.0
"the proof for MVT is not rigorous, there is no proof that there exists a c where tangent exists on the curve. Also when the Professor says f' > 0, we does not specify where, does he mean f' > 0 for all points between [a,b] because the function can be increasing from a to b (ie f(b) > f(a)) and MVT says is there is some point c between [a,b] for which f'(c) > 0 and there can be other points c' where f(c') < 0. so the reverse is not true, ie if f'(c) > 0, for some c between [a,b] that does not specific f is increasing." 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14732.0 0.0 1.0 0.0
"This guy is really a asset. Gonna recommend this interview to couple of my professors." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 10539.0 0.0 0.0 0.0
"This professor got to be the most clueless person when it comes to teaching, I am sorry, it is TERRIBLE! He seems to have an ability to complicate matters that are actually simple to understand. I did this course basically watching youtube videos, I could NOT rely on the classes slides or the lectures. TERRIBLE! He knows his stuff, of course, but you know how some people are just terrible at teaching? That is it.. And he has no idea either that in fact he lost most of the class half way through.. Young still so maybe he can become better but this class was something else I tell you.. It also didnt help that this course should have been divided into 2 or even 3 parts. Anyway, my two cents here." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 10892.0 0.0 0.0 0.0
"This helped alot. Thanks!" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10572.0 0.0 0.0 0.0
"This lecture is basically broken by the fact that there is a continuation mismatch to 1. - references to concepts and theories are made that were never discussed in the previous lecture." C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 10798.0 0.0 0.0 0.0
"Prof. G. S. is awesome" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 8294.0 0.0 0.0 0.0
"so is this for vector calculus or multivariable calculus??? or are they just same?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14336.0 0.0 1.0 0.0
"Shouldn't MIT students already know calc 1?" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8645.0 0.0 0.0 0.0
https://www.youtube.com/watch?v=o2J4KzpsTHw&list=UUJ00ltJb9z260cQFNM7U2eQ&index=1 J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13281.0 0.0 0.0 0.0
"I'm literally in awe of what I can understand thanks to Dr. Strang" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 6346.0 0.0 0.0 0.0
"the virginity is strong there pal..." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14747.0 0.0 0.0 0.0
"The stance in 2:28 though." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 10285.0 0.0 0.0 0.0
"Strang is just the best teacher in the entire world, hands down. Imagine if all teachers had this level and passion for teachin... We would be living in a utopia." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 8908.0 0.0 0.0 0.0
"How wonderful!" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4906.0 0.0 0.0 0.0
"Thanks prof. Strang and MIT, videos are great" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9758.0 0.0 0.0 0.0
"Why don't he show specific examples?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11854.0 0.0 0.0 0.0
Brilliant QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2922.0 0.0 0.0 0.0
"beautifully simple how that Fibonacci worked out" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 12522.0 0.0 0.0 0.0
"It's the first time I've understood everything. Every piece of info is very clearly explained. Thanks" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7075.0 0.0 0.0 0.0
"I wish I could have found these gem of videos much earlier in my life" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6193.0 0.0 0.0 0.0
"Great lecture" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4242.0 0.0 0.0 0.0
"博士，您的研究太深奥了，太多理念集在一功式内?，压力転动能无阻●界处和一大堆，，，，，，，，，SO。
简易人造具为电赫电質使UF0反向为，在地面上翻机体，而吸收有效質量而向上送物体上天国，SO，但，人体机能所须和定立点须捉，但，飲食须像胎内咹乃吸收，因为头罩開後欲食会哪个(自己想像，每人構想不同，SO)，，，SO。" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15617.0 0.0 0.0 0.0
"smart is the new sexy, how you explain the knowledge is so damn sexy" KAySmSEGc9U "3. Regular Pumping Lemma, Conversion of FA to Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 14323.0 0.0 0.0 0.0
"tremendous explanation thank you for sharing ... " vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 14959.0 0.0 0.0 0.0
"I think he made mistake noting that the formula for T prime (Time diliation) is for general Relativity.
" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6017.0 0.0 1.0 0.0
"thansk man" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14621.0 0.0 0.0 0.0
"I just don’t understand why talking about statistics for hours!! It is not that hard to give an introduction!!" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 5602.0 0.0 0.0 0.0
Epic RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 3573.0 0.0 0.0 0.0
"love Prof. Strang!!!" MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13860.0 0.0 0.0 0.0
"So... I was feeling kind of hip so I started simplifying the 1/8 - cos(4x) /8 into terms with only x and I ended up with just sin^2(x) cos^2(x).. 
Now that's pretty interesting right cause it's the same as the integrand plus a constant. 
Anyone tried this?" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8814.0 0.0 0.0 0.0
"I like to hear Prof. Tsitsiklis say ""equally likely""." -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 5696.0 0.0 0.0 0.0
"thanks. I am mexican and I want to say this videos are amazing" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14615.0 0.0 0.0 0.0
"Is this class more for people taking Computer Science or is it more geared towards Engineering or both?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 6858.0 0.0 0.0 0.0
"I hope he lives to AT LEAST 197." Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5586.0 0.0 0.0 0.0
"This guy gives the lecture as if there were a full class of students sitting there. Amazing" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 10509.0 0.0 0.0 0.0
"Professor Jerison, thank you so much for giving such a fascinating calculus series!" TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8332.0 0.0 0.0 0.0
"We cannot see the the top portion of the blackboard.  Who filmed this?  I hope it gets fixed in the next videos." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 11318.0 1.0 0.0 0.0
"Really great lecture! Will start looking at the following videos soon!
One sidenote: In the last twenty seconds there are not CC subtitles.
It's does not effect me, but might confuse people who can't hear." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8515.0 0.0 0.0 0.0
"So much respect and admiration for Professor Strang" cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8780.0 0.0 0.0 0.0
"Do I need to know calculus for this ;(. I will learn that after and watch this again." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 3405.0 0.0 0.0 0.0
"For those who have struggled with the where does -k and -b came from: See that   y^|| = dy^| / dt = -by^| - ky" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 3912.0 0.0 1.0 0.0
"wonderful teaching. the examples he taught at the end makes me laugh. The bus crowdedness example is great!" XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 15398.0 0.0 0.0 1.0
"you mean a mess ^^" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15510.0 0.0 0.0 0.0
"09:30 Example 1: Non-Singular Matrix
28:00 Example 2: Singular Matrix
37:40 Describes components u, v in words" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 299.0 0.0 0.0 0.0
"This guy is definitely PERFECTTTT!!!!" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 10527.0 0.0 0.0 0.0
"The ending of this lecture to reference Black hole was mind blowing !!!" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10090.0 0.0 0.0 0.0
👍👍 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15702.0 0.0 0.0 0.0
"where can I find all lectures of MIT 6.041?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 15223.0 0.0 0.0 0.0
"Distance between Clinton and Monica...🤣lmao that was a good one" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 3403.0 0.0 0.0 0.0
"I did't understand at the first view nor at the 2nd one but at the 3rd or even at the 4th time waw CRAZY approach !" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 5263.0 0.0 0.0 0.0
"There are not n! distinct ways to reorder the matrix.  Only n!/2 I believe.  Because swapping rows 1 and 3 is the same thing as swapping rows 3 and 1.  Consider a 3 x 3 matrix does not have 6 different row swaps.  i can swap 1,2 1,3, or 2,3 that's all." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 10354.0 0.0 1.0 0.0
"Can somebody explain the thing he said at 15:58 ,delta L is equal to delta h by delta L, where did he get that formula" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3063.0 0.0 1.0 0.0
"While deriving the directional derivative, how did we approximate dr/ds=1 ( He said we're moving with unit speed. Firstly, why? And even if we are, how does that make dr/ds=1? )" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 11721.0 0.0 1.0 0.0
"Concept of Eigenvector at 1:02" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 3192.0 0.0 1.0 0.0
"Professor, really respect you ! Thank you and God bless :)
" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8406.0 0.0 0.0 0.0
"I have tried to study differentials through multiple sources and am always confused. In this video, he explicitly addresses the problem of trust in differentials. This is my first time to grasp the concept." 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5566.0 0.0 0.0 1.0
"At 13:20 how he decided the dimension of null space as  2 from x?" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 2588.0 0.0 1.0 0.0
"Now I regret not watching all of his videos although I knew they were available and great videos!" TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 7955.0 0.0 0.0 0.0
"Brainstorming , Mind-boggling  " FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2914.0 0.0 0.0 0.0
"really Mr stang is  osm professor" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 14246.0 0.0 0.0 0.0
"32.43 just wow" zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 922.0 0.0 0.0 0.0
"Master Yoda passed on what he has learnt by fibonacci and 1.618." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 7600.0 0.0 0.0 0.0
EXCELLENT 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3542.0 0.0 0.0 0.0
"Only teacher like him can make average students to extraordinary by his style on subject." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8123.0 0.0 0.0 0.0
"Oh my god literally this guy is smart, my professor just throws information on the white board with no explanation" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8017.0 0.0 0.0 1.0
"Interesting definition of odd numbers at 14:30 as being only positive." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 6726.0 0.0 1.0 0.0
"linear algebra and learning from data 👍👍👍" lZrIPRnoGQQ "27. Backpropagation: Find Partial Derivatives" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13798.0 0.0 0.0 0.0
"the best" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 14663.0 0.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8445.0 0.0 0.0 0.0
"I have a doubt at 12:47 if I have a matrix in M which is [0,0,0; 0,0,0; 1,0,0] which is neither a part of Symmetric matrix or upper triangular matrix, then how come on doing S+U I get all 3x3 matrices?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 5486.0 0.0 1.0 0.0
"we are so lucky 🫶🏼" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 15073.0 0.0 0.0 0.0
"Absolutely well done and definitely keep it up!!! 👍👍👍👍👍" phbw9r1iUDI "7. Parametric Hypothesis Testing" "MIT 18.650 Statistics for Applications, Fall 2016" 2218.0 0.0 0.0 0.0
"Dude you're amazing" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3525.0 0.0 0.0 0.0
"I like the fact that he wrote very big on the board. I have myopia and I can't see anything the lecturer writes in my college." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5682.0 1.0 0.0 0.0
"Just to the point! Clear and Concise! He is my hero!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7200.0 0.0 0.0 0.0
"Everyone is excited for this course but only very few will complete it from start to finish." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 3610.0 0.0 0.0 0.0
"When he says *OK* you know it's about to get good 😂😂" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 11624.0 0.0 0.0 0.0
"I completed the 18.06 today.
I started on 2020.03.16 in Japan(I'm Chinese) and today is 03.29. These 14 days absolutely changed my life and inspired me.
And Math is a whole new thing to me now. 
This lecture was not like a lecture, it's much more like a game, a journey, an inspiring movie.
Thank you, Professor Strang, and thank you, people who made Mandarin subtitles for this video lecture!
Professor Strang, you are the BEST TEACHER in my whole life. And I will remember the lecture 18.06 forever." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5239.0 0.0 0.0 0.0
"I Really Like The Video From Your Divergence theorem (cont.): applications and proof." wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 4953.0 0.0 0.0 0.0
"why were they in a rush to leave the class , man I felt bad @46:35" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 15378.0 0.0 0.0 0.0
"33:36 ""That's what she said.""" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 964.0 0.0 0.0 0.0
"Five five five." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3828.0 0.0 0.0 0.0
"Will the column space of A be a plane if there are only 2 rows, like if A is something like { 2, 1, 1; 1, 6, 3 }? Although the three columns are independent, without a third component, it will only cover a plane, right?" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11946.0 0.0 1.0 0.0
"Thanks to the great people at MIT!" CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9812.0 0.0 0.0 0.0
"Finally those 5 lectures paid off..!!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 3781.0 0.0 0.0 0.0
"Brilliant teaching, a gift to the world. Thank you prof. Strang and OCW" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 2936.0 0.0 0.0 0.0
"A real teacher." t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2154.0 0.0 0.0 0.0
"This lecture made my brain hurt, probably because I don't know anything about physics." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10819.0 0.0 0.0 0.0
"Incredible Teacher!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6702.0 0.0 0.0 0.0
"Very nice way of explaining I hope Lord venkateswara blessed may you long live." 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11216.0 0.0 0.0 0.0
"This lecture was all about flexing the computational power of eigenstuffs. I'm definitely impressed!" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 10830.0 0.0 0.0 0.0
"42:20 prof sipser a real one" m9eHViDPAJQ "4. Pushdown Automata, Conversion of CFG to PDA and Reverse Conversion" "MIT 18.404J Theory of Computation, Fall 2020" 1179.0 0.0 0.0 0.0
"How bizarre. Here I am" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 4806.0 0.0 0.0 0.0
"Thank you 🦋" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 9462.0 0.0 0.0 0.0
"Man! you are an inspiring mathematician. If i become one, full credit to you.....
" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 7581.0 0.0 0.0 0.0
"I find it cool how he slides in some french words without people noticing :)" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5411.0 0.0 0.0 0.0
"he is my hero !
that man made me love linear algebra :)
i can watch his lectures every year !
thx professor Strang!  you are the best teacher we're all dreaming about" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 13097.0 0.0 0.0 0.0
"Thanks MITOpenCourseWare for uploading these beautiful lectures. Even remote students get taught by Prof. Strang.        :)" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 9622.0 0.0 0.0 0.0
"Thank you for sharing! <3" IycOPFmEQk8 "5. CF Pumping Lemma, Turing Machines" "MIT 18.404J Theory of Computation, Fall 2020" 9262.0 0.0 0.0 0.0
"oh I can't stop this class, I watch it all night." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 14101.0 0.0 0.0 0.0
"The cameraman here is now a Senior ML Engineer at Google, California." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10038.0 0.0 0.0 0.0
"thinking about vector spaces, eigenvalues, and eigenvectors are, well, difficult indeed" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14791.0 0.0 0.0 0.0
"At 19:03, 5 minutes of 18.06 is enough to take care of 18.03. That's mathematics prof trash talk for ya." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 2599.0 0.0 0.0 0.0
"just great! This course is the best to clear up all the mess that is all around the testing hypothesis in various sources!" phbw9r1iUDI "7. Parametric Hypothesis Testing" "MIT 18.650 Statistics for Applications, Fall 2016" 13736.0 0.0 0.0 0.0
"Watching this course like i watch a series on netflix :D . This is the best explanation of LINEAR ALGEBRA and today i  finally understood what is actually meant by MATRIX multiplication. Thanks a lot Gilbert Strang." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11299.0 0.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8425.0 0.0 0.0 0.0
"God bless MIT" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4073.0 0.0 0.0 0.0
"thank you for releasing this 🙏" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 14494.0 0.0 0.0 0.0
"what b turns out to b :D" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 15125.0 0.0 0.0 0.0
"It may be worth to note that instead of partial derivatives one can work with derivatives as the linear transformations they really are, and also looking at the networks in a more structured manner thus making clear how the basic ideas of BPP apply to much more general cases. Several steps are involved. 

1.- More general processing units. 
Any continuously differentiable function of inputs and weights will do; these inputs and weights can belong, beyond Euclidean spaces, to any Hilbert space. Derivatives are linear transformations and the derivative of a neural processing unit is the direct sum of its partial derivatives with respect to the inputs and with respect to the weights; this is a linear transformation expressed as the sum of its restrictions to a pair of complementary subspaces. 

2.- More general layers (any number of units). 
Single unit layers can create a bottleneck that renders the whole network useless. Putting together several units in a unique layer is equivalent to taking their product (as functions, in the sense of set theory). The layers are functions of the of inputs and of the weights of the totality of the units. The derivative of a layer is then the product of the derivatives of the units; this is a product of linear transformations. 

3.- Networks with any number of layers. 
A network is the composition (as functions, and in the set theoretical sense) of its layers. By the chain rule the derivative of the network is the composition of the derivatives of the layers; this is a composition of linear transformations. 

4.- Quadratic error of a function. 
...
——-
Since this comment is becoming too long I will stop here. The point is that a very general viewpoint clarifies many aspects of BPP. 

If you are interested in the full story and have some familiarity with Hilbert spaces please google for papers dealing with backpropagation in Hilbert spaces. A related article with matrix formulas for backpropagation on semilinear networks is also available. 

For a glimpse into a completely new deep learning algorithm which is orders of magnitude more efficient, controllable and faster than BPP search in this platform for a video about deep learning without backpropagation; in its description there are links to a demo software. 

The new algorithm is based on the following very general and powerful result (google it): Polyhedrons and perceptrons are functionally equivalent. 

For the elementary conceptual basis of NNs see the article Neural Network Formalism. 

Daniel Crespin" lZrIPRnoGQQ "27. Backpropagation: Find Partial Derivatives" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6977.0 0.0 0.0 0.0
"Who else is still a teenager" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11732.0 0.0 0.0 0.0
"The integral of sinx is pretty easy.
If you want to calculate the area from 0 to n times pi, just check if n is odd or even. If its odd then the area is 2, if its even area is equal to zero." 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10143.0 0.0 0.0 0.0
"I Really Like The Video From Your Lecture 32: Quiz 3 Review." HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 4958.0 0.0 0.0 0.0
"Even though I've learned Linalg from my undergraduate course, it was ages ago. Thanks to Prof Strang, the explanation of the geometry meaning of the matrix is much clearer than what I've ever been given." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3589.0 0.0 0.0 1.0
"it's LeibniTz not Leibniz" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13692.0 0.0 0.0 0.0
"i have learned a lot from these lectures--but i just which prof Auroux would just step throgh the algebra--he always skips steps--then says ""everyone see that""--no one does--and then back tracks--tedious.  Well--i am sure having to do the steps at all is tedious for him.  Overall--he manages to pack a lot of insight into 45 minutes each and every time" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13396.0 0.0 0.0 1.0
"I am having a hard time making sense of the notation at 11:22.  I believe the notation should be the conditional probability P(k|t) rather than P(k,t). I interpreted the latter to be the joint probability and if it is the case, the summation over all k of P(k,t) given a fixed t could not be equal to 1. Anyone, please help knock some sense to my head!" jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 5104.0 0.0 1.0 0.0
"The proofs he used were totally solid. They're also nice because they're very intuitive. L'Hospital's would be premature on the third day (assuming you want to be very rigorous). 

It might help if he explained that, as theta goes to zero (in the limit), the lines of the angle get closer and closer to parallel. Then he could draw the picture with two parallel lines, in which case the 1 - Cos(theta) segment would be gone (zero)." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10260.0 0.0 0.0 1.0
"Don't think you're going to just get away with throwing mad shade at Python. We see you." rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3475.0 0.0 0.0 0.0
"이게 대학교 과정이라니" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15688.0 0.0 0.0 0.0
"What a boss professor. Wish we had these at my school." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 11395.0 0.0 0.0 0.0
20:45 FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 661.0 0.0 0.0 0.0
"when the hell would you use this in a real life situation outside of education?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15211.0 0.0 0.0 0.0
"Wa... Wa... Wa... Are these students really MIT's students?  Wa.... I am flabbergasted by their questions.  How many of them have full SAT scores? :0" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11254.0 0.0 0.0 0.0
"If you are reading this Post Rapture:
Rev 14:6 - And I saw another angel fly in the midst of heaven, having the everlasting gospel to preach unto them that dwell on the earth, and to every nation, and kindred, and tongue, and people,
Rev 14:7 - Saying with a loud voice, Fear God, and give glory to Him; for the hour of His judgment is come: and worship Him that made heaven, and earth, and the sea, and the fountains of waters.

Pre Rapture:
Mark 16:15 - And He said to them, “Go into all the world and preach the gospel to every creature.
 - You've broken 1 of the 10 commandments and are guilty of sin if you've ever lied, or stolen, or lusted.  Works of righteousness will not save you.  Jesus Christ is the only way.
Romans 6:23 - For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord.
Romans 10:9 - That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved.

I ask you to rethink what you know about God.  Rethink what you've been taught.  God wants a relationship, not a religion.  
 - Jesus came to die for all mankind ... not kill them.
 - Jesus came to bring salvation for all mankind ... not condemnation.
 - Jesus came to be an example, a light to the world .. not to force people into submission.

1.  Humble yourself before the Lord
2.  Admit to the breaking of His laws as found in the 10 commandments
3.  Ask for His forgiveness for those sins
4.  By faith, believe Jesus died on the cross for your sins
5.  Confess with your mouth that Jesus is your Lord and Savior
6.  By faith, believe Jesus rose from the dead  
7.  Receive the gift of salvation and the Holy Spirit will fill you" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6536.0 0.0 0.0 0.0
"Exactly. A good friend of mine got a free ride at MIT." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3619.0 0.0 0.0 0.0
"No we don't have to use gradient decent in this case" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7895.0 0.0 0.0 0.0
"I am completely following the mit courseware to study my pre engineering courses awesome > thanks MIT" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5069.0 0.0 0.0 0.0
"Proffesor Auroux talking about Topology kind of made me smile" PnPIqh7Frlw "Lec 24: Simply connected regions; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8412.0 0.0 0.0 0.0
29:30 XtNXQJkgkhI "22. Bayesian Statistical Inference II" "6.041 Probabilistic Systems Analysis and Applied Probability" 854.0 0.0 0.0 0.0
"The last ten minute discussion in a nutshell :
If A has independent columns then Ax=0 only for x=0 
Then multiply A^T on both sides of Ax=0 
A^T Ax=0 only true for x=0
So no combination of columns of 
A^T A gives 0
As A^T A is symmetric 
No combination of rows of A^T A gives 0 hence A^T A is invertible bcz if combination of rows give 0 then determinant is 0" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 10156.0 0.0 0.0 0.0
"i think there is a mistake at 10:44 where it was 1-r“2 and integrate it becomes r“3 not r“4" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13479.0 0.0 1.0 0.0
42:50 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 1189.0 0.0 0.0 0.0
"Maybe it is posible put subtitles spanish,  gracias." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7637.0 0.0 0.0 0.0
"I'm a bit unsure as to why he doesn't like the 10 in the matrix E around 19:00? Are we assuming we already have A and U defined, and just need to find a matrix that relates them? Is it because the L parts, like the E parts (E21, E31, E32) can simply be stated, but to calculate the final L and E, final L can be stated (just like it's parts), where as E has to be calculated?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 6293.0 0.0 1.0 0.0
"Educating the third world in how to develop. Thanks open course MIT for profit and google. Kills us via global warming why don’t you" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3550.0 0.0 0.0 0.0
"Great professor, great lecture although it seems there are no students, great chalk and also great gesture at 20:14! xD" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4326.0 1.0 0.0 0.0
"If gradient is always orthogonal to any tangent plane on the surface then how come the chain rule (grad f dot dr) doesn’t always equal zero? In other words for f(x,y) why doesn’t fxdx + fydy always equal zero." 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 6500.0 0.0 1.0 0.0
"thank you ! Prof. and MIT" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 14473.0 0.0 0.0 0.0
"How is the earth spinning via a magnet field and the moons' rotation locked to the earth?" BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 4873.0 0.0 0.0 0.0
"This is great!" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10666.0 0.0 0.0 0.0
"What book is used for this course?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11472.0 0.0 0.0 0.0
"""Don't take the videotape quite so carefully""... Camera zooms in right after lmao" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 43.0 1.0 0.0 0.0
"@prantare Because delta v represents the change of the value of v from the original v(x) value (in other words, delta v = ""new"" v - ""old"" v). As delta x goes to zero, ""new"" v and ""old"" v become the same (if v is continuous at this ""old"" v value, by the definition of continuity), and therefore the delta v approaches zero. Make sense?" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1980.0 0.0 0.0 0.0
"in the first minute and 30 seconds there were more girls on screen than all of my math classes up to calc 3 " 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13600.0 0.0 0.0 0.0
"RIP. He will be missed." NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8488.0 0.0 0.0 0.0
"16 x Row 1 - 9 x Row 2 = Row 3" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 464.0 0.0 0.0 0.0
"Do the additive and multiplicative inverses have to be unique? The notation -x and x^(-1) suggests so, but the statement of the axiom (""there exists"") seems to suggest there may be more than one." mlPLLXHZ8_U "Lecture 4: The Characterization of the Real Numbers" "MIT 18.100A Real Analysis, Fall 2020" 3412.0 0.0 1.0 0.0
"One day, I will be like this man" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8076.0 0.0 0.0 0.0
"I wish I could make you immortal. You are a legend." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6194.0 0.0 0.0 0.0
"This teacher is awesome, thank you mister Strang, thank you MIT" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10933.0 0.0 0.0 0.0
"spripreis high school premitt" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 14389.0 0.0 0.0 0.0
"@xo20202004  there are lots of videos available from various universities. it depends on what you are looking for. if you are looking for another calculus lecture you can check out ......
Calculus1 Lecture1

its a calculus course offered by the University of Missouri-Kansas City." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2069.0 0.0 0.0 0.0
"46:29 one to the last row in the matrix left side should be x_1^(r1-1), x_2^(r1-1), etc. instead of r-1" JTbZP0yt9qc "6. Maximum Likelihood Estimation (cont.) and the Method of Moments" "MIT 18.650 Statistics for Applications, Fall 2016" 1271.0 0.0 1.0 0.0
"Is it just me, or does this lecture stop working at 2:31? I've restarted, but nothing." UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6785.0 0.0 1.0 0.0
"The normal vector ?" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10204.0 0.0 1.0 0.0
"fantastic explanation!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 12847.0 0.0 0.0 0.0
"39:38 wait, why do you get a line? Why wouldn't it sketch out like a solid circle or something? I don't quite get that" XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1102.0 0.0 1.0 0.0
"Hello, could you translate your videos to another languages, please? Thanks!" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 4664.0 0.0 0.0 0.0
"Thanks for the lecture!!!" p-bXJIa7QVI "Lecture 30: Completing a Rank-One Matrix, Circulants!" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9717.0 0.0 0.0 0.0
"great lecture" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 12974.0 0.0 0.0 0.0
"He is lowbrow" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 4522.0 0.0 0.0 0.0
"35:40 The identity should be n x n" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1017.0 0.0 1.0 0.0
"HAYNES MILLER explains better" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4397.0 0.0 0.0 0.0
"6:57 ""aright"" :D" aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1387.0 0.0 0.0 0.0
"I'm french and I did this when I was 16, not a joke..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6322.0 0.0 0.0 0.0
"intro to linear transformations and horrors of linear algebra haha" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13621.0 0.0 0.0 0.0
"In linear case, regulation for l2 norm is just pseudo inversion! How about nonlinear case say the case in the deep learning?" Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6639.0 0.0 1.0 0.0
"1 shot for every time he says ""the chain rule""" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 317.0 0.0 0.0 0.0
"For the life of me I couldn't ""get"" the final proof, but now I think I get it. If (A^T A) has linearly independent columns, then A has linearly independent columns. The first is (A^T A)x = 0, and the latter is Ax=0. Remember that linear independence means that the only combination that goes to zero is the zero vector. If C(A) is linearly independent, then Ax=0 means x=0." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 3893.0 0.0 0.0 0.0
"If majority of people are interested in science and math like they do in music and cinema, it would literally push civilization to the next level." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6507.0 0.0 0.0 0.0
"VERY slightly" XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11148.0 0.0 0.0 0.0
"this is amazing" H_k1w3cfny8 "10. Continuous Bayes' Rule; Derived Distributions" "6.041 Probabilistic Systems Analysis and Applied Probability" 14852.0 0.0 0.0 0.0
Easy PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3547.0 0.0 0.0 0.0
"I love this guy
professor, you are great. I really enjoyed your lectures and will enjoy and reference them later on. thanks a lot" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 5804.0 0.0 0.0 0.0
"I give up everything, watching film and sufing web just to comprehend this amazing content given by this gifted professor omg." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 5437.0 0.0 0.0 0.0
"da miedo , parece como las series un profesor psciopata" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12703.0 0.0 0.0 0.0
"The way Prof. Strang explains how det(A-λI) = 0 comes is so enlightening! Wish I had taken to this course earlier." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 10321.0 0.0 0.0 1.0
"He forgot to finish PCA." NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4483.0 0.0 1.0 0.0
"Correct me if I'm wrong, it seems to me that in order to account for the empty transitions in an NFA, the proof that NFA languages are regular would need to utilize the result that a union of regular languages is regular. If so, using the regularity of NFA languages to prove that a union of regular languages is regular is perhaps circular, and perhaps the most important aspect of the proof of regularity for NFA was brushed over." oNsscmUwjMU "2. Nondeterminism, Closure Properties, Conversion of Regular Expressions to FA" "MIT 18.404J Theory of Computation, Fall 2020" 3220.0 0.0 1.0 0.0
"Can anyone say why we didn't use absolute value for y after taking the integral?" 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3043.0 0.0 1.0 0.0
"Great teacher. thanks you MIT for the high quality courses you share." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 4345.0 0.0 0.0 0.0
"Isn’t this video supposed to be watched after trying the exam1 ?" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 6903.0 0.0 0.0 0.0
"26:30 start doing algebra furiously :D" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 802.0 0.0 0.0 0.0
"Apparently it's hard to see a teachers who understand the subject and explains it to student, but Dr. Strang just know exactly what he's doing, love it!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2515.0 0.0 0.0 0.0
"Notes: 
32:00 If a matrix A is added by a multiple of Identity, and its eigenvalues will turned out to be the multiple number + A’s eigenvalues.

(A+B)x != (a+b)x because we cannot sure if x is the eigenvectors for both A and B, works the same for (AB)x

39:00 With an example of orthogonal rotation matrix:
1. Trace has to be the sum of the eigenvalues and the det has to be the product of the eigenvalues.
2. There is a trouble in orthogonal rotation matrix since we don’t have any eigenvector parallel to the Ax. The eigenvalues will appear to be the imaginary number.

46:20 With an example of a a11 = 3, a12= 1, a21 = 0, a22 =3 (Triangular matrix)
1. Eigenvalues will appear to be in the diagonal. 
2. The number of eigenvectors could be less than the the number of eigenvalues" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 7940.0 0.0 1.0 0.0
"Can I change the language into arabic!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3003.0 0.0 0.0 0.0
"Thanks mit" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9750.0 0.0 0.0 0.0
"godly lecture" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12935.0 0.0 0.0 0.0
"Accent ❤️" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2226.0 0.0 0.0 0.0
"no wonder my kids now nothing" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 14075.0 0.0 0.0 0.0
https://www.youtube.com/watch?v=98vap_OR7a8 J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13270.0 0.0 0.0 0.0
"@inuyashalivesbaby 

Oh, get over academia already. I'm not being condescending and pompous: I think it's cool that you're a T.A.

You're probably sensitive because you're in academia. I am too." dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 1892.0 0.0 0.0 0.0
"In Poland we call calculus mathematical analysis, and it's trivial." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6616.0 0.0 0.0 0.0
"can anyone share how we get property 9 from the  properties 1-3 ?" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 12614.0 0.0 1.0 0.0
Finally LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 3758.0 0.0 0.0 0.0
"At 3:08 the subtitles are about someone who watched ""How to be a Millionaire""." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 2658.0 0.0 0.0 0.0
"33:31 Minnie Mouse learns Calculus 2. Great lecture!" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 961.0 0.0 0.0 0.0
"Amazing class!" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 2355.0 0.0 0.0 0.0
"Appreciated very much" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2518.0 0.0 0.0 0.0
"My linear algebra class at Columbia used his textbook and my professor even recommended that we watch his videos. Gilbert Strang taught me that mathematics is elegant and beautiful and I ultimately switched from physics to math after this course." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7770.0 0.0 0.0 0.0
"Please, does somebody know what is name's book adopted by this course ? Or, better, a list of books recommended to read during this course by the lecturer ?" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8219.0 0.0 1.0 0.0
"is nobody going to point out the kid with the dyed yellow mohawk at MIT?" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 13642.0 0.0 0.0 0.0
"21:28 Well I shouldn't say anything bad about calculus, but I'll. 😂" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 679.0 0.0 0.0 0.0
"I enjoyed this professor's lecture. It helped me conceptualize a new idea." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5385.0 0.0 0.0 0.0
"just finished the whole course! thank you MIT for giving us the opportunity to learn from the best :)
Chile, 2021." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13732.0 0.0 0.0 0.0
"This guy is awesome." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 10526.0 0.0 0.0 0.0
"Ahh the days when you had to use a separate GPS device to find your location, the days when Nokia ruled the world's pockets, and when YouTube started rising in an elevator powered by cat videos........." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2286.0 0.0 0.0 0.0
"Lol, damn.  Teachers like this make class so much more interesting!  " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7403.0 0.0 0.0 0.0
"@zobazoba69 Yes that would have been a better description of what gradient actually is" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2086.0 0.0 1.0 0.0
"what a great man" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 15106.0 0.0 0.0 0.0
"Thanks ! Sir Prof Gilbert Strang for sharing your valuable knowledge and information on this topic . God bless You 🙏 .
- Real Group of Companies Goa ❤️ India ." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9580.0 0.0 0.0 0.0
"Prof. Strang, you may not a true physicist but you are a true magician." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8313.0 0.0 0.0 0.0
"Lectures like this one make me regret not taking Linear Algebra in college. However, I would probably never have come across Prof Strang's lectures had I did. Such a great teacher for showing how interesting and useful a subject that I once thought was so dull." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7307.0 0.0 0.0 0.0
"@kotofu Ofcourse someone who likes math doesn't need to like every lesson, but the only reason to view this is to learn something, and if you don't learn something from this it's probably because you have already studied this, you aren't on this level yet, or you are just stupid. Theese things are your own fault (possibly parents) and there is no reason to blame the video." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1924.0 0.0 0.0 0.0
"Best professor ever." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2874.0 0.0 0.0 0.0
Dadfagafwgdqgsfshsvywhaggw srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 3291.0 0.0 0.0 0.0
"Those are some wonderful examples you have used professor! I've been following this entire probability series and I would like to say that I am really grateful for these videos. Thank you and keep up the good work!" P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 10989.0 0.0 0.0 0.0
"Stop following the guy around with the camera!!
I want to see the blackboard. We're here to lean to theorems, not to admire the guy's shirt!!" YAo1sd4kuOQ "2. Forbidding a subgraph I: Mantel's theorem and Turán's theorem" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 8900.0 1.0 0.0 0.0
"At 27:00 why follow the direction of eigenvalue? It just comes out of no where" wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2627.0 0.0 1.0 0.0
"Thank you, I am so sorry that I did not watch this video years ago." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9496.0 0.0 0.0 0.0
"Thank you for making rank 1 matrices so clear!" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 9252.0 0.0 0.0 0.0
"I love it love it love it love it" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5759.0 0.0 0.0 0.0
"so, one question for anyone expert on this or understands it,
how does X = [-F I], becomes [-1 -1 1] in the end?
or in the first example, how it does become the c[-2 1 0 0]   +  d[2 0 -2 1]" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 14353.0 0.0 1.0 0.0
"31:05 female function male function" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 904.0 0.0 0.0 0.0
"You are our inspiration. This is amazing." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12176.0 0.0 0.0 0.0
"I like Professor Strang's sweater. Reminds me of Mr. Rogers' Neighborhood." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 5660.0 0.0 0.0 0.0
"And the math is hard to begin with" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2449.0 0.0 0.0 0.0
"48:07 why du/u = ln u?" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1291.0 0.0 1.0 0.0
"""You can come even after monday"", man he is just on a another level." TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 136.0 0.0 0.0 0.0
"47:20 There are various reasons why 0!=1. First to come in mind is that if you work backwards from n! you'll find that (n-1)! = n!/n, so 0!= 1!/1 =1. Then there is the definition of ""empty product"". Empty sum is of course 0 because when you add your first term a to 0 you get a. So in same sense empty product should be 1 as you multiply with your first term a with 1 you get a. And 0! is an empty product, so it value should be 1. Those are reasons totally outside of the rationale that it must be so that the series work but it is consitent with that." wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1279.0 0.0 0.0 0.0
"maybe a subtital  would be better" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13927.0 0.0 0.0 0.0
"Truly amazing. Nice lecture he teaches well. Thanks MIT" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11091.0 0.0 0.0 0.0
"Please , can you give us  the   titles  of the books  you are using  for this?" Yb69dAq4uh8 "Lecture 15: Orthonormal Bases and Fourier Series" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 8196.0 0.0 0.0 0.0
感谢老爷子 MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 15633.0 0.0 0.0 0.0
"Hmm, did Professor Strang copy the first question down wrong? At the end he gets x=2, y=1, and z=-2 but the last row in the question says 4y-4z = 2. Am I missing something ?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4773.0 0.0 1.0 0.0
"why is the probability of P(1head) is 3p(1-p)^2...? Shouldnt it be 2p(1-p)^2, because only 2 probability it would happen instead of 3.... or am i not understanding it clearly? its in 9:14 please help" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 15339.0 0.0 1.0 0.0
"Whats are the advantages of the column method over the row method? Why does the prof like the column method so much?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11595.0 0.0 1.0 0.0
"A birds-eye view of optimization algorithms -> http://fa.bianp.net/teaching/2018/eecs227at/" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2099.0 0.0 0.0 0.0
"@gorgolyt get over yourself buddy.  this ISNT a business letter. ITS possibly the most informal forum that exist and YOUR comment DOESNT even make sense." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1857.0 0.0 0.0 0.0
"All you texters out there should be paying attention in class and not fidgeting on your cell phones/" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2315.0 0.0 0.0 0.0
"Great lecture" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 4244.0 0.0 0.0 0.0
neat J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 14014.0 0.0 0.0 0.0
"in 36:50 , why sequences are defined by c + delta/2n? why not just delta/n? is there reason you divide 2?" V3Wg_jrMSQY "Lecture 19: Differentiation Rules, Rolle's Theorem, and the Mean Value Theorem" "MIT 18.100A Real Analysis, Fall 2020" 13578.0 0.0 1.0 0.0
"Anyone know what the ""32"" and ""21"" stand for in E32 and E21?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2504.0 0.0 1.0 0.0
"I Really Like The Video Polar coordinates; area in polar coordinates From Your" XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4991.0 0.0 0.0 0.0
"wonderful presentation but i wish next time you increase figurative examples" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 15395.0 0.0 0.0 1.0
"I hate linear algebra, I don't like maths in general...but he is just so enthusiastic that I will watch all these videos to study for my upcoming exam." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5481.0 0.0 0.0 0.0
"this MIT guys do not look so smart after all because they get impressed by many simple concepts often times" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14793.0 0.0 0.0 0.0
"Thank you Prof.  An inspiring teacher. Have really enjoyed every one of these lectures.  If I had been fortunate enough to have had you as one of my lecturers 52 years ago - things would certainly have turned out differently.  (Year 1: Math Stats Phil :: offered completion in all 3 :: Years 2-5 Phil)    Career as Math/Computing teacher and software developer. Now retired.  Greetings to you and yours" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9188.0 0.0 0.0 0.0
" " yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 2.0 0.0 0.0 0.0
"Great lectures." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4308.0 0.0 0.0 0.0
"After 45 years, i forgot all, now watch thí video brand new to me" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 2244.0 0.0 0.0 0.0
"Just finished all 35 lectures! It truly was a fantastic lecture thank you prof. Auroux and mit ocw!" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7168.0 0.0 0.0 0.0
"some great inforamtion here thanks" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 14357.0 0.0 0.0 0.0
legend feb9j65Iz4w "24. Linear Programming and Two-Person Games" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13777.0 0.0 0.0 0.0
"How old is the professor? It seems being 80" cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4892.0 0.0 0.0 0.0
"I totally thought phi = pi/4 was a plane heh. . . Woops." RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6112.0 0.0 1.0 0.0
"40:30 The 3B1B perspective of areas and volumes for  determinants." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 1127.0 0.0 0.0 1.0
"For that first example, I don’t think assuming the solution was the Iinear combination of exponentials was the right way to go. Of course, it’s correct, but it’s not very instructive. I solved this example problem in my own, and this is what I did:
Broke the system of odes into a system of difference equations (finite element approximations of the odes). Then I solved for the vector one node away in terms of the first node by reapplying something like u_(n+1)=A*u_n over and over. The computational hack here is that A being middle diagonalizable matrix doesn’t actually need to be multiplied many, many times. Once you get your answer, take the limit of your solution such that the difference equations converge to the original odes, and boom, you have your solution. It blew my mind a lil bit when I got the right answer lol 😅." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 3876.0 0.0 0.0 0.0
"There's a typo in the title :)" PnDtMfyZSIE "Lecture 6: The Uncountability of the Real Numbers" "MIT 18.100A Real Analysis, Fall 2020" 10386.0 0.0 0.0 0.0
"His voice is so cool and relaxing" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 4767.0 0.0 0.0 0.0
"... and they happen to meet, well, they were *arranged to meet* at point x = 1, y = 2! :))" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 261.0 0.0 0.0 0.0
"@chenhsi4 

So what? Who cares how good they are at math? Everyone starts somewhere." YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1813.0 0.0 0.0 0.0
"You ppl gotta give some credit to camera man who decided to zoom out when the death was passing by" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 12232.0 1.0 0.0 0.0
1:01:00 KAySmSEGc9U "3. Regular Pumping Lemma, Conversion of FA to Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 572.0 0.0 0.0 0.0
"what a chalk!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15103.0 1.0 0.0 0.0
"omfg this course is absolutely amazing. I've never seen matrix operations being explained with such pure logic." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14134.0 0.0 0.0 0.0
"this guy is so cool" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14832.0 0.0 0.0 0.0
"Wonderful explanation!" tBUHRpFZy0s "24. Classical Inference II" "6.041 Probabilistic Systems Analysis and Applied Probability" 11986.0 0.0 0.0 0.0
"Now, I can feel calculus" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7962.0 0.0 0.0 0.0
"never get old" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 14017.0 0.0 0.0 0.0
"Can we get an ocw on relativistic quantum field theory by mit on YouTube? Hope for getting reply." uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 3112.0 0.0 0.0 0.0
"Loved your way of teaching sir. It's seems like everything for registered in my memory.😃" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7483.0 0.0 0.0 0.0
"how many boards are there???
" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13244.0 1.0 0.0 0.0
"Nobody told him when he made a mistake at 2:26?

What makes MIT students better than me again?" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7908.0 0.0 0.0 0.0
"I've been watching all the precedent videos understanding most of what happens, but I always found that I had no link between what I saw and what I know already. I could not integrate the new set of concepts to my current knowledge. It was quite puzzling. Now with the first 18 mins of this lecture everything just clicked. It's like I was floating in space having a hard time navigating but still could move from one point to another. Now I got gravity. This is quite impressive." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6410.0 0.0 0.0 1.0
"Thank you. Now I understand Gauss-Jordan method." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9559.0 0.0 0.0 0.0
"SIGN BETWEEN    A.B   WILL ALSO BE POSITIVE IF  ANGLE THETA LIES BETWEEN 270 DEGREE TO 360 DEGREE( OPEN INTERVAL)   ." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8581.0 0.0 1.0 0.0
"Strang: ""You know what that matrix is""
Me: ""I do?.... Wait a minute... I do!""
Classic moments in Linear Algebra with Prof. Strang 👌👌👌" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 8912.0 0.0 0.0 0.0
"Nice lecture. I'm here for review and picked up a couple of things I didn't know. Thanks MIT." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7850.0 0.0 0.0 0.0
"27:30 EUREKA! " srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 820.0 0.0 0.0 0.0
"Really well explained." vcsxCFSLyP8 "6. Szemerédi's graph regularity lemma I: statement and proof" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 8538.0 0.0 0.0 0.0
"wtf is recitation" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15446.0 0.0 0.0 0.0
"thank youuuuu!!!" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14538.0 0.0 0.0 0.0
"Vector space feels a lot more interesting after this class...the column rank is dealt in a much brief manner out here though.." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 11153.0 0.0 0.0 0.0
"There are no topological considerations in here !? Only Maxwell's equations." BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 10352.0 0.0 0.0 0.0
"This man cooked up some vectors AND insulted MIT's floor integrity. Legend" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10847.0 0.0 0.0 0.0
"Nice lecture. I feel that for that last bit it's more useful to say that augmenting a matrix by the identity matrix for the matrix captures the operations done to the augmented matrix in the augmented region of the matrix. In this case we did the operations to produce the identity matrix out of A. That is A inverse. 
If I'm getting this right. First time doing this stuff." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7849.0 0.0 0.0 0.0
"my faculty (FRI UNIZA SLOVAKIA) says we are following MIT curriculum, i spent 2 semesters with algebra and noone explained what is algebra, we just spent 24 weeks by calculating and useles theory. This lecture is made in for me foreign language, and i understand it better than in my mother tongue." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13980.0 0.0 0.0 0.0
"Gravity is 10m/s²?  Oof.
Now let's just say pi ≈3.  e≈ 3.  4 ≈ 3.  ;)" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4189.0 0.0 1.0 0.0
"Oh he is such a great teacher!!! with appropriate pause and a moderate speed!! I'm glad that I learn a lot." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 8008.0 0.0 0.0 0.0
"Те что на стороне Марса" V4xOdtqic3o "15. Regression (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 15556.0 0.0 0.0 0.0
"nice hand writing" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14035.0 0.0 0.0 0.0
"For n different of zero! Since m/n!" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3868.0 0.0 0.0 0.0
"20220526 簽" Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 636.0 0.0 0.0 0.0
"45:15 
I thought only physicists do that." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1251.0 0.0 0.0 0.0
"A very clear spoken professor.
I learned a new word. ""Bashful"" just from the context he used the word in.
I assumed Bashful meant shy because he asked the students that were bashful to sit far back.
Which indicates the word ""shy"" as in the term ""camera-shy""." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2167.0 0.0 0.0 0.0
"In minute 1:12:26 he says ""it's taboo to write on the back board."" Why they don't use the back board and why is it taboo?" V3Wg_jrMSQY "Lecture 19: Differentiation Rules, Rolle's Theorem, and the Mean Value Theorem" "MIT 18.100A Real Analysis, Fall 2020" 6644.0 1.0 0.0 0.0
"Prof. Auroux is the goat" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8289.0 0.0 0.0 0.0
"Wish this guy taught me Math 293 and 294 at Cornell. My guy could barely speak English, let alone explain what we were trying to accomplish. I understood that if we wanted eigenvectors perpendicular to x we'd get lift relative to flow...but this guy would have made the math a bit simpler." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 11961.0 0.0 0.0 0.0
"30:51 there's a face in E32" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 896.0 0.0 0.0 0.0
"Cool video" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3211.0 0.0 0.0 0.0
"you can just substitute new u and v in the formula for (uv)prime
just put 1/v instead of v and you get (u/v)prime" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15499.0 0.0 1.0 0.0
"40:37 ""I got excited thinking about math"". Best" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1130.0 0.0 0.0 0.0
"*Question:* what is the relationship between rank(A) and rank(A^T)? Does rank(A) = rank(A^T) in general?

The professor seems to be hinting at this, but rref(A) only preserves the column space, so it doesn’t seem so trivial to me. Any insight is highly appreciated.

Edit: I found the answer. rank(A) = rank(A^T) by virtue of the fact that linear independence of the columns implies linear independence of the rows, even for non-square matrices. I proved this for myself this evening. The main idea for the proof (at least how I did it) is that if you have two linearly dependent rows, one above the other say, row reduction kills the lower one (reduces number of possibly independent rows). Killing off the row (making the row all zeros) also makes it so that the given row can’t have a pivot. Thus, we’ve reduced the number of potential pivot columns by one. That’s the relationship in a nutshell. The math is only slightly more involved" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 237.0 0.0 1.0 0.0
"I agree about the chalk, really.  I find myself so tired of looking at a computer screen, and having to deal with the 32 or however many flashes of light per second day in, day out.  Somehow the teacher feels more present and more connected to the material when using chalk, I think.  
I dislike online assignments too." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5024.0 1.0 0.0 0.0
"20:28 ""cool trick"" (:
" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 652.0 0.0 0.0 0.0
"WAAAYYY Better than my Linear Algebra prof
" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 11240.0 0.0 0.0 0.0
"I blessed to see the prof.Gilbert strang  lecture. Very thankful to u." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 5177.0 0.0 0.0 0.0
"At 23:34, why should a_1 and a_2 both be perpendicular to  the vector b? How can that be even possible?" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2617.0 0.0 1.0 0.0
"Aww his smile omg" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 2794.0 0.0 0.0 0.0
"how did most of them get the vector and plane problem wrong..these are MIT students right?" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13218.0 0.0 1.0 0.0
"I am curious if there's another statistics class on OCW that is recommended as well as this course on probability?  

This is the class I think will benefit me most but I think a statistics class with video lectures would be excellent." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 5081.0 0.0 0.0 0.0
"The essence lies in the last 6 to 7 minutes. Now I understood schematically hows and whys of Bayes's rule" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 10092.0 0.0 0.0 0.0
"the lecture and the teacher of my life! " 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 14708.0 0.0 0.0 0.0
"Now I'm starting to understand the lanhguage of matrices. Thanks to professor Strang!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7956.0 0.0 0.0 0.0
"The professor Miller's explanations are concise and dead-on." CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10244.0 0.0 0.0 0.0
"Can someone say u-not better than Gilbert Strang?" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 3098.0 0.0 0.0 0.0
"@lenlen1010 do you realize how much subsidies american universities get? the federal government gives our uni's lots of money." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1929.0 0.0 0.0 0.0
留名 RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 15640.0 0.0 0.0 0.0
"I love this guy. He got some jokes :) Good teacher too!" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5812.0 0.0 0.0 0.0
"What's the third kind?" wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 11587.0 0.0 1.0 0.0
"Hailing from the horrible video experience that is Lecture 4, I feel at peace finally" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4417.0 0.0 0.0 0.0
"He covers a lot of ground quickly but it doesn't feel that rushed." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4470.0 0.0 0.0 0.0
"this guy is a master chalk operator" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 14812.0 1.0 0.0 0.0
"No. It should be 5 since we are subtracting row 2 FROM row 3. So i.e 1-(-4) = 5" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7905.0 0.0 1.0 0.0
"6:50 That is the straightest line drawn by hand in the history of humanity." Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1386.0 0.0 0.0 0.0
"16:45 should be a 10.

These lectures are amazing! I've learned so much from these videos. :) And the professor rocks." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 488.0 0.0 0.0 0.0
"I am confused with his proof that 1 = 0 and the reason why it's incorrect. He says that this is because the set of real points is uncountable (i.e. not a sequence).

But what if we take a discrete grid of points (infinitely many), or for simplicity a 1D line of discrete points, i.e. the set of all integers Z. Then again we have that P(i) = 0, because there are infinitely many of them and they are all equally probable. But now, the set is countable, i.e. it is a sequence, and hence 1 = P(Ω) = sum(P(i)) = 0. What is wrong with this reasoning?" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 5075.0 0.0 1.0 0.0
"Chain rule, I don't like you" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3134.0 0.0 0.0 0.0
"Legend ...bow to him" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7318.0 0.0 0.0 0.0
"I completed the course at 18:23 today.
The course is informative and really help me a lot in machine learning and data mining.
Thank you, Professor Strang." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5240.0 0.0 0.0 0.0
"Regarding transformation of REs to NFAs, while I like the method used in his book, I think Thompson's construction is slightly more intuitive..." oNsscmUwjMU "2. Nondeterminism, Closure Properties, Conversion of Regular Expressions to FA" "MIT 18.404J Theory of Computation, Fall 2020" 8545.0 0.0 0.0 0.0
"20:00 a rationale for determining rank (using null space) so that you don't end up with a junk matrix in an engineering application." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 640.0 0.0 0.0 1.0
"I have a math degree and I still enjoy these lectures. Auroux is a great lecturer." tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5494.0 0.0 0.0 0.0
"I've been preparing for college in Italy for a couple months now with the official books and I can't help noticing one fundamental difference between the american and the european teaching philosophy: americans appeal to your common sense to make learning easy and fun, while europeans try to make it as formal and meticulous as possible so that you get used to working your ass off." -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6405.0 0.0 0.0 0.0
"@siggascation There is, and it's the same as f sub xy." 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2014.0 0.0 0.0 0.0
"how can I get the paper's that the professor gave to them?
does anyone upload it to any page?" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13193.0 0.0 0.0 0.0
"I have to say, this one is pretty challenging for me, cuz I have no idea about Kirchoff's Law." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5564.0 0.0 0.0 0.0
w00t 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15049.0 0.0 0.0 0.0
"The white noise in the background is the most irritating part of these lectures. Does anyone know a way to denoise these videos? It's so difficult to focus because of this static noise." TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 10336.0 0.0 0.0 0.0
"Genius. I am so happy this is on the internet." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 4001.0 0.0 0.0 0.0
"Who are these dislikes guys?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11725.0 0.0 0.0 0.0
"excellent lecture." EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 12822.0 0.0 0.0 0.0
20:30 Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 655.0 0.0 0.0 0.0
"finished 18.01 :D 08/12/2020" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12864.0 0.0 0.0 0.0
"Will this be on edX  by any chance?" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11950.0 0.0 0.0 0.0
"MIT OCW has been a blessing for millions of people. However, the logistical problems of posting over 2000 course are HUGE." sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7505.0 0.0 0.0 0.0
"I just came to see the top comment XD " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5597.0 0.0 0.0 0.0
"I didn't get the part where he minimized the L2 norm geometrically, why was it that particular point?" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5269.0 0.0 1.0 0.0
"The best course on Linear Algebra ever made. Infinite thank you to Prof.Strang!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9994.0 0.0 0.0 0.0
"hypothesis testing actually starts at 52:13" phbw9r1iUDI "7. Parametric Hypothesis Testing" "MIT 18.650 Statistics for Applications, Fall 2016" 13319.0 0.0 0.0 0.0
"How do we actually see what sigma1 is the maximum blow-up factor and what v1 is the vector what gets blown up the most? Because i initially thought it would be the first eigenvector, and then it would make sense, but then i realised what sigma is not an eigenvalue after professor said it and i'm struggling a bit with imagening what's happening here" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4849.0 0.0 1.0 0.0
"maybe use a microphone next time" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 13931.0 1.0 0.0 0.0
TOP 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 8999.0 0.0 0.0 0.0
"can someone please tell how was the pivot choosen" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12628.0 0.0 1.0 0.0
"I hate this camera men. Gosh, please just follow Gilbert. He ruined Gilbert's lecture." TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 5485.0 1.0 0.0 0.0
"his geometric explanation of why gradients must be parallel kind of sucked. he stated facts, didn't bother to explain." 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13165.0 0.0 0.0 0.0
"Wow. This looks amazing. Great intro, God bless." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12088.0 0.0 0.0 0.0
"MIT, thank you so much. This is truly a gift." TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7554.0 0.0 0.0 0.0
"@zobazoba69 see first youself before judging others as if your better than the professor, shame on you idiot. upload your lectures to so that well see if which is better.. your just a big mouth idiot.." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2088.0 0.0 0.0 0.0
"When he said "" It's fantastic to have these beautiful clean boards"". I was thinking the same. lol" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11620.0 1.0 0.0 0.0
Great 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4191.0 0.0 0.0 0.0
"skipping this lecture for now...too much messy algebra for me." 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14319.0 0.0 0.0 0.0
"Good overview of Bayesian Statistics" XtNXQJkgkhI "22. Bayesian Statistical Inference II" "6.041 Probabilistic Systems Analysis and Applied Probability" 4150.0 0.0 0.0 0.0
"It was called ""Introduction to Applied Math"" ,  many graduate students had to take it for graduate credits.    It's both Arts and Math." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6998.0 0.0 0.0 0.0
"Oh god! I'm taking this subject in the next 2 months....I don't understand anything! " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8006.0 0.0 0.0 0.0
"Did he choose the b vector (1,5,6) at random, based on 0 = b3-b2-b1? EDIT: yes" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 3369.0 0.0 1.0 0.0
"Very helpful video thank you MIT!!!" ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 11197.0 0.0 0.0 0.0
"@MIT OpenCourseWare, and Dr. Casey Rodriguez: thanks a lot for this.
Now that it has been released, more and more people over the years and over the world will continue to benefit from this." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 1669.0 0.0 0.0 0.0
"thanks, Profesor  Gilbert Strang" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 14613.0 0.0 0.0 0.0
"Came looking for a better understanding of my calculus class and got a better understanding of my physics class, not complaining!" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2993.0 0.0 0.0 0.0
"This teacher is incredibly good..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10936.0 0.0 0.0 0.0
"Sheer genius" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 8636.0 0.0 0.0 0.0
"You'll see that BS on any math video -

""Man, I did partial differential equations and vector calculus in 3rd grade. These college kids are dumb.""

Yeah, whatever, we don't care." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12246.0 0.0 0.0 0.0
"way to go MIT for the high quality videos!" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15071.0 0.0 0.0 0.0
"And for that matter: why are these comments repeated in every single lecture from the course, with the exact same wording and just the title of the lecture swapped?" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 2442.0 0.0 0.0 0.0
"Sweet professor." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8975.0 0.0 0.0 0.0
det(A)=6 U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12737.0 0.0 0.0 0.0
"I never trust substitutes." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5887.0 0.0 0.0 0.0
"I am so surprised that the prof is doing such a great job at explaining things and when he asks a question, nobody wants to respond." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 5143.0 0.0 0.0 0.0
"One of my heroes. I owe a lot to this man. Thank you very much Prof. Strang." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8084.0 0.0 0.0 0.0
"'I was the little brother' lol, great lecture as always" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 209.0 0.0 0.0 0.0
"I have never read political science in my life but is there mathematics in it?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5539.0 0.0 0.0 0.0
"@kevinbollers2 all the classrooms at MIT have blackboards, but they are cleaned by janitors daily" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1920.0 1.0 0.0 0.0
"I Watched all of the lectures and it was an amazing experience thanks!!" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5007.0 0.0 0.0 0.0
"I love this guy! You see a lot of passion on him 😊" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5805.0 0.0 0.0 0.0
"23:33 why the two dimension  plane go through the x particular? I can’t see a way that c1 and c2 could produce it." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 715.0 0.0 1.0 0.0
"I’ve needed this course for a couple of years now. Looking for good open resources regarding such an advanced topic was hard. The search is over. Thanks OCW! You’re da GOATs of open learning." uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 7120.0 0.0 0.0 0.0
"plane or plain? :))))))) just kidding he is the best and i am thankfull for what he is teaching so bright and clear.." RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14185.0 0.0 0.0 0.0
"Why is UtU = I?" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11866.0 0.0 1.0 0.0
"Students asks lot of useful questions ..sometimes I wonder how they come to think that" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8918.0 0.0 0.0 0.0
"The camera man in this one drank some vodka." TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 10031.0 1.0 0.0 0.0
"Anyone else Bingewatching all these lectures?" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 2485.0 0.0 0.0 0.0
"It´s an excellent Math Class professor. Thank youuuu !!!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7097.0 0.0 0.0 0.0
"He is wonderful" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 4553.0 0.0 0.0 0.0
"So I'm literally writing a paper on inverting neural networks. It's fairly direct (yet not trivial) under certain nice assumptions. My plan was to begin to investigate what happens as you relax these assumptions. It's perfectly timed that I'm taking this course :))))" Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8733.0 0.0 0.0 0.0
"Thanks prof. This is one of the best lectures of the course!" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 9760.0 0.0 0.0 0.0
"i think the explanation of the first queston was a little bit wrong it seems. because he wrote the equation  to diagonalize the matxix P even though it does not have 3 independent eigen vectors." QuZL5IKpO_U "24b. Quiz 2 Review" "MIT 18.06 Linear Algebra, Spring 2005" 13476.0 0.0 1.0 0.0
"Thank you!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9472.0 0.0 0.0 0.0
"By educating the world, you directly develop international worker competition as well as international business competition.  The result is that you hurt the American worker and you hurt American business.  Why would you accept US taxes and US donations to promote what is against the national interest?" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2972.0 0.0 0.0 0.0
"Millions of likes <3" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 7665.0 0.0 0.0 0.0
"If you're not getting why those entries turned out to be zero. Here is a proof for it:
 https://ltcconline.net/greenl/courses/203/MatricesApps/cofactors.htm" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 6563.0 0.0 0.0 1.0
"The subtitles are in the way. I would guess they would still be in the way if you were deaf." 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 10290.0 0.0 0.0 0.0
"the real doctor strange" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14739.0 0.0 0.0 0.0
"Thank you Professor and MIT" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9227.0 0.0 0.0 0.0
"The context of the problem on 43:24 is so rude! Why does
 only a king can be born in this family??? Do you have something against female's rights to become a queen?? By the way, the formulation of this problem is so ridiculous. We can not say that there was born a boy or a girl, because a child have not identified its gender yet!!" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 10057.0 0.0 0.0 0.0
"20:05 ""y is changing ten times as fast as"" x, not b." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 642.0 0.0 1.0 0.0
"To everyone being rude to the student, he's actually not completely off like you wrongly assume. Because if you have parentheses around the number in the superscript/exponent it can be used to denote a higher order derivative, like f⁽⁵⁾(x) can be used instead of the much less readable f'''''(x)." TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11034.0 0.0 0.0 0.0
"This is the best mathematics instruction I have EVER experienced. Thanks!" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10742.0 0.0 0.0 0.0
"Can be explained by lambda calculus, much more concise and graceful" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 3054.0 0.0 0.0 0.0
"Awesome Lectures!

I think the solution to the last question in the final exam is wrong on the ocw site. D5=63 and not 207. 
D1=3,D2=7,D3=3*7-2*3=15,D4=3*15-2*7=31,D5=3*31-2*15=63!
You can take a look at the jupyter notebook for the exam here.  You can download and use it for your purpose... 
https://colab.research.google.com/drive/1Am40fnIiocrTVWUen8mZA5DfcsS2SThU" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 2753.0 0.0 1.0 0.0
thanks BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14542.0 0.0 0.0 0.0
"There are X logical statements that explains Y algebra is useful to learn in science and tech; and Y it can be used to do N things in life, for any kinds of operation that 1 can care to image, including the use of imaginary numbers for complex tasks themselves.  It is all about integration and the sequences that have to be followed to achieve equality and reason in all of knowledge, so that we can have the opportunity to be the greatest at numeration and denomition as well as domination of those lessor; for X > Y when X have more knowledge then Y.  Y?  Because of Z!" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 10346.0 0.0 0.0 0.0
"Min 20 and I still understand what he's talking about lol" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7666.0 0.0 0.0 0.0
"Berkeley EECS shall kidnap him
" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2847.0 0.0 0.0 0.0
"@slatz20 
he explains that if you multiply only one row. so he did it correct." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 2018.0 0.0 0.0 0.0
"I think the infinite discontinuity is a type of a jump discontinuity." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6056.0 0.0 0.0 0.0
"i noticed that only when i watch MIT lectures i get not only the definitions but how to imagine the space on which the whole picture is all about!
that's crucial!!!" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 13448.0 0.0 0.0 1.0
"The blackboard and the chalk makes me wanna become a lecturer." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10021.0 1.0 0.0 0.0
"44:04
oh" tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1227.0 0.0 0.0 0.0
"This professor is solid." CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10910.0 0.0 0.0 0.0
"Thanks, Dr. Strang. I always enjoy your lectures." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 9841.0 0.0 0.0 0.0
"Anybody else see that salmon-fluke pun opportunity at 17:25?  Coulda been legendary..." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 2475.0 0.0 0.0 0.0
"very good lecture" wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 15006.0 0.0 0.0 0.0
"Lecture 1: Dot Product
Lecture 2: Determinants
Lecture 3: Matrices
Lecture 4: Square Systems
Lecture 5: Parametric Equations
Lecture 6: Kepler's Second Law
Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds)
Lecture 8: Partial Derivatives
Lecture 9: Max-Min and Least Squares
Lecture 10: Second Derivative Test
Lecture 11: Chain Rule
Lecture 12: Gradient
Lecture 13: Lagrange Multipliers
Lecture 14: Non-Independent Variables
Lecture 15: Partial Differential Equations
Lecture 16: Double Integrals
Lecture 17: Polar Coordinates
Lecture 18: Change of Variables
Lecture 19: Vector Fields
Lecture 20: Path Independence
Lecture 21: Gradient Fields
Lecture 22: Green's Theorem
Lecture 23: Flux
Lecture 24: Simply Connected Regions
Lecture 25: Triple Integrals
Lecture 26: Spherical Coordinates
Lecture 27: Vector Fields in 3D
Lecture 28: Divergence Theorem
Lecture 29: Divergence Theorem (cont.)
Lecture 30: Line Integrals
Lecture 31: Stokes' Theorem
Lecture 32: Stokes' Theorem (cont.)
Lecture 33: Maxwell's Equations
Lecture 34: Final Review
Lecture 35: Final Review (cont.)" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7268.0 0.0 0.0 0.0
"""randomness is a big rug under which we sweep everything we don't understand""
I fucks with this" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 171.0 0.0 0.0 0.0
Art! QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2561.0 0.0 0.0 0.0
"Around 41:33, I think the number of pivots  should be (n pos + m neg) pivots since A is a m by n matrix and (-A*inv(S)*A^T) is a m by m matrix." xaSL8yFgqig "Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2557.0 0.0 1.0 0.0
"yeah , it gets complicate when derivated formulus are thrwon in the mix." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15462.0 0.0 0.0 0.0
"Thanks for posting! @MIT" gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 9695.0 0.0 0.0 0.0
"where was this back last semester >.< this was my subject." 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 15246.0 0.0 0.0 0.0
"Could someone explain if there is a reason for using any other method other then the clasic way to multiply? I mean even the row and column multiplications are using the clasic method, you just take the columns or the rows bit by bit." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3232.0 0.0 1.0 0.0
"""unapropriate"" LOL" seO7-TwXH_I "Lec 30: Line integrals in space, curl, exactness... | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 185.0 0.0 0.0 0.0
"v and w belong to s...v+w belongs to s..but need not belong to intersection of s intersec T...so hows that a proof" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 14989.0 0.0 1.0 0.0
"I follow your videos, Sir. the best of the best." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5423.0 0.0 0.0 0.0
"AX = b
  pivots
  associative law A(BC) = (AB)C
   row ops start at left
   col ops start at right" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2187.0 0.0 0.0 0.0
"apart from the 40'57"" problem i had the rest was brilliant
that's if you're still with us" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12392.0 0.0 0.0 0.0
"I think that's why most undergraduate engineering programs don't require people to go beyond Differential Equations and Linear Algebra; because beyond that it starts getting more and more abstract. " xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6047.0 0.0 0.0 0.0
"He is certainly right that even the best would fare well to add anything. To have the pleasure of his lectures is more than gold." L3-WFKCW-tY "33. Neural Nets and the Learning Function" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4510.0 0.0 0.0 0.0
"Ahhh!!! Mind blown near the end!!!" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 2288.0 0.0 0.0 0.0
"damn girl didn't want to take a seat. disrupting my learning environment. " 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12708.0 1.0 0.0 0.0
"Could you make a playlist of just proofs?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 3245.0 0.0 0.0 1.0
"Just impressive! " RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 7184.0 0.0 0.0 0.0
"""these things are not vectors, but we can cal them vectors""

this guy is not einstein, but we can call him einstein!" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 181.0 0.0 0.0 0.0
"Finished this course on 06/08/2021 :)" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 3811.0 0.0 0.0 0.0
"Thank you very much Professor Strang. I am a medical student, so the last time I did anything involving linear algebra was years ago. But I got pulled in research involving bioinformatics, so this course was very valuable to quickly get a sense of how to think about matrices. Thank you again for your very intuitive, clear and, at times, humorous teaching." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9435.0 0.0 0.0 0.0
"Can't wait for the next one!" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3129.0 0.0 0.0 0.0
"Thanks Prof. Strang!! very clear and easy to understand!" sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9634.0 0.0 0.0 0.0
"thanks Professor Strang, You inspire people to love math, as they should!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 14561.0 0.0 0.0 0.0
"At t = 11:00, finding the complete solution to Ax = b." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 2721.0 0.0 1.0 0.0
"ds 2 = dx2  + dy 2" XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12775.0 0.0 0.0 0.0
"A is mxn matrix b is usually mx1 matrix then how can we multiply Ab in Krylov method" MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2126.0 0.0 1.0 0.0
"well i think every where does that, but man they don't spend an entire module on the basics we do that at high school we get into something in particular very fast. You really don't realise how good teaching MIT students get, they get everything handed to them its crazy un fair!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15092.0 0.0 0.0 0.0
"Quality Of this Video Content is poor" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 8468.0 0.0 0.0 0.0
"Thanks Respected sir" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9643.0 0.0 0.0 0.0
"i wonder how many majors will go into using this shit" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13506.0 0.0 0.0 0.0
"Is this course for beginners." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6862.0 0.0 0.0 0.0
"Thank you, Dr. Strang." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9494.0 0.0 0.0 0.0
"I'm fairly certain x includes 255 in the domain. [4:15]
Can anyone confirm or clarify? 
(should be x is less than or equal to 255, rather than strictly less than)" 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 6321.0 0.0 1.0 0.0
"Οne question about the Reduced Matrix R.

When he says at the end (41:06) again that the pivots of the R should all of them be equal to 1, 
it this the generic rule that:

a) all pivots of any R will be equal to 1
b) OR all pivots of any R will have the same value (e.g all 5 or all 10)?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 15548.0 0.0 1.0 0.0
"super lecture, super teacher" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 14417.0 0.0 0.0 0.0
"For those of you who are absolute beginners, yes this course might be quite hard to follow. However for people like me, who have not took statistics or probability theory courses during their undergraduate studies but have some background whatsoever, this course is very insightful and beautifully brought together." TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 3907.0 0.0 0.0 0.0
"Excellent prof of Mathematics, Sir Your lectures are very attractive." ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3667.0 0.0 0.0 0.0
"I'm not sure what text he uses, but if you're looking for a good calc book I would try the one written by Swokowski (Calculus: Fifth Edition). He has passed away so that is the latest one by him, and you can find a used copy for dirt cheap. They do offer a new version of his fifth edition on amazon, but they charge 60 bucks (as opposed to the 3 bucks I paid at a used book store). It's very well written" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6356.0 0.0 0.0 0.0
"Thank you professor David Jerison for this awesome lectures" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9307.0 0.0 0.0 0.0
"Raise your hand if you are watching it in 2023!" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 8491.0 0.0 0.0 0.0
"very helpful" XtNXQJkgkhI "22. Bayesian Statistical Inference II" "6.041 Probabilistic Systems Analysis and Applied Probability" 15015.0 0.0 0.0 0.0
"he is a lame teacher." Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13087.0 0.0 0.0 0.0
35:19 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 1006.0 0.0 0.0 0.0
"Lecturing to an empty room. I like the honesty. lol" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 7311.0 0.0 0.0 0.0
https://www.youtube.com/watch?v=SYS0-gf-J_M&t=34s VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 13277.0 0.0 0.0 0.0
"I saw that this doesn't require a textbook, but if we wanted a resource to supplement studying with this OCW what textbook would you recommend?" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5957.0 0.0 0.0 0.0
"15:30 lol" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 452.0 0.0 0.0 0.0
"The lecture is marvelous. Thanks, professor John Tsitsiklis." HIMxdWDLEK8 "18. Markov Chains III" "6.041 Probabilistic Systems Analysis and Applied Probability" 10163.0 0.0 0.0 0.0
"I request to instructors or everyone who watches this message. Can you guys suggest to me any good book from which I can study multivariable calculus deeply with intrigue and sincerity?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5951.0 0.0 0.0 0.0
"It is much easier using a discrete random variable X to explain the posterior probability." bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 6958.0 0.0 0.0 0.0
"3:50 ""Useful to have in our hands"" ...But where is his right hand ????    o.O" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 1118.0 0.0 0.0 0.0
"Dr. Strang thank you  for being such an amazing lecturer" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 3510.0 0.0 0.0 0.0
"even the chalk quality is great" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12805.0 1.0 0.0 0.0
"Is it relevant for JEE" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6796.0 0.0 0.0 0.0
"Is this Mr. Sipser himself?  It's been some years that I read his book. Had a love-hate relationship with that subject lol." 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 6848.0 0.0 0.0 0.0
"In the 2009 lectures he is quite young as compared to now. How did he grow so old in 10 years?" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6655.0 0.0 0.0 0.0
"Poor Recording.. can't hear anything" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 8226.0 1.0 0.0 0.0
"I never thought I would be able to comment ""first"" on any Strang lecture O__O Lucky me XD" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5884.0 0.0 0.0 0.0
"His teaching style seems casual and intuitive. I go to a small public college and the course is much more formal and proof driven. These lectures are a great addition to (as well as a nice break from)  formal proofs. Thanks MIT!" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 4765.0 0.0 0.0 1.0
"Not even a single dislike , that's Gilbert strang for you" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7922.0 0.0 0.0 0.0
"In 26:47, Is there any relation between L U and L1 U1 L2 U2?" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6597.0 0.0 1.0 0.0
"48:40 doesn't the rank theorem say that : dim(R^3) = rank(A) + dim(Kernel) ? I guess the kernell here is the nullspace, dim(R^3) = 3 and rank(A) = 2  so dimension of NullSpace should be 1 ?" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 1296.0 0.0 1.0 0.0
"This video is just incredible. I've been watching the Khan Academy LA videos and have covered this over there, but seeing this gives me yet another point of view. Coming at it from a slightly different angle is so good at solidifying the concepts. In this lecture I find Professor Strang keeps things high level and really shows the power of thinking at the high ""linear algebra"" level. Nice to see a video on projection without a cosine in sight :)" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10955.0 0.0 0.0 1.0
"those 9 people who disliked this video..." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14930.0 0.0 0.0 0.0
"Thank you, mitocw. <3" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9521.0 0.0 0.0 0.0
"Looks like netflix got the sound from 37:59" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 7424.0 0.0 0.0 0.0
"this guy is beautiful..." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14823.0 0.0 0.0 0.0
"I'm curious as to what book Professor Strang is referring to. These lectures, by the way, are absolute masterworks." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 6315.0 0.0 0.0 0.0
"32:24 HE WORKS" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 929.0 0.0 0.0 0.0
"EEiigenväktoars. Ich liebe es" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3536.0 0.0 0.0 0.0
"travel(l)ed XD" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14958.0 0.0 0.0 0.0
"Interesting work
" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 6733.0 0.0 0.0 0.0
"going to have to take this whole series cos Real analysis was probably the hardest course I took at UNN" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 12936.0 0.0 0.0 0.0
"Freaking awesome professor. authoritative, concise, clear-makes me want to teach math" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3920.0 0.0 0.0 0.0
"it looks like 1,2,3,4,5 but somehow it doesn't..." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 13679.0 0.0 0.0 0.0
"At 33 surely cos is positive for  360-angle as well?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2648.0 0.0 1.0 0.0
"@pdxginni Yes, it's just me. I had the screen maximized. Wouldn't pass without minimizing." UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1963.0 0.0 0.0 0.0
"god bless this lecturers and the other teachers , i love the way they teach us ,one day ill be financially supporting this guys hay, a large amount" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12928.0 0.0 0.0 0.0
"70th comment :P" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1390.0 0.0 0.0 0.0
"In R^10 we may take a comnination of five vectors in R^10 and what will we have? ..(emming)... God knows.     God: sure..sure, i do know." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 6617.0 0.0 0.0 0.0
"his zeros look like 3eros" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 13172.0 0.0 0.0 0.0
"So Newton's Method is based on using only the first derivative term in the Taylor Series?" nvXRJIBOREc "Lecture 21: Minimizing a Function Step by Step" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8736.0 0.0 1.0 0.0
"this was the best lecture in my life .. so far ))" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14926.0 0.0 0.0 0.0
"Why not until 39:16 did I realize that he was talking alone this whole time? T_T" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11903.0 0.0 0.0 0.0
"I’m in the top engineering school in all the United States and have already learned this yet MIT still makes it intimidating" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 7113.0 0.0 0.0 0.0
"@magdalene512 you have to see the diferential equations course; those stupid questions desappear there :D " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1934.0 0.0 0.0 0.0
"hello, could anyone explains me the difference between energy function ans snorm taught by professor in lecture 8" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13136.0 0.0 1.0 0.0
"Can't you also use the determinant to figure out that Aᵏ → 0 as K → ∞ ? i.e. if det A < 1 then Aᵏ → 0" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 3132.0 0.0 1.0 0.0
"Awesome videos.  Just to let everyne know, you can donate to the open course ware through their website.  Also, you can buy books through amazon where MIT gets money.  I dontated because I really believe in what they are trying to achieve.  " dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 2777.0 0.0 0.0 0.0
wonderful ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 15392.0 0.0 0.0 0.0
"Great Mathematician" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4207.0 0.0 0.0 0.0
"Did he re-film the lectures. I wonder because I see no students in the room." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 3375.0 1.0 0.0 0.0
"i think this guy just likes writing in chalk lol" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13481.0 1.0 0.0 0.0
"thank you so much for the answer" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14515.0 0.0 0.0 0.0
"Is this a part of undergraduate degree or just a after class 10 maths" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6852.0 0.0 0.0 0.0
"@zazzolina 
No money." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2080.0 0.0 0.0 0.0
"Dear can u plz tell me abt other online organizations that ARE already free." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3334.0 0.0 0.0 0.0
"After reviewing probability courses and this one itself many times, I found this lecture to be a great one. Some vague knowledge in real analysis will help. But I still need to come back later after digging deep into other sound footings for foundation. Thank MIT and professor." C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 2251.0 0.0 0.0 0.0
"Thanks legend!!! This course is a key of machine learning area." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9749.0 0.0 0.0 0.0
"@Michciu0911 That's what tutorials are for. (Sessions with graduate students). Hi from NZ" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1677.0 0.0 0.0 1.0
"around 32 min , it should be 99square not 100sq" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 12403.0 0.0 1.0 0.0
"@ShaneHayes123 LOL same... you from england? Thats where I'm from..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1721.0 0.0 0.0 0.0
"come back when you teach at MIT" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12664.0 0.0 0.0 0.0
"How did we get a_31 and b_14?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4845.0 0.0 1.0 0.0
"This attitude of MIT is incredible. Offer the best engineering course in the world to all people. Now, anyone can learn with the highest quality. Thanks, MIT." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10467.0 0.0 0.0 0.0
"This guy is a God. He has blessed himself 😆" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10512.0 0.0 0.0 0.0
"16 people used the wrong hand to calculate cross product :)" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 463.0 0.0 1.0 0.0
"Such nice illustrations of applications of the theoretical concepts presented thus far. One more teaching masterclass from prof. Strang!" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8952.0 0.0 0.0 1.0
"Thanks for the explanation as well as for the jokes :)" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9711.0 0.0 0.0 0.0
"""AHHH, sorry he's still there""

^.^" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 25.0 0.0 0.0 0.0
"When we write X as [ -F I] T, the number of cols in F is n-r and number of cols in I is r so wont there be a condition for n-r=r??? Confused, pls help" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 11640.0 0.0 1.0 0.0
"The subtitles are out of sync..." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10291.0 0.0 0.0 0.0
"Let me write this ""right hand rule down"" while you experiment with it...try not to enjoy yourself"" hahaha" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7335.0 0.0 0.0 0.0
"All of our lectures use projectors and computers, nice to see some good old fashioned chalkboards in education =)" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2304.0 1.0 0.0 0.0
"This SVD business is truly poetry in motion." rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10463.0 0.0 0.0 0.0
"What is the intuition behind Krylov.why does it work?" MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11529.0 0.0 1.0 0.0
"It is better watch some video of Math." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 6941.0 0.0 0.0 0.0
"many many thanks to Gilbert strange" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 13908.0 0.0 0.0 0.0
"Good lecture. When watching it I came up with an idea, how one could have found the method of approximating e much easier. The method in the lecture was explained in the last 7 minutes, and made me think how to do it without calculus and in 10 seconds. Could not have come up with it if I had not watched the lecture :)" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4138.0 0.0 0.0 0.0
"He is able to be so wonderfully passionate because he cares that his students understand. So he is able to be in a one-on-one framework while standing and talking to an entire class." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 4504.0 0.0 0.0 0.0
"I love the cliff hangers" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 5775.0 0.0 0.0 0.0
"Cool vid" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3210.0 0.0 0.0 0.0
"So excited!!! Let's gooooo" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8752.0 0.0 0.0 0.0
"why is Q not on the other side, if we move down (South) from where dh/dx is 0 than also h which decrease  right? I mean dh/dy < 0  for both points right? why only for the upper one?" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15325.0 0.0 1.0 0.0
"9:45
Professor Strang subtly integrates class consciousness into his lecture of the Four Fundamental Subspaces. 
Truly a genius." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1445.0 0.0 0.0 0.0
"I am a physics undergraduate student. Will this course will be helpful for quantum physics and statistical physics?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 5055.0 0.0 0.0 0.0
"first year calculus in most universities" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12873.0 0.0 0.0 0.0
"Man where were these lectures when I was taking my functional analysis class 😭" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 7579.0 0.0 0.0 0.0
"Lecture 1: Dot Product
Lecture 2: Determinants
Lecture 3: Matrices
Lecture 4: Square Systems
Lecture 5: Parametric Equations
Lecture 6: Kepler's Second Law
Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds)
Lecture 8: Partial Derivatives
Lecture 9: Max-Min and Least Squares
Lecture 10: Second Derivative Test
Lecture 11: Chain Rule
Lecture 12: Gradient
Lecture 13: Lagrange Multipliers
Lecture 14: Non-Independent Variables
Lecture 15: Partial Differential Equations
Lecture 16: Double Integrals
Lecture 17: Polar Coordinates
Lecture 18: Change of Variables
Lecture 19: Vector Fields
Lecture 20: Path Independence
Lecture 21: Gradient Fields
Lecture 22: Green's Theorem
Lecture 23: Flux
Lecture 24: Simply Connected Regions
Lecture 25: Triple Integrals
Lecture 26: Spherical Coordinates
Lecture 27: Vector Fields in 3D
Lecture 28: Divergence Theorem
Lecture 29: Divergence Theorem (cont.)
Lecture 30: Line Integrals
Lecture 31: Stokes' Theorem
Lecture 32: Stokes' Theorem (cont.)
Lecture 33: Maxwell's Equations
Lecture 34: Final Review
Lecture 35: Final Review (cont.)" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7266.0 0.0 0.0 0.0
"Amazing. Cannot be explained better." wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 2405.0 0.0 0.0 0.0
"When i connected dots in my head around 15 minutes when professor was talking about why we do this projection thing, it was one of the most mind fucking blown moments in my mind. I felt like going from top to bottom in the tiny brain - galaxy brain meme in a span of a second. Amazing course" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 11628.0 0.0 0.0 0.0
"I can't figure that out either!  I asked the same question for another video." sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5214.0 0.0 0.0 0.0
Nice WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7834.0 0.0 0.0 0.0
"Thanks for the information since it saves time and frustration especially if you need to find Newton's method right away.
" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9713.0 0.0 0.0 0.0
"at 3:15 - 3:20 Instead of looking at the row picture to realize the dependence we may also see that 2*(column 2) - (column 1) gives (column-3) :)" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12450.0 0.0 0.0 1.0
"Sir pls give solution basedvon this chapter" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8702.0 0.0 1.0 0.0
"This is the worst explanation, amazing!" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10758.0 0.0 0.0 0.0
"@OHYEAHDUDES yeah, is nice to sleep" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1695.0 0.0 0.0 0.0
"“Help me out right now,” awesome 👏" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15588.0 0.0 0.0 0.0
"For those curious, the law of cosines is also called “Al-Kashi’s law” (in France and the Arab and Persian world). Al Kashi was a Persian mathematician (I encourage you to check his wikipedia page). Great lecture! I was genuinely surprised that what students in Syria are taught in 11th grade, Americans learn in university.. To those from other countries, when did you learn dot product? Just curious" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3902.0 0.0 0.0 0.0
"Im not sure what is more impressive. What his talking about or that there is a professor strang. Yours sincerely matt strang" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 6576.0 0.0 0.0 0.0
"@dmtang01 Both, but He was Only Evaluating for the Component for Special." BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1825.0 0.0 1.0 0.0
"man, this is good..........." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 13905.0 0.0 0.0 0.0
"I got his linear algebra book in 2011, never really finished it as I had graduated and got into different things. Out of curiosity I started this video, it seems like Strang's hands are shaking and twitchy. I didn't realize he had gotten this frail and old, but its interesting to see that the mind is still as sharp as a razor edge. He has done a lot with his life and I hope that people who watch this lecture series go on to carry his legacy when he isn't around any more :')" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5447.0 0.0 0.0 0.0
"i don't understand people QQ'ing about the blackboard. Math on powerpoint ? really ? lol 
Never seen that. Math is a science where you need to be able, at any time, to demonstrate any calculus you make. I don't see that happening on a power point.
Beside, doing the demonstration forces you to explain it, which is better for understanding." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13367.0 1.0 0.0 1.0
"Damn he's good at teaching!" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 3294.0 0.0 0.0 0.0
"Its the 51st day since I began self study on 18.06 and today I finally completed all lectures, assignments and quizzes
I will begin my 18.02 study next week

Thank you professor Strang, Thank you MIT OCW" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 7092.0 0.0 0.0 0.0
"You did calculus at 7 yo and you still don't understand it HAHA" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12201.0 0.0 0.0 0.0
"Lol, if I ever do this class... I'll have to remember to decide my favourite curve/surface/vector field/scalar field early on, since I'll be using them so often.  

This guy is very good; very clear and efficient explanations.  

Fibonacci" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7405.0 0.0 0.0 0.0
"what a mess" yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 15111.0 0.0 0.0 0.0
"Absolutely well done and definitely keep it up!!! 👍👍👍👍👍" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2211.0 0.0 0.0 0.0
"I think the derivative of U(x)V(x) ,we should add and substract u(x+deltax).v(x) instead of u(x) ..... " 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6052.0 0.0 1.0 0.0
"48:50 1/(1+rho) ~ 1-rho" ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 1298.0 0.0 0.0 0.0
"This is genius! Now I want to go to MIT, but not enough money... guess I will stay at Dalhousie" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 10665.0 0.0 0.0 0.0
"I didnt understand his exmaple of cos and sin. Someone please help." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 5283.0 0.0 1.0 0.0
"The professor's accent sounded exceptionally understandable and familiar to me, and then I saw that this brilliant teacher is from my country! Thank you so much for the lessons, μεγάλο ευχαριστώ από την Ελλάδα!" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 10252.0 0.0 0.0 0.0
"33:11 it's A=3*2^(2/3)*V^(2/3)" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 953.0 0.0 0.0 0.0
"For some odd reason teachers with odd or funny accents make me pay attention more lol. No offense intended of course" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3873.0 0.0 0.0 0.0
"there's something about his lectures that make it so easy for me to concentrate and follow along. I think it's because he thinks out loud; verbalizing the literal thought processes he runs through to compute this stuff, like he himself is learning for the first time and trying to understand what's going on. even though he's on a higher level than all of us mathematically, he still retains such a clear understanding of the basics." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14767.0 0.0 0.0 1.0
"sir, f sub xy is not always equal to f sub yx" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14314.0 0.0 1.0 0.0
"I have learnt those things on my (9--10) th class. w(°ｏ°)w. And I am from Bangladesh." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5535.0 0.0 0.0 0.0
"This guy ist Ubermann.
" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 10550.0 0.0 0.0 0.0
"gr8 vid, thx" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12959.0 0.0 0.0 0.0
"@inuyashalivesbaby haha i know what you mean! i study at LUMS univerity, Lahore, Pakistan and our science department is inspired by MIT.. we have moving boards here too its so much fun haha :D" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 1894.0 1.0 0.0 0.0
"Where can we get the notes of the class which are referred in the lecture so many times?" xaSL8yFgqig "Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11669.0 0.0 0.0 0.0
"at 36.40 how n3/ 3 it hsould be n(n+1)(2n+1)/6" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 12444.0 0.0 1.0 0.0
"MIT has done great service to mankind, by recording his lectures and sharing them online. This are so beautiful, future generations will remember him as the Mozart of this subject" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 7520.0 0.0 0.0 0.0
"The subtle but crucial shift from row space to column space using matrices at the end was just phenomenal!
This lecture has made my day" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10293.0 0.0 0.0 0.0
"I'm too dumb for MIT, but his lectures are so much simpler and easy to understand than my professor's.  #SJSU" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6392.0 0.0 0.0 0.0
"Thanks Proffesor." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9642.0 0.0 0.0 0.0
"ok ?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14123.0 0.0 0.0 0.0
"24:40
was it halloween?
They seemed to have linear algebra on Monday, Wednesday and Friday, and this lecture seemed to be on Monday (professor said ""see you on Wednesday"" in the end)
and I searched halloween of 2005 was also a Monday, so I guess it was halloween then☺️" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 743.0 0.0 0.0 0.0
"Thanks to all for making this possible." 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 9808.0 0.0 0.0 0.0
"@iDiViNeXx his from France, lol" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1884.0 0.0 0.0 0.0
"18:00 where LIMIT starts" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 526.0 0.0 1.0 0.0
"For chebyshev, on the left hand side, the right bracket should close after "">=a""." nrDkb2MAwSA "20. Definitions and Inequalities" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3860.0 0.0 1.0 0.0
"I'm yet to complete this video, commenting in the middle of it. What an explanation, amazing!" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 6400.0 0.0 0.0 0.0
"'gauss given order'  lol" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 210.0 0.0 0.0 0.0
"Very nice lecture" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11208.0 0.0 0.0 0.0
"When the substitute teacher comes in and does the final review, you've gone to MIT." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11636.0 0.0 0.0 0.0
"My textbook covers flux in 10 sentences. Thanks for making this public so it can bolster this kind of trash textbook." _CdoRiNSrqI "Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7794.0 0.0 0.0 0.0
"Awesome..Its much helpful." TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2790.0 0.0 0.0 0.0
"its good to be alive in this era bc of things like this. MIT ocw fucking rocks!" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13709.0 0.0 0.0 0.0
"It is immortal at 2019" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6950.0 0.0 0.0 0.0
"Great Lecture" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 4200.0 0.0 0.0 0.0
"He is gem" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4515.0 0.0 0.0 0.0
"amazing video for chalkboard asmr" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12354.0 1.0 0.0 0.0
"I completely know where you are coming from- differentiation from first principles was taught to me in Year 10 in my Further Maths IGCSE." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5244.0 0.0 0.0 0.0
"I am grateful for seeing this video" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 5099.0 0.0 0.0 0.0
"i understand how they felt when he said Taylor expansion." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13486.0 0.0 0.0 0.0
"Amazing! Hope my professor was like you." YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2397.0 0.0 0.0 0.0
"50:37 Why did not he also calculate the cofactor for a23 in the smaller matrix when he was looking for the cofactor for a21? I know it is still going to be zero because of the zero column on the left but I think he should have made that clear." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 1339.0 0.0 1.0 0.0
"may I ask how was 106 phone lines computed? I tried setting pi_b = 0.01 and substituted some numbers to calculate the i needed using the equation at 30:15, but seems the RHS of the equation is getting larger with larger i..." HIMxdWDLEK8 "18. Markov Chains III" "6.041 Probabilistic Systems Analysis and Applied Probability" 13923.0 0.0 1.0 0.0
"Lecture 1: Dot Product
Lecture 2: Determinants
Lecture 3: Matrices
Lecture 4: Square Systems
Lecture 5: Parametric Equations
Lecture 6: Kepler's Second Law
Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds)
Lecture 8: Partial Derivatives
Lecture 9: Max-Min and Least Squares
Lecture 10: Second Derivative Test
Lecture 11: Chain Rule
Lecture 12: Gradient
Lecture 13: Lagrange Multipliers
Lecture 14: Non-Independent Variables
Lecture 15: Partial Differential Equations
Lecture 16: Double Integrals
Lecture 17: Polar Coordinates
Lecture 18: Change of Variables
Lecture 19: Vector Fields
Lecture 20: Path Independence
Lecture 21: Gradient Fields and Curl Of Vector Fields
Lecture 22: Green's Theorem
Lecture 23: Flux
Lecture 24: Simply Connected Regions
Lecture 25: Triple Integrals
Lecture 26: Spherical Coordinates
Lecture 27: Vector Fields in 3D
Lecture 28: Divergence Theorem
Lecture 29: Divergence Theorem (cont.)
Lecture 30: Line Integrals
Lecture 31: Stokes' Theorem
Lecture 32: Stokes' Theorem (cont.)
Lecture 33: Maxwell's Equations
Lecture 34: Final Review
Lecture 35: Final Review (cont.)" PnPIqh7Frlw "Lec 24: Simply connected regions; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7282.0 0.0 0.0 0.0
"Thanks Dr. Strang. You are the best." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9588.0 0.0 0.0 0.0
"this guy fuckin sucks he has no idia what hes saying ......flmfaoooooo.....moron " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14807.0 0.0 0.0 0.0
"It's great to revisit all linear algebra from a different point view! It really opens my mind! Thank you Professor Strang!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7047.0 0.0 0.0 0.0
"A brilliant prof. God bless you!!!" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2102.0 0.0 0.0 0.0
"I'm the 951 viewer and 2nd commenter!!" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6391.0 0.0 0.0 0.0
"why these lectures look interesting?" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15369.0 0.0 0.0 0.0
"the chalk is about three times thicker than his thumb" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14674.0 1.0 0.0 0.0
"my exam is in 3 days, wish me luck, i am now at lec 12 haha" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13979.0 0.0 0.0 0.0
"Thanks for the lecture." cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 9718.0 0.0 0.0 0.0
"My neurons have started firing again after taking this course...Love from India." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 7778.0 0.0 0.0 0.0
👍👍👍 LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 15703.0 0.0 0.0 0.0
"thanks a lot, that was very intuitive, which is something difficult to do in linear algebra 
:)" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14574.0 0.0 0.0 0.0
"Great videos, and the professor is excellent. However, camera, please film the blackboard and the statements on it, please do not follow the professor. It is not supposed to be a video of him...." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 4363.0 1.0 0.0 0.0
"Thank you Professor Strang and to everyone involved in these videos, this course reignited my love for mathematics." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9217.0 0.0 0.0 0.0
"Thank you Gilbert Strang, thank you MIT." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9111.0 0.0 0.0 0.0
"40:44  (0, -1, 0)" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 1135.0 0.0 0.0 0.0
"Changing the order of integration in double integral is indeed equivalent to using the integration By Parts. Let's see how for this example:
Put $f(x)=\int_x^{\sqrt{x}}\frac{e^y}{y}dy.$ Then $f'(x)=\frac{e^{\sqrt{x}}}{2x}-\frac{e^x}{x}.$ and so
$xf'(x)=\frac{e^{\sqrt{x}}}{2}-e^x.$
The required integral is $I=\int_0^1 f(x)dx.$ Apply By Parts
by considering $u=f(x)$ and $dv=dx$ to get
 $I=(1f(1)-0f(0))-\int_0^1(\frac{e^{\sqrt{x}}}{2}-e^x)dx.$
To find the first integral, use the u-substitution $u=\sqrt{x}$
and the integration By Parts again!" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3141.0 0.0 0.0 1.0
"why singular values are always positive?" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15359.0 0.0 1.0 0.0
Legend QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7314.0 0.0 0.0 0.0
"Great lecture! Thank you so much Prof. Gilbert Strang. But can anyone tell me where to find the following part of PCA?" Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4269.0 0.0 0.0 0.0
"Professor Strang is the Columbo of Linear Algebra" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 8355.0 0.0 0.0 0.0
"19:16, why are all 5x5 matrices in a 25 dimension vector space?" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 557.0 0.0 1.0 0.0
"He's teaching at Berkeley this semester!! I always see him before my Linear Algebra class " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4645.0 0.0 0.0 0.0
"those 2 questions asked at 23:15 and 24:30 can be easily answered by 14 year old middle school student in Asia ! Good job MIT students!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14929.0 0.0 0.0 0.0
"Why are there so many empty seats" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 11781.0 1.0 0.0 0.0
"best  lecture" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12534.0 0.0 0.0 0.0
"Finally 😀" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 3788.0 0.0 0.0 0.0
"how could he derive X^2=sum (Xi)^2+ sum(XiXj) ? please someone explains to me" EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 13209.0 0.0 1.0 0.0
"Why give a boilerplate response that doesn't even address the issue?" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11861.0 0.0 0.0 0.0
"These lectures is too simplified because proof used in lecture is not completely done." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 10417.0 0.0 0.0 1.0
"Really this lecture deserves a bow 🙏 from india, thank you for clear explanation sir" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8531.0 0.0 0.0 0.0
"Phenomenal series, thank you MIT & Prof. Auroux!" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8189.0 0.0 0.0 0.0
"Rediscovering Linear Algebra again with Professor Strang! So intuitive with him." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 8542.0 0.0 0.0 0.0
Fucktorial 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 3947.0 0.0 0.0 0.0
"How is he cheating at 6:55 ?" BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 4867.0 0.0 0.0 0.0
"Ευχαριστώ ΕυχαριστώΕυχαριστώΕυχαριστώΕυχαριστώΕυχαριστώΕυχαριστώΕυχαριστώΕυχαριστώ!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 15545.0 0.0 0.0 0.0
"oh I can't stop this class, I watch it all night." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 14101.0 0.0 0.0 0.0
"I am going to put short 5 minutes clips that will be kind of a 'cliffs notes' to each lecture in this series on my channel " bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5096.0 0.0 0.0 0.0
"Cool hwip" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 3208.0 0.0 0.0 0.0
"29:53 How can you tell the matrix on the left is invertible without using determinants?" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 863.0 0.0 1.0 0.0
"He made life easy for so many people. <3" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4579.0 0.0 0.0 0.0
"I wanna see the board not the (great) professor." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6132.0 1.0 0.0 0.0
"Bohdan Nazarenko
0 seconds ago
I wish there were 4k cameras back then in order to shot this beauty well!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2906.0 1.0 0.0 0.0
"the third pivot is 3, not 5 as shown in the example. Interestingly, in back substitution -6 yielded a -2 for z as did the -10 that was shown" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14746.0 0.0 1.0 0.0
"i wish there would have some full system tap of Mathematical analysis and Physics courses 😁" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 13503.0 0.0 0.0 0.0
"This is cooool... :)" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10657.0 0.0 0.0 0.0
"Ax=b, then AtAx=Atb. awesome!" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2796.0 0.0 0.0 0.0
"15 years later, but the cameraman did not do a good job on this particular lecture. Most of the time the camera was too far zoomed in to see all of the notes on each blackboard slide. Previous lectures did a much better job of zooming out to see the full picture." phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 442.0 1.0 0.0 0.0
"""if one of those is the zero vector, *INDEPENDENCE IS DEAD* ""

not the context i expected those dramatic words in" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 157.0 0.0 1.0 0.0
"31:19 shouldn't that read dy/dt = 10cos(10) because x=10t   =>   x' =10?


Or have I missed something?" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 907.0 0.0 1.0 0.0
"This man is brilliant. A brilliant professor who conveys the true art of teaching. Happy to see this." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 10864.0 0.0 0.0 0.0
"looks like he has memorized the whole lecture instead of letting it come naturally" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13853.0 0.0 0.0 0.0
"Xo = at the intersection of the Y and X axes. He should have used an other symbol or letter whatever." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12100.0 0.0 1.0 0.0
"Dear MIT! What happened at 8:00? An important part of the lecture is missed!!!!" 0Qws8BuK3RQ "34. Distance Matrices, Procrustes Problem" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3325.0 0.0 0.0 0.0
"ear raep" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 12788.0 0.0 0.0 0.0
"What a beautiful human being" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11390.0 0.0 0.0 0.0
"A+ for the teacher" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 2173.0 0.0 0.0 0.0
"Dada ji kmaaal ke guru h aap ❤️❤️❤️" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 3290.0 0.0 0.0 0.0
"People are criticizing how ""easy"" this stuff is . But to be fair I honestly I don't think Prof David Jerison (no offense) is doing a good job explaining  to students that are new to this subject" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8163.0 0.0 0.0 1.0
Fantastic! XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 3740.0 0.0 0.0 0.0
"This is an AMAZING course that just fills the missing link between available courses in Math and courses in machine learning. Many thanks 👍" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10621.0 0.0 0.0 0.0
"Such an amazing course. Thanks MIT OCW and the professors." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8943.0 0.0 0.0 0.0
"Professor Strang, thank you and MIT for this powerful interview.  I hope that that your mind stays sharp." t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8384.0 0.0 0.0 0.0
"amazing lecture, I thought its gonna be crazy hard to understand, yet, I can follow up :) thank you MIT thank you Professor Gilbert!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12347.0 0.0 0.0 0.0
"it's because of his skill at erasing berofe the next blackboard cover it... just funny staff" _CdoRiNSrqI "Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13693.0 1.0 0.0 0.0
"Excellent proclamation! :  36:00 There is no randomness. Randomness is a big rug, underwhich we sweep everything we don't understand." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3666.0 0.0 0.0 0.0
"Like if you don't understand what he say..." C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 7355.0 0.0 0.0 0.0
"I love this guy. Been watching him for years. I am out of the business ( Ex teacher) and working on the railroad for a living now, however I still have an interest in math and science. Dr. Strang is the Eddie Vedder of math." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5811.0 0.0 0.0 0.0
"Is there an error at 32:30? Shouldn't S be multiplied before (lamda matrix)^100?" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 6832.0 0.0 1.0 0.0
"Good Job Professor" sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4117.0 0.0 0.0 0.0
"When do we get to integration?" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11614.0 0.0 1.0 0.0
"why  B group delta x is one?" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15274.0 0.0 1.0 0.0
"Therefore Issac Newton was irresponsible." hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10391.0 0.0 0.0 0.0
"Realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado realizado" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8499.0 0.0 0.0 0.0
"Coming from 18.06, 
Finished the whole Single Variable Calculus course!
Thanks you Prof. Jerison! and MIT
India, 2017
Time for 18.02!" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3171.0 0.0 0.0 0.0
"@30:18""Where did I run into trouble?  Well, then, my final step was to find U... ...and I didn't read the book...  ...so, I did something that was practically right, but I guess practically right is not quite the same...""  8^D" HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 1534.0 0.0 1.0 0.0
"There is an awesome lemma that lets you preserve distances in a high dimensional matrix by projecting it into a lower dimension with a random matrix. Its called Jordan-Lindenstrauss Lemma" z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10370.0 0.0 0.0 0.0
"45:35 is just exuding The Office Vibes" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1257.0 0.0 0.0 0.0
"If a country has teacher like him, that country is bound to prosper..." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6486.0 0.0 0.0 0.0
"Damn i really want that book but it costs like 80$ and only avaliable in paperback" Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3296.0 0.0 0.0 0.0
"37:36 ""Its not I like 18.01 ,but 18.06 is better "" hahhaha. MIT rocks" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 1068.0 0.0 0.0 0.0
Brilliant FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2921.0 0.0 0.0 0.0
"I feel proud to have made it to lecture 20. This course & the book combination has been such a gem" q3xvno_KgRY "20. L and NL, NL = coNL" "MIT 18.404J Theory of Computation, Fall 2020" 5397.0 0.0 0.0 0.0
感谢教授，第一次听这个课还是在网易公开课，没想到时隔多年，老教授还在上这个课，而且与时俱进了，大大的赞！ Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15632.0 0.0 0.0 0.0
"25:09 Toin Coss" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 765.0 0.0 0.0 0.0
"I don't understand clearly if x≠x_0 why we find the answer f'(x_0).(x-x_0=0. ? Can someone explain me?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5338.0 0.0 1.0 0.0
"I'm very thankful for these lectures. Though, the camera movement is sometimes annoying." k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6398.0 1.0 0.0 0.0
"Dear God,

Thank you for Gilbert Strang" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 3322.0 0.0 0.0 0.0
"Cool. Waterloo University has very similar lectures. This one is very clear though and I can understand the professor." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 3215.0 0.0 0.0 0.0
"This guy is something else. I go to my Linear Algebra class and I usually go out feeling more confused than when I went in, then I come watch these videos and things make sense in a minutes. It's not just what he knows, but he knows how to explain it, simple brilliant." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10545.0 0.0 0.0 0.0
"I love the difference in noise from a first year course to a 3rd or 4th year course. I forgot how noisy a class could be :P" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5776.0 0.0 0.0 0.0
"thank  u  sir   for  excellent  lecture  --pls   divide  long   lecture   in  to   short  lectures" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 14448.0 0.0 0.0 0.0
"i simply enjoy watching and listening to this." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13458.0 0.0 0.0 0.0
"Anybody found that there are no Ads in MIT OCW, wow!" xaSL8yFgqig "Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2476.0 0.0 0.0 0.0
"3:38 Did he miss multiplication by singular values?" 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1115.0 0.0 1.0 0.0
"lol, in france we do that at 15 years old." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13839.0 0.0 0.0 0.0
"Single variable calculus (aka Calculus I and II) is equivalent to AP Calc AB and BC.

In AB, there is material from Calc I and a bit from Calc II. In BC, the material revisits Calc I to some extent (that's why there's a B in the course names AB and BC) and then covers the Calc II material. 

Calculus III (multivariable) is not covered in high school because most students don't reach that far (the ones that do might take a special class or they enroll in a college class while in high school)." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8685.0 0.0 0.0 0.0
"infinite blackboards..." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 13608.0 1.0 0.0 0.0
"Por que usa la transpuesta de a en lugar de a? Why you use a transpose instead of a?" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 8230.0 0.0 1.0 0.0
"End of this year Im going to master linear algebra and calculus :)" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 3566.0 0.0 0.0 0.0
"@ 46:45 why did he put a negative in front of ye^y?" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1479.0 0.0 1.0 0.0
"Applied math, which is the same thing as physics but with different notations. Comedy gold." dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 2517.0 0.0 0.0 0.0
"Thanks MIT" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9595.0 0.0 0.0 0.0
"What if a number of pivots columns is not equal to a number of free columns - how can you build the matrix N in this case?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 11502.0 0.0 1.0 0.0
Legend. or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7322.0 0.0 0.0 0.0
"In the last prob we had one free variable and 2 pivot variables, but while concluding XN=0, indicating N = [ -F , I] where in two numbs were filled by free variables each as ""-1"" and the last unknown X3 = 1 !! Can anyone explain me ab this??" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 6674.0 0.0 1.0 0.0
"Where did q and alpha come from?" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 11674.0 0.0 1.0 0.0
"I paid a ton of money in college went there every day for several hours and learned nothing. And here i am learning free of cost from the comfort of home from the best professors in the world. Respect and love to professor strang." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 5895.0 0.0 0.0 0.0
"Some MIT students do not now the law of cosines!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8821.0 0.0 0.0 0.0
"End part is awesome ." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3567.0 0.0 0.0 0.0
"P = A.x(hat) ,right ?
so at 32:10 why is he substituting  P as x(hat).A.
Please help me with the intuition behind that." 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 8146.0 0.0 1.0 0.0
"You've had a new shirt professor :D." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 12256.0 0.0 0.0 0.0
"Watching Dr. Strang is never ever boring" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11293.0 0.0 0.0 0.0
"i love you professor!!!!!!!!!!!!!!!!!" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13439.0 0.0 0.0 0.0
"He is really great!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4535.0 0.0 0.0 0.0
"wasn't physically pressent in the class yet I can't ignore it's snowing outside! :P" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15061.0 0.0 0.0 0.0
"Did I miss anything hha, why is the class only 34 min and 29 min for the last one" cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3364.0 0.0 0.0 0.0
"The Very Hungry Caterpillar - Animated Film
https://youtu.be/75NQK-Sm1YY" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9977.0 0.0 0.0 0.0
"Kanye West in the first row 18.05" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7208.0 0.0 0.0 0.0
"THANK YOU VERY MUCH FOR YOUR GOOD LECTURES.IM WIS wishing you a very Merry Christmas and a HAPPY new year.YOU DESERVE ALOT OF DONATIONS.THANKFUL FOR YOUR LECTURES." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 8986.0 0.0 0.0 0.0
"I'd like a proof of this too. Trapezoids necessarily better fit curves than rectangles, so a midpoint trapezoid better approximates than a midpoint rectangle." jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6277.0 0.0 1.0 1.0
"@Raizdecimal Many of them are there because they work very hgard and make few mistakes, not because if the depth of their insight," kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1706.0 0.0 0.0 0.0
"@juhulk  can we download them problems sets? where?" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1908.0 0.0 1.0 0.0
"43:50 The moment one realise that he is the 😎 and everyone has so much respect for such as beautiful soul. I would be honoured to be one of his ‘pupil’ student or assistant. A 🎩 to a unique gentleman!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1221.0 0.0 0.0 0.0
"I love him " FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5735.0 0.0 0.0 0.0
"Great lecture" 0_w-R_g5lRA "Lecture 10: The Completeness of the Real Numbers and Basic Properties of Infinite Series" "MIT 18.100A Real Analysis, Fall 2020" 4240.0 0.0 0.0 0.0
"have you played any video games recently?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13066.0 0.0 0.0 0.0
"He explained Pendulum better than my PHYSICS teacher!" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4479.0 0.0 0.0 0.0
"This man is the best LA professor ever and these lectures are perfectly made. I really appreciate Prof. Strang and all the team involved." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10874.0 0.0 0.0 0.0
"poor teaching skills" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 14199.0 0.0 0.0 0.0
💖💖💖 QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15722.0 0.0 0.0 0.0
"I don't know what he's doing differently, but everything is easier when I listen to this guy. It might be the way he repeats certain phrases or makes everything less abstract. I'm currently struggling in my Linear Algebra class, so seeing this video and realizing that it isn't as hard as my current professor makes it seem is a huge relief. This guy is great. Thanks MIT. " Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5321.0 0.0 0.0 1.0
"I think my mind just exploded !" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 6036.0 0.0 0.0 0.0
"m is a number of rows, and the column space is in R^m?" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 13892.0 0.0 1.0 0.0
"33:35 three rules" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 963.0 0.0 0.0 0.0
"At 20:36 , I got bit confused and did not understand what was the point Prof.Gilbert made." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2606.0 0.0 1.0 0.0
"I don’t need to take linear algebra in college but it’s 3 am and here I am 1 full lecture deep too late to stop now" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5377.0 0.0 0.0 0.0
"it is very nice lecture i appreciate his hard work" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13676.0 0.0 0.0 0.0
"OMG!
Amazing teaching!" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 7987.0 0.0 0.0 0.0
"This document https://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-c-parametric-equations-for-curves/session-17-general-parametric-equations-the-cycloid/MIT18_02SC_notes_9.pdf has an equation for an ellipse.  Is it correct?" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10499.0 0.0 0.0 0.0
"I wonder if Stoke's theorem generalizes well to even higher, say, n, dimensional space.  " tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6243.0 0.0 1.0 0.0
"Its much easier to think of elimination as the needed row operations in order to produce a reduced row-echelon or at least a row-echelon form !" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7088.0 0.0 0.0 1.0
"Outstanding--Review on June 11th" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8144.0 0.0 0.0 0.0
"Also a great explanation by Gilbert Strang
https://www.youtube.com/watch?v=FtQl1gAo12E&ab_channel=MITOpenCourseWare
Actually I like it better, but this one is good too." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2322.0 0.0 0.0 0.0
"linear algebra by kenneth hoffmann and ray kunze" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13800.0 0.0 0.0 0.0
"I think Prof. Strang forgot to mention his (the) ""secret ingredient"": to love to teach. 
I hope he keeps sharp and healthy for a long time to come!" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6002.0 0.0 0.0 0.0
"Finally  null space  column has a combination of  identity  with free  variables 👏👏" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 3759.0 0.0 0.0 0.0
"MIT students groaning about a Taylor series expansion on a course in multivariable calculus? I don't know how a lot of these students made it into MIT." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7544.0 0.0 0.0 0.0
"No, ImageNet is just a training data. It consists of a bunch of pairs of image and description in words of what's in the image. It has nothing to do with neural networks, other than the fact that CNNs are currently the best tools to do image classification, and thus to win ILSVRC challenges." hwDRfkPSXng "Lecture 32: ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7900.0 0.0 0.0 0.0
老教授还挺精神的。太棒了，希望他长命百岁！他的线性代数课程实在是太棒了！ 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 15652.0 0.0 0.0 0.0
"His teaching technique itself should be teached ." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4766.0 0.0 0.0 1.0
"He writes slow compared to many a professor I have had....." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4621.0 0.0 0.0 0.0
"16:56 got scared by listening to that sneeze now" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 495.0 0.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8424.0 0.0 0.0 0.0
"Why do the local distant universities that we pay for don't give us a solid understanding of the subject, while the free global videos that are between our hands do? Maybe I should've not registered in the uni in the 1st place..." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 11825.0 0.0 0.0 0.0
"Alan Edelman is unmistakably erudite to state the concordance had by Linear Algebra with the applied topics of Machine Learning and Neural Networks." rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2291.0 0.0 0.0 0.0
"well he literally wrote the book!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15089.0 0.0 0.0 0.0
"Is this real? He is the legend.." Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 6876.0 0.0 0.0 0.0
"What was he doing since 22:45? I don't see why was he augmenting." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 11565.0 0.0 1.0 0.0
"""I illustrated patience"" hahaha" CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 57.0 0.0 0.0 0.0
"The real amazing teacher, wish him  a long and healthy life!!" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10267.0 0.0 0.0 0.0
"great lectures,, much better than any paid courses on Udemy or other sites" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 12992.0 0.0 0.0 0.0
"euler is genius" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12801.0 0.0 0.0 0.0
"amazing !!!session once again" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 12344.0 0.0 0.0 0.0
21:00 RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 666.0 0.0 0.0 0.0
"Jumper game on point." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 7145.0 0.0 0.0 0.0
"30:48 it seems to me that the word ""any"" should not be there. This only occurs to the point of max or min.  " 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 894.0 0.0 1.0 0.0
"41:10 thank god there are built-in functions in numpy for this cr***" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1148.0 0.0 0.0 0.0
"Thanks MIT" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9593.0 0.0 0.0 0.0
"DR. Strang thank you for a fantastic lecture to start this new class for MIT and all students in mathematics." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3279.0 0.0 0.0 0.0
"Boring friday night? mit course sounds like a good plan. XD" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 2910.0 0.0 0.0 0.0
"excellent lecture" 4HRhg4eUiMo "8. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 12820.0 0.0 0.0 0.0
"What an amazing Course! Thank you professor Strang for 18.065!" rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11447.0 0.0 0.0 0.0
"heh  RANGLE!  @ 17:15       i never took multi calc, he seems like a good prof" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13127.0 0.0 0.0 0.0
"43:30 Real analysis- sequence and series starts 😊" PnDtMfyZSIE "Lecture 6: The Uncountability of the Real Numbers" "MIT 18.100A Real Analysis, Fall 2020" 1212.0 0.0 0.0 0.0
"I like how you actually put it in the title...
""Theory""
Nevermind he writes with his left hand... enough shown." uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 5674.0 0.0 0.0 0.0
"OK I've watched this. How am I going to use this in the real world. " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7973.0 0.0 0.0 0.0
"Here we are anyhow finding the best approximated solution by this method. 
Then why can't we find the same approximated solution even when the rank(A) < n.  By following the same way. 
Just by projecting the 'b' on C(A) and then solving." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 4676.0 0.0 1.0 0.0
"Best one Yet ! !! !" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 2871.0 0.0 0.0 0.0
"Gauss will quit, but Jordan says keep Going. :D" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3986.0 0.0 0.0 0.0
"Not clear, lengthy, anticipate too much concepts" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7920.0 0.0 0.0 0.0
"mis respetos para el MIT y las clases que imparte saludos desde la Universidad Nacional Tecnologica de Lima Sur - PERU" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13948.0 0.0 0.0 0.0
"What's so funny @17:55?" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11575.0 0.0 0.0 0.0
"Watching in 2022 ! #legends🗿" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 11296.0 0.0 0.0 0.0
"long live professor Strang !!! thanks for your explanation" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13847.0 0.0 0.0 0.0
"I love how he uses different ways of looking at the same thing to help drive concepts home (from the very first lecture). Strang is a fine teacher." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 5750.0 0.0 0.0 1.0
"Mind is officially blown." lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 7669.0 0.0 0.0 0.0
"Can anyone tell me how he gets the coordinates (1/root2, 1/root2?" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3044.0 0.0 1.0 0.0
"students get so excited by something minimal." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14405.0   0.0
"Thank you Professor Auroux, all your videos were so helpful." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9206.0 0.0 0.0 0.0
"The audio is heavy on the right side" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9984.0 0.0 0.0 0.0
"Must watchhttps://youtu.be/lVUVWdECVVM" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 7728.0 0.0 0.0 0.0
"can someone explain me what unit speed is ?" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12621.0 0.0 1.0 0.0
"congratulations is a great class of calculus, I admire you so much; and some day I want visit to MIT.
See you soon
Teacher Jose Luis Benavides Cepeda
Colombia" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12669.0 0.0 0.0 0.0
"@kjkunaljindal24 Yeah.. but everyone forgets stuff and some people catch on faster than others. " ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1922.0 0.0 0.0 0.0
"in the elementary matrix, How we can know the unknown column otherwise (same columns ) which take 100 or 010 or 001   
I really do not understand how he knows this for example, in minute 31:40 
how can he determine that third row should be (0 -2  1 )" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13599.0 0.0 1.0 0.0
"All the presentations by this lecturer is excellent,and well presented for taking notes and to learn by  listening.Well paced ." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2309.0 0.0 0.0 1.0
"9:18

God bless ya" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1439.0 0.0 0.0 0.0
"It's a Zipf, it's a Zipf" XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 7016.0 0.0 0.0 0.0
"What happened to Lecture 10? (Multinomial Chi-square?)" a66tfLdr6oY "11. Parametric Hypothesis Testing (cont.) and Testing Goodness of Fit" "MIT 18.650 Statistics for Applications, Fall 2016" 11497.0 0.0 1.0 0.0
"0:21 outline" P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 304.0 0.0 0.0 0.0
"be nice to have American teachers in American classrooms. I find myself too distracted trying to decipher the accent when my attention should be on the material. " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12513.0 0.0 0.0 0.0
"It's so sad that the camera work is so bad, he's a really good lecturer, so it's frustrating to pause everywhere to take notes. My teachers are nowhere near this standard." 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7071.0 1.0 0.0 0.0
"im 17 and doing this in school..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13561.0 0.0 0.0 0.0
"why is everyone here so old?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15330.0 0.0 0.0 0.0
"What kind of alien language is this? " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11546.0 0.0 0.0 0.0
"About pi. I find it funny that people say that one can calculate the periphery of a circle but not of an ellipse when the periphery of circle is 2*pi*r and ellipse is 4*a*E(e), where r is the radius of the circle, a is the larger semiaxis of the ellipse and e is the excentricity of the ellipse. pi and E(e) are both as difficult to calculate exactly but somehow people say that the other equation is explicit and the other is not." Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2196.0 0.0 0.0 0.0
function👎 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12909.0 0.0 0.0 0.0
"thinking about subspaces of matrices is difficult i couldn't even visualize" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 14790.0 0.0 0.0 0.0
"n^2 + (n-1)^2 + (n-2)^2 + ... + 2^2 + 1^2 = n * (n+1) * (2n + 1) / 6. As n becomes ""big"", this sum approaches n^3 / 3. His approach in the lecture is also good. Plot a graph of y = x^2 and identify the points x = n, x = n-1, x = n-2, ..., x = 1, and you'll find that if n is big enough, the discrete plots start to look more and more like the curve y = x^2, which then allows you to approximate the area under the curve. Again, what you get for a reasonably large n is n^3 / 3. One final thing is, if these operations are performed in a loop, you'll need way more time, because his analysis assumes an operation on an entire row. To achieve this, you would need vectorized code that can operate on the entire row at once. Hope this helped someone :)" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 14010.0 0.0 0.0 0.0
"Thank you Professor Tsitsiklis for this great intro to Probability!" rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 9226.0 0.0 0.0 0.0
"Glad mit still needs sat score to admit students or they would be ruined." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 4054.0 0.0 0.0 0.0
"He is amazingly good teacher but 20:43 He has problems with Gauss :D" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4507.0 0.0 0.0 0.0
"Simply genius" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 8667.0 0.0 0.0 0.0
"My teacher also used visuals like the wheel one to explain standing waves and we too were like... Wooooooahh." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7788.0 0.0 0.0 1.0
"yellow + blue = green , he teach art too!" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 15479.0 0.0 0.0 0.0
"Sir ! .. so much respect to you sir .. !" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8687.0 0.0 0.0 0.0
"Everyone please notice that this course was a first year in 1999. Things change after 14 years. This information is still quite pertinent, but yes, some of you went over this in grade 10/11/12. Good for you." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3611.0 0.0 0.0 0.0
"MIT students, first year.

fuck are you on?" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7546.0 0.0 0.0 0.0
"Mit lectures are futile." YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7678.0 0.0 0.0 0.0
"I've been working on the problem sets for these lectures on the MIT website, but it doesn't seem to give solutions for the part B problems; does anyone know where I could find these? " U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6412.0 0.0 1.0 1.0
"So students at MIT also make noises & talk with each other when the instructor turns his back towards students." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8788.0 0.0 0.0 0.0
"Holy shit, no dislikes." PnPIqh7Frlw "Lec 24: Simply connected regions; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4780.0 0.0 0.0 0.0
Yayaya 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 12115.0 0.0 0.0 0.0
"Very great course! Thanks very much. I hope the 18.102 by Dr. Rodriguez could be released soon😀." u4qQ1oIQcW8 "Lecture 25: Power Series and the Weierstrass Approximation Theorem" "MIT 18.100A Real Analysis, Fall 2020" 11192.0 0.0 0.0 0.0
"so, how old r the ppl he's talking to??" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14351.0 0.0 0.0 0.0
"my brain is on fire!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13971.0 0.0 0.0 0.0
"I don't know why he let I_d  rather than I_n denote n by n Identity matrix since 32:10." WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 5324.0 0.0 1.0 0.0
"The classes are wonderful, excuse me, what linear algebra book do you work with?" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 10046.0 0.0 1.0 0.0
"final call of steve jobs" lZrIPRnoGQQ "27. Backpropagation: Find Partial Derivatives" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12856.0 0.0 0.0 0.0
"Why did he divide (x^10-1) and (x^2-1) by (x-1)? Can someone kindly explain that to me, please? I would really appreciate it. Thanks! :D <3" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11808.0 0.0 1.0 0.0
"10:00 energy
19:00 convex" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 340.0 0.0 0.0 0.0
"26:05 (-1^2=-1?)" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 794.0 0.0 1.0 0.0
"Gotta respect Gilbert Strang!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4173.0 0.0 0.0 0.0
"thank you. it was great experience with linear algebra" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 14535.0 0.0 0.0 0.0
"great lecture!!" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12985.0 0.0 0.0 0.0
"Whelp. He's right that he's staying home and not driving around this year." 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11600.0 0.0 0.0 0.0
"Why take linear algebra if you're not interested?" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 11915.0 0.0 0.0 0.0
"in 30:10 question we can calculate the area of the triangle simple by using 1/2 * base*height and its a right angled triangle so is it necessary to use calculus over here." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13577.0 0.0 1.0 0.0
"This series is making my life so easy" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10923.0 0.0 0.0 0.0
"23:32 different ways to generalize solution for test data use Lipschitz Continuity bound to your loss function(Usually while applying SGD we have a methodology which combines the two using Lipschitz Continuity Constraint Projection." Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 714.0 0.0 1.0 0.0
"Gilbert Strang, you have my love. I love you. The devotion you show for the subjects you teach is rare. One can easily see why an institution like MIT would like to keep you for the rest of your life. Thank you." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4038.0 0.0 0.0 0.0
"Unique and interesting presentation. However, would be difficult if one had not already had basic LA." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11124.0 0.0 0.0 0.0
"He explained in 1 lecture what took my professor 3.... very good teacher" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 4480.0 0.0 0.0 0.0
"Thank you sir,  I understand the importance of checking triangular inequalities. By the way isn't the Distance Matrix  1st row [ 0 1 6], 2nd row [ 1 0 1] and 3rd row  [6 1 0]." 0Qws8BuK3RQ "34. Distance Matrices, Procrustes Problem" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9336.0 0.0 1.0 0.0
"Thank you.......you've shared the worth lesson..." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 9564.0 0.0 0.0 0.0
"Thank you Mr Strang!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9173.0 0.0 0.0 0.0
"Thanks a lot to Dr. Auroux and all the staff behind the making of this series of videos. The course is very insightful and clear. By going through these videos, I cleared up a lot of confusions which were unanswered when I took the course before." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9664.0 0.0 0.0 0.0
"good question" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12950.0 0.0 0.0 0.0
"Does this class include what is generally Calc 2 as well? I see the next class up is multivariable which is often known as calc 3 at some uni's." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3461.0 0.0 1.0 0.0
"Thanks Professor Auroux!" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9639.0 0.0 0.0 0.0
"Prof Stang The GOAT." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8269.0 0.0 0.0 0.0
"You can really feel the weekend's around the corner" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12192.0 0.0 0.0 0.0
"this guy saves my midterm XD" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14838.0 0.0 0.0 0.0
"Dr. strang is too energetic!!!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 3518.0 0.0 0.0 0.0
"Eu estou no ensino médio e já sei fazer essa budega aí...  kkkkkkkkkkkkkkkkk
Seus burros." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3579.0 0.0 0.0 0.0
"who is here in 3018 ?
And thank you for all this videos they are best" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 15262.0 0.0 0.0 0.0
"proof by picture lol haven't heard that one before" H_k1w3cfny8 "10. Continuous Bayes' Rule; Derived Distributions" "6.041 Probabilistic Systems Analysis and Applied Probability" 14225.0 0.0 0.0 0.0
"oops wrong video" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 14157.0 0.0 0.0 0.0
"I don't get it. Don't take it wrong, but why is this course offered? These students got in so they have the grades. AP Calc AB/BC is taught as a junior or senior class." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5308.0 0.0 0.0 0.0
"It  is flux ACROSS the surface.. (hence it's integrated over F.n) means that flux is maximum when the normal vector of the surface is parallel to the vector field." phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6904.0 0.0 0.0 0.0
"i love you MIT opencourseware" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 13436.0 0.0 0.0 0.0
"mind blown through and through" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13945.0 0.0 0.0 0.0
"thank you 4 the video
i've insomnia so i watch this hope i can get sleep" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14474.0 0.0 0.0 0.0
"Wow - the ending was just mind blowing!!! Think I am starting to love Mathematics so much" zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12026.0 0.0 0.0 0.0
"Oh man still confused on how P intersection L is a subspace I mean I get that their intersection will be 0 which is a sub space but if a vector is in P subspace and another vector is in W subspace how their sum and multiplication will be in that intersected subspace." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 8011.0 0.0 1.0 0.0
"yes, it's still harder than the very first lecture at high school tho" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15487.0 0.0 0.0 0.0
"Any prerequisites for this course?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2473.0 0.0 0.0 0.0
"I already bought this book and I can’t wait😍😍😍" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5034.0 0.0 0.0 0.0
"I can't thank you enough, Dr. Strang! :) It's been a wonderful semester." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5225.0 0.0 0.0 0.0
"Sorry to burst your ego but that's really high school level mathematics, and he even explained it in the video." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8858.0 0.0 0.0 0.0
"Dr. Strangelove!!!!!!
please say: ""I can walk it's a miracle!""" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3516.0 0.0 0.0 0.0
"I dont understand... I am really dumb to be in MIT but what the heck is going on with these students... they shouldn't be getting confused over simple shit as that, can someone tell me are MIT students really not that smart as people say?" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5370.0 0.0 0.0 0.0
"@zobazoba69 mal profesor, explica las ecuaiones de forma mecanica, es mejor aprender en la casa." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2087.0 0.0 0.0 0.0
"I love his shirts. Same every class just a different bold color. Dude should have a fashion line" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5744.0 0.0 0.0 0.0
"Professor Suvrit Sra, thank for a beautiful lecture on Stochastic Gradient Descent and it's impact on machine learning.  This powerful lecture help me understand something about machine learning and it's overall impact on large companies." k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8391.0 0.0 0.0 0.0
"thank youthank you very muchI will donate" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14537.0 0.0 0.0 0.0
"nice lectures , very helpful to me an indian student" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 14045.0 0.0 0.0 0.0
"No one calculate the determinant as it is defined, but using some matrix decompostion, like AR=QU or PA=LU. This way, the determinant is in the diagonal of U, less than a change of sign." d32WV1rKoVk "12. Computing Eigenvalues and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7883.0 0.0 0.0 1.0
"Householder: https://www.sciencedirect.com/topics/engineering/householder-matrix
 http://mathworld.wolfram.com/HouseholderMatrix.html" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4793.0 0.0 0.0 0.0
27:44 QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 825.0 0.0 0.0 0.0
"These are very niece explanation of Linear Transformations and  Their Matrices  thanks once again to the godfather of linear DR. Gilbert Strang. I took introductory linear algebra at the University of Maryland Baltimore County  in the late 1980's and my professor was nothing close to what Dr. Strang is. This MIT legend is a rare find." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10398.0 0.0 0.0 0.0
"I have used the Kirchhoff's Law for 6 yrs since studied electrical engineering, and that's the first time I learn it from perspective of matrices, what a great lecture!" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5567.0 0.0 0.0 1.0
"cos^4 (theta) could be integrated by using Wallis formula its easier :) " YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12681.0 0.0 0.0 0.0
"I think I need my subspace radio." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 5997.0 0.0 0.0 0.0
Excellent 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3625.0 0.0 0.0 0.0
"The author of Mathematics for the Million was Lancelot Hogben in 1936. Eric Temple Bell wrote Men of Mathematics in 1937. For decades, both were very popular books on math for the general audience back when computational cost meant paying people to crank mechanical devices and write down the answers. Now a smartphone can invert a giant matrix in the blink of an eye." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 9986.0 0.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change

Lecture 2: Limits
Lecture 3: Derivatives
Lecture 4: Chain Rule
Lecture 5: Implicit Differentiation
Lecture 6: Exponential and Log
Lecture 7: Exam 1 Review
Lecture 9: Linear and Quadratic Approximations
Lecture 10: Curve Sketching
Lecture 11: Max-min
Lecture 12: Related Rates
Lecture 13: Newton's Method
Lecture 14: Mean Value Theorem
Lecture 15: Antiderivative
Lecture 16: Differential Equations
Lecture 18: Definite Integrals
Lecture 19: First Fundamental Theorem
Lecture 20: Second Fundamental Theorem
Lecture 21: Applications to Logarithms
Lecture 22: Volumes
Lecture 23: Work, Probability
Lecture 24: Numerical Integration
Lecture 25: Exam 3 Review
Lecture 27: Trig Integrals
Lecture 28: Inverse Substitution
Lecture 29: Partial Fractions
Lecture 30: Integration by Parts
Lecture 31: Parametric Equations
Lecture 32: Polar Coordinates
Lecture 33: Exam 4 Review
Lecture 35: Indeterminate Forms
Lecture 36: Improper Integrals
Lecture 37: Infinite Series
Lecture 38: Taylor's Series
Lecture 39: Final Review" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8447.0 0.0 0.0 0.0
"Best lecture thus far :D" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2864.0 0.0 0.0 0.0
"he does it not as if he's doing math, but like art, like poetry" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13074.0 0.0 0.0 0.0
"is he the best mathmatician of our times ?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 13633.0 0.0 0.0 0.0
"Great professor" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 4322.0 0.0 0.0 0.0
"I wish I could understand this but am dumb ☹️" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6195.0 0.0 0.0 0.0
"@slatz20 
he explains that if you multiply only one row! so he did it correct" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 2017.0 0.0 0.0 0.0
"God bless MIT and Professor Strang. Such a bright light for a wonderful course!" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 4074.0 0.0 0.0 0.0
"Psh, that example had a much easier solution. Just multiply the first two equations, cancel the xy (as clearly neither can be 0), and you get L^2 = 4.

Glad to finally learn Lagrange Multipliers, though; my teacher skipped over them in AP Calc, so they've always seemed like some magical algorithm I would never know that trivially solves optimization problems." 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8457.0 0.0 0.0 0.0
"Look. I’m going say this. I learned much oh this in Pre-Calculus in 1981 👍🏾" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 7419.0 0.0 0.0 0.0
thanks 4UJc0S8APm4 "23. Classical Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 14541.0 0.0 0.0 0.0
"and the paradox lies in the very nature of curvature itself, which can't be exactly calculated using discrete math (I am claiming the entire real number line is discrete)." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12372.0 0.0 1.0 0.0
"I have a doubt/conclusion that needs rectification as I am no sure about  it. So here it goes. If 2 matrices A and B (both nxn) have the same 4 subspaces then if they are spanning all of n dimensional space(in form of Column and Row Spaces i.e. all cols and rows are independent or rank = n), only then can A and B not be multiples of each other.  If they span a subspace of the column space Example 2D plane in R³, then in that case A and B have to be multiples of each other i.e. A=cB. Am I correct? Pls justify or oppose my conclusion. Thanks for reading :)" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 5490.0 0.0 1.0 0.0
"Am here as a Graduate student who is up for a Behavioral economics interview in two weeks and i need some Econometric analysis background led me here as a foundation and am not even mad.. the Professor is just amazing." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2344.0 0.0 0.0 0.0
"student sitting in mit and no doubt really talented student but got stuck at simple point which is like 7th grade question" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14403.0 0.0 0.0 0.0
와... YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15684.0 0.0 0.0 0.0
"Around #22:30 , why not just do the multiplication by distributing in order, i.e. 
(a+b+c)(d+e+f) = ad+ae+af+bd+be+bf+cd+ce+cf 
instead of what he called ""cross-terms?""
" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2546.0 0.0 1.0 0.0
"I remember in a lecture he suddenly stops for a few seconds then exclaims 'Wait a minute! there's a minus sign here!' It was a funny moment." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5947.0 0.0 0.0 0.0
"Thanks Prof. Strang." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 9636.0 0.0 0.0 0.0
"I am not able to understand how the matrix A is being formed from X and result. Please help" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 5120.0 0.0 1.0 0.0
"30:54 I think he made a mistake when drawing the curve. The top is not matching." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 897.0 0.0 1.0 0.0
"Thanks professor, Thanks MIT." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9768.0 0.0 0.0 0.0
"What a beautiful beautiful lecture! 

Thank you Prof. Suvrit!" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11389.0 0.0 0.0 0.0
"How is his proof for dot product not circular logic? If you believe the law of cosines... then that is a proof for the dot product. If you believe in the dot product, then that's proof for law of cosine. WTF?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4868.0 0.0 1.0 0.0
"Glad the intro properly says ""high quality"" rather than the illiterate ""quality"" so often used now  to describe the video which follows.. At least there is one place left which respects   language. MIT is to be commended for this alone." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4055.0 0.0 0.0 0.0
"He was explaining that you could factor them out, but that would take to long to factor out the 10th power.  That's why he didn't actually do it, he showed the rule." PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4618.0 0.0 0.0 0.0
"Thank you so much! God bless you!" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9384.0 0.0 0.0 0.0
"This give a easiest geometric interpretation of why singular matrices has no inverse. This kind of matrices take n-dimensional vectors as input and the output is in a vector of smaller dimension, and different vectors can have the same output, so you can´t have an inverse transformation because you don't know to wich of all of this original vectors corresponds the vector in the space of smaller dimension. More importat, that's why you need an initial condition in integrals to know the original function, because the derivative is making this same process and only with the inverse ('integral ) you can't tell which is the original function." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10503.0 0.0 0.0 0.0
"Can anyone explain the proof starting at 5:45?" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3026.0 0.0 1.0 0.0
"Linear algebra is used quite frequently in the real world. Especially when countless variables are being dealt with. Computer programs/software are great examples of this." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 7379.0 0.0 0.0 0.0
"Homie, you are not alone.  Having said that, many questions tend to go away with time.  Sometimes you just go through the motions, as it were, now, and hope that deeper understanding evolves later, even much later.   If this stuff was intitive (some of it is,) it wouldn't have taken them 1000 years to 'discover' the Calculus.  " 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4781.0 0.0 0.0 0.0
"Lec 27 is so interesting" phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7260.0 0.0 0.0 0.0
"42:00 Are the things he's saying correct or he was confusing the words ""potential"" and ""potential energy"" during the whole lecture? Shouldn't force be a gradient of potential energy and electric field intensity a gradient of electric potential?" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1168.0 0.0 1.0 0.0
"There's a very specific notation for the junk xD" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10387.0 0.0 0.0 0.0
"@erood8 We'll these courses go by so quickly there barely enough time to understand all the material let alone really appreciate what you're learning. The instructor and educational institution realize that because of the pace of these courses you won't be able to develop a concrete understanding at the same pace. They want to know that you have a fairly well-off foundation and really developing a strong usages of these concepts will be your problem later." PnPIqh7Frlw "Lec 24: Simply connected regions; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1831.0 0.0 0.0 0.0
"Thanks sir!" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 9778.0 0.0 0.0 0.0
"Why audio is muted" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11793.0 0.0 0.0 0.0
"I've just noticed that my teacher never taught me the entire steps...just the short cuts. This is great!" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6418.0 0.0 0.0 1.0
"27:30 oh my god it makes sense" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 821.0 0.0 0.0 0.0
"29:33 should be  you can find a non-zero vector x with Ax=0" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 855.0 0.0 1.0 0.0
"Damn, the explanation to the quadratic approximation is simple but powerful. I just took the CFA Level 1 exam, and the Bond Duration involved such quadratic approximation and I have been wondering where tf was that extra 1/2 coming from. At the end of the day, It was all my own insufficient knowledge in fundamental calculus. I wished I had studied my undergrad in MIT. But it's never too late to study, thank you MIT for the free education." eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3306.0 0.0 0.0 0.0
"Howard Anton’s linear algebra is best. Prove me wrong" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4911.0 0.0 0.0 0.0
"I must say I love his handwriting 😅👌👌" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5875.0 0.0 0.0 0.0
"5:06 did he mean positive semi definite ?" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1356.0 0.0 1.0 0.0
"i'm confused to the extent that i don't know what i'm confused about. ( probably  i'm missing something)" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13511.0 0.0 0.0 0.0
"if I put in 3,3,7. That would be a goof" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 13528.0 0.0 0.0 0.0
"Does he talk somewhere about vector spaces, subspaces, euclidian spaces ?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3454.0 0.0 0.0 0.0
"This comments thread seems to be filled with people reassuring themselves of their intelligence even though MIT rejected them. If you were actually doing multivariable calculus in 6th grade, you wouldn't be complaining on a youtube thread. " 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10486.0 0.0 0.0 0.0
"Thank you professor Gilbert Strang. This lecture's content is very abstract, thank to the previous lectures that helped me to build up foundation knowledge and intuition that I could understand this lecture." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 9310.0 0.0 0.0 1.0
"Gilbert Strang, you have done so much to help me learn linear algebra for my research. Thank you!!" 1pFv7e9xtHo "31. Eigenvectors of Circulant Matrices: Fourier Matrix" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4037.0 0.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8423.0 0.0 0.0 0.0
"I find this course especially a great one. Probably many people will argue that it seems easy, the professor speaks slowly, many concepts are probably studied in high school, and is worried about the critical points in his explanation. And that's the point.. In one of this lectures the students asks more questions than in the complete calculus course I took in mi Spanish university 25 years ago. 
In my course the professor took for granted much concepts that we didn't had, taught for himself (he was a mathematician of course, but we were studying chemistry..), worried more of finishing the lesson in time (at full speed) without taking into account the main key points of confusion a first year college has. I know there's a more theoretical (for mathematicians) courses of calculus in MIT, more formal and pure mathematics, but this is the best calculus course a first year college should have." Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5418.0 0.0 0.0 0.0
"useful for understanding mathematics" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14986.0 0.0 0.0 0.0
"17:03 UA ,cb" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 501.0 0.0 0.0 0.0
"I thun he wanted to emphasize that you can pick e' as small as you want." 3eiio3Tw7UQ "19. Weak Law of Large Numbers" "6.041 Probabilistic Systems Analysis and Applied Probability" 6106.0 0.0 0.0 0.0
"Thank you for this video!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9286.0 0.0 0.0 0.0
"Thank you MIT for sharing this." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9148.0 0.0 0.0 0.0
"20:08 for ftc 2, if anyone is here for it :>" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 644.0 0.0 0.0 0.0
"The comments are always much consolation to see..." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 10052.0 0.0 0.0 0.0
"Great prof..he makes linear algebra makes more sense, and easier to understand..I mean it is suppose to be easier..the purpose of linear algebra is to make complex thing easier to solve...but unfortunately many teachers dont teach it properly, making it seem so hard to learn" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4321.0 0.0 0.0 0.0
"He's absolutely amazing!!!" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4630.0 0.0 0.0 0.0
"Prof Boyd is also very good teacher !
I enjoy his lecture very much." wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8261.0 0.0 0.0 0.0
"Took me some time to realize he was talking about the American version of 'football'." TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 11073.0 0.0 0.0 0.0
"@Merky2k Well, if you watched until 2:30 you would of heard that it is used in ""Science, Engineering, Political Science and Economics"" but clearly since you dont understand that, i doubt you understand differentiation in its simpliest form.
" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1672.0 0.0 0.0 0.0
衆口難防 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15656.0 0.0 0.0 0.0
"Wow just amazing,in 2 and a half minute, u generalized my concept and the use of the dot product was astonishing, hats off professor🙇‍♂️🙇" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12033.0 0.0 0.0 0.0
"Oh God, not another chalk on the blackboard presentation. This is the 21st Century." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 7998.0 1.0 0.0 0.0
"Someone have more clear resource (Lecture videos) that explain everything without skipping some points because i really can't understand this 
can someone please send my some link or something that explain better?" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8835.0 0.0 0.0 0.0
2017 QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 621.0 0.0 0.0 0.0
"@gorgolyt 

That is completely messing with my mind." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1855.0 0.0 0.0 0.0
"Couldn't understand why people are disliking?" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3249.0 0.0 0.0 0.0
"Watching Andrew Ng's Machine Learning course, came here to understand what a low rank matrix factorization is." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 11292.0 0.0 1.0 0.0
"Thank you" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 9085.0 0.0 0.0 0.0
"Lagrange multipliers. Ouch. Starting to make a bit of sense now, but it would have been good if he could have done a different example, preferably one that didn't use up time talking about pyramids and triangles; time that could have been spent going over the actual Lagrange multiplier method again a bit more slowly." 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7246.0 0.0 0.0 1.0
"In italian calculus courses there are better proofs for limits sinx/x=1 and (cosx-1)/x=0... here the explanation is very confused, and in particular how can I say that the limits would be 1 and 0 and not, for example, 0.99 and 0.01? We use instead the theorem of comparison for the first limit (sin x < x < tan x) and a trick for the second limit (1-cos x = 2sin^2(x/2)). Very simpler and clearer." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6638.0 0.0 1.0 0.0
"Eigen vector direction may change between the same and opposite directions  but the eigen value may be increased as a conclusion message of professor." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 3554.0 0.0 0.0 0.0
"Around 21:00,.In general case of R^n, you can not form a determinant of A and B unless n=2. Hmmm " 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2551.0 0.0 1.0 0.0
"Great topic!" Yb69dAq4uh8 "Lecture 15: Orthonormal Bases and Fourier Series" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 4349.0 0.0 0.0 0.0
Nice 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7832.0 0.0 0.0 0.0
"@pedroissler You are right. I did not knew what will happen next and hence was kind of anticipating things. But now I know that I was right
" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1966.0 0.0 0.0 0.0
"In 20:17 .. if the prism is cube why the sum is square 1^2+2^2+3^2 ...." hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6594.0 0.0 1.0 0.0
"A Few days back I emailed Prof. Gilbert Strang,after completing the Linear Algebra course taught by him, showing my gratitude to him for letting us learn these amazing things in a heavenly interesting way. He, in reply, thanked me and informed me of this course. Professor, I wish I could give you my years left." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2093.0 0.0 0.0 0.0
"An Indian edition of this book is available only in India
http://www.wellesleypublishers.com/buy.html" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 2428.0 0.0 0.0 0.0
"Take really good notes and absorb them. Now, try to present the same lecture without memorizing it all like a script. Not so easy, is it?! You see that Strang is not referring to notes. Keep working at it and you will have internalized the idea." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9010.0 0.0 0.0 1.0
"Any of these single variable calculus resently im self teaching myself math and looking for the best software to follow up, I have a pdf on the subject, called by early transdentals, and there is one doing the same subject on Edx, looking for the best resources to continue my math studies. Khan academy is good but to jumpy now for my liking.i am from Scotland uk and hope I can find the right ones." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2471.0 0.0 0.0 0.0
"Beware! Storytelling is enticing enough to make you jump to next one like it's GOT" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 2891.0 0.0 0.0 0.0
"I'm so gonna forget all the homeworks I've done in this course (because it makes me learn how to compute rather than actual knowledge, I'll still remember the ""knowledge"" in the lecture though) 

Confusing part: 
0:00 what does that linear problem really mean? (Why is the solution only u(t) when there're 2 variables u1 and u2? Shouldn't it be u1(t) and u2(t) Maybe that some calculus that I don't know yetf) 
9:55 (Au popping off like a wild Pokemon)
18:48 (What is that value, sine and cosine thingy and why? Maybe that's some calculus problem that I should just agree that it is for now) 

I heard about Taylor series 
Is (1-x)^-1 = 1 + x + x^2 +... true with every x? 
Oh, here's the answer :
http://mathforum.org/library/drmath/view/61847.html
But then how can we judge if At < I, monkaHmm" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 6374.0 0.0 1.0 0.0
"These videos are helpful, but can't see lecture 16?" bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 10432.0 0.0 0.0 0.0
"thanks sir u improved  my math knowledge" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14605.0 0.0 0.0 0.0
"The discontinuity from the first video adds quite some confusion." C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 10076.0 0.0 0.0 0.0
"Thank you, this is mindblowing" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 9536.0 0.0 0.0 0.0
"this guy is awesome the proffs at the university of toronto dont know shit abt math..." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 14821.0 0.0 0.0 0.0
"why do they laugh at the chain?" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15304.0 0.0 0.0 0.0
Legend rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7316.0 0.0 0.0 0.0
"3:07 Why does elimination change the column space? All you do is take rows to be linear combinations of each other (crucially, preserving the original row), which leaves the column space unchanged. The basis vectors you use to form the column space are different, but the space itself should be the same because all combinations are in the original space and no vectors are lost by multiplication by zero." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 1109.0 0.0 1.0 0.0
"thank you Professor Gilbert Strang for these wonderful lectures." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 14488.0 0.0 0.0 0.0
"Best discussion on Baye's, I have come across." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 2855.0 0.0 0.0 0.0
"i can make it, i can make it, i can make it... confidence!!! iam the best, i am beautiful! iam sucvccessful and handsome and sexy!!!!!!!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13347.0 0.0 0.0 0.0
"Thankyou Dr. Strang, been here from Lec 1 to 34. Amazing course" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9865.0 0.0 0.0 0.0
"The v's have points on the bottom. The u's have little round things" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10309.0 0.0 0.0 0.0
"I have all the problems sets but I can´t find the difficult problem that he is showing at 13:15, does anyone know what problem set is that??" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5515.0 0.0 1.0 0.0
"Gil's talking to himself here-" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4009.0 0.0 0.0 0.0
"30:56 https://youtu.be/RQKJBpaCCeo?list=PLUl4u3cNGP60hI9ATjSFgLZpbNJ7myAg6&t=204


43:30: 


cov(X, Y + X) = cov(X, Y) + cov(X, X)

cov(X, Y + X) = E[X*(X+Y)] - E[X] E[X+Y]
              = E[X^2 + XY] - E[X] E[X+Y]
              = E[X^2] + E[XY] - E[X] * (E[X] + E[Y])
              = E[X^2] - E[X]^2 + E[XY] - E[X] E[Y]
              = cov(X, X) + cov(X, Y)" yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 899.0 0.0 1.0 0.0
"This python program shows that total sum is n cube divided by 3

import matplotlib.pyplot as plt

def r(n):
	sum = 0
	for i in range(1,n+1):
		sum = sum + i*i
	return sum
def y_axes(n):
	lst = []
	for i in range(1, n+1):
		lst.append(r(i))
	return lst


plt.plot([x for x in range(1,1001)], y_axes(1000))
plt.show()" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 10913.0 0.0 0.0 0.0
"Thank's MIT, now I don't have to go to my lectures any more! :) " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9570.0 0.0 0.0 0.0
"“Why don’t we learn all Linear Algebra in one lecture? - We just live so long ...” - Gilbert Strang is transmitting and implanting big ideas with Love. 🙏 Students are so lucky to be in his presence - of the real master. And we are lucky to watch it years later... 🙏" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 15600.0 0.0 0.0 0.0
"Just to add, I'm glad I've got YouTube where I can pause video so brain can catch up. I'd fail the course if I was actually at MIT and had to keep up in real-time :)" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7198.0 0.0 0.0 1.0
"Pre-calculus is a great conglomeration of advanced algebra and logical extensions, and is a great buildup to calculus, but usually does not contain concepts or calculations of calculus within itself." eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8238.0 0.0 0.0 0.0
"""Why don't we do all of linear algebra in one lecture""" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 135.0 0.0 0.0 0.0
"Thank you for being who you are and touching our lives!!! I am VERY VERY grateful." Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9248.0 0.0 0.0 0.0
"welll, that was fun!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 15097.0 0.0 0.0 0.0
"bookmark - 30:10" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12550.0 0.0 0.0 0.0
"There are good instructors everywhere, of course. I think it does have to do with the research...among other things." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10348.0 0.0 0.0 0.0
"The beauty of these lecture can't be described in words. It was best 45 days of my life. Hope to take other courses of Dr Strang too." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9989.0 0.0 0.0 0.0
"Thank You 
Education without politics" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 9045.0 0.0 0.0 0.0
"lazy teaching" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13762.0 0.0 0.0 0.0
"What's the difference between verify and test? Seems to me they are not quite different..." iZPzBHGDsWI "15. NP-Completeness" "MIT 18.404J Theory of Computation, Fall 2020" 11580.0 0.0 1.0 0.0
"Take for example something as simple as the circle.  The length of the perimeter/circumference can never be exactly known, since it relies on the product of the length of straight line and an irrational number--it can only be approximated to whatever precision one desires.  Until infinity is more fully understood and embraced in a type of mathematics that allows for continuous exactitude, we are left with the limit." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9009.0 0.0 0.0 0.0
First!😂 O0Tw47okZJM "Lecture 21: The Spectrum of Self-Adjoint Operators and the Eigenspaces of Compact Self-Adjoint..." "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 3824.0 0.0 0.0 0.0
"https://youtube.com/channel/UCDtl_39dIClgkxQOx5Oir8g kindly attention please 🥺 in this link you can comment me anytime for any chapter of class 6 7 8 9 and 10 maths videos 💯👌🥰" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13311.0 0.0 0.0 0.0
"16:05 - ∆L/∆h = dL/dh. This is COOL - derivative 'originated' from real world errors! This has deepened my understanding of the fundamentals of derivatives!" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 469.0 0.0 0.0 0.0
"sir your style of explaining is outstanding...Thanks, to MIT for doing this noble work which benefits hundreds of thousands of students in the world......keep up the great work!!" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 14313.0 0.0 0.0 0.0
"1:55 
LSD vision!!!" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 604.0 0.0 0.0 0.0
"at 22:05 why did he divide 2nd row by 2" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 12425.0 0.0 1.0 0.0
"regarding the mono audio issues, if you are on W10 you can search ''ease of access'' -> ''audio'' and turn on ''mono audio''.
it will work properly that way. (remember to turn it off afterwards)" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 14259.0 0.0 0.0 0.0
"Thank professor, such a great joy to watch your lecture <3" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9068.0 0.0 0.0 0.0
"35:00 This is like a typical home work quiz problem." 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 994.0 0.0 0.0 0.0
"I really find it funny how towards the end of the lecture most students can't wait to go..😂" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 5916.0 0.0 0.0 0.0
"Yes Dr Rodriguez, thousands of people will listen to the your lecture. Thank you for the lectures! Must be more awkward if you imagine yourself lecturing to number of people that is of stadium size." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 12135.0 0.0 0.0 0.0
"@agapitoflores001 me 2...ur not alone" ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1769.0 0.0 0.0 0.0
"always a minus fault .... sqrt(68) not sqrt(60)  , so one eigenvalue neg , yes .... 🤣😊 But now does Matlab opposite , to mine abc formula  : (8 +/- sqrt(68))/2   for eigenvalues 🙄" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12334.0 0.0 1.0 0.0
"Thank you" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 9084.0 0.0 0.0 0.0
"“I won, but it didn’t pay off!”  😂
@TM88 breaks down how @LIL UZI VERT's “P2” was made https://youtu.be/IVLsJ18T8Ds" sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15591.0 0.0 0.0 0.0
"@theRealCheeseCake isn't being good at learning the definition of being smart?" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2038.0 0.0 0.0 0.0
"You could also argue that it isnt a basis because -1 time the first vector plus 2 times de second vector gives us the third vector... You really dropped the ball there professor G. hahahaha just kidding, this man is the best thing that ever happened to Linear Algebra right after Gauss" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12199.0 0.0 1.0 0.0
"dude thats Gilbert Strang!!! " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12778.0 0.0 0.0 0.0
"Is has helped me truly triumph" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6767.0 0.0 0.0 0.0
"That's the best probability teacher ever!" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 9941.0 0.0 0.0 0.0
"why is everyone here so old.....?" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15329.0 0.0 0.0 0.0
"@Schutzstafell If that was the truth, you would probably be smart enough to know that single variable calculus is basic introductory calculus." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1718.0 0.0 0.0 0.0
"Finally completed this course !! Thank You, MIT:)" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3768.0 0.0 0.0 0.0
"Thank you very much for these lectures. They are very useful!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 9441.0 0.0 0.0 0.0
"This is the statistics class we actually wanted to take but didn't get." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 10755.0 0.0 0.0 0.0
"So at 35:23, does that mean that every Vector Space in R^2 must pass through the origin (0,0)" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 8741.0 0.0 1.0 0.0
"I was nodding my head, keeping up just swimmingly, it all made perfect sense.  He wrapped up the diagram and it seemed like we were done.  Then he stepped over to the far board and replaced vectors with matrices and just turned everything upside down.  Didn't see that coming." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6160.0 1.0 0.0 0.0
"that has to be the best damn chalk ever" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14631.0 1.0 0.0 0.0
"I always found it interesting how the US system of teaching calculus has evolved into two subjects - calculus and real analysis. I guess the motivation for calculus is to introduce some of the concepts and build the practical skill of calculating derivatives, integrals and apply them to analysis of functions and generally solving practical problems. The rigorous introduction of the subject is left to real analysis which I guess not all students learn. For me, analysis became clear once I looked into how the subject developed over time, how Newton/Leibniz saw the connection between the derivative and the integral. I always wondered why all those people were so busy with calculating areas and why the tangent was something they were interested in. Also, the limit process always looked as a cheat until the moment someone suggested it was a best approximation, the way to do away with infinity and replace it with the nearest best approximation. Just wondering if calculus presented in such a form rises more questions than it answers.. I guess the joy of applying the method to different problems overshadows the gaps here and there.." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5041.0 0.0 0.0 0.0
"*\ ^^ /*
    ||
   / \" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 243.0 0.0 0.0 0.0
"Do you guys learn about this in 10th grade? I don't know about your system because I'm an Indian and we learnt this before college. Why are they teaching this in MIT tho? Like you guys do study variable calculus before college right? I'm genuinely curious." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3418.0 0.0 0.0 0.0
"In closure in concat, why we don't know where to split?
x is a string in M1, so it has a finite length. Then I think the end of the string x must be the split point." oNsscmUwjMU "2. Nondeterminism, Closure Properties, Conversion of Regular Expressions to FA" "MIT 18.404J Theory of Computation, Fall 2020" 6631.0 0.0 1.0 0.0
"Can The number of operation for n by n matrix be n! ^2" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 3009.0 0.0 1.0 0.0
"As a young undergraduate engineer I had a superb lecturer, Dr. Boswell." hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2567.0 0.0 0.0 0.0
"Please having terrible time solving a problem on linear mapping.

Please who can help so I can drop it" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8204.0 0.0 1.0 0.0
精彩 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15647.0 0.0 0.0 0.0
autodidact vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 12485.0 0.0 0.0 0.0
"Department of Computer Engineering & Informatics
University of Patras, Hellas. 
Thank you, it was really helpful!" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 3355.0 0.0 0.0 0.0
"35:57 - camera guy just had a stroke" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1024.0 1.0 0.0 0.0
"whate beautiful chalk. my teachers here have flimsy chalk that breaks with every use, they go through a box each class (3hs)." -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15199.0 1.0 0.0 0.0
promosm uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 14224.0 0.0 0.0 0.0
"so amazing!" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 14325.0 0.0 0.0 0.0
"Professor Strang was my advisor at MIT. For me he was a lifeline that helped me get through the very difficult process of learning to become who I wanted to be." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8373.0 0.0 0.0 0.0
"16:16 If delw.V is zero because w is constant on a curve on the same level surface .. then delw . any other vector would be zero be it tangent or not .. because del w is always gonna be zero on the level surface.. isn't it ?" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 472.0 0.0 1.0 0.0
"15:25 can anyone please explain how the linear combination of the Special solutions is the null space, intuitively? Thanks" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 451.0 0.0 1.0 1.0
"Is it just me, or does all of this seem a lot easier than derivatives and integrals?" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6784.0 0.0 0.0 0.0
"This man is made by Linear Algrebra materials." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 10870.0 0.0 0.0 0.0
"jerison the beast" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13722.0 0.0 0.0 0.0
"he is the best of all" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 13101.0 0.0 0.0 0.0
"Clear, concise, coherent 
so who disliked this
   " 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 3153.0 0.0 0.0 0.0
"Took me almost 3 hours to get close to ""fully understand"" the lecture." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 11071.0 0.0 0.0 0.0
"I never seen an mathematical lecture this much interesting." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 5883.0 0.0 0.0 0.0
"I was so eager to finish single variable calculus, but now I’m sad that it’s over 😭" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6162.0 0.0 0.0 0.0
"Dumbfounded. Thank you MIT." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3529.0 0.0 0.0 0.0
"ahhahahahahha sin(x+Δx)=sinxsinΔx+.... lmao" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12315.0 0.0 0.0 0.0
TY 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 9001.0 0.0 0.0 0.0
"This is trivial ..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10759.0 0.0 0.0 0.0
"This profesor is nice but I liked Haynes Miller better" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10890.0 0.0 0.0 0.0
"Has anyone managed to complete the 3 heads problem using conditional probabilities?" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 4434.0 0.0 1.0 0.0
Legend 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7313.0 0.0 0.0 0.0
"this guy is awesome, my english is not that good but i somehow manage to understand him clearly! thank god for this lecture and for pause bottons!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14822.0 0.0 0.0 0.0
"how did he find that  b = [1 , 5 , 6] at 06:03.. is there a systematic way to do it ? or just guess?" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 13213.0 0.0 1.0 0.0
"His lecture is not fast, quite helpful for non-native speakers." 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 4754.0 0.0 0.0 0.0
"I enjoyed this lecture.  Professor Strang seems like a congenial person truly interested in imparting his knowledge.  Some professors seem to look down on their students and have the attitude that if you don't get it, tough." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5384.0 0.0 0.0 0.0
"Probability was a very difficult math course when I was in university which was made even harder by the professor who taught it. At least now, I can appreciate the subject more." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 8254.0 0.0 0.0 0.0
"Amazing lecture!!!! I wish they would teach me in my univ. Like this" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2370.0 0.0 0.0 0.0
"Mathematics is comprehensive like these professors." tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7616.0 0.0 0.0 0.0
"when you have to pee with prior belief that you don't know why you put a pie or where it is then the best approach is to squared it with iid. p.s. don't forget to include pmf/pdf." bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 15215.0 0.0 0.0 0.0
"this lecture is insightful" 4HRhg4eUiMo "8. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 14891.0 0.0 0.0 0.0
"Why do U and V mean rotation? Why not reflection?" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11821.0 0.0 1.0 0.0
"I'll have some of whatever you're drinking :)" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 6287.0 0.0 0.0 0.0
"This is certainly God level!
Things he is saying at times, not only predicting the answers to himself but also to the audience, just to assure them that they can do it too. Also, not being there predicting and waiting for more than a few more secs., for others to still follow!" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 10656.0 0.0 0.0 1.0
"So good for doing this, even it's ordinary. Very good self-study material." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8762.0 0.0 0.0 0.0
"Am I the only one who doesn't seem think mr jerison isn't a good teacher? I mean compared to the brilliant herbert gross and christine breiner he seems to not be able to connect with us students and get what might be difficult or need more to students. In one of the lectures he couldn't even understand that the student who asked a question had a problem with negative numbers n that's the freakin basics .. PS I totally get this a purely subjective thing." TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2337.0 0.0 0.0 0.0
"if people know Russian they will be able to use НМУ lectures" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13538.0 0.0 0.0 0.0
"Hey, I know school is back and summer classes are hear with us meaning the essays and assignments are back. I could be of your assistance in handling the papers and I guarantee you value for your money with an A+ essay results. Kindly reach out to me through my email address  kristenchantelle5@gmail.com" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 4697.0 0.0 0.0 0.0
"@beenpimped31 walter lewin" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1790.0 0.0 0.0 0.0
"MIT OPEN COURSEWER  MEANS KNOWLEDGE FOR THOSE WHO WANT IT." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7507.0 0.0 0.0 0.0
"You are great thanks mit" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 12172.0 0.0 0.0 0.0
"I love this guy, he actually shows the FULL way to do things. And his proof for the product rule is beutiful <3" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5809.0 0.0 0.0 1.0
"I'VE GOT A DEVIL'S HAIRCUT IN MY MIND" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6274.0 0.0 0.0 0.0
"The point of this lecture... -> 26:59" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 10230.0 0.0 0.0 0.0
"18:31 conditional pmf" -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 543.0 0.0 1.0 0.0
"Who is in 2019? 
Made easy student? 😘🤗" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11739.0 0.0 0.0 0.0
"I don't understand the addition in the Zero vector only subcpace. How is it closed under addition?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 5345.0 0.0 1.0 0.0
"I am actually amazed at how he writes with chalk so fast but maintains cleanness and legibility." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5058.0 1.0 0.0 0.0
"I'm proud to have found out that he had made a mistake before Mr Strang. It means I've actually undertood the previous lecture (which I had to watch several times to grasp)" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 6362.0 0.0 0.0 0.0
"31:54 Could someone please explain why both of them aren't minus? (which makes outcome plus not minus)" QuZL5IKpO_U "24b. Quiz 2 Review" "MIT 18.06 Linear Algebra, Spring 2005" 918.0 0.0 1.0 1.0
"Only because he was born earlier.... and died earlier... I was like hmmm 🤔" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8117.0 0.0 0.0 0.0
"Thank you Mathematician Gilbert Strang" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9171.0 0.0 0.0 0.0
"This class is packed" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10476.0 0.0 0.0 0.0
"amazed at the little amt of views in these videos" H_k1w3cfny8 "10. Continuous Bayes' Rule; Derived Distributions" "6.041 Probabilistic Systems Analysis and Applied Probability" 12342.0 0.0 0.0 0.0
yes tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15482.0 0.0 0.0 0.0
"Inverse starts at 21:30" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6741.0 0.0 0.0 0.0
"this is really amazing for students today.  i wish i could rewind my current lectures" phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14871.0 0.0 0.0 0.0
Heard VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 4651.0 0.0 0.0 0.0
"You need to crack the calculus textbook first! ..... and if you master vectors you will have earned the right to break out the red bull!" ZwpwmGP5ITM "Lec 34: Final review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12231.0 0.0 0.0 0.0
"EA=R !!!! :D" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3535.0 0.0 0.0 0.0
"could someone tell me 6:48 why is this true?  how can you calculate lambda with trace? Thank youooouuu!" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 12691.0 0.0 1.0 0.0
"Thank you, Dr. Strang. You are a very clear and entertaining teacher. I have thoroughly enjoyed your lectures. I am an old timer just freshening up. I really appreciate your teaching methodology and after watching this series think of you as an 'old friend'." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9495.0 0.0 0.0 0.0
"These lectures are soo awesome!! I'm taking Ap calc right now and my ap test is in less than a month, and these lessons are like a nice review. Thank you soo much for posting them up!!" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10413.0 0.0 0.0 0.0
"if k is not equal to c(assuming k<c or k>c)  isn't it possible that t might still be there?" vqFRAWeEcUs "21. Hierarchy Theorems" "MIT 18.404J Theory of Computation, Fall 2020" 13534.0 0.0 1.0 0.0
"thanks professor" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14600.0 0.0 0.0 0.0
"So french accent :D" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8757.0 0.0 0.0 0.0
"I did it too! With a bit of a bittersweet feeling at the end. 2x is the way to go guys!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5257.0 0.0 0.0 0.0
"@jvc1998 ok, so whats better about a black board vs. a smart board, you can make a smartboard look like a black board. you can scan every thing on a smart board and  send your lecture notes to students via email. you can plug your calculator into a smart board and show your students what you are doing. you can even re-do and un-do mistakes like on paint or photoshop, yes smart boards are the best." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1912.0 1.0 0.0 0.0
"This Lecture seems to be somewhat lacking in examples and illustrations." TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 10457.0 0.0 0.0 1.0
"Amazing limited edition 👍🏻" cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 2381.0 0.0 0.0 0.0
"Excellent lecture, great visual and conceptual explanations, much appreciated!" CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 3655.0 0.0 0.0 1.0
"I think (but am not necessarily sure) that positive definite matrices can have non orthogonal eigen vectors. Symmetric matrices can definitely have non orthogonal eigen vectors.

Posted this as a reply to a comment but reposting it here:

Symmetric matrices don't necessarily require the eigenvectors to be orthogonal, I think the same is also applicable to positive definite matrices.

Consider the identity matrix for example. It can be decomposed into a product of a non orthogonal matrix of two arbitrary (but independent) eigen vectors the the lambda matrix (identity) and the inverse of the first matrix.

It would be great if someone could confirm the same about positive definite matrices." HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 5992.0 0.0 1.0 0.0
"Thank you. it has been fun and love prof Strang humour." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9563.0 0.0 0.0 0.0
"Globaly very Great lecture (19/20), congratulations.
But I notice at 34:30 nevertheless a great confusion, between VECTOR SPACE and AFFINE SPACE. Actualy, the 0 vector MUST indeed be in all vector spaces BUT has NO FIXED ""PLACE"" in the plane. The word ""place"" is in fact irrelevant for a vector in general and the 0 vector in particular. It is a beast that doesn't live in the affine plane, and so has no ""location"" in it. That's a crucial point. A dual way of painting this need understanding that the affine origine has indeed fixe coordinates, namely (0,0), ok, BUT it's location in the plane is ARBITRARY (by homogeneity argument somehow) so as the ""orientation"" of the axes (by isotropic argument somehow).
For similar reasons the straight line OF the origine is NOT LESS a vector space than the one THROUGH the origine. And even much more than that. In fact these two affine lines are EQUIVALENT AFFINE REPRESENTATIONS of the SAME 1-dim vector space which is, by definition, essentialy a DIRECTION (their comon one), and THAT IS what matters. It may seem to beginers that this confusing situation is a paradox. In fact, NOT AT ALL. Nevertheless, to overcome it, it is crucial to understand that a 1 dim vector space is NOT in fact an (affine) straight line (not more the one THROUGH the affine origine than the one OF the affine origine) BUT essentialy a DIRECTION, that is to put it in a rather intuitive and visual formulation, an EQUIVALENT CLASS of infinitely many parallel (all pointing in the same direction) affine straight lines filling the entire plane (in 2 D).
""Complementary"" the ZERO VECTOR is ""LOCATED"" NO WHERE in particular in the affine plane. In fact it doesn't live in it BUT in the infinite family of infinite equivalent classes. To visualize it one could think of it through a pedagogical metaphore of a strange being : an ISOTROPIC ""1 dim"" vector space, that is, a strange ""line"" pointing in all direction equivalently, which is an impossible mission except for a degenerate line reduced to a point. Any affine point can be seen as a equivalent representation of the 0 vector pointing in NO DIRECTION." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4062.0 0.0 1.0 0.0
"I love these lectures. He makes it so easy." tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5798.0 0.0 0.0 0.0
"can someone please let me know of the prerequisites before starting if you have already seen the course." 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 12627.0 0.0 0.0 0.0
"I think the error in 9th lesson was intentional, because this mistake makes you realize that for independence you can look both columns and rows." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6053.0 0.0 1.0 0.0
"Fxy = Fyx if and only if F is continous. 

Denis, why you lyin?" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3963.0 0.0 1.0 0.0
"can anyone please provide the links to the extra videos he said he'll be uploading. Like the Gaussian Distribution one up on stellar. I searched stellar MIT but couldn't find it." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 12607.0 0.0 0.0 0.0
"I'm just watching out of interest, but he explains this muuuuch better than my teacher used to when I was still going to school...." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 6342.0 0.0 0.0 0.0
"opa el machine learning" 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 14158.0 0.0 0.0 0.0
"Do MIT students attend the same lectures or different ??" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 3406.0 0.0 0.0 0.0
"magine the professors brain SHIT!!!! is Huge" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13896.0 0.0 0.0 0.0
"Shreyas e^(-ix) = (c1) cos(x) + (c2) sin(x) when c1 = 1 and c2 = -i" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 8658.0 0.0 0.0 0.0
"My calc professor was similar: young, vibrant, always cheerful and helpful. The enthusiasm and joy rubs off and I really loved learning calculus from her!" jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7739.0 0.0 0.0 0.0
"Flat earth!   Yea baby" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3831.0 0.0 0.0 0.0
Lg hwDRfkPSXng "Lecture 32: ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7346.0 0.0 0.0 0.0
"its been almost a decade, but I remember he wrote the textbook we used." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 13706.0 0.0 0.0 0.0
EZ! cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 3544.0 0.0 0.0 0.0
"If you haven't heard him perhaps you don't know linear algebra !!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6549.0 0.0 0.0 0.0
"MIT did a really good job" QeYUHA0UMVg "Lecture 21: The Riemann Integral of a Continuous Function" "MIT 18.100A Real Analysis, Fall 2020" 7517.0 0.0 0.0 0.0
"thanks for the great lecture :)" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14584.0 0.0 0.0 0.0
"Professor Gilbert strang looks young, omg.:)" cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8329.0 0.0 0.0 0.0
"So simple, I learnt it when I am 14." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8787.0 0.0 0.0 0.0
"Something like (-1)^(n/2) * ((n-1)!!)^2 for the determinant of the even ones?" QuZL5IKpO_U "24b. Quiz 2 Review" "MIT 18.06 Linear Algebra, Spring 2005" 8843.0 0.0 1.0 0.0
"im almost at the end of watching ths series!! so sad!! watching all these lectures has made me feel like im part of the class lol. this instructor is great :D" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13564.0 0.0 0.0 0.0
"round of applause indeed" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14268.0 0.0 0.0 0.0
"Hooray and big ups to MIT for publishing these high quality videos!

Anyone else notice the professor alternates between solid red, blue, green shirts throughout the semester?  hehe." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4785.0 0.0 0.0 0.0
"Hi, Thank you for these nice videos.

One small note : at 27:40, I think that to justify the use of uniform distribution for θ, one should use entropy, so given that uniform distribution (discrete r.v)/Guassian (continious r.v with a given 1st and 2nd moments) has the highest entropy, i.e the highest degree of randomness, if we estimate/detect θ assuming those distributions, the solution would be the best (in randomness sense, so lower probability of error maybe ?) also for other distributions based θ, given that those other distributions have lower degree of randomness.

Cheers
Nabil" 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 4720.0 0.0 1.0 0.0
讲得很好，希望我能坚持看下来 j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 15660.0 0.0 0.0 0.0
"36:00 Basically... 😀" 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 1025.0 0.0 0.0 0.0
"Beta distribution may be bimodal when both parameters are less than 1, and the curve is U shaped. Why they don't use whiteboards but these ugly blackboards?" bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 2885.0 1.0 1.0 0.0
"The tiresome pantry advisably license because peony immuhistochemically produce beyond a  flagrant field. hot huge, demonic peru" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10304.0 0.0 0.0 0.0
"Solution time: Sometimes we can't solve Ax=b but we can solve the nearest solution that is what projection do.
But what is the link between vector b and the projection vector p, it's perpendicular. Then if b doesn't lie in the column subspace of A which will cause no solution, then we can think that the null space is also perpendicular to the column space of A. So p is in null space. Then go back to the original problem to calculate the nearest solution we just need to multiply the A' on both sides.
because A'(b-Ax)=0 where b-Ax finds the A' null space, we just need to solve A'b=A'Ax. Done!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 8819.0 0.0 1.0 0.0
"I wish they would not start packing up and making noises when Professor Strang didn't even finish his last sentence...They should've known how lucky they were to have this education :)" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 6229.0 1.0 0.0 0.0
"After years of using linear algebra, both in fundamental problem formulation, and in numerical computation, I can say that Prof. Strang's approach to teaching the subject is by far the most direct, comprehensible, practical, satisfying, and even beautiful pathway into the subject. In particular he makes front and center key nuggets often ignored or insufficiently emphasized, such as the column picture, the fundamental vector spaces of a matrix, the big, must-see  factorizations of a matrix, and even a most satisfying way of looking at least squares. Going through his lectures, I learned a lot of wonderful things that fell through the cracks during my education." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 2268.0 0.0 0.0 0.0
20220511簽 Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 632.0 0.0 0.0 0.0
"Finally I understood the origin of the least squares method... (i'm in 2nd year of aeronautics and this teacher is a thousand times better than my university ones. A few could learn how to teach additionally to the algebra lesson)" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3761.0 0.0 0.0 0.0
"camera work is the fucking worst" XhSk_Lw2X_U "14. Low Rank Changes in A and Its Inverse" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12592.0 1.0 0.0 0.0
"I'm japanese and an university student. I already learned this kind of things but this proffessor is awsome !
I do hope he is still alive." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6336.0 0.0 0.0 0.0
"Roddy Rich took the box mainstream recently. Professor Strang was clearly ahead of him time" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 8574.0 0.0 0.0 0.0
"welcome to the future of education, the whole people of the world will learn from internet lectures such as youtube. United States got you covered for all your learning needs" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15082.0 0.0 0.0 0.0
"An Indian edition of this book is available only in India
http://www.wellesleypublishers.com/buy.html" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2429.0 0.0 0.0 0.0
"This class kicked my ass.. ok bye before commercials end  🏃‍♀️" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 10477.0 0.0 0.0 0.0
izi kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13718.0 0.0 0.0 0.0
"At around 33:35 he defines the x-int as (2x0,0), following the same logic and using the original point slope form, I got y-int as (0,2/x0). I don't think I am wrong, but can any confirm?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2707.0 0.0 1.0 0.0
"I learned a lot with your videos, they are fantastic. I could not believe that one can watch Legendary Professor Gilbert Strang." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5649.0 0.0 0.0 0.0
"""Less Steep"" was a bit of a confusing word to describe a straight line.
I always thought of steep being like a lines angle to the ground.
I guess here he means height tho" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 78.0 0.0 0.0 0.0
"This guy is so brilliant, that it makes ME think I'm brilliant just by listening and understanding his thoughts." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 10542.0 0.0 0.0 0.0
"I do make this statement, after understanding Polynominal Crystal Algebra IV with the X-Axis,Y-Axis,& Z-Axis Polynominal Cyrstals revolving around""TIME""= 4D Algebriac, & Calculus Limit Questionaires using Newtonian Physics,WHY Don't you run that""STUPID FREEMASON U.S.A.IDIOT Government""!Now that you Fully Understand the Mathematics of Our UNIVERSE,you certainly can adapt it to""SCIENCE SOCIALISM of ELECTRIFICATION-Photons of Physics Calculus-Algebriac I,II,III & Algebriac IV Polynominal Graphing!!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5289.0 0.0 0.0 0.0
"can't believe that a university like MIT have shit professors like these, at the start he makes sense and then the next minute he's during fucking circles chatting shit" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 12642.0 0.0 0.0 0.0
"धन्यवाद सर ..🙏🙏" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15580.0 0.0 0.0 0.0
"Why is arc length not included in volume of solid in revolution whereas it is used in surface area formula?" TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11869.0 0.0 1.0 0.0
"thank you mit for this...to give such a privilege to the world that they can view and learn from your content,...its commendable,..and i am grateful" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 14499.0 0.0 0.0 0.0
"Just wonderful" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7205.0 0.0 0.0 0.0
"Great video, but misleading title. ""Parametric Equations"" in the name, and 40/45 minutes are about arc length and surface area? I kept waiting for the Parametric Equations topic to kick in I didn't realize the video was almost over. " TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4357.0 0.0 0.0 0.0
"How can you create a straight line using only circles. Impossible. Always use circular matrix." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4816.0 0.0 0.0 0.0
"its just gud job" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13713.0 0.0 0.0 0.0
"joe derosa teaches stats?" bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 13725.0 0.0 0.0 0.0
"Who could possibly dislike this?" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11728.0 0.0 0.0 0.0
"Can we get a solutions for problem sets on the mit page?" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3111.0 0.0 0.0 0.0
"The shoes and socks analogy for inverses of matrix products is probably the cutest thing a math genius has ever said." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 10277.0 0.0 0.0 0.0
"harold:cube =12.137:9.
square 4y-65Q.
your area of circumfrence is 18.775. ^2SQ|MEGAPIXELS UNITS [LOARYIES HIDE-GO-SEEK÷(&).]" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 13060.0 0.0 0.0 0.0
"Why not just add a shit load of neurons and features to boost your chances of successful classification?" sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11901.0 0.0 0.0 0.0
"why don't you have magnetic boards in classrooms? are you that poor?" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 15316.0 1.0 0.0 0.0
"Thanks for your insights into linear systems. I struggled to understand the plotting of points in three dimensions but found this video: https://www.youtube.com/watch?v=EzJP9uwV3ms" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 9744.0 0.0 0.0 0.0
"SHUT UP NO HE DID NOT GET THE AVERAGE OF 15 NUMBERS IN 3 SECONDS😧 1:12:59" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8579.0 0.0 1.0 0.0
"awesome...really helpful" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 12498.0 0.0 0.0 0.0
"cool proofs" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12679.0 0.0 0.0 0.0
"why matrix multiplication is Row x Column or Column x Row .....?
why not  matrrix multiplication Row x Row or Column x column......" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 15352.0 0.0 1.0 0.0
"What's with the goddamn a-holes that stroll in 14 minutes late and commence moving furniture and zipping & unzipping their f-kn book bags? I wish Strang had some Sadoway in him and tossed the arrogant morons out." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11590.0 1.0 0.0 0.0
"This is awesome. Absolutely no doubt this is the best i've ever seen. I wish I had known this course at highschool. Pure logic i love it" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10644.0 0.0 0.0 0.0
"For c belongs to (a,b)" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3859.0 0.0 1.0 0.0
"What's the chapter 2 he's referring at #37:30?" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 11576.0 0.0 1.0 0.0
"this guy is brilliant.  it's a shame the video doesn't show the whole board." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14824.0 1.0 0.0 0.0
"Love from India" EBdgFFf54U0 "Lecture 14: Basic Hilbert Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 7437.0 0.0 0.0 0.0
"I so want my professors to have a look at the relevant MIT lectures before they come to class
" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5966.0 0.0 0.0 0.0
"Professor Strang ,this is an awesome lecture on the Derivatives of Inverse and Singular Values using  derivatives from calculus. Students should have a solid understanding of calculus before taking upper level mathematics." AdTvkFsqcDc "16. Derivatives of Inverse and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8340.0 0.0 0.0 1.0
"So, that's the reason for the row versus the column combinations! I could've used this concept in late 1976." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8808.0 0.0 0.0 0.0
"41:58 You don't get M back from ∂M/∂y in cases where M is the sum of a function of x only and another function since you lost all information of how M depends on x only (for example M = x+y, ∂M/∂y = 1, integrating 1dy will never give M back). However, you do get back M(x, f2) -M(x, f1) because what depends only on x cancels out." tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1166.0 0.0 1.0 0.0
"Thanks for these lectures and for the effort in putting together these videos!" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9726.0 0.0 0.0 0.0
"Why am I having such a feeling that no one was in the classroom in this lecture? :P   But the professor is very good and explained the concept of subspace in an easy to understanding way!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11771.0 1.0 0.0 1.0
"I love you so much Mr Strang!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5850.0 0.0 0.0 0.0
"Thank god for MIT, i really hope I get in, hopefully my intel research pays off..." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9065.0 0.0 0.0 0.0
"Thank You for these lectures!
Should be continued!
Greetings from Tübingen, Germany" 6Az1gtDRaAU "16. Cook-Levin Theorem" "MIT 18.404J Theory of Computation, Fall 2020" 9055.0 0.0 0.0 0.0
"Too old to teach. Mumbles too much." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11069.0 0.0 0.0 0.0
"46:37
I just record the timestamp in case I forget the conclusion of this great course in the future." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 1274.0 0.0 0.0 0.0
"Is this the last video of the course?" eEXSv0jChO4 "26. coNP is a subset of IP" "MIT 18.404J Theory of Computation, Fall 2020" 6882.0 0.0 0.0 0.0
"@melque4271 velho vc assistiu o vídeo todo?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1943.0 0.0 0.0 0.0
"I learnt these properties in my 11th grade. Had no intuition for it, nor any particular interest. I knew the rules, knew how to apply them, knew how to solve 'tricky' problems.
This is just sublime! So lovely! I am totally in awe." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 5656.0 0.0 0.0 0.0
"@michalchik trig sub is very very useful... with out it we wouldnt be able to integrate many things...
" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1949.0 0.0 0.0 0.0
"AGGH Brilliant. My Calc teacher forgot the last part. Now I can make the whole thing rhyme!" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2176.0 0.0 0.0 0.0
"Thank you very much, MIT and Professor.
It's been my dream to understand what what each notation, operator means in Math and more so in Calsulus. The geometric and physical interpretations with real life examples helped me experience why is is important to understand and learn Mathematics. I'll be covering all the relevant lectures of Calculus. Thanksa lot :-)" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9450.0 0.0 0.0 1.0
"Hrm, turned into quite the meaty flamewar.
I do indeed feel stuck in the middle. :)

@ thejugglenaut:  It's probably why I learn best self taught.  Also being a visual thinker, it's sometimes difficult to make a brain painting of certain concepts.  It's especially bad when it comes to applying new material.  Really have to drive the nail deep with cement, epoxy and duct tape to get it to stick.  Takes time to work out a memorable picture." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4912.0 0.0 0.0 0.0
"give the text book
" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12922.0 0.0 0.0 0.0
"17:00 disjoint vs independence" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 500.0 0.0 1.0 0.0
#thanks_MIT 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 204.0 0.0 0.0 0.0
"""I guess I have to wish you happy holidays"" hahah. 
Kidding aside, I really appreciate having this series available in its entirety for free- thank you" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 56.0 0.0 0.0 0.0
"I have done my masters and plans for  a phd, but I have come to know that my linear algebra knowlegde fails in my research, Man what i have learnt is nothing.... I need to scarifice my summers listening to these perfect videos.. These guys are really luCky getting concepts in undergrad level......... The third world countries graduates needs to work more inorder to compensate the difference in concepts with developed countries graduates.
Thank you very much...
" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5523.0 0.0 0.0 0.0
"If Taylor's approximation is valid only for small theta, why would we use it here. Since theta increases by 2*pi by every rotation, we can no longer use this approximation. So instead of this, can't we just use dy/dx to find out the nature of cycloid? Is this correct?" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6484.0 0.0 1.0 0.0
"He is lecturing to an empty classroom if you look at time 40'53'' !! Even more wonders!" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4519.0 1.0 0.0 0.0
"I've heard so many silly (from my subjective point of view) questions coming from students about ""differentiability => continuous"" theorem proof. I just don't understand why MIT students are not familiar with basics of maths. But really... How many people in comments did not understand his proof? I'm just curious, because my hypothesis is that everyone here understood him. Am I wrong?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6417.0 0.0 0.0 0.0
"15:00 xDDD everyone clapping" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 445.0 0.0 0.0 0.0
"I have huge respect for him, he teaches in a way to make the subject interesting." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5529.0 0.0 0.0 0.0
"Did anyone else find the premise of the financial question at the end confusing? It seems like he didn't define the function or defined it as something weird like you borrow 1 dollar on day 1 2 on day two, etc... but never really said that." hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3367.0 0.0 1.0 0.0
"Can anyone please explain how the dimension of symmetric matrix is 6?  (at 6:43). I understood we have have 3 diagonal basis, but I do not understand how we get the other 3... [100;000;000], [000;010;000], [000;000;001] is all I can think of now... how the other basis can be a symmetric?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 3040.0 0.0 1.0 0.0
"What if the second derivative in the denominator evaluated at the critical point equals zero...?" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11506.0 0.0 1.0 0.0
"Thanks a lot." ZwpwmGP5ITM "Lec 34: Final review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9670.0 0.0 0.0 0.0
"Thank you professor Strang for the excellent lectures. I think watching all of your lectures on youtube (of course if you are not enrolled at MIT, in that case you could register for 18.06) is THE best way to learn Linear Algebra!

I particularly liked the way you explain using examples and always help us have the big picture, even when we are discussing something specific. You're a great teacher!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9317.0 0.0 0.0 1.0
"Excellent hand writing!" P3tGiT72APw "14. Graph limits I: introduction" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 3644.0 0.0 0.0 0.0
"I feel so lucky to be able to pause, rewind, and re-watch.  I might have struggled trying to take notes while letting the incredible insights sink in.  Are we getting a better education online than even the students in this very course?!" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 5400.0 0.0 0.0 0.0
"It's fun pausing the video and trying to figure out how the process ends before he's shown it ..." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 7040.0 0.0 0.0 0.0
"That exercise at the end did not come out to have average of 67.5 and Std dev of 18....is it me or did t happen with anyone else" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 9884.0 0.0 1.0 0.0
"Thank you G.Strang!
Anyone from Siraj's video?" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9108.0 0.0 0.0 0.0
"Having a competent instructor teach undergraduate mathematics is a key differentiator in college.   Most often undergraduate courses will be taught by either the the incompetent, the unskilled, or by poor communicators.  Often all three in combination.    Requiring your best instructors to indoctrinate the freshmen is seen as a waste by many as the drop out rate is high and the lectures are trivial.   Sadly this logic reinforces high drop out and trivial lectures.    My calculus 1 course had a 50% drop out rate and then a 50% failure rate.   The lecturers generally could not speak English, could not teach calculus, and to give them the benefit of a doubt were completely indifferent to the students (as opposed to entirely incompetent).   It  was essentially a farce.   The best strategy was to read the text, do the problems and attend the labs.   The classes were not worth attending.

The Socratic method was generally not seen till late in the 4rth year when it was far to late to salvage most students from rote memorization and pandering to professors idiosyncrasies.   MOOC's have opened up an opportunity for learning that exceeds the abilities of most universities to provide.    Industry has yet to recognize this,  Universities have yet to recognize this, but there are avid students around the world that will begin to generate new science, mathematics, literature without the benefit of an Ivy league education or even a piece of paper recognizing their accomplishments.

There is a massive barrier to publish based on pedigree that has to be overcome and the establishment is highly motivated to maintain these barriers for as long as they can to protect  themselves but it is likely to come down fairly quickly once there is a critical mass of globally educated students producing meaningful outputs.

... or at least this is my hope." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4450.0 0.0 0.0 0.0
"At 44:00, can someone please explain to me where does he get the 2 from?. I understand that the x^1 comes from x^{n-n+1}, but the 2 that he adds?" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2675.0 0.0 1.0 0.0
"جدا رائع شرح التكامل والتفاضل الي هوه اساساً موجود في السادس العلمي في العراق" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15569.0 0.0 0.0 0.0
"a set of free lectures from one of the top Schools in the world.(especially the highest level of mathematics) God bless YouTube." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12289.0 0.0 0.0 0.0
"Normal people at age 65 or less: 
I am finally had relief from the hustle if life
Gilbert strangs in future at age 90: 
Today we are going to start matrix methods...." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7911.0 0.0 0.0 0.0
"@fasantupp stop trolling. Are you saying that someone who likes math with like every single lectures about math? I dont even know why I bother answering your semi-rhetorical question. You are clearly just trolling" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1833.0 0.0 0.0 0.0
"10 years ago I took OCW for the first time and I am still taking it. Thank you professor Gilbert Strang." Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 333.0 0.0 0.0 0.0
"I Really Like The Video From Your Second fundamental theorem" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4969.0 0.0 0.0 0.0
"CAN SOMEONE HELP ME UNDESTAND THE FUNCTION OF  cos and sine???when are they used?" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2981.0 0.0 1.0 0.0
"al fin alguien escribe español jaja

muy buena la clase!" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12319.0 0.0 0.0 0.0
"This class was going so fast up until this lecture when it started crawling" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 10480.0 0.0 0.0 0.0
"I Really Like The Video From Your Approximations (cont.); curve sketching" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4949.0 0.0 0.0 0.0
"that's a dumb explanation for the name chain rule. that got an applause ?!!" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14645.0 0.0 0.0 0.0
"@11:11:38 What does he meant lambda comes from here? Why does it come from the variance of the limit distribution? After this, where does the next expression come from, the one he divides lambda by, why does he do this?" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 1495.0 0.0 1.0 0.0
"hahhaah 29:53 ""i think of matrices as people at this point"". As we approach the end of the course, i just want to thank you AGAIN, amongst the plethora of other appreciations. This have been a remarkable journey, I dont think any other lecturer in the entire world would have made this as enjoyable as you have Mr Strang. Case-in-point: the comment at this time stamp just adds that additional layer of novelty and enjoyment that makes the whole experience just remarkable." TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 13057.0 0.0 0.0 0.0
"The  Boss Baby has a determinant of zero" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 9952.0 0.0 0.0 0.0
"A mesmerizing amazing person ever. I am really astonished to see his dedication to linear algebra. A big salute to him." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2142.0 0.0 0.0 0.0
"is  there some mistakes in 3+9=6? i think dimensions can't be added directly." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 13623.0 0.0 1.0 0.0
"24:42 I really hope camera man zoom in professor's face. His face is always a mood XDD" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 752.0 1.0 0.0 0.0
"The way he says ""Kill"" makes him sound serious @ 25:56" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 10330.0 0.0 0.0 0.0
"For a student like me, having engineering background, these lectures are just blessings." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3847.0 0.0 0.0 0.0
Excellent 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3626.0 0.0 0.0 0.0
"good job em" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12945.0 0.0 0.0 0.0
"Learning math is so... delicious!! :D
I'm not even a math genius. Thanks Prof. Strang, MIT, and YouTube." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 7255.0 0.0 0.0 0.0
"This man is old" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10872.0 0.0 0.0 0.0
"Such a great lecture!!" phbw9r1iUDI "7. Parametric Hypothesis Testing" "MIT 18.650 Statistics for Applications, Fall 2016" 8928.0 0.0 0.0 0.0
"From this latest lecture , I am learning more about eigenvalues and eigenvectors in relation to diagonalization of a matrix. DR. Strang continues to increase my knowledge of linear algebra with these amazing lectures." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 3936.0 0.0 0.0 1.0
"whats wrong with the cameraman this lec." -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15202.0 1.0 0.0 0.0
"6 more lectures, 2 more psets, 1 more exam. We're almost there!" seO7-TwXH_I "Lec 30: Line integrals in space, curl, exactness... | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1371.0 0.0 0.0 0.0
"Just finished the whole Single Variable Calculus course.
Thank you MIT OCW for making this possible.
Brazil, 2015." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7172.0 0.0 0.0 0.0
"great sir! i learned something new. thank you very much." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13003.0 0.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8429.0 0.0 0.0 0.0
"The good way to learn math is to do exercises." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 10125.0 0.0 0.0 1.0
"At 28:11 ,How can we assume Nullspace to be 0,if free variables are 0,in Reduced echleon eqn=[-F I] to find nullspace F=0 as free variable is 0,But I can still write 1 in place of I to get Nullspace non zero???" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 2633.0 0.0 1.0 0.0
"Sur how to find out volumme of tetrahedron using triple integral.what is procedure for limits>?" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8970.0 0.0 1.0 0.0
"People claiming it is fast. Me watching at 2x speed :p" phbw9r1iUDI "7. Parametric Hypothesis Testing" "MIT 18.650 Statistics for Applications, Fall 2016" 8165.0 0.0 0.0 0.0
"Thank you very much Professor!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9436.0 0.0 0.0 0.0
"In 38:30  Inverse Matrix" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6601.0 0.0 0.0 0.0
"I love this man!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5825.0 0.0 0.0 0.0
"Can anyone tell me why can't we obtain the Lower triangular matrix L directly from the combined E which could just be derived from using gaussian elimination? Thanksss" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 3050.0 0.0 1.0 0.0
"36:48 I legitimately was wondering this. Thank Professor Strang for answering my questions from beyond the screen" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 1043.0 0.0 0.0 0.0
cool 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12674.0 0.0 0.0 0.0
"Thank you MIT" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9119.0 0.0 0.0 0.0
"Sir you're a legend, and yet so humble. Thank you sir for your efforts and your love for mathematics. I will forever be grateful for the knowledge you've imparted to us. Stay healthy and cheerful like you always have been :)" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8707.0 0.0 0.0 0.0
"Have u observed
First lecture got Million's of views
And views count is slowly reduced from video to video" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 4448.0 0.0 0.0 0.0
"Coming from lecture 4 I feel like my ears are being sensually caressed." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 3172.0 0.0 0.0 0.0
"35:05 hahahah" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 999.0 0.0 0.0 0.0
"15:40 Why were the second and third columns of A equal to -1 -2 -1, 0 0 0 respectively?" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 457.0 0.0 1.0 0.0
"I think it's the first I follow a course where the teacher takes 5mn at each class to review and exemplify briefly what was done the last time. This stuff is quite easy as I already saw it in 6.042 for me, but it adds a level of clarity that is just amazing!
If any teacher sees this comment: what this guy does is a GREAT idea, borrow it! We can allways spare 5mn in a 1--hour course." 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 6031.0 0.0 0.0 1.0
"which book to refer along with lecture" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 15249.0 0.0 0.0 0.0
"Hi tbarker5252, 
Do you think that the word cycle and loop are different? 
And this discussion contribute with some development ... I dont think so." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4715.0 0.0 1.0 0.0
"Feynman would have loved Prof Strang." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3755.0 0.0 0.0 0.0
"The way Dear professor smiles at the end is so beautiful. I love you dear teacher. God bless you and :) . Love from Kashmir" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 10319.0 0.0 0.0 0.0
"Ah yes, 1+1=1²" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2278.0 0.0 0.0 0.0
"Just ""nice sets"" instead of the definition of a sigma-algebra? No mention that one must use Lebesgue integrals and not Riemann integrals in general case? I understand it's not a ""theoretical"" course but I didn't expect they cut corners this way at MIT too..." mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 7147.0 0.0 1.0 1.0
"35:25   you kick ass!!" wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 1011.0 0.0 0.0 0.0
"Wow!  I'd have to learn how to manipulate matrices before I'd taken this course.
" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12049.0 0.0 0.0 0.0
"why does the sum part have Sum(XiXj) instead of 2*Sum(XiXj) which is the correct formula of square of a sum?" EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 15313.0 0.0 1.0 0.0
"very understandable and fluent . I ilked it. thank you" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 15038.0 0.0 0.0 0.0
"Fantastic way to introduce Pseudoinverse.  GS is a great teacher.   Thanks OCW for making this available" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 3737.0 0.0 0.0 0.0
"I wonder where these students now are 🙂" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6252.0 0.0 0.0 0.0
"@michalchik i don't know....if you think about it trig substitutions in the context of the arclegnth formula are pretty intuitive" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1947.0 0.0 0.0 0.0
"Cliffhangers are not ethical" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3159.0 0.0 0.0 0.0
"I LOVE THIS GUY" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 4927.0 0.0 0.0 0.0
"@JohnyAngelo It's the worst thing when teacher won't be delayed. He or she wants at all costs finishes subjects before exact date. I should have been happy that my maths lecturer reserves how much time he wants in compare to other teachers. Maths is the most important subject at technical univeristies." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1645.0 0.0 0.0 0.0
"Really enjoyed this course -- thanks!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 8510.0 0.0 0.0 0.0
"The rate of change of distance" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10266.0 0.0 0.0 0.0
"I am afraid because Sir  Gilbert  you are 83." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5059.0 0.0 0.0 0.0
"20:11 When Proffessor Strang transformed from a Mathemagian to a Magician." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 645.0 0.0 0.0 0.0
"Thank you very much" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9425.0 0.0 0.0 0.0
"Your linear algebra OpenCourseWare has been benefiting millions. I know I am one of them. Thank you Professor Strang. You are an inspiration and my role model." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 12262.0 0.0 0.0 0.0
"Hard lecture to get through personally but does illustrate some of the cool machinery for applying eigenvectors" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 4423.0 0.0 0.0 1.0
"i think he admitted sine rules" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13469.0 0.0 0.0 0.0
"I love the way he is just being himself with Math, giving the pure logistic to student. I was really desired for a lesson like this." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5791.0 0.0 0.0 0.0
"This lecture is the hardest one in 18.06." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 10814.0 0.0 0.0 0.0
"11:57   guy eating in the front row... how disrespectful. I would kick him out of the lecture." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 383.0 1.0 0.0 0.0
"Dennis Auroux is a really good teacher. The one important quality that a teacher want is to explain things in a manner that is as simple as possible and I bet, he is excellent at that." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3354.0 0.0 0.0 0.0
"19:17 'well don't all speak at once.' ....superb" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 558.0 0.0 0.0 0.0
"If a pair of dice is rolled 5 times then find out the probability that three times we get some more than 9
Please help me" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 6487.0 0.0 1.0 0.0
"Thx MIT" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11005.0 0.0 0.0 0.0
"29:07 moment of respect" IycOPFmEQk8 "5. CF Pumping Lemma, Turing Machines" "MIT 18.404J Theory of Computation, Fall 2020" 850.0 0.0 0.0 0.0
"numerically incorrect. I accepted that the units were correct over a month ago. learn to read please." jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14093.0 0.0 1.0 0.0
"Is this the same as introduction to statistics for economists???" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 6885.0 0.0 0.0 0.0
"Thank you very much for this effort , I watched all the playlist and it was very helpful to me ,, Thank you MIT and Thank you prof. Auroux, I wish to you the best !!" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9443.0 0.0 0.0 0.0
"Best Calculus teacher ever" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2850.0 0.0 0.0 0.0
"If the average life span of humanity is stretched to say 150 years old or even longer..what rate of progress would we have achieved?? Anyway, thank you for the service Prof Strang." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6518.0 0.0 0.0 0.0
"Actual math lecture starts at 13:20" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 2231.0 0.0 0.0 0.0
"31 people don’t know what a determinate is. :/" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 901.0 0.0 0.0 0.0
"He made me fall in love with linear algebra. I studied at an engineering college where the subject was taught very mechanically. His lectures were like a breath of fresh air." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4580.0 0.0 0.0 0.0
Enlightenment 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3572.0 0.0 0.0 0.0
"Lecture 1: Rate of Change

Lecture 2: Limits
Lecture 3: Derivatives
Lecture 4: Chain Rule
Lecture 5: Implicit Differentiation
Lecture 6: Exponential and Log
Lecture 7: Exam 1 Review
Lecture 9: Linear and Quadratic Approximations
Lecture 10: Curve Sketching
Lecture 11: Max-min
Lecture 12: Related Rates
Lecture 13: Newton's Method
Lecture 14: Mean Value Theorem
Lecture 15: Antiderivative
Lecture 16: Differential Equations
Lecture 18: Definite Integrals
Lecture 19: First Fundamental Theorem
Lecture 20: Second Fundamental Theorem
Lecture 21: Applications to Logarithms
Lecture 22: Volumes
Lecture 23: Work, Probability
Lecture 24: Numerical Integration
Lecture 25: Exam 3 Review
Lecture 27: Trig Integrals
Lecture 28: Inverse Substitution
Lecture 29: Partial Fractions
Lecture 30: Integration by Parts
Lecture 31: Parametric Equations
Lecture 32: Polar Coordinates
Lecture 33: Exam 4 Review
Lecture 35: Indeterminate Forms
Lecture 36: Improper Integrals
Lecture 37: Infinite Series
Lecture 38: Taylor's Series
Lecture 39: Final Review" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7286.0 0.0 0.0 0.0
"What is the restriction on the number of decision variables and constraints in an lpp ?" feb9j65Iz4w "24. Linear Programming and Two-Person Games" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11536.0 0.0 1.0 0.0
"Looks like a Monte Carlo method, doesn't it?" z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7423.0 0.0 0.0 0.0
"@Anonymiusen I was going to wager Moroccan, but six of one and...but his English is clear, so I don't see the need for the subtext." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1588.0 0.0 0.0 0.0
💖💖💖 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15721.0 0.0 0.0 0.0
"Thank you for you videos andlLecture notes I wish I  could donate, but maybe if i .m succeful in this n earn better pay by the Grace of Allah" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9292.0 0.0 0.0 0.0
"Lol I was watching this and my little cousin randomly comes and starts watching with me, he then says, ""all I hear is , blah, blah, blah,"" then leaves, lol funny part is the prof. Actually does say blah blah and blah xD" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7397.0 0.0 0.0 0.0
"Thank you!" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9463.0 0.0 0.0 0.0
"i like the way he prepares to introduce a topic. very thoughtful and enjoyable." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 13420.0 0.0 0.0 0.0
"A fantastic way and new Era to see linear algebra tks form CH" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2112.0 0.0 0.0 0.0
"It's good." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7045.0 0.0 0.0 0.0
"You are a great teacher!" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 12164.0 0.0 0.0 0.0
"At 40:46, if b is the greatest of lower bounds, should it say b < b_0, whereas it says b ≤ b_0 for both second cases of least upper bound and greatest lower bound? I checked the notes for the lecture after and the second case; whilst using c and c_0, it says c < c_0. I wondered if it should strictly be less given c_0 or b_0 is considered the greatest lower bound." nbENJ-Ce7Nc "Lecture 3: Cantor's Remarkable Theorem and the Rationals' Lack of the Least Upper Bound Property" "MIT 18.100A Real Analysis, Fall 2020" 2661.0 0.0 1.0 0.0
amazing! VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 12355.0 0.0 0.0 0.0
"Thank you MIT. Now I can learn from anywhere using my laptop or smartphone." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9168.0 0.0 0.0 0.0
"it would have been better to prove fundamental theory of calculus rather than an intuitive explanation" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13690.0 0.0 0.0 1.0
"Only respect for you sir and looking forward to study your books too and I hope they're as inspirational as these lectures♥️♥️♥️I'd love to meet you once in life!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 8122.0 0.0 0.0 0.0
"I am lost..." XhSk_Lw2X_U "14. Low Rank Changes in A and Its Inverse" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5114.0 0.0 0.0 0.0
"This was a much easier lecture than the previous ones.  Thank god for the break." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10963.0 0.0 0.0 0.0
"the first term of the taylor expansion shouldn't be primed right?" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14692.0 0.0 1.0 0.0
"Thank you MIT OCW and Gilbert Strang for making these lectures entertaining! I enjoyed it a lot." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9127.0 0.0 0.0 0.0
"Very nice lectures. Thank you for posting. The thing is I can't donate and money now cause I am poor, but if I have money in the future, I will remember to donate, and I hope others will do the same." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11210.0 0.0 0.0 0.0
"In the king's example in the end, shouldn't bg and gb mean the same thing since it does not matter how you have ordered them? So that according to that logic you still get 1/2 like how you had got intuitively." 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 6670.0 0.0 1.0 0.0
"It is so easy to differentiate I got e^(xarctan(x))[arctan(x)+(x/(1+x^2))] in about 1 minute and this is right because I checked it on Wolfram Alpha and they are only doing it at the end of this degree level unit.I thought USA was good at education.I'm in Year 12 in the UK by the way.
" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6966.0 0.0 0.0 0.0
"does anyone else find this fun?? its 2:30am right now and im watching this... (i think this means i have no life) hahaa
" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12762.0 0.0 0.0 0.0
"DR. Strang thank  you for a another awesome lecture on Multiplying and Factoring Matrices in linear algebra. I really enjoy this part of linear algebra." or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3277.0 0.0 0.0 0.0
"HELP! I think Strang might have got WRONG around 05:40. I think P U L is a SUBSPACE of P as P & L itself is a subspace of P.

Think like this: let p & l be a vector from P & L respectively. than u=p+l belongs to
P U L and u lies within P as p is within P and l is also within P.

Also c*p & c*l belongs to P & L respectively where c is scalar as P&L are subspace. so c*u=(c*p + c*l) belongs to P U L. 

Finally, zero vector lies in both P & L. so Zero vectors belongs to P U L.

So P U L is subspace." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 4401.0 0.0 1.0 0.0
"Professor Strang, You are immortal !! 🙏🙏🙏" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 8381.0 0.0 0.0 0.0
"Clearly the best teacher on the planet!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3157.0 0.0 0.0 0.0
"To anyone watching: This first video is introductions to vectors including rules and applications." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11025.0 0.0 0.0 1.0
"The Business Analytics admission director for McCombs school of business told me to watch these videos for a understanding of linear algebra." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 9958.0 0.0 0.0 0.0
"""They're nice formulas, but I just don't want you to use them."" - Prof. Strang on Cramer's Rule." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 126.0 0.0 0.0 0.0
"my right ear really enjoyed this lecture" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14002.0 0.0 0.0 0.0
"Too easy." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11062.0 0.0 0.0 0.0
"Removed long video delay after the title." 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 8552.0 0.0 0.0 0.0
"The practical application of linear algebra in real life? Thats easy: Linear Algebra is the basis for solving equations in numerical analysis. Numerical analysis uses the principles of linear algebra in order to solve systems of equations as fast as possible, as well as approximating functions, integrals, and even solving differential equations. Whats that used for? Its used in every software, every computer game, every simulation, every airplane, car, train, space shuttle etc etc etc" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10231.0 0.0 0.0 0.0
"brilliant!! Thanks for great videos
 " FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12557.0 0.0 0.0 0.0
"O Conselho de Administração do PRISA (grupo que publica o EL PAÍS) aprovou os termos para o refinanciamento da dívida, que alarga o prazo até 2025 e reforça a liquidez da empresa. Ao mesmo tempo, acordou a venda do negócio de educação da Santillana de Espanha à finlandesa Sanoma por um valor do ativo de 465 milhões de euros, informou à Comissão Nacional do Mercado de Valores, órgão regulador do mercado de ações espanhol.

“Estas operações permitirão acelerar a transformação digital do Grupo, centrada nos sistemas de aprendizagem Ed-Tech, na América Latina, e nos modelos de subscrição dos seus negócios dos Média”, salienta em comunicado.

O acordo de refinanciamento da dívida prevê alargar o prazo até março de 2025, com um custo inicial de 5,5% e um custo total médio de 7% durante a vigência do contrato. Contempla a amortização de 400 milhões de dívida (ficando a dívida líquida total cortada em mais de 30%) e estabelece um marco para uma futura separação efetiva dos negócios da Educação e dos Meios de Comunicação. Com este refinanciamento, a empresa contará com cerca de 275 milhões para reforçar sua liquidez e facilitar o desenvolvimento dos planos estratégicos de negócios.

O preço pela venda da Santillana Espanha foi estabelecido sobre um valor de empresa de 465 milhões de euros, o que representa 9,6 vezes o EBITDA médio do ciclo educativo do período 2017/2019, para além dos múltiplos das principais transações comparáveis no setor. O preço será liquidado integralmente em dinheiro, na data de encerramento da operação, uma vez descontada a dívida líquida, a 30 de junho de 2020, do negócio objeto da transação, estimada em 51 milhões de euros. A venda gerarà um ganho de capital estimado em 385 milhões de euros.

O diretor-executivo do PRISA, Manuel Mirat, considera que “com estas operações, o Grupo demonstra a validade do percurso delineado, que mereceu também a confiança dos credores”. “Com a venda da Santillana Espanha, verifica-se a capacidade da PRISA de criar valor. Além disso, ao eleger a Sanoma, conseguimos que a Santillana contribua de forma notória para a conformação de um dos grandes líderes europeus no setor da Educação”, assinala Mirat em comunicado.

O encerramento da operação está pendente da obtenção da respetiva autorização das autoridades competentes espanholas, da autorização da Assembleia Geral de Acionistas da PRISA e da formalização do refinanciamento.

Após a venda do negócio da Santillana Espanha, que representa 21% do negócio do Grupo Santillana, o Grupo concentrará os seus esforços no impulso dos sistemas de aprendizagem na América Latina. A Santillana é a única operadora global de educação presente em todos os países da América Latina, onde tem uma posição e proposta de valor únicas, projetando para outros mercados os modelos de subscrição desenvolvidos no Brasil e alcançando através deles um total de 1,7 milhões de alunos na região, com um crescimento de 25% no último período anual." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7964.0 0.0 0.0 0.0
"Finished (24/01/21, London), thank you very much MIT for keeping me entertained during lockdown. Both are fantastic lecturers. See you in 18.02." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3803.0 0.0 0.0 0.0
"In India we study this in Kindergarden 😥😂" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 6612.0 0.0 0.0 0.0
"4:49 There is an error in the subtitles. Should say 'It's symmetric', not 'It's a metric'" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1327.0 0.0 1.0 0.0
"Thanks mit" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 9751.0 0.0 0.0 0.0
"mannnnnnnnnn profs. with accents..." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13906.0 0.0 0.0 0.0
"Is this basic statics??
I am worried that i don't understand....
Can i have the stellar ink wheee the notes and assignment are loaded" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 6856.0 0.0 0.0 0.0
"Finally we can understand
""with respect"" means
 ""small changes of""
For example let find the derivative of 
the function f(x)=x+y with respect to x..
Means when x is moving slowly ..
What is the gradient between z and x
i.e 
z/x =?" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 3786.0 0.0 1.0 0.0
"why is there no echo in my left ear?  but there is in my right ear..." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 15345.0 0.0 0.0 0.0
"Wow... and this is the high profile, 'first world' education??? ... goshhhh ... I learned this stuff two years before ending highschool!!, is obviously presumed to be known in order to enter university! well... I guess I'll go for Lomonov State University of Moscow... I guess this is why the USSR got first into space xD .. and what's with the exposition?!? beyond if the guy uses or not PowerPoint... it's like reading a crappy colorful textbook!!!
" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12089.0 0.0 0.0 0.0
"I love him so much,
He is an amiable man and he's a good teacher.  
I'm sad to see him getting old in the first video,
I hope he can live forever." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5731.0 0.0 0.0 0.0
"obviously to groom your cats and dogs" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 14099.0 0.0 0.0 0.0
"In the linear LMS estimation part... it is nowhere mentioned that E[theta hat] = E[theta] which is a pretty important/basic property. Seems it is not in the book too (Section 8.4). I was bumping my head around proving something else... until I realized that this property holds true. Anyway... This is a perfect lecture series and I am so thankful for being able to ""attend them""." XtNXQJkgkhI "22. Bayesian Statistical Inference II" "6.041 Probabilistic Systems Analysis and Applied Probability" 6676.0 0.0 1.0 0.0
"The way you teaches here , why don't you teach in the same fashion in your book?

Regards,
DSE MA ECONOMICS student" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10335.0 0.0 0.0 0.0
"finally, Zodiark EX Prog" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12859.0 0.0 0.0 0.0
"That it is snowing outside makes everything even better :))" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9902.0 0.0 0.0 0.0
"shouldn't the multiplier be -3 ?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14298.0 0.0 1.0 0.0
"11:45 the disappointment" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 379.0 0.0 0.0 0.0
"this guy is amazing" mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 14815.0 0.0 0.0 0.0
"i wish to have a lecture like that in my university.." RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13505.0 0.0 0.0 0.0
"HOCAM BETON YETMEZ BETON" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4405.0 0.0 0.0 0.0
"Gilbert Strang is one of my heroes of Linear Algebra (teaching)! He‘s a really great teacher and human! ❤️" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4023.0 0.0 0.0 0.0
"An error is made at 21:50, but is then corrected at 23:48." Tx7zzD4aeiA "20. Central Limit Theorem" "6.041 Probabilistic Systems Analysis and Applied Probability" 2438.0 0.0 1.0 0.0
"thank you" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 14463.0 0.0 0.0 0.0
"44:30 Probability va Statistics" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 1237.0 0.0 0.0 0.0
"If your prof had his phone on the side. Lecture was going to be immaculate." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6565.0 1.0 0.0 0.0
"very helpful" 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 15014.0 0.0 0.0 0.0
tnx a1ZCeFpeW0o "20. Principal Component Analysis (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 14941.0 0.0 0.0 0.0
"can someone please explain how he got from R = [1 2 0 -2; 0 0 1 2; 0 0 0 0] to R = [I F; 0 0] ?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 12625.0 0.0 1.0 0.0
"Vietnamese student: easy peasy" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 11235.0 0.0 0.0 0.0
"I like to think of it as ""Naive Gram Schmidt"" vs ""Strategic Gram Schmidt""" MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5697.0 0.0 0.0 0.0
"Very nice." dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 11221.0 0.0 0.0 0.0
"0      Vectors
1 Dot product
2 Determinants; cross product
3 Matrices; inverse matrices
4 Square systems; equations of planes
5 Parametric equations for lines and curves
6 Velocity, acceleration
8 Level curves; partial derivatives; tangent plane approximation
9 Max-min problems; least squares
10 Second derivative test; boundaries and infinity
11 Differentials; chain rule
12 Gradient; directional derivative; tangent plane
13 Lagrange multipliers
14 Non-independent variables
15 Partial differential equations
16 Double integrals
17 Double integrals in polar coordinates; applications
18 Change of variables
19 Vector fields and line integrals in the plane
20 Path independence and conservative fields
21 Gradient fields and potential functions
22 Green's theorem
23 Flux; normal form of Green's theorem
24 Simply connected regions
25 Triple integrals in rectangular and cylindrical coordinates
26 Spherical coordinates; surface area
27 Vector fields in 3D; surface integrals and flux
28 Divergence theorem
29 Divergence theorem (cont.): applications and proof
30 Line integrals in space, curl, exactness and potentials
31 Stokes' theorem
32 Stokes' theorem (cont.)
33 Topological considerations, Maxwell's equations
34 Final review
35 Final review (cont.)" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 272.0 0.0 0.0 0.0
"Wel, this matrix here is doing its best to be the inverse. Actually, everybody here is just doing the best to be an inverse. (c) 


This phrase really describes me fighting my procrastination all the day." ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11342.0 0.0 0.0 0.0
"is he even human? Beautiful!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13629.0 0.0 0.0 0.0
"Fun fact: This prof started his masters leading to his Ph.D when he was 14 

:| " dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 3952.0 0.0 0.0 0.0
"Ellipsoid :D

Its like the UFO from the Movie Independence Day :D
" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 3562.0 0.0 0.0 0.0
177.5 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 499.0 0.0 0.0 0.0
"""Ok!""

^_^" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 95.0 0.0 0.0 0.0
"What is the question at 30:51?  Oh, and the word Parallelipiped sounds funny." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11533.0 0.0 1.0 0.0
"11:55 when you try to guess answer on multiply choice test" nrDkb2MAwSA "20. Definitions and Inequalities" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 382.0 0.0 0.0 0.0
"16:00 i love this professsor" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 465.0 0.0 0.0 0.0
"Thank you for existing Gilbert Strang. I am grateful to you for showing me the beauty and elegance of mathematics" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 9250.0 0.0 0.0 0.0
"I'm struggling so much with the paradigm of linear transformations. I can do with matrices just fine. ""See"" the concepts even - but throw in the T(x) whateverthefuck and I can feel myelf melting with tears. Hoping this will be the click for me!" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6381.0 0.0 0.0 0.0
"IMPORTANT!! Make sure you have the picture quality up (preferably to 480p). Because of the length if you have the settings on auto the picture quality is very low....I was on the verge of sarcastically asking if MIT couldn't afford a decent camera!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6447.0 1.0 0.0 0.0
"he constantly says yesterday and tomorrow, do these guy have lessons all days ?
when do they do the homework ?!

however if they only have 1hs of calculus thats not such a pain. having 4hs x 2 days is the same pain or worse, but you can at least do the homework between these two days !" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13071.0 0.0 0.0 0.0
"He's absolutely amazing! I do wonder, however, if a non MIT - like class of students would be able to appreciate his teaching style." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4629.0 0.0 0.0 0.0
"(1/3)*n^3, magically! hmm! But hey, it makes sense, that is a sum of all (n-x)^2, and as he assumed for all pivots it is a continues variable then the discrete sum of continues variables turns into integral and there you have it, 1/3n^3." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 216.0 0.0 0.0 0.0
"Just when I thought he ran out of blackboard to write he moves to the right and lo and behold there's more of them" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7204.0 1.0 0.0 0.0
"even my grandma can undestand" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12803.0 0.0 0.0 0.0
"Isn't the order of complexity for multiplication b/w 2 n x n matrices O(n^3) and not O(n^2)?" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 6897.0 0.0 1.0 0.0
"so e being perpendicular to p means that e is truly the smallest difference between b and p" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 14328.0 0.0 0.0 0.0
"I believe that Mr. Strang is really amazing and incredible, but I got stuck when he said of ""the pivot and free variables"" , I mean he told us about the algorithm very well, but I am not able to connect these with that what does it mean to?? Why does non pivot columns can be considered anything?? And what are its effect on my graph if I wish to plot it on?? And what's the concept behind these pivot and free variables, how did it occur from anywhere??
So , if you guys could help me out with this , it would really be appreciated!!" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 5170.0 0.0 1.0 0.0
":D
" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1452.0 0.0 0.0 0.0
"33:52 " IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 971.0 0.0 0.0 0.0
"finally finished all of Lewins physics lectures and Auroux's math lectures. Thank you MIT for helping me start my classes well prepared! Would love to go here for graduate school." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12858.0 0.0 0.0 0.0
"How did he get the equation at 23:01 ?
I don't understand .
Did he differentiate with respect to ds, or what?
Please help." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4835.0 0.0 1.0 0.0
"€~Thankyou~$
Thanks a lot..." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15601.0 0.0 0.0 0.0
"26:44 
haha thats awesome" tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 807.0 0.0 0.0 0.0
"Who is here before world War 3" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 11738.0 0.0 0.0 0.0
"No news to worry. We are listening." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 7877.0 0.0 0.0 0.0
"Aha! If wikipedia is good enough for Prof. Strang it's good enough as a source for my Master's Thesis." Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2283.0 0.0 0.0 0.0
"Does anybody know what movie or book title he is talking about in the last minutes of the lecture at 43:47 ?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 3430.0 0.0 0.0 0.0
"Well I got my finals in 1 month so I really hope that this will safe my ass. Complex numbers, linear algebra and differential equations in 10 weeks time, they must be nuts XD" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11345.0 0.0 0.0 0.0
"32:52 ... You're welcome !" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 943.0 0.0 0.0 0.0
"3 days before finishing linear algebra... I finally understand linear algebra" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 877.0 0.0 0.0 0.0
"I Really Like The Video From Your Orthogonal Vectors and Subspaces" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4964.0 0.0 0.0 0.0
"the movement of the camera is so annoying" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 14719.0 1.0 0.0 0.0
"Thank you sir :)" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9330.0 0.0 0.0 0.0
"Awesome lectures however I call bullshit to the following: At 32:03 he says the following: ""you can make it formal (the argument about the memoryless property) by just manipulating PMFs formally"". And then proceeds up to 34:04 by which time he's supposedly ""proven formally"" the memoryless property of the geometric distribution and declares victory. Except of course he's actually proven absolutely nothing at all. Either that or I am plain thick and have failed to see the ""proof""." -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 2764.0 0.0 1.0 0.0
"I am in platonic love with this teacher." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5109.0 0.0 0.0 0.0
Skyrim 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8720.0 0.0 0.0 0.0
"was this more difficult than previous 14 lectures?" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 15058.0 0.0 0.0 0.0
"Thank you verhhy much))))" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9424.0 0.0 0.0 0.0
"Such delightful and divine lectures." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8950.0 0.0 0.0 0.0
"@datHulkinZ 
thats the equation of a circle whose origin is at (a,0) and radius a" ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1821.0 0.0 1.0 0.0
"this lecture rocks!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14897.0 0.0 0.0 0.0
"These teachings resemble those I have been seeing in Africa the difference is who studies" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 10428.0 0.0 0.0 0.0
"@non523 Hard to find realy fat dry erase markers" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1960.0 0.0 0.0 0.0
"So... why do people pay to go to college? Why not just watch it on youtube, download the textbook, and take some standardized tests? No college bullshit, learn at your own rate. You could learn so much faster too." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8815.0 0.0 0.0 0.0
"Has to be vertically simple in all three directions." wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 4437.0 0.0 0.0 0.0
"I love Dr. Strang and rewatch his classes just to see what an accomplished teacher he is." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5713.0 0.0 0.0 0.0
"The camera movements are really jarring, and my eyesight isn't great so the white on grey writing is hard to read." yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 10032.0 1.0 0.0 0.0
"dead simple, low quality, messy handwriting. Could have been explained way simpler, easier and quicker" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12729.0 0.0 0.0 0.0
"Super clear explanation of conditional probability and Bayes' theorem. Loved every minute of this video." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 8955.0 0.0 0.0 0.0
"30:46 The real joy of mathematics !! Thank you Prof. Strang :)" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 893.0 0.0 0.0 0.0
"A lot of viewers here stating that they wish they had a lecturer like Gilbert. I am one of those viewers. But as a lecturer myself, I sometimes find myself in a room full of students who don't give a sh.t about anything I say or anything I explain, and it comes to a point where I want to quit my job. When you click on a link to learn math you are fully motivated. Gilbert has a full room of MIT minds who are open to learning. But when you face a group of students who are just looking for loopholes in your syllabus, who don't give a sh.t about your lessons, always fight for 0.01 points every time you conduct an exam, you began to question things. Yeah, I wish I had a lecturer like him and I am equally sorry that I cannot be a lecturer like him." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 2138.0 0.0 0.0 0.0
"44:10 use a diagram to replace the equation, or encoding of the equation" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1229.0 0.0 0.0 1.0
"33:52 Professor Strang hasn’t taught the 18.06 for a while and he observes the lectures these days at MIT are taught in a very abstract way, unlike how he presented concepts such a column space 20 years ago. That’s why he said what’s going on? So the ‘range’ terminology of these days is the same as our good friend C(A)!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 972.0 0.0 0.0 1.0
"21:12 I believe that if c was i, the matrix is symmetric. It is complex and symmetric, while non-Hermitian." HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 674.0 0.0 1.0 0.0
"The key part of Zolotarev numbers explanation (sets of eigs are separate), unfortunately dosen't explain anything for me. Can anybody give a good intuition, why Zolotarev boundary works? The smoothnes at least makes sense, but while i kinda feel what Sylvester eq does, the end result is kinda deep math for me." 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10149.0 0.0 1.0 0.0
"What is the edition of this textbook?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11524.0 0.0 0.0 0.0
"1:38 ohh man this linear algebra series couldn't have a better ending" 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 595.0 0.0 0.0 0.0
"I love this prof" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 5831.0 0.0 0.0 0.0
"Got B+ haaa  for class 2015" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 4167.0 0.0 0.0 0.0
"alright, let's talk about math, but first, I am going to give a speech like a good engineer should ... then I repeat myself over and over again, trying to get as redundant as I can ... and then I give you stuff that high school student do ... in their first year ...

I might be totally wrong saying it like this, but this is the kind of feeling I get ... In France, in ""seconde"", when we are 15 we learn about this. In some school, it's even earlier than that ... 

Is this video a catch-up?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12331.0 0.0 0.0 0.0
"Explain some wrong" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3706.0 0.0 1.0 0.0
"I find these videos quite interesting, however the disorder at the time of writing that many teachers deal with bothers me. Unclear and messy handwriting. It would be nice if they could improve on those aspects." C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 5417.0 0.0 0.0 0.0
"why is this lecture not being downloaded by Idm and only some of lectures of these lectures are able to be downloaded." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15347.0 0.0 0.0 0.0
"mind blowing!" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 13944.0 0.0 0.0 0.0
"Guaranteed everybody watching this has a final tomorrow" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4384.0 0.0 0.0 0.0
"greater interactive teaching than iits.here we sleep in lectures n in mit they took interest but still iitians can complete the whole courses in one nightn after that both end up with equal level" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13021.0 0.0 0.0 0.0
"Profesor Strang : Muchas Gracias !!!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8320.0 0.0 0.0 0.0
"The operation where you say 3R1-R2 i believe your R2 should (0,-2,2) not R2-3R1 (0,2,-2)
the solution is (2;1;-2)
the basic idea is to substract the row you are changing...." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10217.0 0.0 1.0 0.0
"@HunterDX77M Thank you, I don't get why people can't understand that Lec 1 stands for the first lecture lol
" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1633.0 0.0 0.0 0.0
"@harmansingh101 it is MIT, an ivy league school and arguably the best school on the planet, its the school that Matt Damon's character went to in Good Will Hunting. I would say it is recognized as the best school among most Ivy League students but I'm not positive, there is no doubt that it is on the level of Harvard, Princeton and Tokyo University." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1862.0 0.0 0.0 0.0
"Worth watching and enlightening" rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12001.0 0.0 0.0 0.0
"can you give me the link of ebook needed for the course?" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12636.0 0.0 0.0 0.0
"12 years later, I finally got here" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 384.0 0.0 0.0 0.0
"I don´t notice the identity matrix  at around @22:00" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 5373.0 0.0 1.0 0.0
"Did you know that 93% of people make up their own statisticks?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3394.0 0.0 0.0 0.0
"take speed 0.5 , it sounds like he is dissing the shit out of some1" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 14434.0 0.0 0.0 0.0
"At the 1:05:30 time mark, why is it at most 4/alpha^2 steps? This seemed immediate to both the student and the prof, but I'm not seeing it." buEtwpGvQpI "18. Roth's theorem I: Fourier analytic proof over finite field" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 2724.0 0.0 1.0 0.0
"Very much intuitive ❤️❤️❤️❤️" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11201.0 0.0 0.0 0.0
"Could you provide the solutions to the assignments and recitation materials?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3247.0 0.0 0.0 0.0
"wow.... unbliveable." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15435.0 0.0 0.0 0.0
"Such a nice prof!" L3-WFKCW-tY "33. Neural Nets and the Learning Function" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8937.0 0.0 0.0 0.0
"Thank you,
Professor and MIT." rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 9489.0 0.0 0.0 0.0
"@t=24, H12 is a PlacketBurman design. All H matrices, and subsets of these, are very useful in experimental design. (ref Box Hunter Hunter Statistics for Experimenters 2nd Edition)" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2033.0 0.0 0.0 0.0
"Thank you Gil for getting me through Linear Algebra. You have saved so many people's college careers, a true hero." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9109.0 0.0 0.0 0.0
"haha my prof doesnt teach shit " yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 13040.0 0.0 0.0 0.0
"25:37 Horizontal lines plotted is incorrect?" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 783.0 0.0 1.0 0.0
"was the great seeing the humor come alive in this one." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 15057.0 0.0 0.0 0.0
"Loved it so much...." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 7476.0 0.0 0.0 0.0
"Hey +MIT OpenCourseWare thanks for another amazing video. I did a short little explanation of the intuition behind FToC and would seriously love some feedback, if you get the chance. I think you might like the different approach I take. I hope so anyway :) https://youtu.be/gSA4K8xzrKc" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4686.0 0.0 0.0 0.0
"At 32:00, the prove is just the component e and p equal to b. But I think the e should be perpendicular to the line, not to take the y components... i.e. at 32:00, for the proof, there is an assumption that the x component of b,e,p are the same.
Anyway, it is a great video series for review. :>" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 2644.0 0.0 1.0 0.0
"Guys! Checkout 3blue1brown video on Taylor series." BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4391.0 0.0 0.0 0.0
"its funny how Lady Gaga is a related video..." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13708.0 0.0 0.0 0.0
"The simple algebraic mistakes tho  :)" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 10279.0 0.0 0.0 0.0
cool! aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12680.0 0.0 0.0 0.0
"After seeing julia language..  I think it is most suitable for Machine Learning Researcher or AI Researcher job title.." rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2252.0 0.0 0.0 0.0
"reply to ishan dave i m frm iit  bombay n my brnch is cs" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14262.0 0.0 0.0 0.0
"Expertise your engineering knowledfe here" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3704.0 0.0 0.0 0.0
"I'm so grateful for his classes. Thank you, Professor!  Hugs from Brazil! =)" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6375.0 0.0 0.0 0.0
"i mean why even give the free variables values and not just let them be and solve the equations, for the transpose you would just get x1=-x3 x2=-x3 and x3 as free variable, i guess im missing the point with the identity and swapping the -F but i dont really get why you want to do that instead ..." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 13441.0 0.0 1.0 0.0
"I hope the content of this course and a few other DL courses enables me to make a superresolution version of 18.06 video. Man I love this guy" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5592.0 0.0 0.0 0.0
"You are one among the best teachers sir
Great regards good health from india..." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 12175.0 0.0 0.0 0.0
"Did he just start by saying this is a lot simpler and more intuitive?? Then why did my lecturer always sound like he was from outer space???" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 3373.0 0.0 0.0 0.0
"Professor miller tends to say things he doesn't mean and not realise. But I can't really judge him, as I do that a lot too." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8400.0 0.0 0.0 0.0
"For a person who is not privaleged enough to study into such presitigious universities, but his courses on Linear Algebra made me fall in love with Mathematics and Computer Science. 

Sir honeslty you made my career." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 3844.0 0.0 0.0 0.0
😭😭😭😭😭😭😭😭 J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 15739.0 0.0 0.0 0.0
"if we take the outer length, that is, d(theta).(r + dr) , then
 dA = d(theta). (r + dr) * (dr) 
       = r.dr.d(theta) + r.dr^2.d(theta)
the last term contains a square of dr, which is much smaller than dr when dr is very small itself. Hence the last term is very dispensable. 
so the first term, r.dr.d(theta) prevails." 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13546.0 0.0 0.0 1.0
"Excellent Teacher... I learned a lot fromhim" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3633.0 0.0 0.0 0.0
"Why does the blackboard of a professor must be so badly made?  Why are there so many impossible to be read notes???? Could he just make it readable for his students???? I ask that because I myself had already teachers and professors that made their blackboards impossible to read and messy! Despite that detail, this interview was awesome!!!!! This man is a legend to whom may like linear algebra!!!! I myself just love it!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11845.0 1.0 0.0 0.0
"At BYU right now. Chem E.

Studying this material for the past few days now to get ahead. This lecture is an excellent tool for taking all these concepts and placing them in a clear and simple context. 

I have greatly benefited from listening to this lecture. Thank you." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2702.0 0.0 0.0 0.0
"Pay attention, he is one of the best profs you will ever see!" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 8159.0 0.0 0.0 0.0
"i don't get what is he trying to say at 43:28" EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 13363.0 0.0 1.0 0.0
"Not necessarily. The only guarantee is that they know work hard and study, while Einstein's could choose to be a slacker and be going to worse colleges.

Isn't the education system America has set up great??? work your ass off for us and you will be payed! if you're smart... well no one really cares we just want you working for us." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7928.0 0.0 0.0 0.0
"This man is an artist." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 10862.0 0.0 0.0 0.0
"my favorite anime episode so far, what a plot twist. very twisty." 3eiio3Tw7UQ "19. Weak Law of Large Numbers" "6.041 Probabilistic Systems Analysis and Applied Probability" 13981.0 0.0 0.0 0.0
"I don't understand why he thinks x is fixed and ""delta"" x is moving in here: https://youtu.be/9v25gg2qJYE?list=PL590CCC2BC5AF3BC1&t=448
Can anybody explain me pls?" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5354.0 0.0 1.0 0.0
"It is a very good series of videos, but it has a caveat. Professor Sipster seems to try to explain in detail without first giving a definite answer...." 1VhnDdQsELo "14. P and NP, SAT, Poly-Time Reducibility" "MIT 18.404J Theory of Computation, Fall 2020" 6930.0 0.0 0.0 0.0
"People, this is the fifth lecture of an introductory course to calculus, right after the freshmen are coming out of high school. It's no surprising that the teacher lays a good  foundation before moving on to more complicated things, it's a sort of equalizer for the students. To say you did this in high school doesn't prove that MIT classes are bogus, that's just a dumb statement to make." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8174.0 0.0 0.0 0.0
"""So again I'm getting a little ahead because it's in section 3.2, but that's ok 🤷🏽‍♂️""" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 107.0 0.0 0.0 0.0
"He looks like a reincarnation of Euler" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4571.0 0.0 0.0 0.0
"To find d(A^2)/dt, we can simply write it as d(A.A)/dt and use product rule." AdTvkFsqcDc "16. Derivatives of Inverse and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11035.0 0.0 1.0 0.0
"Ohhh Liam Neeson teaching stats." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8037.0 0.0 0.0 0.0
"Thank You, Professor and OCW for making this available." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9059.0 0.0 0.0 0.0
"Good refreshment for my calc based physics class. Thanks MIT" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4153.0 0.0 0.0 0.0
"I NEED SOME SPACE AFTER THIS!!!" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 4934.0 0.0 0.0 0.0
"I love how confident and spontaneous Professor Strang is. He is not afraid to make mistakes in front of his students and term them as “to finish” examples for later examination as he moves forward and tries another example in hope of “doing it right” the second try. His hesitation which is a result of high brain activity may confuses you sometimes and throws you off tangent, but it emphasizes the need for continuous examination and pondering while you are presenting the material. He could to the naive critic have prepared better for his lectures to have a smoother sail, but he seems on purpose to present himself like a student who is just doing it for the first time, which is really quite sly and entertaining if you don’t find it confusing. You may for that reason have to wind back his lectures and watch it a second or even third time to get a full appreciation of his style. Thank a bunch for having such a brilliant instructor with decades of teaching and research experience!" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 5746.0 0.0 0.0 0.0
"where are lectures: 8,17,26 and 34???" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15218.0 0.0 0.0 0.0
"in which lecture has he explained the l""hospital  rule" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13603.0 0.0 1.0 0.0
"Why isn't the infinity application in some of these." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 11895.0 0.0 0.0 0.0
"Thank you, sir!!! 

It has started with a simple matrix and look it is creating the whole universe, explaining the existence. That's the beauty of it!!!
It feels amazing when I spend my time with the abstract world.
My intuition says ""There is something still hiding and right now you are in the dark place so either you can't get out from that place or you can't stand still"". 

Let's look at these beautiful connections:

A matrix has some columns and these are called vectors. The vectors are independent if their combinations give no zero except if they are zero vectors {How???) and dependent if the opposite of the statement is true. 
What is the connection between independence and null space and the rank of a matrix?
the vector are Independent when the Null space of that matrix = zero vector and
the rank is no of columns (Think !!!) =Invertible = nonsingular matrix.
For dependence of vectors there exists at least one free variable ( Do you know what is free variable?) and rank is less than the number of columns. ( Singular???)

The linear combination of the whole vectors forms space. (Here your existence, experience, can be explained!!! Can you visualize it in your imagination? )

The basis for a vector space is the sequence of all the vectors with two properties
1) They are independent ( look independence again comes here!!!)
2)They span a space ( what is span??? Think!!!) ( What space can be formed from these vectors (1,0,1),(1,1,1),(0,1,1)? )

The basis!!!  The children of a space!
In a three dimensional space with any two vectors, what is the basis for that space?
(Is it  a plane or a space or a line???)

Every basis for a vector space has the same number of vectors given space and that's called
the dimension of the space. The number of vectors is very important.(why??? Think!!!)

The Dimension of a column and a null space???

The dimension of the column space=The rank of matrix =Number of pivot columns. Remember, it does not depend directly on the dimension of the matrix. 

The dimension of the null space = number of columns - rank of the matrix = The number of free variables.
The basis of the column space is generated from the all the linearly independent vectors of a matrix given a space. If We know the dimension of the space then a couple of vectors that are independent be a basis.

Algorithm
1)Matrix -> row reduced echelon form->no of pivot columns->rank->dimension of column space
2) free columns = no of columns - rank= dimension of the null space." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 9530.0 0.0 0.0 0.0
"Great class, helping me a lot in Calculus III. Greetings from a studant from Polytechnique School of the University of São Paulo, Brazil!!" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4216.0 0.0 0.0 0.0
"True ... the next generation will be much more intelligent than us ... because eventually every major university will be doing OCW ... and students will get to listent to so many different professors on the same subject" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11086.0 0.0 0.0 0.0
"life saver for my final" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 13788.0 0.0 0.0 0.0
"I can't expect enormous answers. Like it a lot. " yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 5211.0 0.0 0.0 0.0
"I missed the formal definition of vector spaces. Too many references to it without writing them down. They were mentioned shortly, but..." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 5874.0 0.0 1.0 0.0
"Well don't all speak at once :)" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11348.0 0.0 0.0 0.0
"thank you MIT , thank you professor Strang" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14479.0 0.0 0.0 0.0
"Thank you a lot you are a good man to give us this barnch in mathematics" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9243.0 0.0 0.0 0.0
"personal index:
def of finite automaton : 20:00
regular lang def : 29:00" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 14181.0 0.0 0.0 0.0
"what did he say, why is Fx and Fy equal to zero in local maxima or mimima " UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15130.0 0.0 1.0 0.0
"By the way, at 50:04 it is said that comparing the likelihood ratio L(x) with the threshold xi is the same as comparing x with the threshold xi which is not entirely true (pedantically speaking). Instead, this is true: it's the the same as comparing x with D(xi) where D is the inverse function of L(x) (since L is monotonic it has an inverse function). In other words the xi on the x axis on the drawing is not the same number as the xi from the LRT slide. Leaving this note here just for future viewers. Again: great course and professor!" tBUHRpFZy0s "24. Classical Inference II" "6.041 Probabilistic Systems Analysis and Applied Probability" 2977.0 0.0 1.0 0.0
"Finished 16/02/2021 ;DDD" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3805.0 0.0 0.0 0.0
有没有讲汉语的小伙伴 VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 15636.0 0.0 0.0 0.0
"17:47 blows my mind that people are coming late to this class. They have NO idea how lucky they are to be at MIT and to be taught by the world's premier Linear Algebra instructor." d32WV1rKoVk "12. Computing Eigenvalues and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 518.0 0.0 0.0 0.0
"hahahaha, 18:49" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 13054.0 0.0 0.0 0.0
"This might help others trying to learn this material. 
I found it easiest to watch a few lectures, but without being overly concern about learning exactly whats going on. This gives you a basis to work from.
Then get the text book and work though it slowly. Write down the examples in the book as you encounter them and get used to forming a mental picture for whats going on. 
The column picture is key.
The row picture is probably what your school math teacher taught you. This just confused me a lot. I don't like dot products, but the ""combinations of columns"" is very intuitive once you can visualize why it works. 
The reason I found this easier is that the concepts introduced in the videos are a bit loose, its just an overview. The real learning comes from the text book." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10883.0 0.0 0.0 1.0
"Good contents. But I don't think he has a very systematic way to interpret things. It's kind of hard to understand what he is trying to say." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4125.0 0.0 0.0 0.0
"This si such a treasure. Thank you so much." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 10926.0 0.0 0.0 0.0
"I study Computer Engineering at IPN in Mexico and I'm taking Linear Algebra after this summer. I can't believe I just found these videos, It's like taking a course at MIT! There's no way I could fail that course now. Thank you for sharing this helpful information." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5979.0 0.0 0.0 0.0
"I wish he was my teacher :(. He explains things so clearly and thoroughly! " ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6220.0 0.0 0.0 0.0
"at minute  19:30 what if the function was not (1/ 1 + c) but more complex function where its hard to find the minimum value and the maximum value 

should we then sketch the curves and find out how the function looks like and  then find the max and min value for the function" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12472.0 0.0 1.0 0.0
"i am iranian and i watch this study , it was good" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13334.0 0.0 0.0 0.0
"my right ear feels wholly educated" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 14001.0 0.0 0.0 0.0
"00:00-03:00
Review

03:00-10:00
Finding the component of a vector in the direction of a unit vector using dot product

10:00-24:10
Determinant in 2D
det(a,b) = |a| |b| sin(theta)
det(a,b) = +- area of parallelogram formed by a and b

det(a,b) = | a1 a2 | = a1*b2 - a2*b1
                  | b1 b2 |

24:10-32:45
Determinant in 3D
det(a,b,c) = | a1 a2 a3 |
                    | b1 b2 b3 |
                    | c1 c2 c3 |
det(a,b,c) = +- volume of parallelepiped formed by a, b, c

32:45-47:00
Cross product is a vector, only defined in 3D
a x b = |  i    j    k  |
            | a1 a2 a3 |
            | b1 b2 b3 |
Cross product is perpendicular to the plane formed by a and b
Length of cross product is area of parallelogram formed by a and b
Right hand rule

47:00
Volume of parallelepiped using triple product instead of determinant

Triple product 
a dot (b x c)

det(a,b,c) = a dot (b x c) = +- volume of parallelepiped" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 284.0 0.0 0.0 0.0
"What a superb Professor." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 11432.0 0.0 0.0 0.0
"how is the number of operations n^2. 
2x2 ----> 1 operations
3x3 ------>1+2=3 operations
4x4 -------> 3+3=6 operations
5x5-------->6+4=10 operations
6x6--------->10+5 = 15 operations
7x7---------> 15+6 = 21 operations


So it should be 1+2+3+4+5+6+.....n = n(n+1)/2 
Correct me if I am wrong" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 13241.0 0.0 1.0 0.0
"yeah mate, let me tell you something, where I live we don't have AP classes, so here we only learn calculus in college, well I'm not yet in college, I've just finished highschool and I'll start my first year in college in 2 months, and I've been studying calculus by myself, and dude, MIT classes/problem sets/exams are TOO easy as you pointed out. I read on some forums people saying MIT is the hardest college in the U.S. and that some people spend 10+ hours on problem sets LMAO

MIT is a joke [2]" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15467.0 0.0 0.0 0.0
"Thank you." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9543.0 0.0 0.0 0.0
"@Michciu0911 I havent experienced any ""interactive"" math lessons on Brno University Of Technology either. And as you can see, it's not america. But in fact, I have a feeling that teacher has always just... too much to say that he/she hasn't want to be delayed ..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1676.0 0.0 0.0 0.0
"I think in the proof of the pumping lemma, p needs to be (at least) 1 + [the number of states in M]: only in that case is the input string guaranteed to repeat a state." KAySmSEGc9U "3. Regular Pumping Lemma, Conversion of FA to Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 6025.0 0.0 1.0 0.0
"thanks for this opportunity you have created for poor people :D" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14589.0 0.0 0.0 0.0
"A link to the Matlab simulation prof Suvrit shows would be great" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2133.0 0.0 0.0 0.0
"sounds drunk on 0.5 speed" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14386.0 0.0 0.0 0.0
"just hope you remember the minus F on the test." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 13737.0 0.0 0.0 0.0
"so much fun, so much love. Thank you Professor Strang and MIT for inspiring more people around the world. I truly enjoy learning linear algebra with Professor Strang :) we know he's done it!" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14339.0 0.0 0.0 0.0
"How did it go?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4839.0 0.0 0.0 0.0
"I've never had a chance to learn determinants this way. It was always that teachers gave out a bunch of formulas and methods and made students memorize without further explanations. Thanks for walking us step by step through this wonderful concept, Prof. Strang." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 6425.0 0.0 0.0 1.0
"thank god someone uploaded a better audio/video quality version the other one was abysmal" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 14456.0 0.0 0.0 0.0
"Helped me a great deal to get the method and tricks straight for transform math" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4670.0 0.0 0.0 1.0
"Conclude the lecture: The solution will exist only when rank(A)=rank(A|b), which would be x=x(particular)+x(nullspace), x(nullspace) exists only when rank(A)<n, where n stands for the number of columns." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 3193.0 0.0 0.0 0.0
"@beenpimped31 My multi variable prof is asian and its verry very hard to understand him" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1789.0 0.0 0.0 0.0
"it feels great to be getting in on the ground floor of the singularity" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13672.0 0.0 0.0 0.0
"I'm in PreCal now, I've been at it for almost 2 full months. I have a 93 average, and it is definitely not as hard as I thought it would be." jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6330.0 0.0 0.0 0.0
took 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14954.0 0.0 0.0 0.0
13:00 YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 403.0 0.0 0.0 0.0
"Too bad not technical enough" feb9j65Iz4w "24. Linear Programming and Two-Person Games" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11059.0 0.0 0.0 0.0
"I've learned more in this hour than in a four-months course" X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 6420.0 0.0 0.0 0.0
"I think statistics is branch of mathematics" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 6040.0 0.0 0.0 0.0
"Respected sir,Lectures 8,17,26,34 lectures are missing..Were theory was taught in these lectures??" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8567.0 0.0 1.0 0.0
"no proofs, this looks more like a recipe than real mathematics." 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14072.0 0.0 0.0 0.0
"20:48 ~~ That was cute grandpa sigh!!!" p-bXJIa7QVI "Lecture 30: Completing a Rank-One Matrix, Circulants!" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 662.0 0.0 0.0 0.0
"After proving line integral for gradients is end point - start point, weren't the consequences already obvious?" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2249.0 0.0 0.0 1.0
"Please we want also a differential geometry and partial differential equations courses ❤🙏" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8218.0 0.0 0.0 0.0
"In 26:51, the professor writes Gradient(f) = entries of X^-1. Do anyone know how to get that equation? Thanks!" AeRwohPuUHQ "22. Gradient Descent: Downhill to a Minimum" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6598.0 0.0 1.0 0.0
"how can i download  these vedios plzz any one help me" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13197.0 0.0 0.0 0.0
"Now I know why the figure was this way in the 10th lecture." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7953.0 0.0 0.0 0.0
"Gauss invented the elimination method just because he born earlier :D The confidence !" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3982.0 0.0 0.0 0.0
"""Gauss would quit; but Jordan says keep going"" 😂😂" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 49.0 0.0 0.0 0.0
"Wow wow" lWW54ts9Ubo "24. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 12046.0 0.0 0.0 0.0
"Hi:

I think in the example talks about electric Networks, so LOOP is correct. In fact OPEN LOOP and CLOSED LOOP is used frecuently in electric Networks or in Control Systems to study things that Stability,etc.
Cycle is used in the time domain to know the frecuency and in fact, the frecuency is measured in CYCLES/SEG or Hz." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4733.0 0.0 0.0 0.0
"The cameraman here is now a Senior ML Engineer at Google, California." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10037.0 0.0 0.0 0.0
"17:29 by the way a rangle is a bit of gravel fed to a hawk" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 507.0 0.0 0.0 0.0
"did you hear someone in the class burp loudly about two minutes before the end? How gross!" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12742.0 0.0 0.0 0.0
"thanks for the great lecture !" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14583.0 0.0 0.0 0.0
"I've got a question. Geometrically, vector coordinates calculated as vector's endpoint coordinates minus vector's beginning coordinates, which would make all parallel vectors of the same length and direction have same coordinates. When we talk about vector spaces and subspace in geometric sense, do we only mean thos who have (0,0) as their origin? I mean, that makes sense, since if we take into account literally all geometrical vectors, the whole notion of spaces wouldn't make sense, but that wasn't explicitly clarified, was it?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 6416.0 0.0 1.0 0.0
"Wonderful explanation. 
Taylor's formula evaluated at 0 is just Maclaurin's formula. 
The generalization would be to evaluate at each x=a, so one would replace the x^n term with (x-a)^n within the Taylor formula and evaluate the differentiations at a." wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11987.0 0.0 0.0 0.0
"we really need doctors like him in our university cause most of our doctors cant even explain 10% of what he said.... most of the students taking the same course are failing because of our bad doctors" CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15079.0 0.0 0.0 0.0
"Thanks for sharing it with us! I found it very useful! Amazing explanation" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9698.0 0.0 0.0 0.0
"“Think of probability as cream cheese…”.  😂 This was such a a helpful lecture, thank you!" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 15598.0 0.0 0.0 0.0
"6:03 A_1, b_1 ->  A_l, b_l" L3-WFKCW-tY "33. Neural Nets and the Learning Function" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1374.0 0.0 0.0 0.0
"""... it's because your sister knows..."" Okay, that's creepy!" gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 18.0 0.0 0.0 0.0
"for those who want to know Mike Sipser is author of the book that in detail explains those fundamentals of computer science, make sure you watch these playlist they have a huge value for those who want to learn theory of computation." 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 12893.0 0.0 0.0 0.0
"Pretty incredible to be sitting in my living room while learning from a world class professor. Thank you MIT for sharing these!" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8249.0 0.0 0.0 0.0
"Such a nice teacher😢🙏" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8938.0 0.0 0.0 0.0
"Please I can't see well..." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 8198.0 0.0 0.0 0.0
"to be honest, the blackboard is better than my uni" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 14944.0 1.0 0.0 0.0
"Beauty of mathematics lies in the proofs, the arguments made for proof rather than mugging the result and finding the answer :)" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2829.0 0.0 0.0 1.0
"Impressed ❤️" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6586.0 0.0 0.0 0.0
"Same, what was so funny!?!?" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8599.0 0.0 0.0 0.0
"Its always exciting to understand  non determinism." oNsscmUwjMU "2. Nondeterminism, Closure Properties, Conversion of Regular Expressions to FA" "MIT 18.404J Theory of Computation, Fall 2020" 7081.0 0.0 0.0 0.0
"Love his teaching! His previous Linear Algebra course has helped me a lot!" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7442.0 0.0 0.0 0.0
"your lectures make me understand linear algebra soo well
i was starting to dislike maths beacuse of this but now iam motivated to study it , thanks alot :)" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 15526.0 0.0 0.0 0.0
"Nicely done, prof! Some people are just good at Linear Algebra, some can make others be good at Linear Algebra!" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 7869.0 0.0 0.0 0.0
"Thank you for the great lecture. This is really helpful for me!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 9264.0 0.0 0.0 0.0
"Who is watching 👀 his video in 2x speed ? 😃" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 11745.0 0.0 0.0 0.0
"nazgul wanted to learn determinant." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 14013.0 0.0 0.0 0.0
"Very ordinary lectures !!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11224.0 0.0 0.0 0.0
"Thank you." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 9556.0 0.0 0.0 0.0
"11:34 made a typo in  b as it should be  [1, 2, 2] right?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 376.0 0.0 1.0 0.0
"This guy is the man!" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 10547.0 0.0 0.0 0.0
낼 YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15672.0 0.0 0.0 0.0
讲的不错 cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 15661.0 0.0 0.0 0.0
"Can someone explain to me when we should use Frobenius norm and when we should use the nuclear norm ?" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3074.0 0.0 1.0 0.0
"For anyone watching this who doesn't feel like they are completely getting the concept, Prof Strang has an updated lecture in 18.065 on the SVD, which I think lays it out in a cleaner way: https://youtu.be/rYz83XPxiZo" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 3855.0 0.0 0.0 0.0
"What an amazing teacher" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11453.0 0.0 0.0 0.0
"I hate math." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5482.0 0.0 0.0 0.0
"When you combine those lectures with the ones from 3 Blue 1Brown you get a superb class that opens the doors to mastery. Tank you. I am teching myself math just for the fun of it thanks to You Tube!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11644.0 0.0 0.0 0.0
"I olny had math until 6th form  (around 12th grade) and i was invited one day to see a matrix class. 
And let me tell after the first 14 minutes of this video i really felt in love with maths" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5891.0 0.0 0.0 0.0
"I have a doubt in Difference equations part. He writes u_0 as a combination of eigen-vectors of A. Why should this be true?" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 5487.0 0.0 1.0 0.0
"I think profs in my college shld go through these lectures before lecturing the students." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6039.0 0.0 0.0 0.0
"Thank you for the lectures, they are very helpful." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 9269.0 0.0 0.0 0.0
"44:58 What is E times A? EA sports" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1245.0 0.0 0.0 0.0
"This third quiz seems very fair in comparison to earlier quizzes. DR. Strang there is a heavy thought goes into answering questions  correctly on quiz 3. I understand quiz 3 really well in comparison to quiz1 and two. For an ivy league school like MIT, your students are very fast learners for  all technical classes." HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 10944.0 0.0 0.0 0.0
"my prof. can come and learn from this prof.
" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 13997.0 0.0 0.0 0.0
"Copyrighted in 2000, made in 2005...

Has MIT discovered time travel??" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 3218.0 0.0 0.0 0.0
"21:11 there is a subtitle error, he doesn't say anything about complex numbers. It could cause confusion for people who are deaf." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 672.0 0.0 0.0 0.0
"i love the sound of the chalks" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13429.0 1.0 0.0 0.0
"Just must​ use stat with wordly evens." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7188.0 0.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8437.0 0.0 0.0 0.0
"lecture = n * (the real question is)" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 13772.0 0.0 0.0 0.0
"30:00 its2 and  -1 right since its in right position" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 881.0 0.0 1.0 0.0
"""Any f'n know"" sounds more like ""Any f**king thing you know""" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 29.0 0.0 0.0 0.0
"Whats the ""cheat sheat for exam"" thing?" -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 11596.0 0.0 0.0 0.0
"good camera work on all of these MIT lectures" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 12942.0 1.0 0.0 0.0
"Wowwwwwww.....Amazing....My dream is go to mit.....How can I go???which condition mit wants?" asjAc90L8rE "12. Time Complexity" "MIT 18.404J Theory of Computation, Fall 2020" 12095.0 0.0 0.0 0.0
"This max and min method makes intuitive sense but does anyone have a proof showing that if the gradient is zero and the matrix is positive definite then the function is a local minimum?" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 10882.0 0.0 1.0 1.0
"Very interesting video, thank you!
A very good teacher too, but when the time of demonstration comes the explanations are less understandables!" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11200.0 0.0 0.0 0.0
"So I was a bit confused by his (a,b) notation but I think I got it. 
So in his 'practice' example we have mean = 1/2 (a,b). (a,b) is really the matrix [a b]. With probabilities 1/2 we pick either the matrix [a 0] or [0 b]. So we average the matrices to get 1/2 [a,b]. Now two samples means we get two matrices randomly with the above probabilities and add them. If X is a random variable, mean(2X) = 2 mean(X), so we multiply the mean by two to get [a b], the original matrix. 
Hope this helps someone." z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8732.0 0.0 0.0 0.0
"In the fisher scoring algorithm, why do we only take the expectation of the hessian and not also of the gradient. I mean, we want to minimize the KL divergence, i.e. the expectation of the negative log likelihood that we approximate by a second order taylor expansion. Then we should take the expectation of the whole approximation, right?" OYcdw5vOgIc "23. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 6667.0 0.0 1.0 0.0
"Why are people still using chalk on blackboards?" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11777.0 1.0 0.0 0.0
"great lecture" vcsxCFSLyP8 "6. Szemerédi's graph regularity lemma I: statement and proof" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 12976.0 0.0 0.0 0.0
"10:31 the [INAUDIBLE] thing is ""Weight""." k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 350.0 0.0 0.0 0.0
"In the example of y = x ^ 3, can we still say that the sum of the probabilities of all y can sum up to 1? I ask this since the curve clearly tends to infinite when y approach 0." H_k1w3cfny8 "10. Continuous Bayes' Rule; Derived Distributions" "6.041 Probabilistic Systems Analysis and Applied Probability" 6664.0 0.0 1.0 0.0
"he simplified my life!!!!

" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13113.0 0.0 0.0 0.0
"Man he sure looks old" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7572.0 0.0 0.0 0.0
"""Let's check our intuition using definition"" - this should be the obvious rule on how i should learn from now on" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 79.0 0.0 0.0 0.0
"These students must be really spoiled for not clapping their hands after each of this brilliant mans lectures. I am even forced to do it sitting alone in my room! :)" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 10427.0 0.0 0.0 0.0
"Good Video about Norms. Thank you Prof." NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4122.0 0.0 0.0 0.0
"to get Pi to a final digit multiply Pi  my a number say 8 and then dived it out by the same number ,if that's the desired exponent for required expansion or contraction" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14945.0 0.0 0.0 0.0
"Yes! Smart = ability to apply intelligence (which includes learning), intelligent = Knowing something already; Your intelligence quotient (iq) measures your level of ""smartness"" not your intelligence. Therefore the op meant intelligent. And for some people it takes more than one or two exposures to a topic to fully learn it, but once they do, they can apply it well." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12142.0 0.0 0.0 0.0
"42:43               45:56" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1186.0 0.0 0.0 0.0
"42:19 P = {{1/5, 0, 2/5}, {0, 1, 0}, {2/5, 0, 2/5}}" QuZL5IKpO_U "24b. Quiz 2 Review" "MIT 18.06 Linear Algebra, Spring 2005" 1178.0 0.0 0.0 0.0
"Geez...I like how his lecture is so slow" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3991.0 0.0 0.0 0.0
"Math is against the word of God we need to ban math, it goes against gods law" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7607.0 0.0 0.0 0.0
"linear approximation is what i like to call a ""taylor series striptease"" :D" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13804.0 0.0 0.0 0.0
"WTH IS T HIS, THIS ISN'T WHAT I LEARNED" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 11251.0 0.0 0.0 0.0
"Best linear algebra professor in the world. <3" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 2867.0 0.0 0.0 0.0
"Why is our world considered three dimensional? Why couldn't it be n-Dimensions?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11882.0 0.0 1.0 0.0
"Aaahhh Calculus was never fun before, Thank you Mr. Jerison. Lots of Love from Pakistan." PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2189.0 0.0 0.0 0.0
"i didn't catch ""rangle"" until the students pointed it out" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13356.0 0.0 0.0 0.0
"alot less people talking about how smart they are in this comment thread compared to pt1. :)" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12329.0 0.0 0.0 0.0
"Great course! Thanks a lot!" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 4220.0 0.0 0.0 0.0
"Blessing to all peoples those are related to mathematics field" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2903.0 0.0 0.0 0.0
"Without solving the problem, how could we tell that a matrix has an inverse?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11972.0 0.0 1.0 0.0
++ RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 250.0 0.0 0.0 0.0
"just say wow.
" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 13741.0 0.0 0.0 0.0
"oh whats that? tinyurl com/c93b4vv Imperial being higher than CALTECH in YOUR profession? by a US source(more likely to favor US unis) .. dont call other unis shit for no reason. Even though it is an old comment the ignorance is just amazing and managed to ruin my mood." 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14113.0 0.0 0.0 0.0
"excelente clase del producto punto, me encantan las clases del MIT." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12810.0 0.0 0.0 0.0
"The voice clarity is very clear . Awesome work by MIT OCW." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10317.0 0.0 0.0 0.0
Thanks! 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9821.0 0.0 0.0 0.0
"small Ps and capital Ps could have been written better on the board. But, a great lecture as always!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14321.0 1.0 0.0 0.0
"miyvarxar gilbert MIYVARXAR" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 13955.0 0.0 0.0 0.0
"@Santakingkong Sorry, now i think i got what u were saying. i think u meant to write ""I think P U L is a subspace only IF ( not 'in') line L lies in the plane."" That makes completely sense. Thanks." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 1716.0 0.0 1.0 0.0
"Funny accent" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3957.0 0.0 0.0 0.0
"Do not all speak at once...in vacant class😅😅" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 3410.0 0.0 0.0 0.0
Ć NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15538.0 0.0 0.0 0.0
"41:41, their ""Gauss given order""... that's a way to put it" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1158.0 0.0 0.0 0.0
"54 dislikes, 2400 likes, there is a 54/2454 = 2.2% chance someone watching this will be unhappy" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 1350.0 0.0 0.0 0.0
"You're clearly too smart for one of the best science universities in the world if you know what the first lecture in a class is about. You could probably ace every subject at MIT without studying." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12249.0 0.0 0.0 0.0
camera... VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 12593.0 0.0 0.0 0.0
"Very clearly explained!" EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 11165.0 0.0 0.0 0.0
"There are no students...!!!" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10351.0 0.0 0.0 0.0
"love seeing teachers look at notes" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13871.0 0.0 0.0 0.0
"Can someone, please, provide the link to full playlist for this course?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3104.0 0.0 0.0 0.0
"he really looks like a genious..amazing lecture.." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13111.0 0.0 0.0 0.0
"maybe he just appreciated guys having fun with math xD" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 13928.0 0.0 0.0 0.0
"@@ I guess I'll just skip this cos sin stuff since I'm not really in physics. " kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1579.0 0.0 0.0 0.0
"I am not clear about Prof Strang's explanation at 37:22. He said we choose the eigenvector basis [0 1]^T and [1 0]^T, but this is the standard basis in R^2, right?

Does he mean that if the input and output basis are the eigenvector basis, then the transformation matrix A is just Λ?

Thanks." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5122.0 0.0 1.0 0.0
"I am econ Student and have studied Regression in my statistics class but never was able to understand how exactly was it connected to Nullspace and Column Space . Totally a new persepective  , Thanks a lot for this series Prof Strang and MIT" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 5086.0 0.0 0.0 1.0
"It is so beautiful when you finally understand and can figure out those  e matrices quickly and put it together into one transformation matrix." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6965.0 0.0 0.0 0.0
"How come at 45:55 when -2*(-y) it's -2 instead of +2" aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4821.0 0.0 1.0 0.0
"i guess there are no students because strang did this on sunday and said look my video for lecture 10 on monday :D" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 13384.0 0.0 0.0 0.0
"Normies in the comments can't understand MIT lectures, nothing incredible about this xD" yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 7912.0 0.0 0.0 0.0
"Could any one please tell me why the vector f towards outside of the circle? Isn't the rule of physic tells that the force is towards inside the circle? Thank you very much." xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3223.0 0.0 1.0 0.0
"Is there a link to the notes Prof. Strang keeps alluding to?" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6819.0 0.0 0.0 0.0
"I wish this guy was my teacher :() " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6231.0 0.0 0.0 0.0
"You are the best professor, thank you." rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12181.0 0.0 0.0 0.0
"""If you have good eyes you can see that's a linear equation.""
39:40

😂😂😂" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 70.0 0.0 0.0 0.0
"Does he want students to shout out answers?  Because I'd be talking a lot.  I'd have to ask him, if he just meant us to think about it or to say it." Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 3455.0 0.0 0.0 0.0
"OMG I failed algebra. Now I'm listening to MIT math....." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7979.0 0.0 0.0 0.0
"I am finally learning the basics of linear algebra." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5088.0 0.0 0.0 0.0
"actually logarithm is the deviation of the name of some arabian scientist called al khwarizmi  " _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12304.0 0.0 0.0 0.0
"I think I could watch this like TV" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 5996.0 0.0 0.0 0.0
"thanks mit 
I'm form Iran" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14593.0 0.0 0.0 0.0
"thank you Mr Strang for your lecture!!! i don't understand yet the fact that with 2 millions subscribers, only 4000 folow your lecture!! Your chain is one of the best i found regarding basical science, congratulations!!!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 14486.0 0.0 0.0 0.0
"Why do i think that the class is totally dumb." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 11823.0 0.0 0.0 0.0
"Respect to you, professor ! Now I'll get AA in this subject." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 8561.0 0.0 0.0 0.0
"First comment;
I am preparing for AP exam, and this helped me alot to get me a full mark 5/5
Thank you Mr.Jerison!" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3815.0 0.0 0.0 0.0
"Why some people thumbed down on this? This is just priceless." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11912.0 0.0 0.0 0.0
"It's an extraordinary and amazing one.. No other lecturer are as good as Gilbert... 
Thank you sir........" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7028.0 0.0 0.0 0.0
"您是我见过的最好的老师，祝您身体健康   
You are the best teacher I have ever met. I wish you good health" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15629.0 0.0 0.0 0.0
"Hyothesis testing is the weakest subfield in mathematics" phbw9r1iUDI "7. Parametric Hypothesis Testing" "MIT 18.650 Statistics for Applications, Fall 2016" 4917.0 0.0 0.0 0.0
"skip from 26:00 to 35:00" yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 14316.0 0.0 0.0 0.0
"Full respect to Prof. Strang. So excited to see his insights to trendy technologies and he breaking down how it works." hwDRfkPSXng "Lecture 32: ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3950.0 0.0 0.0 0.0
"Thank you, Professor Strang! I've learned a lot from your lectures! Stay healthy!" rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9513.0 0.0 0.0 0.0
"sorry for much comments i am searching a chartable relationship to Japanese method of multiplication pardon, so excited" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 14373.0 0.0 0.0 0.0
"@phurt89 @xnbentari
yeah im learning the basics of this in yr 9 in australia, and came here to learn more before i go into senior school" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1974.0 0.0 0.0 0.0
"at time 1:12:36, the instructor stated the expectation to be P. What is P representing here? In the case of the statistical model, P represents the Family of Distributions......" TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 12478.0 0.0 1.0 0.0
"32:39 when you run into your ex" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 935.0 0.0 0.0 0.0
"interesting exciting" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 13617.0 0.0 0.0 0.0
"Thanks,very clear" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 9854.0 0.0 0.0 0.0
"It doesn't affect the teaching, but if affects the learning (especially of those who were late)" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6914.0 0.0 0.0 0.0
"Awesome video sir! Thank you!" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2774.0 0.0 0.0 0.0
"MIT students haven't seen the law of cosines ... smh" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7545.0 0.0 0.0 0.0
"12:56 paraboloid" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 400.0 0.0 0.0 0.0
"What does it mean min(X,Y) and max(X,Y) in 22:00 ?" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 11491.0 0.0 1.0 0.0
"The question he actually meant/wanted to ask is the one he asked at 26:00 which is essentially the same as the one you pointed out and would equal your second interpretation. Because if all columns are INdependent the subspace would be 3D (in R4) but if the 3e column would be Dependent the subspace would be 2D (in R4) and the 3e column would just be a variation (linear combination) of the 1e and 2e columns. By the way, the only 4D subspace in R4 possible is R4 itself." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 10263.0 0.0 1.0 0.0
"Few people get here" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 3754.0 0.0 0.0 0.0
"Why were there so many dislikes?" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11932.0 0.0 0.0 0.0
"32:40 A misktake here: shoule be SΛ^100C" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 936.0 0.0 1.0 0.0
"@junior1984able do you clearly know what cos and sin are?" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1909.0 0.0 1.0 0.0
"I dont even know why I'm watching this .." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5363.0 0.0 0.0 0.0
"At which time do the blackboards become visible?" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 2733.0 1.0 0.0 0.0
"Dear Professor, Linear algebra is fascinating. I had difficulty understanding Algebra because I could not see beyond the symbols and notations. But I did not realize before that algebra is a symbolic language to express geometric shapes." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3333.0 0.0 0.0 0.0
"10:25 Can somebody explain why did he say that S union U doesn't form a subspace??" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 347.0 0.0 1.0 0.0
"I live in Minnesota and when I try to watch these it tells me this video is not available in my country. Why is that?" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5710.0 0.0 0.0 0.0
"After reading so many texts finally some actual geometric interpretation of L1 and L2 ...he explains it so beautifully.Came here only to understand definition but his charsima made me watch whole 50 mins" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2250.0 0.0 0.0 0.0
"I wish you were my actual teacher, but I guess this will do! Great vids, great teachers." 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6237.0 0.0 0.0 0.0
"lol this guy's accent is hilarious." 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 13833.0 0.0 0.0 0.0
"I actually consider Professor Gilbert Strang to be one of my heroes 🏆❤️🙏🏽🎊" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 5011.0 0.0 0.0 0.0
"i hated this class. I found it useless." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 13392.0 0.0 0.0 0.0
"This is what we learn in 4 classes of same length" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 10771.0 0.0 0.0 0.0
"""Me and the guys in the nullspace""" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 87.0 0.0 0.0 0.0
"Always interesting to hear how bad the questions are from the students. Really begs to question the standards they have for admissions." Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2331.0 0.0 0.0 0.0
"""today was all letters, numbers next time"" 😌😌" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 184.0 0.0 0.0 0.0
"You repeat for the rest. Remember You now have not only the number that zeroes lets say A but also B that you can use! see the second part of the video to learn why!" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12234.0 0.0 1.0 1.0
"Thank you, MIT OCW and Professor Strang." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9497.0 0.0 0.0 0.0
"Spivak's calculus might be to confusing for someone that's starting, but is an awesome book." dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 8870.0 0.0 0.0 0.0
"I think Indian teachers are far better than mit teachers. And we study this in our 12 grade." V3Wg_jrMSQY "Lecture 19: Differentiation Rules, Rolle's Theorem, and the Mean Value Theorem" "MIT 18.100A Real Analysis, Fall 2020" 5999.0 0.0 0.0 0.0
"He explains it so clearly its amazing. Instead of just throwing around the definition of it all he actually explains and gives examples on why and how it works, in a simplified manner." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4482.0 0.0 0.0 1.0
"This is amazing thank you for sharing this, I'm taking a computation course based on Michael Sipsers book, and having these lectures from the author himself is very nice change of pace sometimes if I feel like watching a lecture instead of reading the book. Both the book and the way Michael explains the material in these lectures are simply top notch. Again, thank you so much!" MGqoLm2aAgc "10. Computation History Method" "MIT 18.404J Theory of Computation, Fall 2020" 10613.0 0.0 0.0 1.0
"I m in love with  how humbly he finishes his lecture.His lecture will be Immortal." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5863.0 0.0 0.0 0.0
"In the case where x approaches 0 in the expression of (cosx-1)/x, one can find the value of the expression using geometric intuition.

When ""angle x"" approaches 0 then the arc length ""x"" becomes equal to sinx, just as Professor explained in the video. But (cosx-1)/x is another nut to crack.

Let there be a *single* triangle made by the radius of the unit circle and the x-axis with hypotenuse ""H"", adjacent side ""A"" and opposite side ""P"". Let the angle made by the radius to the x-axis be ""x"". Now let's take a look at (cosx-1)/x

We know from Professor's explanation that Arc length *""x""= sinx* (when x approaches 0), so put the value of x=sinx in (cosx-1)/x, and we can write (cosx-1)/x as:

*(cosx-1)/sinx*
Rearrange it as:

*(Cosx/sinx) - (1/sinx)*
Note that (Cosx/sinx)=A/P and (1/sinx)=H/P {basic definitions}

(cosx-1)/x=
(A/P)-(H/P)=(A-H)/P

Now take a look at Hypotenuse and the Adjacent side.
As angle x gets smaller and smaller, Hypotenuse moves towards the adjacent and when x becomes infinitesimally small, *Hypotenuse ""H"" will nearly become equal to Adjacent ""A""* ( or you can say that ""H"" will nearly superimpose on ""A"")

Therefore *H=A* for a very small angle x.
So :
(cosx-1)/x       =(A-A)/P=0

P.S》I thought about sharing this because there were a lot comments regarding this problem. I'm not trying to act like a nerd or genius, as I have been learning calculus for only some time and and it is pretty obvious that my skill is infinitesimally weak with respect to that of the Professors of MIT. This is what I've leart from his geometrical approach." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6659.0 0.0 0.0 1.0
"I actually just took a formal linear algebra class at my university and it's crazy how the lectures are so similar. So I feel at least I'm getting a good education from my uni for a good price." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 5017.0 0.0 0.0 0.0
"this guy so cool" tBUHRpFZy0s "24. Classical Inference II" "6.041 Probabilistic Systems Analysis and Applied Probability" 14840.0 0.0 0.0 0.0
"omg... this cameraman..." YAo1sd4kuOQ "2. Forbidding a subgraph I: Mantel's theorem and Turán's theorem" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 14144.0 1.0 0.0 0.0
"I wonder how many people in this class have actually taken calculus before. Something tells me that the level of the presentation is not intended for an introductory level. Feels more like a master class" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6241.0 0.0 0.0 0.0
"This class was so good and his explainations are so lucid." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10482.0 0.0 0.0 0.0
"looking like Jimmy Dore on the thumbnail" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 13851.0 0.0 0.0 0.0
"This is his first lecture that I watch about a topic that I didn't previously know. Now I can finally see how brilliant he is at explaining because I have never heard any of this stuff before and it still makes sense the first time I hear it. My brain almost exploded at the complex and yet simple beauty of what he's explaining. It's almost like he's doing a magic trick because we know all the laws of math and he can just take them and make something possible that I never would have thought possible." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10675.0 0.0 0.0 0.0
"So nine columns is a plane with vectors that normalize the matrix to be a sort of 8th dimensional plan e in a 9 dimensional space that would be simple to resolve with every right hand side manipulation and will not be at all difficult to understand as shown here.  Let me create a matrix and a fabricated vector and think of it as one of these and two of those and get a component of a 1 and a 6 or 7 plus a 12 and a 3 - but that's not the right way to do it." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8783.0 0.0 0.0 0.0
"@ Brian Ebers: As he said, can be used to solve problems in physics. More generally, multivariable calculus is a stepping stone to more advanced topics like differential forms and tensor calculus." 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1484.0 0.0 0.0 1.0
"Thank you so much for releasing this course :)." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9366.0 0.0 0.0 0.0
"A este hombre ,le deseo mil vidas mas a su vida ,es una gran persona con un amor a expandir el conocimiento  hacia todo rincón del planeta ,Que con decir millones de gracias no es suficiente .Gracias por existir,gracias por tu contribución desinteresada a ayudar al projimo ,Dios  te bendiga grandemente" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2110.0 0.0 0.0 0.0
"Great job. What's more, Professor Miller's voice is like Steve Jobs'. It's beautiful." Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4238.0 0.0 0.0 0.0
"I don't get it, why does he subtract 2? 18:05" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5307.0 0.0 1.0 0.0
"thabk you subtitles T_T" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14446.0 0.0 0.0 0.0
"sorry i got lost at 32""14 what exactly happened with how he got the last row of that matrix which was almost an identity ?
" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14375.0 0.0 1.0 0.0
"This guy is a good teacher, but he leaves some points out, in which case you really have to just sit down, pause the video, and go through the steps he's doing very carefully. Especially for the geometric proof. But it's very understandable." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10516.0 0.0 0.0 1.0
"27:00
To find the combination you're going to scale the first one by a and the second one by b, then try to find c:
From first column: 2a+3b=5
From second column: a+b=7
Working on first:
2(7-b)+3b=5
b=5-14=-9
Working on second:
a=7-(-9)=16
So:
16.r1 - 9.r2 = r3" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 811.0 0.0 1.0 0.0
"Lots of love" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7429.0 0.0 0.0 0.0
"First Solved Example: 20:42" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 3814.0 0.0 0.0 0.0
"What fascinates me are some stats you can find below this video. Maybe it's some bug but youtube tells us that this video is most popular among:
1) men 45-54 yo
2) men 35-44
3) men 25-34
Which I find really strange cause I've thought that most of viewers would be actual students.
Also, popularity by region is interesting stat." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 11493.0 0.0 0.0 0.0
"Please record mathematical statistics 18.655, thanks!" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8211.0 0.0 0.0 0.0
"This is maybe the best lecture in the entire course." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 10689.0 0.0 0.0 0.0
"Frobenius norm squared = trace of (A transpose times A) = sum of eigenvalues of (A transpose times A) = sum of squares of singular values" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3923.0 0.0 0.0 0.0
"Thanks for you great lecture!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9742.0 0.0 0.0 0.0
"Even though, It was not complicated at all, I  felt so overwhelmed." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3592.0 0.0 0.0 0.0
"thats easy lol" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14651.0 0.0 0.0 0.0
"La matriz adjunta debiera de estar transpuesta en la fórmula. minuto 44:40 and beyond.                     adj()^T.                                                                          El profesor lo infiere en el cálculo (por cierto, gracias por su trabajo)" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7244.0 0.0 1.0 0.0
"xD it was tough, but WE MADE IT THROUGH!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 15456.0 0.0 0.0 0.0
"Hope you are alright professor alex. You are really a star in this field. 
I will probably work on this number once I reach 32." 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4789.0 0.0 0.0 0.0
"Fisher proof is awesome!" JTbZP0yt9qc "6. Maximum Likelihood Estimation (cont.) and the Method of Moments" "MIT 18.650 Statistics for Applications, Fall 2016" 3826.0 0.0 0.0 0.0
"a*X +b*Y=c*Z :FIND X,Y,Z AS FUNCTIONS OF a,b,c Mr. Professor if you are so smart!
 I am the first person who discovered these functions and I AM AN AMATEUR!!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12297.0 0.0 1.0 0.0
"can anyone help me how  he got  values 0 and 1 during  derivation of cosine and sine" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12606.0 0.0 1.0 0.0
"Where's the pdf for the exam that he is going through in this video?" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 11701.0 0.0 0.0 0.0
"after 10 years, I still cannot clearly understand why the dimension of the null space is n-r..." or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12305.0 0.0 1.0 0.0
"Why do physicists avoid using/thinking in terms of basis? why are they unwilling to bring them in?" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11824.0 0.0 0.0 0.0
"I really want to thank MIT OCW fore the opportunity to really learn calculus, and even better, from one of the best places in the world. We don't have this kind of teatching here in Brazil, not anywhere near this. I'm very thankful for you opening this class to everyone." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5937.0 0.0 0.0 0.0
"@IIAOPSW umm KwH is energy.  If it wasn't multiplied by hours, then ya it would be per unit time.  Also he lives in the U.S." jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1639.0 0.0 1.0 0.0
"why are lectures 8,17,26,34 missing from the playlist?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15282.0 0.0 0.0 0.0
"so many chalkboards!!!
" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 14338.0 1.0 0.0 0.0
"holy shit....18.06 for life" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 13184.0 0.0 0.0 0.0
"How are the students getting picked up on the microphone? I think that it is neat as it is usually difficult to hear the students’ questions." or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4802.0 1.0 0.0 0.0
"love it
" P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 13866.0 0.0 0.0 0.0
"So much better than watching Netflix...Thanks a million both teachers are awesome!" CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8776.0 0.0 0.0 0.0
"This lecture is what MIT means in this world!" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10815.0 0.0 0.0 0.0
"Sometimes Maths feels like a religion. Have faith on me till I prove it. At least he proves it." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8846.0 0.0 0.0 1.0
"Amazing lectures" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 2377.0 0.0 0.0 0.0
"Cutest teacher! EE starts counting from 0, we start counting from 1. Actually they probably right." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 3269.0 0.0 0.0 0.0
"thank you mr steve jobs!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14502.0 0.0 0.0 0.0
"Plus, diversity is awesome!" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8221.0 0.0 0.0 0.0
"Who is Monica?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 11737.0 0.0 0.0 0.0
"We are already study in class 11th
And they study in college
Indian education is higher than America" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11312.0 0.0 0.0 0.0
"I cant get the link of the complete course :/" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5233.0 0.0 0.0 0.0
"1A-5 What are the ij-components of a plane vector A of length 3, if it makes an angle of 30 degrees with i and 60 degrees with j. Is the second condition redundant?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 605.0 0.0 1.0 0.0
"Thanks!!! I am from Brazil and is very wonderful see videos like this!!!" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9838.0 0.0 0.0 0.0
"ROFL THE GUY FROM 38:30 TO 38:50 AT THE BOTTOM IS SLEEPING" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8489.0 0.0 0.0 0.0
"If Denis Auroux was my math teacher all my life Euler would be eating my dust." sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6463.0 0.0 0.0 0.0
"19:40 ""Mewtwo is below lambda one"" I've never heard of that Pokemon, is it new?" AdTvkFsqcDc "16. Derivatives of Inverse and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 565.0 0.0 0.0 0.0
"I'd advise you to read Dr. Strang's chapter on Integration before you attempt to make sense of this lecture.  The lecture moves quickly and instructor assumes the students understand integration" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6275.0 0.0 0.0 0.0
"what is the textbook for this course?" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15173.0 0.0 0.0 0.0
"I'm not sure what you're talking about. If you look at any of the other lectures in this series you can see people in seats while he is talking. & at the end of some of the lectures you can see students getting up from their seats. That doesn't happen in this video. Also, in this video, he makes some comment like ""Don't all speak at once"" which seems to be a reference to the fact that there is no one there. What does the fact that you can't see them have to do with how good they are as students?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 6357.0 1.0 0.0 0.0
"Toller Vortrag! Vielen Dank Professor!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11055.0 0.0 0.0 0.0
"excellent lecturer, but terrible cameraman!.. The cameraman, has no mathematical background of whatsoever, and it is frustrating how s/he either to slow or to fast to zoom in and out of the pictures, during the respective lecture!.." 3eiio3Tw7UQ "19. Weak Law of Large Numbers" "6.041 Probabilistic Systems Analysis and Applied Probability" 12824.0 1.0 0.0 0.0
"Why did he take the example of China rather than French 😂" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11810.0 0.0 0.0 0.0
"very sad way to explain polynomial decomposition, I'de rather go with the french way ""members identification"", its way easier and faster" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15034.0 0.0 0.0 0.0
"On 21 minute I don't understand where these matrices come from and why we need them. Anyone care to elaborate?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 8065.0 0.0 1.0 1.0
"Great course! I really enjoy it :-) Especially the lectures about cyclic and toeplitz matrices are very interesting. Mostly because I came across toeplitz before and wondered that Lapack doesnt seem to have any special routines for block toeplitz and alike.( if I now remember correctly what I was searching for...) 
Seems like there are some structures behind these matrices such that calulations reduce quite signigicantly ... even for block-Toeplitz? And therefore only quite a few codes out there for block toeplitz?   Talking about big to very big Ax=b systems (1 Mio unknowns on a normal laptop computer), inverse of Hessian matrices, fairly sparse, nearest neighbour interactions" hwDRfkPSXng "Lecture 32: ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4219.0 0.0 1.0 0.0
"Best Explanation" CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 2852.0 0.0 0.0 0.0
"this is the most usless think i have ever seen in my life...here let me tell you what the answer is . WHO! the EFF! cares, over, what a waist of time, to the, LAME!!! to the 25th power of i feel sorry for whoever finds this interesting." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14885.0 0.0 0.0 0.0
"Best Class I have ever seen...Wish I could be one of the students sitting in the classroom." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2851.0 0.0 0.0 0.0
"Automated motion-tracking is a solution searching a problem. :/" BYR1fXW95zY "Lecture 13: Lp Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 2748.0 0.0 0.0 0.0
"16:56 IT'S CORONA TIME *_*" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 494.0 0.0 0.0 0.0
"https://www.youtube.com/watch?v=13r9QY6cmjc#t=29m29s how does one know that u0 can be expressed in terms of eigenvectors, i.e. how do we know what u0 is in the span of eigenvectors?" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 13269.0 0.0 1.0 0.0
"It has been an honour, Prof Strang" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 6917.0 0.0 0.0 0.0
"Please @mitopencourseware. Please label each video with the content covered in the video! I'm begging you!" WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8197.0 0.0 0.0 0.0
"why is it that (N + 1) Cn + 1 / N +1  simplifies to Cn + 1 / (N+1) rather than just simplifying to just Cn + 1 ?" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15333.0 0.0 1.0 0.0
"why is a numerical low rank matrix hard to invert? he mentioned it briefly when introducing the vandermonde matrix but didn't clarify later." 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15327.0 0.0 1.0 0.0
"I don't understand why E[X|X>1]=1+E[X] if the first try fails? if the first try fails then how come there is +1 because +1 means that you obtain the HEAD at the first try? And if so how can we add 1 to that?" -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 5351.0 0.0 1.0 0.0
"Congratulations to all who made it, 🎉🎉🎉




and thanks to mit ocw for providing such high quality content" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3201.0 0.0 0.0 0.0
"What an amazing teacher, thank you!" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 11454.0 0.0 0.0 0.0
"Statistics are about knowing the distribution of the entire poppulation given the distribution of one dataset" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8891.0 0.0 0.0 0.0
"This guy's awesome." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10566.0 0.0 0.0 0.0
"Never in my entire life, i would have been able to convert that Fibonacci sequence in matrix form. Untill, he did it." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 7814.0 0.0 0.0 0.0
"at 5:56 he says that x1,....,xn are gaussian? what is each Xi denoting in this case?" phbw9r1iUDI "7. Parametric Hypothesis Testing" "MIT 18.650 Statistics for Applications, Fall 2016" 12466.0 0.0 1.0 0.0
"thanks again!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 14577.0 0.0 0.0 0.0
"Thank you, Prof. Gilbert and MIT OCW for the lectures." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9510.0 0.0 0.0 0.0
"People strolling in late to one of the greatest linear algebra lectures ever given." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 8172.0 0.0 0.0 0.0
"Thank you Dr. Gilbert, you made me fall in love with math,I hope everything is well.❤️🍀" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9100.0 0.0 0.0 0.0
"It's really crazy that rational, integer and natural sets are all the same cardinality" 9_xG0AGRa-w "Lecture 2: Cantor's Theory of Cardinality (Size)" "MIT 18.100A Real Analysis, Fall 2020" 7067.0 0.0 0.0 0.0
"@vex123 That's precisely my point. I'm putting in doubt how true it the 'world class' character or MIT, supousedly an institution reserved to high profile minds. If this is what you have for the first year, and if how you say, alumni have to learn 'by writing things down', thanks but I'm staying here in my free-of-charge public university, and I'll head to Lomonosov Univ. of Moscow for my post-grads! And I was more specific... not about writing things down or not, but about The Exposition..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2061.0 0.0 0.0 0.0
"Love you sir" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7467.0 0.0 0.0 0.0
"Are you teaching to an empty classroom for this class? Your ""I'm going to assume you're laughing"" comment led me to believe you were! Which is very impressive." 78vN4sO7FVU "Lecture 2: Bounded Linear Operators" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 2544.0 1.0 0.0 0.0
"i HAVE FAST TODAY. I really dont want to do any thing but i started your lecture and just get busy in dimensions. kudos to you Sir. you are my mood changer." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13321.0 0.0 0.0 0.0
"this woman seems really in love judging from the way she looks at him and talks to him haha :D" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 14927.0 0.0 0.0 0.0
"42:00 use SVD, the smallest SVD and square SVD" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1170.0 0.0 1.0 0.0
"Excellent episodes i watched them all, i learned a lot thank you MIT, thank you  Prof Auroux, sorry bye for now 18.02 :( , hey wait for me 18.03 i'm coming :D .. HAHA!" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3640.0 0.0 0.0 0.0
"thanks alot" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14578.0 0.0 0.0 0.0
"OMG! Like everyone else here the whole lecture series has been mindblowing! I have been obsessed with it for the past week putting around 5 hours per day just absorbing the material, it is magnificent! I always had problems with Linear Algebra and I have a Computer Vision Exam in two weeks that depend a lot on linear algebra. I tried somehow to get around it like I did with other courses but I then decided that enough is enough and I need to understand what Linear Algebra really is about. Never expected it to be that elegant and that simple! This is ART!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 7988.0 0.0 0.0 0.0
"not all." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14079.0 0.0 0.0 0.0
"What a beautyfull person" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11392.0 0.0 0.0 0.0
"East or West, Prof Strang is the best!" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3546.0 0.0 0.0 0.0
"4:51 geometric interpretation of differentiation
12:00 steps in computing slopes
21:50 check for the plausibility of computed slopes
25:30 the hardness in solving a problem involving calculus
33:50 use symmetry as a shortcut
37:00 the hardest part of calculus, the resolving of variable names" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1328.0 0.0 0.0 0.0
"Quality teaching!" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8471.0 0.0 0.0 0.0
"I HOPE THAT I COULD GIVE 2 THUMB UP!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4924.0 0.0 0.0 0.0
"You are doing so many people a favor by posting this. Seriously." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 12169.0 0.0 0.0 0.0
"43:16 I think there is a mistake here. That is not Newton's notation (which is usually noted with a dot on the top). The ""f prime"" notation like the professor wrote it should be Lagrange notation." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1200.0 0.0 1.0 0.0
"Hello sir I have a doubt in math 
Can you please help me" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4659.0 0.0 0.0 0.0
"Best chalk I have ever seen" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2854.0 1.0 0.0 0.0
"I'm proud to live on one planet with this honorable man. Both his lectures and his textbook are wonderful. The only textbook which was actually fun to read. And it was quite deep into the subject. Thank you, Professor." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6363.0 0.0 0.0 0.0
"Quite interesting." uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 8483.0 0.0 0.0 0.0
"Thanks so much, Professor Strang!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9791.0 0.0 0.0 0.0
"Well this is an awfully unknowledgeable math class. How does one get to multivariable calculus without a firm knowledge of trigonometry and vector geometry?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11361.0 0.0 0.0 0.0
"Are graphs build in Mapple? Recognized the commands, that were used" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 2524.0 0.0 0.0 0.0
"The first 5 minutes is like professor speaking alien language to me :'(" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 10107.0 0.0 0.0 0.0
"What is written on the board is not clear" V3Wg_jrMSQY "Lecture 19: Differentiation Rules, Rolle's Theorem, and the Mean Value Theorem" "MIT 18.100A Real Analysis, Fall 2020" 11544.0 1.0 0.0 0.0
"a great prof..   abstract maths can so easily taught .... Its amazing...... Great ..... hats off to u 
U should come up with simillar lect in analysis" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 12283.0 0.0 0.0 0.0
"Who else watched in 1.5x or 1.75x ?

Thanks, Prof. Strang.
Thanks, MIT OCW." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 11733.0 0.0 0.0 0.0
"Dear guys : any books recommended for accompanying this excellent course ? Thanks" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3335.0 0.0 0.0 0.0
"Thanks a lot for posting all this, it's really appreciated!" ZwpwmGP5ITM "Lec 34: Final review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9656.0 0.0 0.0 0.0
"Am getting an SVD tattoo." rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2343.0 0.0 0.0 0.0
"Column space is span of  pivot columns and dim(Colspace) (rank)= number of pivot cols
BUT !
Even tough dim(nullspace) = number of free variables, nullspace is not span of free variable columns. Have I just get it right? " yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 3165.0 0.0 1.0 0.0
"Great lecture, but i am confused by positive theta opening in clockwise direction." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4279.0 0.0 1.0 0.0
"If this is linear algebra.  I don't know what rubbish they are teaching in schools and colleges." TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 6528.0 0.0 0.0 0.0
"mathematics well thought" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13918.0 0.0 0.0 0.0
"One of the best teachers I've had pleasure to learn from - only online, but thanks to quality of content and ease of acces it feels almost as good.
THANK YOU MIT!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8093.0 0.0 0.0 0.0
"This Professor is simply amazing. So humble to teach and so thorough. Thanks for this!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10462.0 0.0 0.0 0.0
"thank you Prof. Strang for these" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14487.0 0.0 0.0 0.0
"I was skeptical seeing all the comments how he'd be. Considering how hard it is so jump en media res into a set of lectures and be clear, he does ok... But the moment he takes out the chain and they applaud him is one I'll never forget till I die. And that's why he gets the gold star. He may not have had the best technique in this one day, but I'll forever have that memory tethered into this topic." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6161.0 0.0 0.0 0.0
"Also at about 21:00 there is a good question from a student. He is confused on the variables x=x'(t) and y=y'(t), in some calculus books they try to avoid the confusion and represent it as x=f'(t) and y=g'(t)." XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2323.0 0.0 1.0 1.0
"basis of R^n spans the space of R^n, but at 43:46, the column space is R^3 and we had only 2 linearly independent vectors so how can it create a basis? because with only 2 vectors we cant span R^3." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 12512.0 0.0 1.0 0.0
"Liars figure & figures lie. Not quite what he said in the intro but pretty close--close enough in fact." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7347.0 0.0 0.0 0.0
"I should have begun this course earlier instead of turning it down because of the recording quality." 4UJc0S8APm4 "23. Classical Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 5965.0 1.0 0.0 0.0
"I'd say without any doubt that Professor Strang is the best Algebra professor in the entire world. I'm sure he has helped tons of students all around the world to understand the beauty of algebra" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6283.0 0.0 0.0 0.0
"JT  is an excellent lecturer! Easy to follow his explanations on stochastic processes!" P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 7122.0 0.0 0.0 0.0
"its not even fair how much better this guy is than my prof" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13714.0 0.0 0.0 0.0
"Mr Strang and MIT ,thank you so much." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 7709.0 0.0 0.0 0.0
"Math Rules :)" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7604.0 0.0 0.0 0.0
"Way of solving ❤️" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11310.0 0.0 0.0 0.0
"Man, it's crazy. I watch these MIT lectures on biochemistry or computer science, and they make me feel dumb. Then, I come to math/stats/machine learning (my areas of study) and suddenly they seem palatable and even easy at times. Knowledge can be so deep and so specialized that there is just no way any one person can have enough time to learn all of these topics!" hwDRfkPSXng "Lecture 32: ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7585.0 0.0 0.0 0.0
"I used this course for passing my Exam P from SOA. Great great course! Cannot recommend it enough. Prof. Tsitsiklis has an amazing ability to make abstract concepts super intuitive. e.g. Never had to remember any formulae for discrete space conditional probability. Transforming into the sub-universe was enough to compute all probabilities. All the TAs are great as well. 

Big Thank you to Prof. Tsitsiklis and everyone involved and of course MIT OCW for making this available to everyone! I am heading straight to the donations page :-)" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 6126.0 0.0 0.0 1.0
"50:45    [-1 0]
can be the vector space?" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 1340.0 0.0 1.0 0.0
"I Really Like The Video The Four Fundamental Subspaces From Your" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4997.0 0.0 0.0 0.0
"who else sees double and triple integrals as nested for loops..." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15260.0 0.0 0.0 0.0
"Can anyone help me understand, why the professor keep saying at 19:01 that we can't solve 4 equation with 3 unknowns?

Simple rule is if you have as many equation as unknowns then it's easy to solve but above statement has one extra equation so easy to solve.

Right?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 3037.0 0.0 1.0 0.0
"Sorry had a typo! o.o" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8854.0 0.0 0.0 0.0
"Linear Algebra useless? Silly boy, the very computer you're writing this comment on wouldn't exist without it... heck, nothing in the modern world works without the linear algebra being utilised in the background. Learn something before you share your lack of knowledge." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 7374.0 0.0 0.0 0.0
"Beautiful lecture. Thanks" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 2825.0 0.0 0.0 0.0
"Good Job Professor" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4110.0 0.0 0.0 0.0
"Adamın dibi" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2240.0 0.0 0.0 0.0
"I'm a freshman in college and I'm only taking BASIC ALGEBRA" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6295.0 0.0 0.0 0.0
"@Deliratio Good point, I had forgotten about that." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1614.0 0.0 0.0 0.0
"This must be the best lecture I have ever had." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10884.0 0.0 0.0 0.0
"Cool video
" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3212.0 0.0 0.0 0.0
"I don' even know why I go to my linear algebra lectures anymore. This guy is amazing." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 5295.0 0.0 0.0 0.0
"listening to professor Strang is like watching a sci-fi movie, time to time i start seeing the exact same concept in different view points." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 13809.0 0.0 0.0 0.0
"If all youtube content would be deleted today, the most upsetting thing for me would probably be losing this series of lessons." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6490.0 0.0 0.0 0.0
"He has clearly deep understanding  about what is he saying...excellent lecture!!🇧🇩🇧🇩" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 4489.0 0.0 0.0 0.0
"Really well explained! Thank you!" iZPzBHGDsWI "15. NP-Completeness" "MIT 18.404J Theory of Computation, Fall 2020" 8537.0 0.0 0.0 0.0
"these statistics do not suit for psychology" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 14782.0 0.0 0.0 0.0
"What are 8 rule for vector space.. which he never wrote. Any answer ???" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 11462.0 0.0 1.0 0.0
"oooow , he speak like the banana in rick and morty ! that satisfact me" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 14156.0 0.0 0.0 0.0
"no french" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14068.0 0.0 0.0 0.0
"Excellent teacher. The little touches like reinforcing important concepts as he's moving on to new ones that make use of them is very helpful." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 3675.0 0.0 0.0 1.0
"The course is so slow, and isn't this high school math, which we all had already taught in high school?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10062.0 0.0 0.0 0.0
"this was recorded in 1999." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14925.0 0.0 0.0 0.0
"If I need to understand this lecture to proceed with the rest of the course, I’d better just give up maths for life..." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 6471.0 0.0 0.0 0.0
"I remember my college years when sometimes I really needed to go back in time and check what the teacher just said, when the material was hard for me to understand, or I needed to draw a better conclusion. It's great that we have videos nowadays." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5948.0 0.0 0.0 0.0
"A lecture on the unit disk would be appreciated!" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 2129.0 0.0 0.0 0.0
"Sorry to say how small your brain is TBArKER, you check the MIT lectures only to check how many blacks are in there? That is incredibly unreal." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8859.0 0.0 0.0 0.0
"through single matrix transformation, the whole subspace will expand or shrink with the rate of eigenvalues in the direction of its eigenvectors, suppose you can decompose a vector in this subspace into the linear combination of its eigenvectors, so after many times of the same transformation, the random vector will ultimately land on one of its eigenvectors with the largest eigenvalue." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 14934.0 0.0 0.0 0.0
"Thank you for uploading these. It's always great to be able to watch education for free :)
I have a question about the course tho: I'm still very irritated that there hasn't been a single proof so far. Could someone please explain to me how the courses there work?
Like, is only half of the course uploaded? Or are the proofs in the books and they omit them in the lecture?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 9290.0 0.0 0.0 1.0
"I have seen many online lectures from Mister Strang when he was younger, and it saddens me to see him this old, yet still remarkably shrew. 
I hope he stays with us for a few more years until i can go to the USA and see him live." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5554.0 0.0 0.0 0.0
"Thank, Prf. Strang. 03/10/19" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9573.0 0.0 0.0 0.0
"Mit is doing a phenomenal job by uploading these" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7677.0 0.0 0.0 0.0
"Too much goog vedio" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 11066.0 0.0 0.0 0.0
"@RingWarrior12 maybe its for you, it helped me a lot!" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1709.0 0.0 0.0 0.0
Bravo! Xn8wL2ItzZw "Lecture 9: Limsup, Liminf, and the Bolzano-Weierstrass Theorem" "MIT 18.100A Real Analysis, Fall 2020" 2916.0 0.0 0.0 0.0
"Brilliant! helped me a lot...SKIP THAT PROOF LOL!!!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 2940.0 0.0 0.0 0.0
"I'd like have a Grammpa iquals him" QuZL5IKpO_U "24b. Quiz 2 Review" "MIT 18.06 Linear Algebra, Spring 2005" 6278.0 0.0 0.0 0.0
"28:28 Pushdown automata." m9eHViDPAJQ "4. Pushdown Automata, Conversion of CFG to PDA and Reverse Conversion" "MIT 18.404J Theory of Computation, Fall 2020" 837.0 0.0 0.0 0.0
"😂 ""extremely awkward lecturing to an empty classroom"" 😂 Good job though ..." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 15733.0 1.0 0.0 0.0
"King Gilbert Strang 🙏" lZrIPRnoGQQ "27. Backpropagation: Find Partial Derivatives" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7217.0 0.0 0.0 0.0
"Teaching in empty class and still remaining cool. Great professor!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9019.0 1.0 0.0 0.0
"Can anyone tell me why is it a must for (A^T)(A) to have an inverse? o.O" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3051.0 0.0 1.0 0.0
"""Einstein can do it."" I love it when he said that :)" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 44.0 0.0 0.0 0.0
"Would be nice to update the requirements of this course in https://ocw.mit.edu/18-217F19 because you start using concepts that you don't define (concepts that are easy to find the definition, but the course page says you don't require previews knowledge) this isn't true. With the simple concepts as colouring and stuff like that. Maybe a link to a Discrete Maths course would be good for the people that want to see this course and doesn't have the basic. This type of approach may discourage people of studying Maths because they would think they can follow and is because they don't know simple concepts that can be referenced or at least commented.
In any case, thanks for the free course." RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 12007.0 0.0 0.0 0.0
"2,3,8,9,10,11,12,13,15,16,25 - these are topics needed for economics&finance majors" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 614.0 0.0 0.0 0.0
"Thanks a lot !" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9650.0 0.0 0.0 0.0
Thanks! rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9827.0 0.0 0.0 0.0
"Usually it is a bit noisy in the beginning... I guess it is because the students open the door or something... But in this lec seems like the door was opened in the middle of the lecture... Late to the class maybe O.o...  :P " IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 11140.0 1.0 0.0 0.0
"Audio channels fixed!" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 2738.0 0.0 0.0 0.0
"Just finished the whole Single Variable Calculus course.
Thank you MIT OCW for making this possible.
Ukraine, 2016." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7174.0 0.0 0.0 0.0
"@sponsoredwalk1 
synechism
drupal/cfsv

The pdf there has a great derivation of it using the dot product & the idea of a normal vector ;)
" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2024.0 0.0 0.0 0.0
"well i got impressed at the begining, but when he stated the second eigenvalue i realized it is just the golden ratio... That does not demerits him, he's great!" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 15091.0 0.0 0.0 0.0
"In LU decomposition he assumed that l1*u1 will cancel first column of A. And he took u1 as the first row of A. But what if the first row of A have first element as zero." or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6614.0 0.0 1.0 1.0
"I got 0 0 -5 too. I don't know if we're right though?
" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5440.0 0.0 1.0 0.0
"I’d solve the cone problem like this:
The radius=r of a cone increases linearly at height=h, so if r goes from 0 at the h=0, to 4 at the h=10, then r=2 at the h=5.
The surface area of water is just a circle, so at h=5, it is 2pi*2 = 4pi.
The instantaneous speed of the height increase is the same as that of a cylinder with base area equal to the surface area of water at that height, so it’s just volume/time divided by area or 2/4pi = 1/2pi.

Or in other words: just calculate the surface area of water at appropriate height and divide the added volume speed by it." sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7108.0 0.0 0.0 0.0
"One to One 24:00" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 8115.0 0.0 0.0 0.0
"what are you talking about a cough?" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 15124.0 0.0 0.0 0.0
"The best math teacher" WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10003.0 0.0 0.0 0.0
"great teacher .........:)" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 13006.0 0.0 0.0 0.0
"44:18 He's still here 😂😂" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1233.0 0.0 0.0 0.0
"7:14 , error in subtitles.
He said ""recursive"" , not ""very cursive""" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1395.0 0.0 0.0 0.0
"17:30, ""You could have your car's milage counter count backwards from the point where the car will die and start walking."" Don't you just hate those walking dead cars?" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 510.0 0.0 0.0 0.0
"If the gradient is a vector, why isn't there any arrow on top of it?" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 6519.0 0.0 1.0 0.0
"Such amazing lecture ... this may be helpful too    https://youtu.be/XkY2DOUCWMU?list=PL2QY0xcsWhz6ghPUixeNQm47xapSKw4SM" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8942.0 0.0 0.0 0.0
"Thank You very prof. strang for this lectures. I always thought if prof. strang would have taught this lectures then it would be the best. Now we have this. Now I will get up early and my first task will be to complete prof. strang lectures. Thank You very much professor. Be healthy and long live." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9056.0 0.0 0.0 0.0
"I wish I had this guy for Calculus I and II. I can't believe how much of a difference something like having nice and clear handwriting makes!" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6203.0 0.0 0.0 0.0
"H is a n by n matrix, and v is a d-element column vector. H can not multiply v" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 4393.0 0.0 1.0 0.0
"The determinand-by-box definition was simply brilliant!" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 10074.0 0.0 0.0 0.0
0:50 FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 308.0 0.0 0.0 0.0
"Farmer Brown had two bushels of apples and one had twenty five apples and the other thirty apples - how many apples did the Government  allow him to sell?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3745.0 0.0 0.0 0.0
"@TheMadFedje I'd want this video in 1080p just for that." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1740.0 0.0 0.0 0.0
"Bizim okullarda anlatılan derslere bak bide bunlara bak, sonra ülkeler arasındaki farklara bak; sebebi belli oluyor." 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 2896.0 0.0 0.0 0.0
"anas hatem: If you think of the integral as the area below a curve, and you're splitting that area into infinitely narrow rectangles, then the height of such a rectangle is the value of the function f, while the width of that rectangle is dx. Taking the integral means you're summing up the area of all of those rectangles with area f(x) dx." sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12364.0 0.0 0.0 1.0
"why is there no explanation on what the pivots are and why you need them? It doesn't make sense to me why you only need to make the bottom left 0's when doing elimination

nvm i see that its because you need to eliminate one variable in one equation, two in the next, and then plug in the values for the third" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15346.0 0.0 1.0 0.0
Thanks 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9574.0 0.0 0.0 0.0
"20:32 I FuXX" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 658.0 0.0 0.0 0.0
"There should be a way to directly thank this professor after the lecture. So lucid and clear. Hats off Sir." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10383.0 0.0 0.0 0.0
"In the function
     w=a.x^2 + b.xy + c.y^2
x and y play the same role, there is a form of symmetry.
That means the sign of c would matter the same as the sign of a, right?
But how he ends up discussing only the sign of, and not that of c?!!

Anyone?" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6668.0 0.0 1.0 0.0
"I’m taking calc AB right now as a senior in high school and so far I know all this stuff but I plan on watching all the vids until I can understand it through these and then go over it again in class to make me double prepared this year, thank you so much MIT for this opportunity." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7117.0 0.0 0.0 0.0
"He is teaching probability through telling a story instead of saying again the formulas and definitions - what most teachers do." IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 4545.0 0.0 0.0 1.0
"Kids saw first time cycloid, and JEE students in INDIA remembering after solving ROTATION questions :)" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7214.0 0.0 0.0 1.0
"This seems like a good introductory course and I'm finding it helpful to review and refresh my previous knowledge. There is also a wonderful series of lectures from MIT done in 1970 by the amazing Herb Gross, called ""Calculus Revisited."" Herb is still alive and doing new videos on K-12 math. If you comment on his calculus videos, he might well reply. He is truly a unique and marvelous lecturer, and I highly recommend that series. You can find it on YouTube or on the same site this lecture series is on." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10918.0 0.0 0.0 0.0
"It's not big-Oh, I think it's big-omega" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7060.0 0.0 1.0 0.0
"SUPER LOGIC" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 8585.0 0.0 0.0 0.0
"36:49 it's (1/3)n^3 + (1/2)n^2 + (1/6)n for those wanting to know the exact answer." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 1045.0 0.0 0.0 0.0
"I love this sir teaching. Sir is so good at teaching" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5837.0 0.0 0.0 0.0
"37:11 It was I ... Dio!" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1055.0 0.0 0.0 0.0
"Finally, an intuitive understanding of plane equation Ax + By + Cz = D: all points (x, y, z) that have the same dot product D with the normal vector (A, B, C). It really drove me crazy when the first time I saw this equation in my textbook. Thank you!" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3793.0 0.0 0.0 1.0
"Derivatives are cool and all.. but have you ever tried a stuff crust pizza?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3357.0 0.0 0.0 0.0
"A city
records a population of 23,000 in 2006

The
statistical agency projects that by 2011, the city will hit a population of
34,000

1.      How can we calculate what the
population may have been in 2007, 2008, 2009, 
and 2010

2.      How can we calculate the percentage
of increase in each of these years?

3.      How can we estimate the population
in 2012, 2013, 2014, 2015 and 2016?

Thank you" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 2104.0 0.0 1.0 0.0
"@T22Lee Most unis" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1736.0 0.0 0.0 0.0
"@kaga13 I'm at 8hrs maths / week " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1914.0 0.0 0.0 0.0
"This is the greatest lecture of math i have ever attended" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10750.0 0.0 0.0 0.0
"Where's the hyperbolic functions...? " eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11700.0 0.0 1.0 0.0
"horrible. Don't max out your volume. There's nothing till you get a huge surprise at 1:15. 
One of the cameras is tracking the movement of the lecturer, and it makes me dizzy. The view of the blackboard is enough. Even in 2016, the camera man at OCW still can't master how to record good video lectures." WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 13188.0 1.0 0.0 0.0
"why is the third pivot number 5???" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15343.0 0.0 1.0 0.0
"Thank you so much, professor, for making these lectures free. I simply want to learn the logic and these videos seriously help. I realize that people have criticized the fact that we haven't quite gotten to some of the more difficult stuff yet. But I understand the value of a solid foundation." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9402.0 0.0 0.0 0.0
"Sadly I haven't watched all of his videos yet but does anybody pay attention to the fact that he almost never used fancy terminologies?  At least those terms like:  vectors being closed under addition, vectors being closed under scalar multiplications... are not being used at all this lecture and many other later lectures.  In 100 math professors, maybe 1 or 2 does thing like what this professor does.  I see this is how he made himself a highly respected professor.  That is simply  because he cares for and focuses on the understanding of the materials he is delivering rather than focusing nearly half a class time to explain what those terms are." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 8591.0 0.0 0.0 0.0
"3:13  ""going way back to greeks..."" :) well, sir, i think greeks are still in the world." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1112.0 0.0 0.0 0.0
"WHAT CHALK USES?" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11243.0 1.0 0.0 0.0
"Course starts on 13:23..." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3253.0 0.0 0.0 0.0
"2:48 if he said to differentiate everything, we could differentiate the absolute value function" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 873.0 0.0 1.0 0.0
"Lecture 1: Dot Product
Lecture 2: Determinants
Lecture 3: Matrices
Lecture 4: Square Systems
Lecture 5: Parametric Equations
Lecture 6: Kepler's Second Law
Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds)
Lecture 8: Partial Derivatives
Lecture 9: Max-Min and Least Squares
Lecture 10: Second Derivative Test
Lecture 11: Chain Rule
Lecture 12: Gradient
Lecture 13: Lagrange Multipliers
Lecture 14: Non-Independent Variables
Lecture 15: Partial Differential Equations
Lecture 16: Double Integrals
Lecture 17: Polar Coordinates
Lecture 18: Change of Variables
Lecture 19: Vector Fields
Lecture 20: Path Independence
Lecture 21: Gradient Fields
Lecture 22: Green's Theorem
Lecture 23: Flux
Lecture 24: Simply Connected Regions
Lecture 25: Triple Integrals
Lecture 26: Spherical Coordinates
Lecture 27: Vector Fields in 3D
Lecture 28: Divergence Theorem
Lecture 29: Divergence Theorem (cont.)
Lecture 30: Line Integrals
Lecture 31: Stokes' Theorem
Lecture 32: Stokes' Theorem (cont.)
Lecture 33: Maxwell's Equations
Lecture 34: Final Review
Lecture 35: Final Review (cont.)" wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 7281.0 0.0 0.0 0.0
"The permutation matrix is the matrix needed to exchange rows. Such matrix must be the transpose of the identity matrix and it should be right multiplied by the input matrix. To do column exchange, we left multiply by the input matrix." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10225.0 0.0 0.0 0.0
"35:21 how does he come up with that solution? Sounds so random" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 1008.0 0.0 1.0 0.0
"In the computation of the Eigen values for A², he used A = SʌSˉ¹ to derive that ʌ² represents its Eigen value matrix. However this can be true only if S is invertible for A², which need not be always true.

For example, for the matrix below (say A), the Eigen values are 1, -1(refer previous lecture). This would imply that A² has only one Eigen value of 1. This would imply that S has 2 columns which are same (if it has only one column then it is no longer square and hence inverse doesn't apply) and hence non invertible. This implies that this proof cannot be used for all the cases of the matrix A.
 _       _ 
│ 0  1 │
│ 1  0 │
 ¯       ¯
Is there something I'm missing here?" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 6660.0 0.0 1.0 0.0
"could someone help me in this part 47:40, why it cannot be expressed and what does that mean?" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12689.0 0.0 1.0 0.0
"Computational Linear Algebra course" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 3189.0 0.0 0.0 0.0
"Professor Strang's introduction to projections using Fourier Series as an example generalizes to other orthogonal functions (Legrendre Polynimials, Bessel Functions, etc.).
This is pretty cool, because you'll see this stuff ad nauseum in electrodynamics, quantum mechanics and statistical mechanics." lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 8377.0 0.0 0.0 0.0
"Prof. Auroux, Thank you for these wonderful lectures" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8290.0 0.0 0.0 0.0
lmao 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13814.0 0.0 0.0 0.0
"hahahhahahahahaha I checked the comments after I watching the video of right ear.... poor me.." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13056.0 0.0 0.0 0.0
"He ties up all the loose ends in this lecture and in lecture 6, except that I don't know where lim k->infinity (1 + 1/k)^k comes from" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4616.0 0.0 1.0 0.0
"I am a computer science undergrad watching these lectures because I felt I needed to understand Linear Algebra better for two fields: Machine Learning and Quantum Information. It's incredible that both of these get some overlap with this linear algebra course (ML was touched on when we did projection matrices as that is exactly the closed form solution to linear regression), and now QI which uses Complex vectors spaces is being covered. 

:)" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 5051.0 0.0 0.0 0.0
"Since you claim you are so good in math, I suggest you go work on your English. It sounds garbled and fuzzy. 

After that, why won't you try to find your humility. I could probably guarantee you aren't as smart as you claim yourself to be/" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8681.0 0.0 0.0 0.0
"I am so glad that he is still blessing this world with his presence! I have hated maths all life until I encountered 18.06 last year!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5141.0 0.0 0.0 0.0
"man's a genius" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 13904.0 0.0 0.0 0.0
"A Taylor polynomial is series of increasingly close approximations." BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2096.0 0.0 0.0 0.0
"Every time I see a backboard in a thumbnail I think Aphex Twin meme." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 3602.0 1.0 0.0 0.0
"Gill gets savage on Trig 2:30" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4044.0 0.0 0.0 0.0
"Lecture 17 was not recorded because of Exam 2.  The next lecture is 18. " 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7264.0 0.0 0.0 0.0
"Is Gilbert Strang the God of Linear algebra? I loved this lecture :)" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6747.0 0.0 0.0 0.0
"I take much more time to finish watching the lecture , its about double time of the lecture if not more" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5988.0 0.0 0.0 0.0
"Ty for uploader" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 11107.0 0.0 0.0 0.0
"This series is Breaking Bad level high. Same highs and lows and tension and mystery and excitement" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10921.0 0.0 0.0 0.0
"The beauty of calculus is that the machinery itself is not complicated, there are limited tools, but the scope and application has been as wide as humanity's imagination.
You just have to develop the intuition and everything is easy then, good lectures by OCW, as always" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9988.0 0.0 0.0 0.0
"This lecture is especially beautiful.." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 10801.0 0.0 0.0 0.0
"Oh I voted for the fourth answer the plane as well, but I thought it was because 2 vectors(<1,2,3> and <x,y,z>) form two lines so they could define a plane which contains both of them, I was so wrong haha." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8000.0 0.0 0.0 0.0
"OK so this is really the area of a section of a hyperboloid from the last lecture." 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7974.0 0.0 0.0 0.0
"Thank you for this wonderful lecture" P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 9287.0 0.0 0.0 0.0
"this lecture of MIT is for electricl engenering student" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14895.0 0.0 0.0 0.0
"+1 for this :)" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 251.0 0.0 0.0 0.0
"in min 23:04 why didn't he apply the product rule to xy" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13591.0 0.0 1.0 0.0
"2020.5.8
From Korea🇰🇷" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 628.0 0.0 0.0 0.0
https://www.youtube.com/channel/UC4bDpTs5tRVdSQuPRn7Mv1g VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 13265.0   
충성충성 QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15691.0 0.0 0.0 0.0
"Thank you Prof Gilbert and thank you MIT OCW.

P.S: I just noticed that the comment section is dominated by men.... Come on girls, we can do it." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9178.0 0.0 0.0 0.0
"I took this class at community college. Aced it" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 6111.0 0.0 0.0 0.0
"I am very grateful to this teacher, this teacher's lecture has given me a strong interest in linear algebra. (In counting the number of viewers in this class, there are actually many Chinese viewers who watch it in other ways - like me, we all like your teaching style and think you are a good teacher!)😁😁😁" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5150.0 0.0 0.0 0.0
"Timestamps and Summary of Lecture 1: Basic Banach Space Theory 

0:00 - Motivation and Introduction 
Functional analysis works with vector spaces that are sometimes infinite-dimensional, using the techniques of analysis to study their structure & functions defined on them. Besides existing as a pure mathematical discipline, it finds applications in partial differential equations and physics. 

5:27 - Review of Vector Spaces
Vector spaces are defined over a field (here, R or C) and are closed under addition and scalar multiplication. Every vector space has a basis, or a maximal spanning set; its dimension is the cardinality of any basis (this is well-defined). e.g. Finite-dimensional vector spaces over R: R^n (n-fold Cartesian product)

13:46 - An Infinite-Dimensional Vector Space
The set of continuous functions from [0, 1] to the complex numbers forms a vector space (sum, multiple of any elements are still in the VS). But the countably infinite set {1, x, x^2,...} is linearly independent in C([0, 1]). 

16:26 - Norms 
To perform analysis, we require a concrete notion of ""proximity"" or ""size"" on our spaces. A norm assigns to each vector in a vector space some nonnegative real number; as a map it is positive semidefinite, homogeneous, and satisfies the triangle inequality. 
A seminorm is similar to (but weaker than) a norm; it satisfies the latter two conditions but is not necessarily definite. A vector space endowed with a norm is a normed vector space: these are central objects of study in functional analysis.

21:15 - Metric Spaces
A metric on a set provides a notion of distance between its points. It is an identity-indiscernible, symmetric, and triangle inequality-satisfying function; a space with such a distance function is called a metric space (has the metric topology) 

23:08 - Norms Induce Metrics
Given a norm on a vector space, it induces a metric in the natural way. This allows us to talk about ideas like convergence, completeness, etc. with regards to normed vector spaces. 

26:11 - Examples of Norms (and NVS) 
Euclidean norm on R^n, C^n provide us with the most familiar notion of distance. We can consider more broadly the family of norms called p-norms, of which the Euclidean norm is a special case (taking p = 2). When p = ∞ we consider the norm that picks out the maximal component of a vector in n-space. 

32:45 - The Space C_∞{X}
From a metric space X we consider the space C_∞{X} of all continuous, bounded functions from X to the complex numbers. This indeed forms a vector space - on it, we can introduce the supremum norm that measures the maximal value a function takes. This turns C_∞(X) into a normed vector space. If we take X to be some compact interval like [0, 1], the boundedness of continuous functions are automatic.

39:24 - The Supremum Norm and Uniform Convergence
When asking what convergence in this metric means for functions in C_∞(X), we find it translates to uniform convergence in the familiar sense from real analysis. 

42:20 - l^p-Spaces
The l^p spaces consist of p-summable sequences. When p = 2, these are square-summable, etc. and these are all defined to be the sequences on which the respective p-norms resolve finitely. 

46:38 - Banach Spaces
We are interested in special cases of normed vector spaces that mimic the situation/structure in Euclidean spaces, namely, their completeness. We have seen that norms (on vector spaces) give rise to metrics, with respect to which we make sense of convergence of sequences. Cauchy sequences are those whose terms tend arbitrarily close; every convergent sequence is Cauchy, but the converse doesn't necessarily hold (the rationals have many ""holes"": one can construct a sequence of rationals that close in on sqrt(2) but can't converge to it in Q). Spaces for which the converse does hold, i.e. Cauchy sequences converge, are complete with respect to that given metric. Banach spaces are normed vector spaces that are complete with respect to the metric induced by the norm. 

49:52 - Examples of Banach Spaces
R^n, C^n are Banach spaces with respect to any of the aforementioned p-norms. These provide relatively trivial examples, but foundational ones. 

50:39 - C_∞(X) is Banach 
A useful nontrivial example - the normed vector space of continuous, bounded functions X -> C actually forms a Banach space with respect to the supremum metric. The process of showing that it is a Banach space amounts to exhibiting completeness, and is instructive in demonstrating the general procedure for showing that a space is Banach: first take a Cauchy sequence & come up with a candidate for its limit, then show that this proposed limit lies in the space, and finally show that the convergence does occur." uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 11016.0 0.0 0.0 0.0
"Up to lecture 6 done" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11129.0 0.0 0.0 0.0
"Great teacher" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4335.0 0.0 0.0 0.0
"what happens in this slot, stays in this slot.." gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 15143.0 0.0 0.0 0.0
"how could he define the last 2 A's columns? 15:10" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 13208.0 0.0 1.0 0.0
"This guy is great.  I studied engineering at a university less prestigious than MIT, and I remember professors refusing to explain their algebra steps.  They were like ""you should know this already""." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10535.0 0.0 0.0 0.0
"basically, I got lost after 1:30 xD" X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 12510.0 0.0 0.0 0.0
"""No mathematics went on there; we just got some vectors that were lying down to stand up.""" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 91.0 0.0 0.0 0.0
"If you're struggling to understand the Product Rule proof (he skips alot of steps) check out this video by Eddie Woo.  Much more clear :) https://www.youtube.com/watch?v=Xkm-V59j8Zw" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6564.0 0.0 0.0 1.0
"What a lol this stuff is studied in India in high school (even harder than this)" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11424.0 0.0 0.0 0.0
"13:00 subspace S is orthogonal to subspace T means: every vector in S is orthogonal to vectors in T.

Can anyone explain what is going on there?" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 404.0 0.0 0.0 0.0
"Thanks, Teacher !" AeRwohPuUHQ "22. Gradient Descent: Downhill to a Minimum" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9844.0 0.0 0.0 0.0
"@PhilOrzechowski he does it to make first order difference equations system out of second order
" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 1700.0 0.0 1.0 0.0
"Thanks for you good work sir, this is the technique which every civilian should keep in their tool bag." ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 9741.0 0.0 0.0 0.0
"linear algebra is immortal" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 13801.0 0.0 0.0 0.0
"Love the lecture, thanks Professor" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7453.0 0.0 0.0 0.0
"Any Indian is here" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2466.0 0.0 0.0 0.0
"I loved his sincerity when he thanks god @32:58" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 5856.0 0.0 0.0 0.0
"That matrix multiplication on minute 42 is on fire!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9906.0 0.0 0.0 0.0
25:26 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 780.0 0.0 0.0 0.0
"The law of cosines can be derived from the law of sines.  The law of sines can be derived from trigonometry." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10159.0 0.0 0.0 0.0
"Nice video thanks will use information to finish my book" 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 7865.0 0.0 0.0 0.0
"Words would not suffice the knowledge that you have given us Dr. Strang
Thank you very much for these lectures." hwDRfkPSXng "Lecture 32: ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11999.0 0.0 0.0 0.0
"As a non English native speaker university student, the first minute of the video is like the professor speaking alien language to me :|" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 2565.0 0.0 0.0 0.0
"27:07 minimizing something with a constraint Lagrangian Formulation." NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 815.0 0.0 1.0 0.0
"""The simmetrical is the king of the matrices and the Orthonormal the Queen""... and the Queen and her twin sister get together with their greek lover(*beat starts at background*) listening Isaac Hayes and... wait! what we're talking again?" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 123.0 0.0 0.0 0.0
"I never get sick of them; they're really cool to me." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5879.0 0.0 0.0 0.0
"I suggest anyone viewing this now goes and watches 3blue1brown's video on Duality... dot products / projections all make sense now in how they are encoded within each other... will help you understand what x = aTb / aTa actually means the ratio of the projection of b onto a : the length of a... but this is one hell of a lecture!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5981.0 0.0 0.0 1.0
"At 36:22, it is fascinating how he got a bit into the orbital mechanics, saying there are 6 unknowns (which is rightly known at the State vector, which is a 6 by 1 matrix with Position (x,y,z) and velocities (xdot, ydot, zdot))." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2651.0 0.0 0.0 0.0
"Where can I find lectures that are missing?" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11658.0 0.0 0.0 0.0
"Thank you, professor Strang and all guys insist on this perfect linear algebra lecture.
I started this lecture on 23/12/2021 and completed it on 08/01/2022 in Hong Kong, just before my new semester. I will remember this 18.06 forever, and professor Strang will be the best linear algebra teacher in my heart!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9523.0 0.0 0.0 0.0
"interesting video and very informative" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 13620.0 0.0 0.0 0.0
"Wow! The way he teaches is amazing...Thanks a lot.." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12054.0 0.0 0.0 0.0
"Finally watched all 36 lectures, this was quite intuitive and helped me to understand LA better, thank you Prof. Strang and MIT OpenCourseWare!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 3785.0 0.0 0.0 0.0
这个代课老师思路清晰，而且沉稳多了，比之前的那个老师好 Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15662.0 0.0 0.0 0.0
"A better zoom on the board please" EBdgFFf54U0 "Lecture 14: Basic Hilbert Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 2097.0 1.0 0.0 0.0
"Thanks MIT! You are giving chances for those who can't afford to go to expensive schools!

-Rommel from the Philippines" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9614.0 0.0 0.0 0.0
"I am so fascinated by the way that professor G. Strang  gives his lectures, he does it in such a  great way that even a 5 years old boy could understand , on the side , teachers from my university make the subject so complicated, that even highly above the avarege students struggle to understand the concepts poperly." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5140.0 0.0 0.0 0.0
"Georgia Tech > MIT

Our lectures and Calc 3 class is way harder..." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4004.0 0.0 0.0 0.0
"Not a single dislike. This video bring my faith to humanity back." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7914.0 0.0 0.0 0.0
"I Really Like The Video From Your Elimination with Matrices" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4954.0 0.0 0.0 0.0
"Is this for real undergradutes or is it an introductional course?" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6870.0 0.0 0.0 0.0
"(3, 3, 8) = -(1, 1, 2) + 2 * (2, 2, 5).
These three vectors are not linearly independent.  " yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 220.0 0.0 1.0 0.0
"I have to disagree with people on this....I think the lecture starts off good but then he speeds onto areas without clear explanation.....I was thinking that if there are any new students in his room to stats then they may struggle ....but then again it is MIT so I guess all the students in there are pretty much top of their class" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 5562.0 0.0 0.0 0.0
"@poyanator no. High School Calculus is nothing compared to a good freshman engineering calculus class. I assure you of this." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1978.0 0.0 0.0 0.0
"who are the 3 ignorant folks?" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15257.0 0.0 0.0 0.0
"Can someone tell me the meaning of 18.01,18.02 etc...." Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3100.0 0.0 1.0 0.0
"That was pretty good.

""Extra shipping charges apply to boxes with negative dimensions.""" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9923.0 0.0 0.0 0.0
"Wow, 15 years ago.. Prof. Strang looks like a kid!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12060.0 0.0 0.0 0.0
"Isnt grad(f) supposed to be [x by] instead of [2x 2by]?" AeRwohPuUHQ "22. Gradient Descent: Downhill to a Minimum" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6901.0 0.0 1.0 0.0
"Is this a good course for data analytics" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 6849.0 0.0 0.0 0.0
"Hi guys - I wrote an article on Inverse Matrices which was influenced by this lecture http://www.orrymr.com/post/inverse-matrix/ 
Writing it helped me understand a little better. Hopefully reading it can also be helpful." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4711.0 0.0 0.0 0.0
"Like watching someone like Aristotle teach" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 7362.0 0.0 0.0 0.0
"some of their behavior is really childish" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14359.0 0.0 0.0 0.0
"Why I hate math!  Where else is there guess work in math. 2+2=4 No guessing. Just do the procedure until the answer is revealed. But here, as you see in the video, we guess. We substitute, we try this and that. Pain in the butt!!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11766.0 0.0 0.0 1.0
"41:21 it would help if it were in shot" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1151.0 1.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8440.0 0.0 0.0 0.0
"Will the rest of this course be posted also?" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 11949.0 0.0 0.0 0.0
"I think this video further proves my point of view." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6078.0 0.0 0.0 0.0
"Compelling lecture (as always), but I'm unsettled about one thing: much of it is based on the fact that the first singular vector of A is the maximizing x in the definition of ||A||2. However, this fact just seems to be mentioned without proof or argument, and accordingly it doesn't feel as though the proof that ||A||2 = sigma1 is complete. Thoughts?" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3177.0 0.0 1.0 1.0
GOAT cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 3968.0 0.0 0.0 0.0
"The formula h= 80 -5t^2 is wrong but his principles are correct" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10115.0 0.0 1.0 0.0
"Can you please explain your question?" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3120.0 0.0 0.0 0.0
"Thank you so much, great teacher, I had to retake Probability subject 2 times, and never quite grasped it, teacher only followed what was written in the book, there were no added insights, with this single lecture I got it so much better." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 9401.0 0.0 0.0 0.0
"I actually liked the fact that he did an informal proof. Much better than doing the formal proof, cos that requires invoking Rolle's Theorem etc, which they don't cover in this course, presumably. 

Obviously, this course isn't meant to be extremely difficult. It's sort of a survey course, where the difficulty of the material is not so much. In that way, people who don't want to major in that subject don't have to face a difficult time if they want to learn something new." 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5018.0 0.0 0.0 1.0
"i'm sad for my left ear because it couldn't enjoy this fantastic lecture!!!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 13516.0 0.0 0.0 0.0
"Integrate from 0 to (1/2) x^3 arctan(x) dx to 4 decimal places." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6719.0 0.0 1.0 0.0
"Somehow after some thought I figured out why Prof says all upper triangular matrices are subspaces of 3X3 Matrices! If we add any 2 upper triangular matrices we are still in that space as also if we multiply with scalar any upper triangular matrices we are still in that space. Same with Symmetric and Diagonal matrices. But Prof assumes that all students will decipher this and he did not spell that out. Otherwise its a privilege to hear from a genius!" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 8832.0 0.0 0.0 1.0
"Better than my prof." phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2888.0 0.0 0.0 0.0
👍👍👍👍👍👍👍👍👍 l4NoMKEHQwM "11. Derived Distributions (ctd.); Covariance" "6.041 Probabilistic Systems Analysis and Applied Probability" 15711.0 0.0 0.0 0.0
"he is a fucking gift of god thx gilbert" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 13085.0 0.0 0.0 0.0
"i learned linear regression in a statistical lecture, but i think the linear algebra way of doing it is nicer and neater." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 13411.0 0.0 0.0 0.0
"i feel better about not having mastered taylor expansions now..." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13373.0 0.0 0.0 0.0
"Great summary in the first part of this lecture! Simple examples." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4334.0 0.0 0.0 1.0
"formula ,multimeter alternator," J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12895.0 0.0 0.0 0.0
"professor and MIT... the world stay better with this actions... thank you... thank you... Yes, he's a legend...." cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14219.0 0.0 0.0 0.0
"Is there a way to find the problem sets for this class?" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6829.0 0.0 0.0 0.0
"being confused for more than 20mins with FFT, still watched the whole lecture oops haha, omgg, good jobbbbbbbbbb!" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 12531.0 0.0 0.0 0.0
"Thank you very much professor, l love you" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9446.0 0.0 0.0 0.0
"If you made it till here, you are the best <3" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 6553.0 0.0 0.0 0.0
"Lol @ 41:15" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7394.0 0.0 0.0 0.0
"I have reached that step!!! Thank you Professor and MIT. And Congrats for all who also complete the course~" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5551.0 0.0 0.0 0.0
"good explaination though a little more rigorous derivation wud have helped lot... intended for overview" jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 12943.0 0.0 0.0 1.0
"Every time this guy says ""Poisson"" I think of Carl saying croissant
https://www.youtube.com/watch?v=dg2S08WAIAo" TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 3606.0 0.0 0.0 0.0
"LOL - you sound like a zoo in there!  (Et! Merci, docteur!)" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7232.0 0.0 0.0 0.0
"Thank you." OHiu2F18dFA "Lecture 7: Sigma Algebras" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 9546.0 0.0 0.0 0.0
"04/01/2022

I FINISHED IT!" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 291.0 0.0 0.0 0.0
"This is a heck of a lecture. The flags example is really great. Thanks Professor Townsend." 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10596.0 0.0 0.0 0.0
familiar-airity M2d4HsBsu8Y "Lecture 5: The Archimedian Property, Density of the Rationals, and Absolute Value" "MIT 18.100A Real Analysis, Fall 2020" 12840.0 0.0 0.0 0.0
"did you know your dream speed of thinking is faster than light speed you can test this using math immersion so you do calculus in your dreams then slip into lucid dreaming you might like to use the juice of safu even queens gambit" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12743.0 0.0 0.0 0.0
"Great lecture. Thanks a lot for posting this!" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4295.0 0.0 0.0 0.0
"Finished 18.06 on 05-06-2021. Thank you MIT OCW! Prof. Strang's enthusiasm is infectious and the entire series was amazing <3 
Anmol, India" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 3807.0 0.0 0.0 0.0
"He looks rather unsecure." WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 4573.0 0.0 0.0 0.0
"I dropped out of electrical engineering degree, and here it is, following me around with no chill. Maybe this is a sign lol" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 5378.0 0.0 0.0 0.0
"OMG I love dz!!! Thank you 4 posting this treasure" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 7980.0 0.0 0.0 0.0
"Incredible class. Thanks for the content and go on!" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 6703.0 0.0 0.0 0.0
"can I do this way ? : sinx.cosdx + sindx.cosx - sinx / dx  dx→0 =
sinx.cos0 +sindx.cox - sinx /dx dx→0 =
using aproximation that sinx = x = tgx when x is too small, we have:
sinx - sinx + dx.cosx /dx dx→0 =
0/0 + dx.cosx /dx dx→0 = 
cosx dx→0 = cosx !

can I ?" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12595.0 0.0 1.0 0.0
"omg retarded algebraic questions ....." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14140.0 0.0 0.0 0.0
"can't believe mit still uses blackboards..." PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12641.0 1.0 0.0 0.0
"Prof Gilbert Strang, I was supposed to attend your courses - Linear algebra and Matrix methods for ML as a prerequisite for my graduate program in Electrical engineering at UBC, Canada. I must say, I lost in track of time attending your lectures and you changed my perspective of thinking mathematics. Many Thanks and I owe you a lot for inspiring me. I wish to become a professor like you in future. Wish me well if you happened to see this message! Lots of love, from Simran Suresh, India" rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8265.0 0.0 0.0 0.0
"You are emancipation of Algebra thank you sir." lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 12170.0 0.0 0.0 0.0
"I fall" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 5389.0 0.0 0.0 0.0
"I don't know why but listening to prof Strang brings me so much inner peace" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5323.0 0.0 0.0 0.0
"Watching final lecture (done with course) 17 sep 2020 Libya. Thank you MIT" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11294.0 0.0 0.0 0.0
"It took me 3 months to finish this parllel to my college courses but worth it.
Thank you So much MIT and especially Professor Tsitsiklis for this amazing Series Of lectures" rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 6990.0 0.0 0.0 0.0
"back when ""who wants to be a millionaire"" was not popular" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 12506.0 0.0 0.0 0.0
"Thanks MIT" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9598.0 0.0 0.0 0.0
"24:13 Let's move to space <3 :D" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 729.0 0.0 0.0 0.0
"long time no see, dr.strang! 2year ago i watched linear agebra vedio" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13849.0 0.0 0.0 0.0
"thanks prof. now I can imagine what eigenvectors and eigenvalues are like." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 14599.0 0.0 0.0 0.0
"This is a masterclass. Thanks truly" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10598.0 0.0 0.0 0.0
"DR. Strang thank you for counting and verifying the Parameters in SVD, LU, QR and Saddle Points in numerical linear algebra." xaSL8yFgqig "Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3283.0 0.0 0.0 0.0
"nice, we covered a lot of multivariable calculus this year (a first for junior students in Hawaii) it was awesome, but since we also took AP Calculus BC during this year, it was a bit difficult to switch back for the exam and I ended up trying to use MV calc on the BC exam lol.  Smart idea to spend time reviewing the course materials ^^" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14057.0 0.0 0.0 0.0
"I’m trying to relax listening to this in bed but the chalk slamming is so aggressive in my headphones XD" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7118.0 1.0 0.0 0.0
"I wish I had instructors like him!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6199.0 0.0 0.0 0.0
"45:50
Why does he add the constant c1?" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 1260.0 0.0 1.0 0.0
"oh, these classes are so awesome, I wanted to clap at the end of the video." 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 14118.0 0.0 0.0 0.0
"Hats Off Professor, You are an inspiration!" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 4438.0 0.0 0.0 0.0
"Really nice way to break down formalism into geometrical interpretation. The linear algebra script of my university (germany) is extremly formal/theoretical (theorem + proof, theorem + proof,... etc), took me a while to build up geometrical interpretations on my own but I had some gaps, filled by Gilbert Strang and other sources (from books/web), => I say thank you ;)" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8528.0 0.0 0.0 1.0
"here you go: /watch?v=eHJuAByQf5A" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13143.0 0.0 0.0 0.0
"Nice prof. Wish I had this guy when I was struggling in my own Stats class years ago." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 7853.0 0.0 0.0 0.0
"why did he make the columns space equal to m rather than n i didnt't understand isn't supposed to column space is equal or less than the number of columns  in the matrix. he wrote the column space to be the number of rows dimension 38:04" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15297.0 0.0 1.0 0.0
"this is the easy way to introduce linear algebra, and all profs should do it like that. not with groups, homomorphisms and vector spaces..." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14881.0 0.0 0.0 1.0
"hope to see one planimeter someday, which seems cool. " tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13185.0 0.0 0.0 0.0
11:02 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 362.0 0.0 0.0 0.0
"@gellscream2009 True but the rest of us don't understand you. It's ok though, artists aren't understood either  ;D" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1847.0 0.0 0.0 0.0
"He's talking about multiplying a matrix by a vector, which is O(n^2)." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 4644.0 0.0 0.0 0.0
"Im a beginner in Linear Algebra, what books can you recommend for me to read?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6566.0 0.0 0.0 0.0
"Dual Picture -> Mind = Blown" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 3521.0 0.0 0.0 0.0
"I can't believe I am here
First time I feel passion about learning during my colleage time
I believe people who ever listen to your course will appreciate deeply
Thank you! really! Thank you so much!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5203.0 0.0 0.0 0.0
"I really need indepth statistical knowledge for applications from a Proficient Tutor even if it's within a short period of time as I can learn anything fast if I am serious and really interested. Not all these confusion they're giving us in school." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 5932.0 0.0 0.0 0.0
"The fascinating part is I took this course 30 years ago and it’s all flooding back." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10102.0 0.0 0.0 0.0
"hocam kralsınız" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13181.0 0.0 0.0 0.0
"Thank you so much MIT OCW and Professor Strang! Huge fan! Hugs from Brazil!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9348.0 0.0 0.0 0.0
"Your teaching is amazing. I am a teacher myself and I know that teaching is not easy but it seems very easy to you. Thank you for these videos. I am very grateful for them :)" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 12263.0 0.0 0.0 0.0
"I like how he calls vectors or columns ""this guy"" and ""that guy""" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 5663.0 0.0 0.0 0.0
"process has memorylessnessf property (provided the person entered the room doesn't see the future)   
continuous time variations    
definition of the poisson process and we use the concept of memorylessness in here
time homogenity as time is continuous.
Lambda*Tau will be the rate at very small interval
diff time slots are independent of each other 
NUMBER of arrivals in the disjoint time interval will be independent of each other.

delta is very small.
pmf have the binomial pmf
here we are taking a big interval and we are splitting that interval into many infinitesemely small interval.

now prob of one of the intervals will be same as the bernoulli distriubution
for poissson we take lambda tends to 0.
merging of the poisson process" jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 14208.0 0.0 0.0 0.0
"I suggest every colleges' linear algebra course using this course video. Prof Strang makes linear algebra so intuitive, interesting and easy to understand. He plots the pictures and tells you what's going on in the vector space and then he will go back to the theory to make you have a deep comprehension" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 5982.0 0.0 0.0 1.0
"@ 24:30 why is row operation able to preserve row space and not column space? as Prof Strang mentioned that 111 can longer be found in C(R) so column space is not preserved. However, I don't see any row in A being found in R as well?. To put my question simply, how do I know if certain space is preserved after certain operation?" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1471.0 0.0 1.0 0.0
Yayy rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 12116.0 0.0 0.0 0.0
"I'm interested in this but the application is more as predictive software that can take the data that's collected and make predictions based on everything my question comes in at is it possible to use several other programs I guess like they use in Linux pipeline many large programs together to create a super program I'm interested in a program that can predict everything from everywhere and trying to get the predictive error down to less that 1 percent" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 6334.0 0.0 0.0 0.0
"use the chen lu!" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14985.0 0.0 0.0 0.0
"I love this man" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5821.0 0.0 0.0 0.0
"isnt first and third quadrant of x-yplane together a subspace of R2 ?
second and 4th together also is one" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 13668.0 0.0 1.0 0.0
"1. ? 2. 21:49 3. 40:00 4. 39:49 5. 47:13" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 322.0 0.0 0.0 0.0
"Amazing lecture. Great" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2374.0 0.0 0.0 0.0
"yeah of course the lecture is more older than me" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15469.0 0.0 0.0 0.0
"Just saying.
He says that the additivity axiom needs strengthening, and uses the same to prove that P(A) <= 1.
Does he mean to say that the axiom is correct but needs more depth of explanation?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 7192.0 0.0 0.0 0.0
"where is lectue 34?" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15236.0 0.0 0.0 0.0
"Liloy lilay" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7367.0 0.0 0.0 0.0
"Start with this." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8881.0 0.0 0.0 0.0
"It was a great journey with you professor. Thank you for gifting such a nice course." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 6994.0 0.0 0.0 0.0
"I have now a clear idea of Fisher" JTbZP0yt9qc "6. Maximum Likelihood Estimation (cont.) and the Method of Moments" "MIT 18.650 Statistics for Applications, Fall 2016" 5548.0 0.0 0.0 0.0
"Everything is so clearly explained and laid out! Thank you so much Prof. Strang!" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 3615.0 0.0 0.0 0.0
"Making my day" ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7567.0 0.0 0.0 0.0
"I completed the whole course today, 2021.08.27
Can't remember when I started, but the first chapter gave me a bunch of intuition and those encouraged me to keep studying until the end of the course
Thank you, Prof. Gilbert Strang. You are my great Mathematics teacher. You inspired me to keep moving on these pieces of stuff
I really hope that I can meet you one day" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5243.0 0.0 0.0 1.0
TY 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 9002.0 0.0 0.0 0.0
"Please excuse me. I don't know what I'm doing wrong, but when I took the determinant of matrix A at the end, I got 9, not 3. Because I got det(A)=2(3)-3(-1)+3(0)=9. I'm really hoping someone can help me out." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8202.0 0.0 1.0 0.0
"dirty!! dirty!!! dirty!!! 
rock n rolla
best teacher ever
if you think you're too old to rock n roll then you are \m/ 
#love #respect" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12748.0 0.0 0.0 0.0
"For the benefit of others, the action begins at 33:56" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3883.0 0.0 0.0 0.0
"at runtime 36.40 mins, why cant a horizontal line be a perpendicular to vertical vector and why it must be a horizontal plane instead ?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12474.0 0.0 1.0 0.0
"Thank you for uploading this video. You've made linear algebra 100x easier" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9291.0 0.0 0.0 0.0
"if i had this class........   i would fail it." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 13533.0 0.0 0.0 0.0
"Nice hair cut ;) And great lecture of course!" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 7844.0 0.0 0.0 0.0
"Everytime I'm stuck in a problem I should ask myself ""What would MatLab do?""" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3618.0 0.0 0.0 0.0
"Means the curve itself,is a mirror integral" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7651.0 0.0 0.0 0.0
"Another amazing course, thank you professor and thank you mit" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2457.0 0.0 0.0 0.0
"@russelljbarry15 I agree, he is an absolutely wonderful lecturer." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 1994.0 0.0 0.0 0.0
"HIS DESK IS PHOTOSHOPPED INTO THAT VIDEO!!!
" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4404.0 0.0 0.0 0.0
"Sir I never knew how simple the big equation of linear algebra was until you uttered it elegantly showing how it unfolds from first principles with the determinant rules. May God bless you exceedingly!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8692.0 0.0 0.0 1.0
"25:39 Ins´t there an error with the symbol T (for transpose)? Why transpose the rows? Please, explanations!" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 784.0 0.0 1.0 0.0
"Amazing information and clarity of explanation !!" a1ZCeFpeW0o "20. Principal Component Analysis (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 2362.0 0.0 0.0 0.0
"Starts at 10 minutes" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 8885.0 0.0 0.0 0.0
"Lecture 1: Dot Product
Lecture 2: Determinants
Lecture 3: Matrices
Lecture 4: Square Systems
Lecture 5: Parametric Equations
Lecture 6: Kepler's Second Law
Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds)
Lecture 8: Partial Derivatives
Lecture 9: Max-Min and Least Squares
Lecture 10: Second Derivative Test
Lecture 11: Chain Rule
Lecture 12: Gradient
Lecture 13: Lagrange Multipliers
Lecture 14: Non-Independent Variables
Lecture 15: Partial Differential Equations
Lecture 16: Double Integrals
Lecture 17: Polar Coordinates
Lecture 18: Change of Variables
Lecture 19: Vector Fields
Lecture 20: Path Independence
Lecture 21: Gradient Fields
Lecture 22: Green's Theorem
Lecture 23: Flux
Lecture 24: Simply Connected Regions
Lecture 25: Triple Integrals
Lecture 26: Spherical Coordinates
Lecture 27: Vector Fields in 3D
Lecture 28: Divergence Theorem
Lecture 29: Divergence Theorem (cont.)
Lecture 30: Line Integrals
Lecture 31: Stokes' Theorem
Lecture 32: Stokes' Theorem (cont.)
Lecture 33: Maxwell's Equations
Lecture 34: Final Review
Lecture 35: Final Review (cont.)" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7270.0 0.0 0.0 0.0
"thanks :)" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14551.0 0.0 0.0 0.0
"I swear, these lectures with the Schaum's Outline of Linear Algebra can really help anyone learn the subject." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5986.0 0.0 0.0 0.0
"What does 'when A is singular' mean at 29:00?" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 11484.0 0.0 1.0 0.0
"For what major would this course be taken for?" asjAc90L8rE "12. Time Complexity" "MIT 18.404J Theory of Computation, Fall 2020" 3914.0 0.0 0.0 0.0
"We're using Professor Strang's book in my linear algebra class and I really cannot understand my professor's teaching style. My friend pointed me to these lectures instead and I already feel like I actually understand a lot more from this one lecture than I have the past two weeks in my class. Thanks Professor Strang!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11341.0 0.0 0.0 0.0
"The column by row example at around 14 mins really hit home with the whole linear combination point. Something so simple can flick a switch in your head so it all makes sense, so kudos." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10050.0 0.0 0.0 1.0
"I remember him!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5946.0 0.0 0.0 0.0
"I heartily agree!  When I took linear algebra at Penn State in winter term 1976-7, I had such a hard time with it.  I think now it was the approach (too analytical) and the lack of time I put into the concepts (too much time on details).  I don't like getting so much thrown at me.  I like to mull over the concepts and place them into my longterm memory.  Cliff Notes also help!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5574.0 0.0 0.0 1.0
"Absolutely well done and definitely keep it up!!! 👍👍👍👍👍" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 2219.0 0.0 0.0 0.0
"@stiglaa 
X value - any value on a graph's horizontal axis
Y value - any value on a graph's vertical axis
slope - the value which is the change of x and y values between two points
tangent line - the slope of a curve at any given single point.

In this video he estimated the tangent line by looking at how the graph curved in that area. (Geom. Interp.)" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2028.0 0.0 0.0 1.0
"Thanks a lot MIT OCW for this free lectures.and i am grateful to MIT for introducing the TEACHER Mr. Gilbert to the world. I wish him happy and healthy life. You are a wonderful teacher. Thanks." Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 9655.0 0.0 0.0 0.0
"In the middle of my PhD, with all the stress, Dr. Strang's lectures are the only relaxing time I have. Nothing else really feels so great. What a legend. I wish I could attend his lectures physically." lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 6677.0 1.0 0.0 0.0
"A million times better than my professor" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 2143.0 0.0 0.0 0.0
"tan and arctan has the same slope at 0 as opposed to the drawing at 38:30." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14436.0 0.0 1.0 0.0
"Thank you is not enough to express how lucky we get to access to this great lecture! Still, thank you Prof Strang and MIT :')
And cheers to those who appreciate knowledge up to this point!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9297.0 0.0 0.0 0.0
"I am not so clear about why the R in CR is sure to be a basis, how to make sure that it's independent?" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5126.0 0.0 1.0 0.0
"Thanks MIT And Prof . Gilbert Strang!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9606.0 0.0 0.0 0.0
"What is meant by ""basis""?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 11519.0 0.0 1.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change

Lecture 2: Limits
Lecture 3: Derivatives
Lecture 4: Chain Rule
Lecture 5: Implicit Differentiation
Lecture 6: Exponential and Log
Lecture 7: Exam 1 Review
Lecture 9: Linear and Quadratic Approximations
Lecture 10: Curve Sketching
Lecture 11: Max-min
Lecture 12: Related Rates
Lecture 13: Newton's Method
Lecture 14: Mean Value Theorem
Lecture 15: Antiderivative
Lecture 16: Differential Equations
Lecture 18: Definite Integrals
Lecture 19: First Fundamental Theorem
Lecture 20: Second Fundamental Theorem
Lecture 21: Applications to Logarithms
Lecture 22: Volumes
Lecture 23: Work, Probability
Lecture 24: Numerical Integration
Lecture 25: Exam 3 Review
Lecture 27: Trig Integrals
Lecture 28: Inverse Substitution
Lecture 29: Partial Fractions
Lecture 30: Integration by Parts
Lecture 31: Parametric Equations
Lecture 32: Polar Coordinates
Lecture 33: Exam 4 Review
Lecture 35: Indeterminate Forms
Lecture 36: Improper Integrals
Lecture 37: Infinite Series
Lecture 38: Taylor's Series
Lecture 39: Final Review" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8446.0 0.0 0.0 0.0
"Its really sad that old people are still working they should be retiring but can't because of the economy :(" feb9j65Iz4w "24. Linear Programming and Two-Person Games" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7091.0 0.0 0.0 0.0
"I expect that Professor Strang could explain the rank decomposition for calculating the pseudo-inverse. Damn time limit." Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 5388.0 0.0 1.0 0.0
"MIT really needs to change those blackboards to something more modern." mc1y8m9-hOM "22. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 7541.0 1.0 0.0 0.0
"I Really Like The Video Lecture 33 Exam 4 review From Your" BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4985.0 0.0 0.0 0.0
"I am from the Dominican Republic , 
Thank you very much to MIT Open courses.
we are using yours Lectures at the rural area of Barahona city  wich is at the South area from Santo Domingo. 
Thank you very very much.
God Bless all of you.!!!!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5093.0 0.0 0.0 0.0
"So cool to see" xaSL8yFgqig "Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8747.0 0.0 0.0 0.0
"16:57 bless u" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 496.0 0.0 0.0 0.0
"At 19:50 he said ""When is a line through the origin orthogonal to whole plane? Never"" but I think if we take any line through origin and a plane whose normal vector is parallel to that line then they both will be orthogonal. For example x-axis and y-z plane. Help me out please." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2600.0 0.0 1.0 0.0
"When I got a problem as a student in Maribor from the USA to help solve a problem from postgraduate studies and after I solved it in 5 minutes I never watched what Americans do in mathematics.
1986-7
This professor is a classic European mathematician and not to teach you how to solve everyday problems symbolically so that you are cool." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11604.0 0.0 0.0 0.0
"this one lecture covers most of my math and control engineering module. guys a genius" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 14907.0 0.0 0.0 0.0
"the class is so rambunctious.. it must be that sexy french accent" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14676.0 0.0 0.0 0.0
"@alquiora i assume he just did this one again for the recording! maybe the regular recording got somehow screwed up!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 1777.0 0.0 0.0 0.0
"nice lecture, thanks mr auroux" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14044.0 0.0 0.0 0.0
"Watching this in 2019. Revising for Machine Learning. That guy is brilliant" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 11300.0 0.0 0.0 0.0
"Greatness at its maximum expression." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4379.0 0.0 0.0 0.0
"What a wonderful professor! May God bless his soul." YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11438.0 0.0 0.0 0.0
"I love the way Americans keep on saying that they did this when they were 15-16 ext.
But then Michio Kaku say's that America sucks rhinoceros balls at science. Anyone see the discrepancy?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5789.0 0.0 0.0 0.0
"I started watching this back in April as a college freshmen and it inspired me to study and take my first actuary exam.   I passed this September.  Thank you MIT" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 5973.0 0.0 0.0 0.0
"Where can the problem set of 30 questions that he mentioned be found?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 11666.0 0.0 1.0 0.0
"After the first lecture, I was expecting to see the Gauss method to emerge along the same kind of ideas. Something like, we look for a transformation that turns the vector multiplied by x into (1, 0, 0). This reduces the dimensionality of the problem. We repeat the procedure until we arrive at az = b, and then we roll back. Well, I guess, we all have our preferences." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2257.0 0.0 0.0 0.0
"Thank you Prof Strang, hope to meet u in person one day." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9184.0 0.0 0.0 0.0
"31:42 A doesn't have an inverse because Ax=0 can't recover the vector 3,-1 on multiplication by A inverse if it existed. Why does Prof Strang find this such a compelling illustration that A doesn't have an inverse?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 915.0 0.0 1.0 0.0
"It's a .... superbowl " vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 7014.0 0.0 0.0 0.0
"His lecture is very good. But his lecture is not complete. He didn't prove the fact that n eigenvectors are linearly independent if the matrix A has n different eigenvalues. He lectured only the case in which the eigenvectors are linearly independent. He always omits difficult cases." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 4756.0 0.0 1.0 1.0
"Such an amazing presence of mind and sharpness at 84 years old ... Respect to Prof Strang" cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8944.0 0.0 0.0 0.0
"Is teacher French?" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6802.0 0.0 0.0 0.0
"Hi, I would like a sandwich with x" Xn8wL2ItzZw "Lecture 9: Limsup, Liminf, and the Bolzano-Weierstrass Theorem" "MIT 18.100A Real Analysis, Fall 2020" 4718.0 0.0 0.0 0.0
"great material!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 12995.0 0.0 0.0 0.0
"The best joke of all occurs at 19:00.

“Five minutes of 18.06 is enough to take care of 18.03.”

And it’s not a joke, provided you have a thorough understanding of 18.06.
" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 9998.0 0.0 0.0 0.0
"I didn't understand it until I saw the chains." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5279.0 0.0 0.0 0.0
"I am a graduate student majored in electrical and computer engineering. Though most of us have learned linear algebra in undergraduate study, I would like to highly recommend this course to those who are interested in machine learning and signal processing. Thank you Prof.Strang!" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 5052.0 0.0 0.0 0.0
"This man is a wonderful Guru" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 10860.0 0.0 0.0 0.0
"At 43:46, what if you chose a different slice in the xz plane? Wouldn't df/dx change because you would get different curves? Or, would all the curves be the same general shape: a parabola, making it not change after all? Thanks." dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 2673.0 0.0 1.0 0.0
"Any one here at 2020?" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2472.0 0.0 0.0 0.0
"I'm taking the course Probability (EDX MITx) which really worth it. His book is one the best. Introduction to probability, highly recommended." IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 6387.0 0.0 0.0 0.0
"Yo tambien soy de Mexico y estudio en EU. En EU eres forzado a tomar 2 semestres de matematicas, pese a que no sean necesarias en tu carrera. Muchos estudiantes que estudian ingles o politica deciden llevar este curso porque es de los mas sencillos, otros porque quieren ""refrescar"" los temas, u otros porque quieren un promedio alto. El curso se volvera complicado, por ejmplo no recuerdo haber visto la regla de l'hopital en Mexico, pero como dicen, todo depende en la persona, no en nacionalidad." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12156.0 0.0 0.0 0.0
"you're awesome professor thank you." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 15523.0 0.0 0.0 0.0
"""Ok, so...that's the end.""  haha....ends just as matter-of-factly as he began.  How poetic." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 97.0 0.0 0.0 0.0
"Thank you Lord that I saw these lectures now. It's a shame that is late, but it happened none the less. God bless you Professor Strang" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9117.0 0.0 0.0 0.0
"why did YouTube recommend this? Mathematics scares me" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 15295.0 0.0 0.0 0.0
"Who tf disliked this video?" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11751.0 0.0 0.0 0.0
"You're the master of Linear Algebra! 
All your students every corner of the world love you too much ♥️" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 12255.0 0.0 0.0 0.0
"Thank you." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 9557.0 0.0 0.0 0.0
36:10 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 1031.0 0.0 0.0 0.0
"Linear algebra is used in almost all areas of mathematics, thus making it relevant in almost all scientific domains that use mathematics.
Your course isn't only helping students to pass linear algebra class, your course is helping humanity prof. 🙏❤️
We owe you so much.
Big thanks from Sudan." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7378.0 0.0 0.0 0.0
"수강 날짜: 21 Oct" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 15679.0 0.0 0.0 0.0
"Are you kidding me right we do lim at 16 Years old in Greece and you make it in MIT............-.- pffff ok........." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2539.0 0.0 0.0 0.0
"Is the text book important? Besides the recommended text book “Edwards, Henry C., and David E. Penney. Multivariable Calculus. 6th ed. Lebanon, IN: Prentice Hall, 2002. ISBN: 9780130339676.“, is there any other text books good for this course?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6816.0 0.0 0.0 0.0
8:05 Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1414.0 0.0 0.0 0.0
"I love the polar coordinates explanation and how the non-rectangular region can be treated as rectangular in the limiting case." 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5781.0 0.0 0.0 0.0
"I don't have the pleasure of attending MIT, but I think MIT professors are the best. Including this guy." Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5316.0 0.0 0.0 0.0
"I Really Like The Video From Your Level curves; partial derivatives; tangent plane approximation" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 4959.0 0.0 0.0 0.0
"I wish Strang was my grandfather" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6216.0 0.0 0.0 0.0
"Superb video. Amazing" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8965.0 0.0 0.0 0.0
"ok I'm still not fully understanding how to get the equation of the plane at about 10:30  he tells about it but i must be missing something anyone wanna give me an example?" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14124.0 0.0 1.0 0.0
"He is the most Amazing teacher .The way he shares the knowledge it becomes very easy understand and imagine which is a beauty of his teaching" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4551.0 0.0 0.0 0.0
"""...perhaps we're splitting hairs here, but perhaps it's useful to keep the concepts right.""  I have always wanted to have a Professor like him." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 20.0 0.0 0.0 0.0
"Emergency question! Can we describe a basis for non-subspaces? For example a plane doesn't go through the origin???" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 3564.0 0.0 1.0 0.0
"dat MIT chalk" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12723.0 1.0 0.0 0.0
"I love the videos, i understand the english but some cuts no, but I like" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5788.0 0.0 0.0 0.0
"@thejugglenaut91 as I mentioned, there is no floating point exactitude for the circumference of a circle.  It all rests on the work of Dedekind and his attempt to create continuity in the number line by using his Dedekind Cut.  Even if his logic holds true, it only holds true for a straight line.  It does not hold true for a curve.  You would again be stuck with limits and tangent lines." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2042.0 0.0 0.0 0.0
"~ 45 people are burger flippers" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15532.0 0.0 0.0 0.0
"What a Guy!" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 11387.0 0.0 0.0 0.0
"Heaps of dot-connecting  mental exercises for me. Thanks professor.  Hopefully, your High-Dimensional Statistics course will be available on youtube as well." JBIz7UadY5M "14. Regression (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 4650.0 0.0 0.0 0.0
"Is this the last lecture or are their more coming." zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6881.0 0.0 0.0 0.0
"This prof is fantastic. Thank you." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10889.0 0.0 0.0 0.0
"Bravo!!! Very much the best and premium stuff." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 2918.0 0.0 0.0 0.0
"This is awesome :D" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 10643.0 0.0 0.0 0.0
"Why couldn't you re-record lecture 4?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11803.0 0.0 0.0 0.0
"Is 25:00 justification true?" AdTvkFsqcDc "16. Derivatives of Inverse and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6744.0 0.0 1.0 0.0
"very interesting lecture" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15023.0 0.0 0.0 0.0
"8:14 plus tri lol." 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1417.0 0.0 0.0 0.0
"great video!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 13014.0 0.0 0.0 0.0
"He's so bad at cleaning the board omg" JTbZP0yt9qc "6. Maximum Likelihood Estimation (cont.) and the Method of Moments" "MIT 18.650 Statistics for Applications, Fall 2016" 4642.0 1.0 0.0 0.0
"This guy makes more sense in 50 minutes than my lecturer does in 2 hours." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10553.0 0.0 0.0 0.0
"just funny that 14 of the reactions are What?..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13733.0 0.0 0.0 0.0
"Maybe we can come up with a linear algebra hip-hop artist. We might call her/him PosDef.

*me and my ho's, we like to transpose...*" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 7642.0 0.0 0.0 0.0
"Mister Alan Edelman if you can hear me .   Would it be possible to implement ""physical datatypes"" which contains value as well as unit. wehre for example units wood be as well multiplied as values (in Multiplications)  i think this would also be a great relief. i for my self work with quantum mechanics and units are always a problem. i try to implement the above explained concept in python" rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7673.0 0.0 1.0 0.0
"Because of the extensive amount of programming I've done with OpenGL, I feel that the axis are all messed up x.x... I like z-axis positive direction to be ""out"" and x-axis positive to the right, and y-axis positive up." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2832.0 0.0 0.0 0.0
"He always asks permission from some unseen student in the sky that only he can hear:  “can I give an example here?  OK, can I try this?”  It’s a pleasure to take his course." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 4460.0 0.0 0.0 1.0
"If you distance to Monica is less than three, you are in trouble.😀" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 6540.0 0.0 0.0 0.0
"Much respect To Professor Gilbert Stang." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7722.0 0.0 0.0 0.0
"Can't wait to start this course, budding ML engineer here. Wish me well!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3130.0 0.0 0.0 0.0
"agree!
that's what I plan to use in my teacing" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 12312.0 0.0 0.0 0.0
"I actually don't get that one" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 5012.0 0.0 0.0 0.0
"Phenomenal teacher.....  He has the ability to covey concepts in a very clear and understandable way.  Wow....what a joy to learn from him." 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 8190.0 0.0 0.0 0.0
"3 good lectures so far, but I'm questioning my will to live with this delivery.  I'm not really interested in ANYTHING this guy is saying.  If you're not going to be examined on the first 15 minutes of dross, why lecture on it?" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 878.0 0.0 0.0 0.0
"I didn't get the joke at the end" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5268.0 0.0 0.0 0.0
"Way better than my online class (and way better then the textbook that is needed for the class)" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 11309.0 0.0 0.0 0.0
"I love this logical teaching" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5820.0 0.0 0.0 0.0
"This article is about mathematicians finding that the fastest way to multiply is n*log(n) steps versus the usual n^2.
https://www.quantamagazine.org/mathematicians-discover-the-perfect-way-to-multiply-20190411/ Professor Strang shows you how that is in this lecture." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 10465.0 0.0 0.0 0.0
"I always dreamed (and still continue) about studying at MIT, but I am not a genius and not a daughter of some deputy, so instead of university lectures I watch this course and imagine myself studying there))" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5039.0 0.0 0.0 0.0
"Please spread this school on your wall and your friends because students need to see it.
So will you.
There are more than 4 000 tasks and theorems for primary and secondary school students.
Thank you for your contribution.
Respect!                                                                                                                                                                                                              ...........................................                                                                                                       .Të lutem shpërndaje këtë shkollë në murin tuaj dhe miqve tuaj, sepse nxënësit kanë nevojë ta shohin.
Kështu do të kontribosh edhe ti.
Janë më tepër se 4 000 detyra e teorema për nxënës të shkollave të nivelit fillor dhe të mesëm.
Faleminderit për kontributin tuaj.
Respekt!
https://www.youtube.com/channel/UCELXh5_dCYX6umKP3qlOL9g" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8213.0 0.0 0.0 0.0
"this guy has the most soothing voice. like if he were saying ""i am going to kill you now"" in that voice i would be like ""ok man thats cool""" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14808.0 0.0 0.0 0.0
"Electric current flows from (+) to (-), from higher potential to lower potential. But starting node of each edge is marked with -1 in the matrix and end node marked with +1. Why not other way around?" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3561.0 0.0 1.0 0.0
"Style ❤️" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8920.0 0.0 0.0 0.0
"Not sure why this professor sounds always angry, and keeps hitting the chalkboard as much as he can like trying to release his childish anger. Other than that, he is OK. Sorry to say, my GaTech professors were 10x better than this. e.g check out Prof.  D.Goldsman." X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 7931.0 1.0 0.0 0.0
"The mic noise and hiss is distracting in this lecture, I hope someone could fix it .." aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10188.0 1.0 0.0 0.0
"The last problem is easier if you take the derivative (dy/dθ)/(dx/dθ)  and then use L'Hospital's Rule, rather than using Taylor expansion" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10155.0 0.0 0.0 0.0
"...and, where do you think that software came from? What do you you think is running the Google search engine? Why does the jpeg file format exist and is widely used? You probably need to open your mind to applying math to some field and not limit your thinking that what you learn in a math class is all you need to pay your bills." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 267.0 0.0 0.0 0.0
"how is the quality so good for a video shot in 2005" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13242.0 0.0 0.0 0.0
"he writes super fast :D" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13119.0 0.0 0.0 0.0
"auroux's handwriting is so hot" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12484.0 0.0 0.0 0.0
"we solved for all results that lead us to zero" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 15080.0 0.0 1.0 0.0
"Oh my God Prof. Strang has gotten old. I remember watching 18.06 lectures like 2 years ago. He is one of the best professors out there. I have learned *SO MUCH* from him. He's a legend!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8014.0 0.0 0.0 0.0
"thanks prof" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14596.0 0.0 0.0 0.0
"I don't get how that the equation for the last part was a plane since even a line can be perpendicular to a vector ? @33:44" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5303.0 0.0 1.0 0.0
"IT'S ALL WOW! THANK YOU SIR WITH WONDERFUL EXPLANATION! 
BEST REGARDS FROM AFGHANISTAN" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 6452.0 0.0 0.0 0.0
"hell yeah nullspaces!!" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 13130.0 0.0 0.0 0.0
"I found it very helpful to first go through Chapter 7.1 - Image Processing by Linear Algebra, from the Introduction to Linear Algebra by Strang, Fifth Edition. At first, I could not catch on with the lecture even though I have seen most of his past lectures and read the book. 7.1 really helped me." TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 5431.0 0.0 0.0 1.0
"Where is lecture no 28?" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 11688.0 0.0 0.0 0.0
💛💛 t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15724.0 0.0 0.0 0.0
"@SynthMelody Maybe a simpler example helps. We take the X axis as one subspace and the Y axis as another subspace. So the union of those two spaces is all vectors on either axis, but nowhere else. For example (1 0 0) is on the X axis and (0 1 0) is on the Y axis. But the sum of the (1 1 0) is not on either of those lines. It's outside of it, so the union can't be a subspace, as otherwise you'd stay inside it when you add two vectors." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 1734.0 0.0 0.0 1.0
"Indeed, can't have a critical point *at* infinity.." twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6705.0 0.0 1.0 0.0
"Can i get homework of this course ?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3055.0 0.0 0.0 0.0
Superb. QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8968.0 0.0 0.0 0.0
"Great lecture. I am so happy that i found this.:)" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 4290.0 0.0 0.0 0.0
"Not at all (assuming you are about in the top 10%).  The people at MIT have shown dedication, interest, ingenuity as well as being fairly clever.  Most students at top universities are not brilliant at all.  They are simply hard better students." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7919.0 0.0 0.0 0.0
"34:26 when inequality is sus" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 980.0 0.0 0.0 0.0
"i hope this professor doesnt get any sexual assault charges with that much winking because his lectures are awesome." xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13404.0 0.0 0.0 0.0
"Check-in 8.1> b! Even the logic we use is arbitrary but math is just deduction from arbitrary axioms. The only way you could decide this question is to make it empirical. That is to say, whatever logic and whatever set of axioms we use should be the one that is most predictive of observed experience!" 3PzuSPQPEU4 "8. Undecidability" "MIT 18.404J Theory of Computation, Fall 2020" 3147.0 0.0 0.0 0.0
"you would think MIT students would learn this in highschool" TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15517.0 0.0 0.0 0.0
https://bookerystore.com/downloads/introduction-to-linear-algebra-2nd-ed-1986-edition/ J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13255.0 0.0 0.0 0.0
"I am grateful for your lectures and your teaching.. ""oh,  it's no big deal, maybe that's what' Schmidt did"".  :) :)" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 5101.0 0.0 0.0 0.0
"area between two curves" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12402.0 0.0 1.0 0.0
"You can change the world by providing free education for elite courses that most of the people can not pay for. Thanks so much, amazing explanation." mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 12187.0 0.0 0.0 0.0
"Good lecture. Intuitive explanations with specific illustrations" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4137.0 0.0 0.0 1.0
"This isn't Taylor, it's McLaurin" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10776.0 0.0 1.0 0.0
"At 25:17 is it necessary to transpose the rows of A before multiplying with X ( since the dimensions match already )?" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2624.0 0.0 1.0 0.0
"Can anybody explain thruva and Athruva matrices using 8/16 column row compressions do auto replication of any genetic systems with reference to motion and no motion systems using Barbara Mclintock cytogenetic compression by solar light pressure producing more genetic replication by changing cytogenetic informations into cryogenetic modulations as observed in nature.
Jesus Christ has done such a genetic replications by volumetric increase in grape juice and in more fishes." 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 3011.0 0.0 0.0 0.0
"When proving that (1-cosθ)/θ tends to 0 as θ goes to 0 in the geometric interpretation, shouldn't he be using 2θ in place of θ, as he duplicated the theta when he mirrored it upon what looks to be the x-axis? Also why does he look to be using what looks to me like sinθ (the green line that signifies the height of a specific point on the unit circle) when proving that the numerator of the function decreases significantly ""faster"" than the denomonator, as θ should be the length of the arc from 0 to a specific angle on the unit circle?" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11631.0 0.0 1.0 0.0
"That's right... I speak spanish but I understand this better in english with this professor." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 9936.0 0.0 0.0 0.0
Chalk? vMaKx9fmJHE "12. Testing Goodness of Fit (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 3140.0 1.0 0.0 0.0
"Outstanding lecture from Prof. Tsitsiklis" ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 8142.0 0.0 0.0 0.0
"a privilege to take part in such a distilled lecture. no confusion at all." Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12288.0 0.0 0.0 0.0
"@amarenpdas1975 
Huh? That's not english" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 1778.0 0.0 0.0 0.0
"why cannot simple steps to get upper triangle? still don't get it from this lecture" d32WV1rKoVk "12. Computing Eigenvalues and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15293.0 0.0 1.0 0.0
"Sir, You have shownDOT product applications in very nice order.  Is there any physical significance of DOT Products? Or what does happen when dot product is taken between two vectors? Or is this only a tool facilitating mathematical calculations?" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8712.0 0.0 1.0 1.0
"Has anyone else noticed a drop in views?" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4433.0 0.0 0.0 0.0
"what would happen if  we apply L'ohpital's rule with respect to p  at 32:12 as p approaches 1? would this still be valid?" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15191.0 0.0 1.0 0.0
"it's very useful 

" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13701.0 0.0 0.0 0.0
"@sgba17 Taught myself from a book I found at the public library." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2008.0 0.0 0.0 0.0
"informative without excess fluff, intrinsically entertaining, and well paced. i hope the rest of the lecture series is as well done as this first introduction" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 13609.0 0.0 0.0 0.0
"Ojala a alguien se le ocurra algun dia doblar estas clases al español" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8038.0 0.0 0.0 0.0
"i did matrices at Uni and not s single course / lecturer ever explained what they meant. most books dont either. ive learned more in 2 lectures about this subject than I did in 3 years" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13354.0 0.0 0.0 0.0
"This is for the love of gilbert strang" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 10663.0 0.0 0.0 0.0
"Thank you a lot . also we need physical organic chemistry .because chemistry subjects in channel is a few" V3Wg_jrMSQY "Lecture 19: Differentiation Rules, Rolle's Theorem, and the Mean Value Theorem" "MIT 18.100A Real Analysis, Fall 2020" 9242.0 0.0 0.0 0.0
"@Zeke8762 That's sooo unfair! Where I live we had to go extra fast though some stuff last year because Norway is far behind (but not this far) -.- I'm moving! :D" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1761.0 0.0 0.0 0.0
"At the end of this lecture, the explanation on the fisher information relating to curvature is the best I have seen." 0Va2dOLqUfM "5. Maximum Likelihood Estimation (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 2727.0 0.0 0.0 0.0
"because ur not steve jobs :( neither am i." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12528.0 0.0 0.0 0.0
"I do remember now. It was on video /watch?v=1Datf4AZwTw (Edward Tarte Tries to Extend Dialogue with Father TJ). That is a coincidence!

Cold drink please." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 5293.0 0.0 0.0 0.0
"2+ 2 = 4?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 612.0 0.0 1.0 0.0
"I hate seeing this damn spinning circle while I wait for the internet feed to come in.   " ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5483.0 0.0 0.0 0.0
"Does anyone can explain the origin of such formula for the circumference of a part of a circle? I mean ""a times feita""." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3433.0 0.0 1.0 0.0
"Gilbert Strang is gifted in two ways. Not only he possesses the knowledge and expertise necessary to be a math professor, but also he has the charisma that encourages people to both listen and enjoy what he is talking about." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 4022.0 0.0 0.0 0.0
"Look everyone. Here's that douche bag who's either lying or desperately needs attention that you can find on every video of upper level mathematics or science classes." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7416.0 0.0 0.0 0.0
"Even though i'm studing in Europe, it's still interesting, useful and easy to understand, thx for making these leactures available" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 3590.0 0.0 0.0 0.0
"""The idea of elimination ... I mean you would have thought of it "".It is so funny" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 117.0 0.0 0.0 0.0
"Why expectation = [Y-(a+bx)]^2,  I think i should be = [(a+bx) -Y ] ^2,   or real value - predict value , maybe it same, so Can I use two formulas?. Can anyone explain it for me? Thanks <3" yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 11860.0 0.0 1.0 0.0
"Engenvalues go!!!" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 3568.0 0.0 0.0 0.0
"Hands Down one of the most intersting lectures, The way Professor showed reseach ideas here and there and almost everywhere just blows me away, It was very very intersting, and best part is it is afforable to non-Math guys too, (thought its coming from a maths guy, however I feel like math part of very little, it was more towards intuitive side of SGD)" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4418.0 0.0 0.0 1.0
"Mic ❤️" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7663.0 0.0 0.0 0.0
"A great lecturer! Love the way how you teach!" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2122.0 0.0 0.0 0.0
"22:14 , *""""usually sometimes during the semester i drop one of these erasers behind there. That's a great moment. There's no recovery. There's -- centuries of erasers back there.""*  I like prof gilbert's sense of humor." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 696.0 1.0 0.0 0.0
"This is a very bad quality video, moreover screen size is also shortened now in his every video. I am not able to make what is written on board" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 10604.0 1.0 0.0 0.0
"Who is watching this video in 2020 october." YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11744.0 0.0 0.0 0.0
"Thanks for this MIT - a great aid for me." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9727.0 0.0 0.0 0.0
"sorta got the general idea of this whole lecture, im still not so good at the details. Reading the book and summary might be a good idea to solidate the knowledge if needed. Thank you Professor Strang and MIT! great lecture!" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 14382.0 0.0 0.0 1.0
no TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14062.0 0.0 0.0 0.0
黑色素 hwDRfkPSXng "Lecture 32: ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15669.0 0.0 0.0 0.0
"Why always 2?? is there a prove?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11769.0 0.0 1.0 0.0
"Thanks a lot :)" H_k1w3cfny8 "10. Continuous Bayes' Rule; Derived Distributions" "6.041 Probabilistic Systems Analysis and Applied Probability" 9652.0 0.0 0.0 0.0
"ERROR: stability regions are meesed up. Unit circle is for degrees, and left half-plane is for exponentials." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 3540.0 0.0 1.0 0.0
"being poor doesn't necessarily keep you out of a school like MIT if you otherwise qualify, these schools usually have good financial aid for people that can't afford the tuition." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12532.0 0.0 0.0 0.0
"That is barely a proof of chain rule" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9895.0 0.0 1.0 0.0
"23x
/(x-1)*(x-2)=    A/(x-1)  +  B/(x-2)" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 721.0 0.0 1.0 0.0
"He's just showing applications of linear algebra, not teaching them. That's why it seems ""sloppy"". You just can't teach Fourier Transform in 30 mins." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 4638.0 0.0 0.0 0.0
"Some of those students don't deserve to go to MIT. " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8824.0 0.0 0.0 0.0
"He's such a great instructor" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4643.0 0.0 0.0 0.0
"Gracias. Saludos" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 4180.0 0.0 0.0 0.0
"is there solutions to the asignments?" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13656.0 0.0 0.0 0.0
"22:30
Law of cosines" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 699.0 0.0 0.0 0.0
"@ 24:39, that epic moment. :P" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 1472.0 0.0 0.0 0.0
"Wow.....how beautiful it is! How beautiful!!!" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 12090.0 0.0 0.0 0.0
"prof strang is by far the best teacher i've ever known in my life, he's teaching things that is very much complicated and teaches those things like there're super easy. thank to MIT OpenCourseWare for making this lecture, your job is priceless" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 14211.0 0.0 0.0 0.0
"How can be the dimension of a 3*3 new vector space be 9, can anyone explain this to me ???" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 4811.0 0.0 1.0 0.0
"Ok I don't even know what is going on and don't know where to start learning calculus lol" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8040.0 0.0 0.0 0.0
"Did you record 18.03 for professor Jerison ?" 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3395.0 0.0 1.0 0.0
"I stumbled upon this playlist and it really made my day. This is so good." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5980.0 0.0 0.0 0.0
"The thing is Calculus seems hard when you first take it, but afterwards when you move on take even higher level classes, you realize that Calculus is just the introduction to higher level math. My favorite math has always been Differential Equations." jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10302.0 0.0 0.0 0.0
"In bayes theorm if I know the value of p(symptoms/disease) let's 0.3 so,can I take  p(~ymtm/dise)= p(ymtm/~dise) = (1-p(symtm/dis))?" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 6625.0 0.0 1.0 0.0
"A course in multivariable calculus and the comments center around the sound of the guy's voice. Nice." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2108.0 0.0 0.0 0.0
"Typo at 39:00? The max shouldn't be there? It's by definition the TV, so we want to say the TV is larger or equal to any other difference of probabilities of A." rLlZpnT02ZU "4. Parametric Inference (cont.) and Maximum Likelihood Estimation" "MIT 18.650 Statistics for Applications, Fall 2016" 11109.0 0.0 1.0 0.0
"@blakescello the irony" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1797.0 0.0 0.0 0.0
"have to review the text book. too much information" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 13065.0 0.0 0.0 0.0
"So brilliant lecture, help me a lot!" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8743.0 0.0 0.0 0.0
"why am i being recomended this" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15278.0 0.0 0.0 0.0
"Lol you kidding me? Thats what I'm learning right now in 11th year" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7401.0 0.0 0.0 0.0
"@j4ckjs What I mean, is that around minute 14:00 he says that the error is vertical instead of orthogonal to the line. I thought we were trying to minimize the error by orthogonal projection. I'm probably mixing things up, but I don't see it." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 1896.0 0.0 1.0 0.0
"34:58 would using perpendicular distance (instead of vertical distance) make better sense? 
" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 990.0 0.0 1.0 0.0
"Fundamental ideas ;)
Thanx" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3953.0 0.0 0.0 0.0
"12:54 Lol professor could actually do that, but a little bit different by instead of the conjugate equation, we can use orginal equation. He actually pointed it out but mistook it a little bit. Just multiply both side of the tranpose equation by x, change A*x to Lambda * x, then we end up with the equation where Lambda = Conjugate(Lambda) . I actually followed his guide that moment and it worked, but he instead ended up with a mess XDD." UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 398.0 0.0 1.0 0.0
"We did this in class one week ago. My sucks ass. This is soooo much better and clearer. This guy should be given ""best teacher in the world"" award. He should win a noble prize in teacher. All other teachers should bow to him and call him ""teacher god!""" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 11319.0 0.0 0.0 0.0
"americans do this in college?
LOL
in australia we do this in year 11 / sometimes year 10" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12360.0 0.0 0.0 0.0
"""Ok...we're 'executing' a determinant for formula here""...quality content!!" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 99.0 0.0 0.0 0.0
"this dude is NOT human :O" XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14801.0 0.0 0.0 0.0
"Thanks professor for this amazing lecture." -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9765.0 0.0 0.0 0.0
"Very useful course! You can learn Linear Algebra yourself! Let knowledge spread to everyone, free and efficiently." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 11227.0 0.0 0.0 0.0
"Well,you have the slope (m) of the tangent which is -1\x^2
and the equation of any tangent is y-y0 = m(x-x0)" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11375.0 0.0 0.0 0.0
"if someone could explain what he is saying at 34:35, that would be great. I don't really understand it. I  wish I could be more specific in explaining my confusion!" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13539.0 0.0 0.0 0.0
"It may be worth to note that instead of partial derivatives one can work with derivatives as the linear transformations they really are. 

Also, looking at the networks in a more structured manner makes clear that the basic ideas of BPP apply to very general types of neural networks. Several steps are involved. 

1.- More general processing units. 
Any continuously differentiable function of inputs and weights will do; these inputs and weights can belong, beyond Euclidean spaces, to any Hilbert space. Derivatives are linear transformations and the derivative of a neural processing unit is the direct sum of its partial derivatives with respect to the inputs and with respect to the weights. This is a linear transformation expressed as the sum of its restrictions to a pair of complementary linear subspaces. 

2.- More general layers (any number of units). 
Single unit layers can create a bottleneck that renders the whole network useless. Putting together several units in a unique layer is equivalent to taking their product (as functions, in the sense of set theory). The layers are functions of the of inputs and of the weights of the totality of the units. The derivative of a layer is then the product of the derivatives of the units; this is a product of linear transformations. 

3.- Networks with any number of layers. 
A network is the composition (as functions, and in the set theoretical sense) of its layers. By the chain rule the derivative of the network is the composition of the derivatives of the layers; this is a composition of linear transformations. 

4.- Quadratic error of a function. 
...
——-
With the additional text down below this is going to be excessively long. Hence I will stop the itemized previous comments. 

The point is that a sufficiently general, precise and manageable foundation for NNs clarifies many aspects of BPP. 

If you are interested in the full story and have some familiarity with Hilbert spaces please google for our paper dealing with Backpropagation in Hilbert spaces. A related article with matrix formulas for backpropagation on semilinear networks is also available. 

We have developed a completely new deep learning algorithm called Neural Network Builder (NNB) which is orders of magnitude more efficient, controllable, precise and faster than BPP. 

The NNB algorithm assumes the following guiding principle:
The neural networks that recognize given data, that is, the “solution networks”, should depend only on the training data vectors. 

Optionally the solution network may also depend on parameters that specify the distances of the training vectors to the decision boundaries, as chosen by the user and up to the theoretically possible maximum. The parameters specify the width of chosen strips that enclose decision boundaries, from which strips the data vectors  must stay away. 

When using the traditional BPP the solution network depends, besides the training vectors, in guessing a more or less arbitrary initial network architecture and initial weights. Such is not the case with the NNB algorithm. 

With the NNB algorithm the network architecture and the initial (same as the final) weights of the solution network depend only on the data vectors and on the decision parameters. No modification of weights, whether incremental or otherwise, need to be done. 

For a glimpse into the NNB algorithm, search in this platform our video about : 
NNB Deep Learning Without Backpropagation. 

In the description of the video links to a free demo software will be found. 

The new algorithm is based on the following very general and powerful result (google it): Polyhedrons and Perceptrons Are Functionally Equivalent. 

For the conceptual basis of general NNs in see our article Neural Network Formalism. 

Regards,
Daniel CrespinP" lZrIPRnoGQQ "27. Backpropagation: Find Partial Derivatives" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6978.0 0.0 0.0 0.0
"The video was awesome. Now it is perfect.
(Now my left ear can be as intelligent as my right ear.)" TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 10315.0 0.0 0.0 0.0
"pmsl this is not im im 15 and english lol i need to sort this out
" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14196.0 0.0 0.0 0.0
"Seeing this lecture.....i say it's enough in linear algebra.....i am done with it.....most of the points are unclear in this lecture.....bt before this,every lecture was extraordinary..." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 8617.0 0.0 0.0 0.0
"Is there an MIT course where they focus more on the theory(Proofs) of the subject ,a rigorous treatment ?or any Channel?" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 6830.0 0.0 0.0 1.0
"Can we prove e is convergent using this taylor series of e" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3116.0 0.0 1.0 0.0
"The problem comes out from a student at 19:29 is the concept of conditional independence.  P(A and B | B) = 0 = P(A|B) * P(B|B) = 0 * 1." 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 10235.0 0.0 1.0 0.0
"This was a really good lecture. It was packed with insights.  I love how everything is coming together." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 10965.0 0.0 0.0 0.0
"I Really Like The Video Hyperbolic functions (cont.) and exam 1 review From Your" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4974.0 0.0 0.0 0.0
"So glad you put these up" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 8761.0 0.0 0.0 0.0
"great lectures....thanks
" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12993.0 0.0 0.0 0.0
"Nothing new in my comment. EE Grad - did all of this math in undergrad. Don't remember any of it, and never developed an intuition for it. 
This is so friggin' amazing!! Dr. Strang is a rockstar!" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 7944.0 0.0 0.0 0.0
"linear combination of just two special vector will produce only 2D vector space. How do you know that's the complete solution? " VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 13805.0 0.0 1.0 0.0
"I just read the latest edition of the book for this course and it is brilliant , the best Linear Algebra textbook! Thank you Dr. Gilbert Strang! But I like the cover of older edition with the houses being transformed. Is there any software for online hw for the book? Please let me know." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 5612.0 0.0 0.0 0.0
"I love professor Strang's great lectures. 

Just one small correction at 32:30: It should have been S * LAMBDA^100 * c instead of LAMBDA^100 * S * c." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 5767.0 0.0 1.0 0.0
"https://youtu.be/tzoYhe3H5dM?t=1692
""Except that at that time we called things M&Ns""" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13308.0 0.0 0.0 0.0
"If James Stewart taught at MIT he'd be Prof. Strang. " FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6478.0 0.0 0.0 0.0
"Absolutely precious! Excellent in explaining details! Thank you." WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 2208.0 0.0 0.0 0.0
"simplex method 11:00" feb9j65Iz4w "24. Linear Programming and Two-Person Games" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14303.0 0.0 0.0 0.0
"IT ALL CONNECTS, THIS IS BEUTIFUL!!!!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6450.0 0.0 0.0 0.0
"can someone explain how he got 24P's at the end?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 12620.0 0.0 1.0 0.0
"17:10 The word is his name Rigollet in French" JTbZP0yt9qc "6. Maximum Likelihood Estimation (cont.) and the Method of Moments" "MIT 18.650 Statistics for Applications, Fall 2016" 503.0 0.0 0.0 0.0
"yakınsama olmasa baban kim bilemezdin şerefsiz" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15459.0 0.0 0.0 0.0
"This is not teaching. This is just copying the textbook to the blackboard and reciting the textbook text. A real teacher would give concrete examples which showed with integers how these functions worked." 78vN4sO7FVU "Lecture 2: Bounded Linear Operators" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 10700.0 0.0 0.0 1.0
"Fantastic lecture series!" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 3729.0 0.0 0.0 0.0
"Wow this guys awesome! I hate it when I have professors who don't know wtf they're doing!" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12040.0 0.0 0.0 0.0
"Thnx sir, I am from Assam, India and I am now in 11th standard" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10985.0 0.0 0.0 0.0
"I love this man the way he teach and connects the subject with reality. .. Last 5 min... 💚" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 5824.0 0.0 0.0 0.0
"▲
Aside from what Professor Strang teaches great, he also has a refined sense of humor. Gauss discovered before us, not only because he lived before us, but also died before us. Well, then, because of the ""mistake"" in the third row and the second column, when he ""promised"" A to one of the students at the exam." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15602.0 0.0 0.0 0.0
"Yes high quality! (Veterans of Lecture 4 will understand)." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 12138.0 0.0 0.0 0.0
"Why does the US college start from middle school? Do you guys learn anything before college?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11844.0 0.0 0.0 0.0
GOAT 9_xG0AGRa-w "Lecture 2: Cantor's Theory of Cardinality (Size)" "MIT 18.100A Real Analysis, Fall 2020" 3967.0 0.0 0.0 0.0
"thank you sir." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 14509.0 0.0 0.0 0.0
"The proof for why v1,v2,... ,vr are orthogonal means u1,u2,... ,ur are orthogonal by A*v=sigma*u at 23:00." rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10257.0 0.0 0.0 1.0
"Great stuff. I was able to do my homework with this lecture. I will definitely be getting Strang's book." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 4333.0 0.0 0.0 0.0
"Cheat sheets and notes to tests where do I sign up...👍" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3143.0 0.0 0.0 0.0
"Lecture 4 must have been the ""weeding out"" lecture for the course. hah" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 7289.0 0.0 0.0 0.0
"The null space consist of those vectors at the end and [0,0,0] but he said at the start, if [0,0,0] is a vector in the space then it's not independent since you can take any coefficient of it and 0 for the others. So how does the nullspace have a basis?" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 10206.0 0.0 1.0 0.0
"this guy teaches well!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14842.0 0.0 0.0 0.0
"i know i know its juvenile but that's what she said  @ 42:34" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 13410.0 0.0 0.0 0.0
"This really cleared up some terms I was having trouble with." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 10915.0 0.0 0.0 0.0
"Thank you!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9470.0 0.0 0.0 0.0
"I passed Linear Algebra in 1989 but I did it by correspondence. I had no idea really what it was about but I learnt some algorithms to pass the exam! This is better. Now I see to understand it kind of intuitively. I the Maths 1 paper I passed was part of a BA including English Literature, Philosophy etc But I had intended possibly to do mathematics or engineering. It is interesting. As a NZr I keep wanting to tell him to say ""zed"" instead of ""zee"". I found this lecture by chance." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5896.0 0.0 0.0 0.0
"Good lecture." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4135.0 0.0 0.0 0.0
"Left it on a cliffhanger" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7312.0 0.0 0.0 0.0
"That is correct, it's not a linear transformation.
For me, it helps to think of this in terms of similar triangles: T(2v) takes two times the original vector but only adds one times v0 to it.  For the resultant vector to be proportional (i.e., =2T(v) ), one would have to add 2v0 to T(2v)." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9898.0 0.0 1.0 1.0
"Gradient Descent is at 34:33" AeRwohPuUHQ "22. Gradient Descent: Downhill to a Minimum" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4182.0 0.0 0.0 0.0
"I am hoping for a discussion about conventions of derivatives.  Much of the stuff I've seen would make the gradient a row vector, which leads to the derivatives being the transpose of what he shows.  In his example, the derivative a'x is 'a' which is contrary to intuition from single variable calculus though he uses intuition for x'Sx." AeRwohPuUHQ "22. Gradient Descent: Downhill to a Minimum" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5106.0 0.0 1.0 1.0
Legend 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7313.0 0.0 0.0 0.0
"Mental Gymnastics (Y). " P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 7655.0 0.0 0.0 0.0
"V = Q squared.  Well, Q is area (distance squared).  How do you square that and end up with volume (distance cubed) ???" zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11146.0 0.0 1.0 0.0
"who is watching it in 2017 Christmas holidays ?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 15265.0 0.0 0.0 0.0
"So they learn this at the MIT?
Lol, that's too easy, but thanks for sharing (;" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8793.0 0.0 0.0 0.0
"What TAs stands for?" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11386.0 0.0 0.0 0.0
"i didnt understand this lecture guess i need to read a book...." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 13361.0 0.0 0.0 0.0
"Excuse me, does it mean that the basis of the input space and that of the output space is the same {v1, v2, ..., v8} at 45:25?
Then, if this is true, when does change of basis happen?
I get confused here, please help me, thanks a lot!" 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 3698.0 0.0 1.0 0.0
"it is..." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13678.0 0.0 0.0 0.0
"It's a weighted average, so you have to multiply the previous center of mass by the number of blocks, not just compare the center of mass at the previous block to the new block. When you have 2 blocks and add a 3rd, the 3rd block is (2+1)/3=1/3 of the total mass, then the 4th block is (3+1)/4=1/4, and so on." wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7023.0 0.0 1.0 0.0
"This is the easiest course ever" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10749.0 0.0 0.0 0.0
"lol im here becaue my calc3 professor at purdue gave the worst 2 course review lectures EVER!! going to do make a ratemyprofesor account just to talk about hiim" ZwpwmGP5ITM "Lec 34: Final review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13828.0 0.0 0.0 0.0
"Oh my, his integral signs are...delicious lol" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8021.0 0.0 0.0 0.0
"Excellent teacher...deserves an award if already not earned some." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3676.0 0.0 0.0 0.0
"@DNYAP 
It's because the length of the curve gets closer and closer to the length of the line (infinitely close gives the same length and therefor the ratio between the curve and the line tends to 1) where the linelength = sin x and arclength = x. " kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1609.0 0.0 0.0 0.0
"I would personally go up and shake this man's hand after every lecture... he's that damn good" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6267.0 0.0 0.0 0.0
"i'd never learn a thing with this guy as my professor. He's so incredibly boring and doesn't explain things well at all. Half the time he just sayswhat he's writing and then explains none of it" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13510.0 0.0 0.0 1.0
"Hard to tell if this is before or after the exam was sat?" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 4429.0 0.0 0.0 0.0
"1:50 My favorite part of this video.

""PERPENDIC||  ULA  ||R""
===========           ====" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 603.0 0.0 0.0 0.0
"in case we had two constraints, x>0 & y>0, should we add another variable for x & y too? i guess in this case when x & y are bigger than 0. this variables(gamma_x,gamma_y) would be 0. thanks in advance" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13581.0 0.0 1.0 0.0
"Still remember the silly definition of a matrix as rows of number? Too silly when all you have encountered was scalars and vectors. Thinking of matrices as rows or columns each of which represents a vector makes all sense and could creatively be used for a variety of applications. A matrix seen as a collection of column vectors represent the basis of a vector space is a great tool to define and compute coordinate transformations. Einstein’s General Relativity could have not existed without such concept. Imagine a continuous transformation of coordinates where each subsequent coordinate change is a differential vector and the transformation is continuous." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8899.0 0.0 0.0 0.0
"This is also USA. A very impressive part of it. Sharing wisdom. Thank you professor Strang, and thank you MiT." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10609.0 0.0 0.0 0.0
"Full Metal Jacket! ha! HA!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3948.0 0.0 0.0 0.0
"Good review for ap calc even though it’s multi variable" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4154.0 0.0 0.0 0.0
"Wow thank you" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 12034.0 0.0 0.0 0.0
"It is an incredible gift to have this course open to the public, truly a service to the world." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6936.0 0.0 0.0 0.0
"It's always a pleasure listening to lecture of a Legend." 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 7026.0 0.0 0.0 0.0
"why he select x2 and x4 as free cols? why not x1,x2 or x1,x3?Why x2,x4 can be free cols and why we can set any values to them?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 15319.0 0.0 1.0 0.0
"16:53. The sequential v. matrix representation of the sample space looks like a game in extensive form and normal form." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 491.0 0.0 0.0 0.0
"Glad to see this posted. Hoping of going to the Eastern Half of Australia next semester so that I can study this." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 4060.0 0.0 0.0 0.0
"I don't understand why E[X_i, X_j] = P(X_1 X_2 = 1). Where does that come from? Also, don't we need to know also P(X_1 X_2 = 0)?" EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 5350.0 0.0 1.0 0.0
"This man just truly loves linear algebra, and it's fantastic." or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10875.0 0.0 0.0 0.0
"please post the course for introduction to probability! :D thank you for the videos btw!" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 14189.0 0.0 1.0 0.0
"Why is there no Lec 8?" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11892.0 0.0 0.0 0.0
"No words for sir strang ,he is my favorite teacher" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 7897.0 0.0 0.0 0.0
"This man has dedication!
Also, that girl in the beginning must have been a sharp genius." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10850.0 0.0 0.0 0.0
"1 done" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 315.0 0.0 0.0 0.0
"I really admire him for being able to give improvisation answer to students' questions so fluently." ZwpwmGP5ITM "Lec 34: Final review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5903.0 0.0 0.0 0.0
"Good Job Professor" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4114.0 0.0 0.0 0.0
Thanks! 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9819.0 0.0 0.0 0.0
"7 people took statistics" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1388.0 0.0 0.0 0.0
"this is lullaby to me" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 14866.0 0.0 0.0 0.0
"How did he work out at 12:50?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 4838.0 0.0 1.0 0.0
"He didn't finish the example from the previous lecture did he?" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4472.0 0.0 1.0 0.0
"okay, I know a lot of people have already said this already...but this is from the heart

Thank you MIT" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14132.0 0.0 0.0 0.0
"Allah razı olsun ...." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 2316.0 0.0 0.0 0.0
"this course is normal" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 14798.0 0.0 0.0 0.0
"Thank you Professor Strang!! You made linear algebra my favourite course this semester :D Love your passion for teaching" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9224.0 0.0 0.0 0.0
"I would agree with you were it not for the FACT that MIT is asking not the Chinese, not Europeans, not those in the Southern hemisphere, nor the Northern hemisphere, but specifically Americans to foot the bill to, as you said, increase global standards, help mankind, educate ALL students, blah, blah, blah.  Americans should not be continually asked to sacrifice their own flesh for such endeavors.  Why should I pay taxes to pay for schools who turn out only foreign grads?" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6254.0 0.0 0.0 0.0
"25:11 outrageous" _CdoRiNSrqI "Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 770.0 0.0 0.0 0.0
"intelligence is the possession of knowledge...smartness = good at learning and/or good at applying or using knowledge." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13615.0 0.0 0.0 0.0
"Dr. Strang I see this matrix from a finite point of view.  W is a generator 7 and P is 49 with a range 1 to p-1.  
7^8 = 5764801,  5764801 / 48 = 120100.0208,  120100.0208 - 120100 = .0208 3333,  .02080333 (48) = 1.  I suppose this matrix is part of a discrete log problem. finding the exponent in Zp^*.  this matix looks awfully close to the array for finding primitive roots.  If so would numerical sequences that do not have a repeating pattern  of numbers be Eigenvalues.  Could you bring this cluster mess all together and show the short cuts." 1pFv7e9xtHo "31. Eigenvectors of Circulant Matrices: Fourier Matrix" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3505.0 0.0 1.0 0.0
"The ONE TRUE KING 😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍😍" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 9973.0 0.0 0.0 0.0
"do not forget about heat transfer and thee laws of thermodynamics." jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12753.0 0.0 0.0 0.0
"Very nice video. Please do watch my video "" Indeterminate forms and l’hospital’s rule in Hindi- 0/0 Form "" Complete Explanation is in Hindi. 
link is here.

https://youtu.be/TgWaex0RUOQ" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11215.0 0.0 0.0 0.0
"This guy goes really fast, I love it, finally a real challenge. " 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10510.0 0.0 0.0 0.0
"Thank you Sir Mr. Jerison
" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9233.0 0.0 0.0 0.0
"Someone please explain why if x <> x0, we still get x - x0 = 0? Should it be just a very small number that approaches 0 but never does?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8838.0 0.0 1.0 0.0
"Why, oh why did I come to Cornell to study math= =" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11942.0 0.0 0.0 0.0
"Do you have the REAL video player. If you don't get that and you will be able to record them. Usually it would only take about 10 minutes or so to record this video for instance. When you are watching a video the REAl logo will be somewhere on the screen click on it and it will have an option to record." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3419.0 0.0 0.0 0.0
"I am confused about the calculations of variance in the practice example. If the variance is the distance from the mean, it seems to be 1/2(a^2+b^2) instead of 1/2(a^2,b^2)." z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5072.0 0.0 1.0 0.0
"But why does it look like it was filmed in the 1980's ?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 2968.0 0.0 0.0 0.0
"love the ending..." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 13873.0 0.0 0.0 0.0
"love it, thanks!" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13868.0 0.0 0.0 0.0
"This is making such big difference. My math professor said that we won't have any video lectures while she's teaching. I think this is kinda backwards thinking, because sometimes you can't come to the lecture at the given time, but still need to go through it. If you miss, you're doomed and the more you miss, the more chance there is to fail the class. So this is great. Thanks MIT!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 10688.0 0.0 0.0 0.0
"I really appreciate 18.06. It is my first lesson in linear algebra." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5904.0 0.0 0.0 0.0
"Die-agrams x)" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 3398.0 0.0 0.0 0.0
"the lectures are getting more and more exciting. Differential was rather boring." ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14712.0 0.0 0.0 0.0
Albegra....-_- HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2292.0 0.0 0.0 0.0
"at around 14:04, regarding flux what if curve is also moving? how to tackle that?" _CdoRiNSrqI "Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12470.0 0.0 1.0 0.0
"Okay, see you wednesday!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 8054.0 0.0 0.0 0.0
Prerequisites?? VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8243.0 0.0 0.0 0.0
"Can anyone clarify why (at 48:01) he sets sin(θ) ≈ θ  θ^3/6, leaving out the second degree term (θ^2/2) as it seems should have been next according to the Taylor expansion? He doesnt do that when setting cos(θ) ≈ 1  θ^2/2. I keep thinking about it but cant figure out what Im missing." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3016.0 0.0 1.0 0.0
"Dang - He's good!" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3311.0 0.0 0.0 0.0
"I can't help applauding at the end..." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 5218.0 0.0 0.0 0.0
"Great Lectures!! Really nice
But Reading the same books for this along made it more comprehensible 
Thanks MIT. for your great help" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 4206.0 0.0 0.0 0.0
"aprendi mas con este video que lo que me enseñan en clases " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12395.0 0.0 0.0 0.0
"thankyou professor!! thanku MIT!!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 14617.0 0.0 0.0 0.0
"41:09 for some insane blackboard duster action" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1147.0 1.0 0.0 0.0
"I loved this amazing lecture. Great professor, and great content. Thanks for sharing it openly on YouTube." wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5859.0 0.0 0.0 0.0
"Oh my god. These lectures are horrible." yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 8020.0 0.0 0.0 0.0
"I was so frustated with my math Professor of my university, cuz every he teach us, it slips from our heads. Thanks to Sir David, he supported me." 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6163.0 0.0 0.0 0.0
"Thanks again to the people who put this up. I liked this guy even better though the regular guy is good." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9675.0 0.0 0.0 0.0
"@SwissJustMe 

honestly i noticed that too....i think the professors  are just easier.." z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1733.0 0.0 0.0 0.0
"Finally! Such an exceptional set of lectures. Thank you, Prof. Strang. I can finally move on to machine learning with some serious confidence!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 3789.0 0.0 0.0 0.0
"@datHulkinZ its the general frmula for a circle O-O" ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1822.0 0.0 0.0 0.0
"haha, i like this guy" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13047.0 0.0 0.0 0.0
"very helpful to understand those of theory" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 15017.0 0.0 0.0 0.0
"Thank u sir❤️" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9078.0 0.0 0.0 0.0
"I really appreciate that gilbert strang give such an intuitive course to us. After I see some courses of American colleges I think American's college education  is much better than China's." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5905.0 0.0 0.0 0.0
"Hello all. I had to watch Khan Academy's Trigonometry videos to get back up to speed with this lecture. The law of sines and cosines didn't stick with me from high school." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4656.0 0.0 0.0 0.0
"Will this course cover jacobian and hessian matrix?Just asking." k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11951.0 0.0 1.0 0.0
"I honestly think that his handwriting is really good. It's got it's own swag within itself." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5580.0 0.0 0.0 0.0
"No one bothered to asked him how 2*Xo*Yo turned out to be equivalent to 2. not good." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7882.0 0.0 1.0 0.0
"Gilbret Strang !" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 4043.0 0.0 0.0 0.0
"Best teacher of Linear Algebra ever!!" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2879.0 0.0 0.0 0.0
"that asian guy with the time stamps is gone now." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 14625.0 0.0 0.0 0.0
"is sir Gilbert strang still alive??" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 13643.0 0.0 0.0 0.0
"He is literally teaching me my whole class.....maymester is no joke" mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 4521.0 0.0 0.0 0.0
"2:15 he begins making a really good point. Start with the symbols...then state what does it mean...then say why it is true. I really don't like how many professors start with proofs. They lose students" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 867.0 0.0 0.0 1.0
"The students in the lecture are truley showing great self-control cause if I were taking this class I would be cracking up incessantly." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 10289.0 0.0 0.0 0.0
"@bobdagangster 
immature comment" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1802.0 0.0 0.0 0.0
"22:03 ""Where in calculus, you really, you know, you're trying to visualize these things, well 2 or 3 dimensions is kind of the *_limit_* ...""
Professor Gilbert Strang: Come for the fantastic teaching, stay for the fantastic puns." Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 695.0 0.0 0.0 1.0
"Basics of vector calculus understands properly." dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 2810.0 0.0 0.0 0.0
"although i really admire MIT OCW, what bothers me is that the majority of videos covers easier undergraduate stuff. i would like to see more advanced lessons if there are any filmed." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12333.0 0.0 0.0 0.0
"If we take the matrix A times with the zero vector of R^4, do we get a four-dimensional space ?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 6533.0 0.0 1.0 0.0
"Great lesson from a  humble Professor with a sense of humor." k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4311.0 0.0 0.0 0.0
"I guess this is why MIT is the best. " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5457.0 0.0 0.0 0.0
"There is an important piece of information missing in the lecture; The fact that any particular solution p_i is reachable from another particular solution p_j + some combination of nullspace. Now one can claim that all solutions are included in x_p+x_null" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 10371.0 0.0 1.0 0.0
"What a beast." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 11388.0 0.0 0.0 0.0
"What a brilliant lecture !!!" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 11397.0 0.0 0.0 0.0
18:07 FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 529.0 0.0 0.0 0.0
"my thanks to MIT for providing not only a proffesor whose interested in teaching.... but good at it.. and .. providing it for free. Some day.. i hope to attend

thanks" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 14007.0 0.0 0.0 0.0
30:00 BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 880.0 0.0 0.0 0.0
"that large chalk is interesting." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 14637.0 1.0 0.0 0.0
"Well pi is not 3 and a little more *if you ask an engineer" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11356.0 0.0 0.0 0.0
"Thank you so much Professor Strang and MITTTTT, my best summer friendddd! yahoo! Linear Algebra!" QuZL5IKpO_U "24b. Quiz 2 Review" "MIT 18.06 Linear Algebra, Spring 2005" 9359.0 0.0 0.0 0.0
"Really great professor" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8516.0 0.0 0.0 0.0
"Great point on comparing matrix Nuclear norm with vector L1 norm, which tends to find the most sparse winning vector. I guess the matrix Nuclear norm may tend to find 'least' weights during the optimization." NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4319.0 0.0 0.0 0.0
"עכשיו אני בוגר הנדסת אלקטרוניקה. אָמֵן" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 15562.0 0.0 0.0 0.0
"I just want to say to all those guys watching this series on linear algebra to checkout 3blue1brown essence of linear algebra first then come back to this again . 3B1B videos literally helped me understand these videos in much easier way with much less efforts." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5626.0 0.0 0.0 1.0
"at 10:00 he says ""columns of C are combination of columns of A""
I think is might be mistake there..  it should be like  ""columns of C are combination of rows of A""..
if no then please clear my doubt" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12410.0 0.0 1.0 0.0
"This guy needs to take an English course." WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10557.0 0.0 0.0 0.0
A53858 PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2174.0 0.0 0.0 0.0
"Finally，firstly time in this course saw so many cleaner writing XD. Eraser is horrible!!" bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3795.0 0.0 0.0 0.0
"10/05/2020 thanks" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 334.0 0.0 0.0 0.0
"humbled and honored to learn from you sir." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 13317.0 0.0 0.0 0.0
"HAHA, every single video has different white balance and contrast. I've never seen the same room so many different ways." hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4394.0 1.0 0.0 0.0
"How is one to know what each lecture is on?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4871.0 0.0 0.0 0.0
"It's not that what he's teaching is wrong or anything he its just that he gives no motivation for why he knows this, why there is a need for it and what the intuition is. That is valuable for students who are knew to this & 5 minutes on the intuition connected to previous knowledge is better than 50 mins of confusion.

He's a good teacher but I think most people would have to be already familiar with the concept to appreciate any of it, most would go to khanacademy videos to get the intuition :p" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7063.0 0.0 0.0 1.0
"Why the skew-symmetric matrix have zero or imaginary eigenvalue?" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 11922.0 0.0 1.0 0.0
"@UKGaming360 yeah word me too... wtf" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1747.0 0.0 0.0 0.0
"@muslim86mus It mentions it once because that was on the schedule. And partial derivatives aren't related to partial differential equations? Then I guess variables aren't related to algebraic equations." ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1956.0 0.0 1.0 0.0
"@ShaneHayes123 The first year(s) of Uni are very similar in work to A levels and equivalent qualifications" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1722.0 0.0 0.0 0.0
"I Really Like The Video Left and Right Inverses; Pseudoinverse From Your" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 4986.0 0.0 0.0 0.0
"1:09-1:14 Notice both what he's saying and whether or not someone is walking through the door behind him." XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 581.0 1.0 0.0 0.0
"thaaaaaaaaaaaaaaaaaaank you professor" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14445.0 0.0 0.0 0.0
"This is not a lecture, this is art." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10696.0 0.0 0.0 0.0
"I'm into the fifth minute and wondering whether he made that mistake in last lecture knowingly" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6335.0 0.0 1.0 0.0
thanks eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14544.0 0.0 0.0 0.0
"I love his sense of humor - the flashmob lol" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 5743.0 0.0 0.0 0.0
"Thank you so much for providing these lectures for free. This course is awesome." a66tfLdr6oY "11. Parametric Hypothesis Testing (cont.) and Testing Goodness of Fit" "MIT 18.650 Statistics for Applications, Fall 2016" 9363.0 0.0 0.0 0.0
"This dude speaks fluent" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10500.0 0.0 0.0 0.0
"Nice to brush up the fundamentals" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7859.0 0.0 0.0 0.0
"Were you not paying attention the whole time?" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11381.0 0.0 0.0 0.0
"Wierd algoritm. Suddenly I finally get what I actually subscribe. 👍🤷‍♀️" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 11944.0 0.0 0.0 0.0
"Professor Strang ,thank you for an awesome lecture on Distance Matrices , structure of Neural Nets and the Learning Function. All these mathematical concepts improves  my understanding of Machine Learning." L3-WFKCW-tY "33. Neural Nets and the Learning Function" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8337.0 0.0 0.0 0.0
"Thank you so much Prof. Strang, i learnt so much from the course and implemented a lot of in C++." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9358.0 0.0 0.0 0.0
"Dr. Gilbert Strang is a truly great professor" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3498.0 0.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8426.0 0.0 0.0 0.0
"I Really Like The Video From Your Partial differential equations review." ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4966.0 0.0 0.0 0.0
"I Really Like The Video Newton's method and other applications From Your" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4990.0 0.0 0.0 0.0
"@hunglikehuang 

Lol, you must accept one or the other, but not make an explanation about how you can get to that point from simpler math.

I agree, it would have made it simpler, but I'm not complaining because this is as simple as it gets in a college lecture. Maybe it's somewhere else on the internet." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1872.0 0.0 0.0 0.0
"Hm, MIT got  good chalks... =O" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4772.0 1.0 0.0 0.0
chalkboards! 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12649.0 1.0 0.0 0.0
"Great professor, great human!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4325.0 0.0 0.0 0.0
"I'm so excited! I'm now at the tail end of a Master's program for Data Science in part due to Dr. Strang's linear algebra lectures. My future job heavily uses CNNs and I get to keep improving with Dr. Strang. I literally owe him my livelihood. <3" hwDRfkPSXng "Lecture 32: ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6373.0 0.0 0.0 0.0
"Truly amazing how professor Strang keeps on teaching despite his age." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11089.0 0.0 0.0 0.0
"Who would have guessed, when this guy explains it, it almost sounds easy! You, dear dr. Strang, are a master at what you do..." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 11756.0 0.0 0.0 0.0
"Option Code 8
Junction Junction Sigma Equal 8 promoted Queen Of Chess Proof.," MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8131.0 0.0 0.0 0.0
"How is |C|^2 = (A-B) ???" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4877.0 0.0 1.0 0.0
"Simple made perfect." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8660.0 0.0 0.0 0.0
"Why are we throwing out the column three? I mean we reduce any column to zero by elimination. C1 = C3 - C2  and   C2 =  C3 - C1 . Can somebody explain this please?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 11788.0 0.0 1.0 0.0
"Thanks professor ! It really really helps understanding 3D computer vision works." Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 9761.0 0.0 0.0 0.0
3:47 VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 1117.0 0.0 0.0 0.0
"@hesham3540 yes" seO7-TwXH_I "Lec 30: Line integrals in space, curl, exactness... | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1867.0 0.0 0.0 0.0
"This lectures makes the idea of linear regression crystal clear." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10838.0 0.0 0.0 0.0
"his chalk on the blackboard sounds are just so satisfying 😍 why doesn't all chalk sound like this??" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 13160.0 1.0 0.0 0.0
"listening to those lectures while studying networking is my new hobby, am I okay?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 13811.0 0.0 0.0 0.0
"He just non-chalantly planted the idea of Group Theory in at the very end of the lecture - Genius!
If only one can make a math playlist of all the best lecturers in the world... may be I will do this." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 4558.0 0.0 0.0 0.0
"Who needs live teachers anymore when you can just see the whole thing on youtube?
Why pay them to give the same class over & over? 
You can just watch whenever you want." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11750.0 0.0 0.0 0.0
"Although the audio is low in this video, DR. Strang relay the information on differential equations and exp(At) very well. Matrix exponential is very important in linear systems." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 2328.0 0.0 0.0 0.0
"graduated with a degree in data science, I still have to be here" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12960.0 0.0 0.0 0.0
"20:00 ""There are many paraboloids in life"" ~Auroux" WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 639.0 0.0 0.0 0.0
"I feel like a kid on christmas ;)
I have enjoyed his Lin. Algebra and the CSE course so much, I can't wait till I find the time to do this course!

Thumbs up from Bavaria!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5393.0 0.0 0.0 0.0
"you are amazing!~" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15491.0 0.0 0.0 0.0
"Prof Gilbert Strang is a legend by his own right!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8263.0 0.0 0.0 0.0
"100 students in a class. each pay 50USD a day aprox for university. perhaps 25USD for this lecture alone. (2500USD total!) 
And we get it for free!
This really helps those without opportunities to learn and advance." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 336.0 0.0 0.0 0.0
"this can't be ther full course their not even done differentiation yet." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14797.0 0.0 1.0 0.0
"Good job sir I am also math teacher in india" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4129.0 0.0 0.0 0.0
"I found it more interesting and time saving for me to watch these lectures on 2x speed." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 5430.0 0.0 0.0 0.0
"Gilbert Strang's lectures are wonderful and have saved me in several classes where they (were supposed to) teach the same stuff!  I'll most definitely keep watching anything he teaches.  I did, however, cringe when he put an equal sign between Q0R0 and R0Q0 :-(." d32WV1rKoVk "12. Computing Eigenvalues and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4032.0 0.0 1.0 0.0
"Thank you!..every thing makes sense now!" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9488.0 0.0 0.0 0.0
"It's great that there are over 100000 views even on the 5th video. I'd like to think that it's because people just love learning and discovering math, but probably most people just need it for a class. Still, it's good that people are learning these things." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 7046.0 0.0 0.0 0.0
"Is he Markov? :P" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 6768.0 0.0 0.0 0.0
"My work doesn't require linear algebra, so I'm studying this to understand what my colleagues are up to and how some of the instrumentation I work with operates.  After looking at the textbook I thought this would be over my head, but the lectures are excellent. Plus, there is no stress in this course or in the presentation.  When I don't understand something I would look it up on line elsewhere, but that wasn't often necessary.  In other lectures we get the mechanics, but not enough to go through understand the concept behind the mechanics.  

I stop either before or after a new concept is presented and try to play with the example matrix on a piece of paper trying to figure out the next bit of the lecture before Prof. Strang explained it.  More than half the time I was wrong, but I got it enough times to gain confidence. In order to make the matrix manipulations easier I did all the calculations for each entry  in row by column dot products.  This made for a messy piece of paper, but avoided arithmetic errors and communicative multiplication errors.  After doing this, my error rate went way down.

Thank you. MIT!  Thank you Professor Strang!
(Suggested retitle: James Stewart teaches Linear Algebra.  It's like listening to Elwood P. Dowd.  A gentle explanation that makes me happy just listening to it. What's not to like? )" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7797.0 0.0 0.0 0.0
"@interxavierxxx How did they save your life?" wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 1889.0 0.0 0.0 0.0
"It's pleasure to learn maths from an MIT professor" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7065.0 0.0 0.0 0.0
"My favorite way to inverse a matrix of any n×n is to find its determinant (to make sure that it can inverted), then write an augmented matrix such that aug(A)= [A | I] and do row reduction until you get aug(A)= [I | A] where the A on the righthand side of aug(A) is the inverse of A, if the matrix is invertible that is. xD" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7750.0 0.0 0.0 1.0
"And thanks MIT for this content" jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2447.0 0.0 0.0 0.0
"Oh.... its just Mathematics living through him....🙏 Respect." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8035.0 0.0 0.0 0.0
"5:45 group the terms to get 0/0
11:50 remarks about sin & cos's derivatives
15:00 geometric proofs" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1365.0 0.0 1.0 0.0
"but then WHAT IS DETERMINANT?" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 12574.0 0.0 1.0 0.0
"Why Julia Alone, Could be Python or Octave or Matlab. Its just another language." d32WV1rKoVk "12. Computing Eigenvalues and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11768.0 0.0 0.0 0.0
"Can't someone reedit it and remedy its semi-ear-sound problem?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 3126.0 0.0 0.0 0.0
"so this is that Michael Sipser whose book we all read and love" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 14348.0 0.0 0.0 0.0
"make the video 2X ... you will thank me" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13897.0 0.0 0.0 0.0
"arrogant scrub" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12404.0 0.0 0.0 0.0
"do you want them (the videos) to be not 50 but 95 minutes?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 12760.0 0.0 0.0 0.0
"@Rrumiiii take the partial derivative with respect to x, then to y...." 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1710.0 0.0 1.0 1.0
"muito bom... pra quem aprender cálculo de verdade..." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13964.0 0.0 0.0 0.0
"Thanks you!" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9818.0 0.0 0.0 0.0
"Consulted several books before, finally understood Bayes in continuous case in this video." H_k1w3cfny8 "10. Continuous Bayes' Rule; Derived Distributions" "6.041 Probabilistic Systems Analysis and Applied Probability" 3205.0 0.0 0.0 0.0
"Hey you guys, I am looking for someone who has the book and check a specific example please on page 28 example 1.14. 
Probability of Alice being up to date if she was behind the previous week is given as 0.6 but writing the equations they have written P(U3|B2) as 0.4 . Is it a mistake??? It must be? I am confused. If someone can look into it, would be much appreciated. Thank you!!" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 4695.0 0.0 1.0 0.0
"For those interested here is an intuitive way of deriving the heat equation from 3Blue1Brown:

https://youtu.be/ly4S0oi3Yz8" wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 3904.0 0.0 0.0 0.0
"boğaziçililere selam olsun" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 12553.0 0.0 0.0 0.0
"Future employer: where did you study?
Me: MIT
Future employer: you’re hired!!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3962.0 0.0 0.0 0.0
"I came back to this after seeing a Domain/Codomain description of subspaces in row perspective/column perspective tied to the rank-nullity theorem.  This is so much clearer than the introduction I had to this material.  I would love to see his description of the link between row rank/col rank" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 5179.0 0.0 0.0 0.0
"his chalk work is beautiful, smooth" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13161.0 1.0 0.0 0.0
""" I don't know what Schmidt did""  ahhh priceless." 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 14.0 0.0 0.0 0.0
"Thank you OCW and Prof. Aureux." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9176.0 0.0 0.0 0.0
"He made it easy to understand!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 4578.0 0.0 0.0 0.0
"@39:29 how did he get rad 5 so quickly. I heard “16-11” I don’t know how he got the 16. If he used the quadratic formula, that was some light speed calculation of b^2-4ac, sqrt, and divide by 2" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 1549.0 0.0 1.0 0.0
"still uploading 480p in 2017" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 14399.0 0.0 0.0 0.0
"Can anyone explain why at 44:41 why the integral is what it is" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3031.0 0.0 1.0 0.0
"wonderful lecture thank you so much!!!
" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15394.0 0.0 0.0 0.0
"you have changed lives of millions." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 15505.0 0.0 0.0 0.0
"You save my life. You save my whole grade. I do think my professor should have watched this. Thanx." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 12236.0 0.0 0.0 0.0
"Who can guess where the next black board might come from." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 11726.0 1.0 0.0 0.0
"I hope I saw this lecture way more earlier! Just amazing and fun! :)" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5582.0 0.0 0.0 0.0
"airplane example was awesome ...." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 12317.0 0.0 0.0 0.0
"He got me when he said: ""can I just right [ IF]""" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 4487.0 0.0 0.0 0.0
"Even though the lectures cover same material as the textbook, it's nice to listen to the lectures for additional insights that aren't written in the book." H_k1w3cfny8 "10. Continuous Bayes' Rule; Derived Distributions" "6.041 Probabilistic Systems Analysis and Applied Probability" 3591.0 0.0 0.0 0.0
"It does help to have a geometric view of it. Great lecture!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6912.0 0.0 0.0 0.0
"Thanks Prof Jerison! 18.02SC here I come!" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9626.0 0.0 0.0 0.0
"This is another beautiful lecture that summaries Probability, Mean, Variance and Lagrange Multipliers by the grandmaster of linear algebra." z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10631.0 0.0 0.0 0.0
"Super lucky students getting taught by a Legend" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8957.0 0.0 0.0 0.0
"Finally done with the course, was a pleasure learning from you baguette man, worth the hundred hours." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3769.0 0.0 0.0 0.0
"Would be nice to make an insight on the functions over random variables. If i have Y=e^X for example" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 12006.0 0.0 1.0 0.0
"Hello, if anyone is aware where it's possible to access those Julia homework assignments, which Prof. Strang mentiones, I would appreciate if you can let me know :)) thanks in advance (it's not on course official page unfortunately)" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4666.0 0.0 0.0 0.0
"When I observe a human being like that developing his profession, I have the mind that it would be difficult for me to establish a corelate value of salary for a being like that. What metrics I would have to use to in no time fail to be fair with the exception value of it." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 11605.0 0.0 0.0 0.0
"it is the first time that I have made sense of the determinant's meaning, great!" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 13675.0 0.0 0.0 0.0
"is there any material i can use to practice by myself i can find anywhere?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13651.0 0.0 0.0 0.0
"why my teacher is not like him!!!????" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15353.0 0.0 0.0 0.0
"I think the formula for the derivative of a singular value is wrong because d sigma/dt is a diagonal matrix and U^T dA/dt V is not in general. 
The mistake comes because dU^T/dt U + u^T dU/dt = 0 and not each term separately.   The correct formula is d sigma/dt = diag(U^T dA/dt V), the diagonal the stated result." AdTvkFsqcDc "16. Derivatives of Inverse and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6054.0 0.0 1.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8441.0 0.0 0.0 0.0
"24:40 , can anyone tell me why x1 and x2 have a hat ? x has a hat because x is a vector consisting of x1/x2. But x1 and x2 are just scalars that multiply the basis vectors a1 & a2  right ?" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 745.0 0.0 1.0 0.0
24:18 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 730.0 0.0 0.0 0.0
"DR. Strang your first Quiz is very challenging. Professor Strang it  seems to me that you force the students to think about linear algebra in an abstract  sense, however solving problems from the text book should help each student to perform well on quizzes and exams." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 3285.0 0.0 0.0 1.0
"shawn studbbs cosin" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 14290.0 0.0 0.0 0.0
"why is it that the integration of x^2 turns out to be 1/3 when the series divided by n^3 is Less than and greater than 1/3. I did not understand this part, if any of you could explain I would be really grateful" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15334.0 0.0 1.0 0.0
"I have one doubt. If EA = U where E is elimination matrix and U is upper tringular , then det(EA) = det(E)*det(A) = det(U). However at property 7 it was discussed that we first carry out elimination , get U and then use property 7 since it is easier that way and determinant of U will be same as A. That's only possible if det(E) = 1 (by using property 9). Is that always the case?" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 5549.0 0.0 1.0 0.0
Thx. cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 11010.0 0.0 0.0 0.0
"@20.:40 you are still wrong it’s 3.3 not 33" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 1511.0 0.0 1.0 0.0
"@SacredSteve You only need to go as deep as you care to.  Exactitude in any application is never without uncertainty.  Most things are non-linear, which from an exactitude standpoint equals infinite infinities. Sorta hard to put in numbers you can apply to something.  Though infinity is a useful thing, it's hard to describe something tangible accurately with infinity." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1713.0 0.0 0.0 0.0
"@floppyorange Me too, I'm tired about today's youth have it made. The problem is that these OLD ROTTING FOSSILIZED CORPSES of yesteryear believe that nonsense. They're all just right wing ""pick yourself up by your bootstrap"" fanatics, LOL." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1839.0 0.0 0.0 0.0
"33 mijutes" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 947.0 0.0 0.0 0.0
"Great illustration" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4231.0 0.0 0.0 0.0
"love Prof Strang's lecture, enlighten me on the depth of linear algebra" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13859.0 0.0 0.0 0.0
"damn good explanation" Xn8wL2ItzZw "Lecture 9: Limsup, Liminf, and the Bolzano-Weierstrass Theorem" "MIT 18.100A Real Analysis, Fall 2020" 12709.0 0.0 0.0 0.0
"Thanks M.I.T. for making these lectures available to us. It is enlightening to see such talented teachers teach. It is mentally stimulating to think about these concepts. It is satisfying to learn." aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9591.0 0.0 0.0 0.0
"I forgot how to integrate that final integral on stick breaking example. LOL" CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 5427.0 0.0 1.0 0.0
"Randomness is relative, it does not have a absolute meaning. It is wrong to say that something is random or that something is not random. You could say that something is more random or less random depending on the criteria that is being used. You could even eventually consider a scale do measure ""randomness"" depending on the outcome distribution type of a variable.  The true meaning of ""randomness"" would be, for instance, a discrete variable whose possible outcomes have EXACTLY the same probability of happening. The more random a discrete variable is the more likely it's outcome distribution follows a certain type (independently of the specific values that it will assume). A uncertain outcome of a discrete variable may reveal or prove itself as being more or less random considering the type of outcome distribution that it will take. All the exercises that are done resolving binominal, polinominal, multinominal, call them what you want distributions are assuming that all possible values of a discrete variable have exactly the same probability/chance of happening. In other words they' re assuming that the variable is actually random to it's fullest extent. The truth is that the correct answer to these problems is only theoretic because in application it would be impossible in most cases to replicate randomness. This would mean that the actual practical, real life answer to all these exercises would have to consider a more likely convergent distribution type in comparison to the more likely theoretic random distribution type. A random variable is indeed a variable but should not be initially considered random until  proven, through a certain number of trials (the more the better),  to have a more likely theoretical random outcome distribution type . A random variable could be associated with a function (with no input values and with a given range of possible outcome values that follow a certain distribution type).  The possible values that a discrete variable could take doesn't necessarily have to be numbers. They could be anything including shapes, colors, objects, symbols. In other words they could represent anything. This would be the big difference compared to continuous variables.Take the example of dices that, as everybody knows, assume the following outcomes ""1,2,3,4,5,6"". You could consider the numbers as being symbols and not numbers. In this particular case the outcome values ""1,2,3,4,5,6"" could be looked at as being symbols without any arithmetic value. In this case any correlation between the sequence of these symbols and their distribution should be seen as a coincidence. Meaning that there is no sense to calculate the mean or the variance in this particular case, because there is no arithmetic correlation value between symbols or things independently of a more or less random outcome." 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 8493.0 0.0 0.0 0.0
"7:50 Nondeterministic behavior." oNsscmUwjMU "2. Nondeterminism, Closure Properties, Conversion of Regular Expressions to FA" "MIT 18.404J Theory of Computation, Fall 2020" 1404.0 0.0 0.0 0.0
"hey folks, It went smooth for me until min. 36, though I am stucked there.
I was thinking Taylor Series Expansion is a quadrization around a Fixed Point, and Mr. Strang simply uses the t = 0 as the fixed point for his linearization.. For what ı know this Expansion should only approximate around the limited neighbourhood of t=0.

Am I mistaken somehwhere ?
How come is this Taylor Expansion a general thing ? How can it represent the whole e^At for all t ?" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 13148.0 0.0 1.0 0.0
"Thank you Prof Gilbert!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9179.0 0.0 0.0 0.0
"If 1/2 the class does not know that independent columns in an n by n matrix is always solvable then 😅" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 6459.0 0.0 1.0 0.0
"@bjret 

Lecture 8 was the first test, there was no lecture that day. As for lecture 17, I believe it was the mid term. I hope this helps." YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1792.0 0.0 0.0 0.0
"Can someone please explain, how the variance equation is simplified @14:16. What multiplication is it ? Is it inner product ? Don't we get a covariance matrix of size 2 x 2." z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3093.0 0.0 1.0 0.0
"mit challange is awesome, i love the abillity to view this in the 10th grade, love you mit" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13951.0 0.0 0.0 0.0
"*Takes a break from studies*




















*Accidentally learns more*" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 239.0 0.0 0.0 0.0
"32:36 talks hypothetically about 9 dimensional space.
""it's going to be hard to visualize those... i don't pretend to do it.""
...
""pretend you do""
i can't though." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 933.0 0.0 0.0 0.0
"Completed the course, thanks MIT OCW & prof. David Jerison.  I couldn’t find any bibliography listed in their webpage. What book is recommended for this course?" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3183.0 0.0 0.0 0.0
"please upload the rest of the semester" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14191.0 0.0 0.0 0.0
"1.5 x Gilbert Strang = Gilbert Strong" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 326.0 0.0 0.0 0.0
"The camera guy really sucks!" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10030.0 1.0 0.0 0.0
43:44 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 1218.0 0.0 1.0 0.0
"See here for a recap of the main formula and a python implementation of inferential statistics for multiple linear regression: https://xavierbourretsicotte.github.io/stats_inference_2.html" yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 8613.0 0.0 0.0 0.0
"The exam can be found here
https://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/ax-b-and-the-four-subspaces/exam-1/MIT18_06SCF11_ex1.pdf
I always feel the homework and exam problems are a lot harder than what he covers in lectures. I don't have a problem with that - just making an observation. This post was meant for those that think MIT is a cakewalk based on the lectures and this review only." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 10093.0 0.0 0.0 0.0
"And I thought Algebra 2 was hard...." _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2441.0 0.0 0.0 0.0
"Are the notes available somewhere?" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2526.0 0.0 0.0 0.0
"It actually helps you to focus on what is important. :-)" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6905.0 0.0 0.0 0.0
"So I have to draw a 4-D picture on this MIT cheap balckboard - Einstein could do it..:D
" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 8730.0 1.0 0.0 0.0
"I don't follow how x^r = e^rlnx. can anybody help me understand? i didn't follow the explaination in lec6" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5301.0 0.0 1.0 0.0
"If A^T A V = V S is the spectral decomposition of A^T A with S diagonal and V orthogonal, we have that (A V)^T (A V)= S. Hence, the nonzero columns of AV, which is associated with the nonzero columns of A, is orthogonal with all other nonzero columns of AV. Hence, is possible to find an orthogonal matrix U such that A V = U sqrt(S) -- note that the diagonal of S give us the squared norm of each column of AV, which means this is completely fine. Now, this means A=U sqrt(S) V^T. Completing U, if necessary, we have the SVD decomposition. In practice, after the calculation of the spectral decomposition of A^T A, we would calculate the Kern of (AV)^T -- orthogonal to Im(AV) -- and find an orthogonal basis to it, and of course, all the singular values associated with this process would be zero." rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6462.0 0.0 0.0 0.0
"This lecture is a Tour of Force, every sentence he says, including the ancillary comments, are so well crafted that makes everything click with ease. Least Squares open the gates for the siamese fields of Optimization and Inverse Theory, so every bit of insight he shares has deep implications on those fields (and many others). It's not exaggeration to say that the whole lecture is an aha! moment. Very illuminating, thank you Professor Strang" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10790.0 0.0 0.0 0.0
"thank you" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 14469.0 0.0 0.0 0.0
"Sir you  are father  of linear algebra. Nice teaching sir." ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8705.0 0.0 0.0 0.0
"Great Lecture!" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 4202.0 0.0 0.0 0.0
"i didnt get the graph of ln(-x)" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13359.0 0.0 1.0 0.0
"I think that you are wrong." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6045.0 0.0 0.0 0.0
"i ask our lourd to preseve you and your whole familly .and thanks MIT open courseware for  all" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 13342.0 0.0 0.0 0.0
"This guy could be the worst professor of all time" ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10507.0 0.0 0.0 0.0
"do matricies span a space if they do how ?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 12751.0 0.0 1.0 0.0
"Loved your way of teaching sir. It's seems like everything for registered in my memory." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7482.0 0.0 0.0 0.0
"the boy in the front row looks like Harry Potter.." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14671.0 0.0 0.0 0.0
"please explain the example 33:38 in particular iam not satisfied with your explanation on it" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14188.0 0.0 1.0 0.0
"MIT 18.06 Linear Algebra, Spring 2005
Instructor: Gilbert Strang
View the complete course: http://ocw.mit.edu/18-06S05
YouTube Playlist: https://www.youtube.com/playlist?list...

5. Transposes, Permutations, Spaces R^n

License: Creative Commons BY-NC-SA
More information at https://ocw.mit.edu/terms
More courses at https://ocw.mit.edu" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 7501.0 0.0 0.0 0.0
"fantastic man, really I love thatv shit. sympathic, professional, nice homes." p-bXJIa7QVI "Lecture 30: Completing a Rank-One Matrix, Circulants!" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12849.0 0.0 0.0 0.0
"you are actually claiming to be smart when in fact you sound like a cretin with a chip shared between both shoulders... shut the fuck up..and dont make any comments" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15490.0 0.0 0.0 0.0
"At 26:42, he said Eminem" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 2626.0 0.0 0.0 0.0
"Doesn't he make a big mistake in the first example of the video (when he calculates the work done from the field on the particle that is doing the closed path)?

To me it seems as if he completely ignores the effect of the vector field when he calculates c2 and c3, as no mention is made of the look of the vectors and their direction in relation to the trajectory. Instead, as he never gave any algeabric description of the vector field, he implicitly assumes (and I think by mistake) that the vector field is tangent to the trajectory along the entire trajectory (i.e. F dot dr = |F||dr|).

 " z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3468.0 0.0 1.0 0.0
"First, let y=f(kx) and u=kx. This makes y=f(u). Then deploy chain rule so: --- dy/dx = (dy/du).(du/dx). Now compute the derivatives du/dx = k and dy/du = f'(u) Therefore, y' = k f'(u) substitute back in u=kx. This gives - y' = k f(kx). Hope this helps. : ) " 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3825.0 0.0 1.0 1.0
"I LOVE THIS GUY!!! AWESOME TEACHER" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4928.0 0.0 0.0 0.0
"Seriously, when will I use this in real life?" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 8633.0 0.0 0.0 0.0
"In french : Une tête de premier de la classe !" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6635.0 0.0 0.0 0.0
"Why can you just multiply a row by a certain number, and then subtract that multiplied row from another row AND keep the original row in the next step matrix?  Also, why can you multiply the pivots to find the determinate?  " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11795.0 0.0 1.0 0.0
"a blackboard with chalks & dusters ... haven't seen one of these in some time !! ... 

Surprised this lecture doesn't make use of whiteboards / powerpoint " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12280.0 1.0 0.0 0.0
"Its weird cause, i learned this in grade 11 :/" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7096.0 0.0 0.0 0.0
"Hey Yuxuan Wang
I am going to https://www.youtube.com/watch?time_continue=3&v=j9WZyLZCBzs next. See you there" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 4691.0 0.0 0.0 0.0
"@anhhuyalex123 
When a function has absolute value you recreate the function making it with multiple branches depending the number of absolute values.And then you differentate it.
Also Propably your function will not be differentiable where the function changes through the branches." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1781.0 0.0 1.0 1.0
"Also interesting is the num of watching from 1st episode to the last one, what’s the distribution? Is that a exponential decay?" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 2324.0 0.0 1.0 0.0
"Again, I wish I had a calculus professor like him........instead of professors writing and teaching calculus using their own textbook purely with mathematica....it was so hard for me to get the intuition when I was in college..." UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2272.0 0.0 0.0 0.0
"This handwriting is very refreshing." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10568.0 0.0 0.0 0.0
"in notice box why both of equations don't produce same identity matrix? 43:30" ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13593.0 0.0 1.0 0.0
"nice i'm finaly learning stuff xD" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14037.0 0.0 0.0 0.0
"After watching this course, I wonder if the linear algebra I studied in college was of the same discipline..." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 2265.0 0.0 0.0 0.0
"nice lect
" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 14041.0 0.0 0.0 0.0
"@Arturcook 
I would recommend Bob Proctor as your linear algebra professor. He may not be qualified to teach math specifically, however he understands math is nothing more than adding, subtracting, multiplying, and dividing. He will also get your mind in harmony to achieve good grades." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 1594.0 0.0 0.0 0.0
"It really feels like if you know more,  you can get more from this class. Many thanks~" JBIz7UadY5M "14. Regression (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 6980.0 0.0 0.0 0.0
"Man that joke in the last 😂😂😂😂" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 7574.0 0.0 0.0 0.0
"40:45 its a shame to see that such a brilliant professor  is teaching a class of 0 strength, this is sad,really sad" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1136.0 0.0 0.0 0.0
"It's funny how courses at a more prestigious university is somehow easier to understand." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7041.0 0.0 0.0 0.0
"Why are there no students in the class? They have such great professors and students who attend classes! Unimaginable!!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11780.0 0.0 0.0 0.0
Goood 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 4165.0 0.0 0.0 0.0
"Crazy how this course is not even as difficult as University of Toronto's equivalent multivar. calc class :O" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3259.0 0.0 0.0 0.0
"Vaggos2195 thats why Greece is bankrupt." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11150.0 0.0 0.0 0.0
"great lecture.  why on earth do they clap every single time he erases something ! " tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12986.0 1.0 0.0 0.0
"might want to add that x-1 is a natural number" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 13942.0 0.0 1.0 0.0
"I think the reason why Professor Strang's courses are so popular lies with his personality. He is very considerate so he would try all means to find a way to explain linear algebra concepts easy to understand. This is the same at workplace. Nice people who always take other people's feelings into account tend to provide popular products and services. Some professors offer hard-to-understand, unpopular courses since they don't care about how their students feel at all. They mainly care about whether they are promoted or receive more funding." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6062.0 0.0 0.0 0.0
"simple reason, people make mistakes. Use your own brain at times." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14302.0 0.0 0.0 0.0
愛我了個去～頭一次看見騎自行車上課的，可以的這很MIT，抱拳了。 TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 15631.0 1.0 0.0 0.0
"How the last prob. Can be solved when u put y=acos(theta) ?. Actually, y=asin(theta) so how y can be acos(theta)?

" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4897.0 0.0 1.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8444.0 0.0 0.0 0.0
"Group. They are a nice little GROUP." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 4383.0 0.0 0.0 0.0
❤️ k2inA31Gups "18. Bayesian Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 15608.0 0.0 0.0 0.0
"Do you know what ""to execute"" means? It's not a monosemic word. The context within which it is used here is entirely appropriate:)" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 3421.0 0.0 0.0 0.0
"Why is it necessary that the subspace P or L of R^3 must go through the origin [0,0,0]???

What if this plane P doesn't go through the origin? Isn't it still a subspace???" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 11875.0 0.0 1.0 0.0
"why is multivariable calculus actually hard 
i love his french accent but man i understand less and less of what hes saying as we go deeper into the lectures" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15337.0 0.0 0.0 0.0
"Very good lecture!" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11179.0 0.0 0.0 0.0
"I didn't understand x at @38:00.
Is it a mixed column or one randomly picked? Thanks." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5280.0 0.0 1.0 0.0
"Where did I claim to be smart? I never explicitly claimed to be smart, I only said MIT is not worth 100K a year, which is undeniably true" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11670.0 0.0 0.0 0.0
"thanks proffesor
" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 14604.0 0.0 0.0 0.0
"Coolest chalkboard ever." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3216.0 1.0 0.0 0.0
"Woooow explica bastante bien, es muy claro y lo hace interesante, muchas gracias" feb9j65Iz4w "24. Linear Programming and Two-Person Games" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11996.0 0.0 0.0 0.0
"Like an idiot, I just realized that all this available on the MIT webpage. I think I'm migrating there." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7351.0 0.0 0.0 0.0
"I always found it hard to grasp the concepts of limits, especially when it looked like 0/0 but I learned that you should never think of it as 0/0 because really, that is an undefined number and what is important is that the quantity in the limit tends towards 0, infinity or some other number for that matter.

The professor should maybe have emphasised this when addressing the students question about sin(dx)/dx -> 1 because sin(0)/0 is really an undefined number." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5040.0 0.0 1.0 0.0
:0 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1450.0 0.0 0.0 0.0
"Engineering students must love this" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3569.0 0.0 0.0 0.0
"35:36 I found it disrespectful, why on earth is erasing blackboard worth laughing at?????????" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1015.0 1.0 0.0 0.0
"This type of differentiation seriously blew my mind! :-))) Something that I think can be seriously seriously useful. A bit difficult though to understand it right from this presentation.... 

Where this technique should really score is when you need to do derivatives on numerical functions that you cannot really differentiate by calculus to get high accuracy derivatives. Meaning for example calculating derivatives for parameters when using ode solvers and other alike stuff.

For those you would have to either do finite difference approximations which are quite bad (and meaning also simulating the ode twice at least, thus effectively doing same amount of calculations) , or well how on earth would you calculate an analytical derivative for the whole chain of operations? This would be rightout crazy it seems yet maybe not impossible ... ? 

Is there any comparison for how well the differentiation method performs with the log function which is calculated as a continued fraction? I mean how accurate is the dual component of log(x_dual) compared to 1/x?  And in case 1/x is better would it then make sense to implement a custom derivative part returning 1/x to the dual component?" rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10947.0 0.0 1.0 0.0
"Nice videos, good exam reviews. Too bad interval of convergence wasn't covered, R can be easily found by the Ratio test most of the time so it was surprising to see it not covered." wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7867.0 0.0 1.0 0.0
"10:23 In the u-v coordinates, should the parallelogram still be referred to as Delta A, instead of Delta A'? " UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 346.0 0.0 1.0 0.0
"Just came here from 18.06. I'm so excited :)" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7161.0 0.0 0.0 0.0
"Beautiful connection to the cycle space of a graph. Thank you!" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2815.0 0.0 0.0 0.0
"I thumbs up this video because the vectorial product is positive" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6105.0 0.0 0.0 0.0
"Got extremely confused when he brought transformations in at the end. Why did the original basis vector ""x"" change to ""v"", then why does he compute a T(x) from ""knowing"" T(v1), ... T(v8) BEFORE writing what the actual values of T(v1) .. T(v8) are, and what is this T(x) even used for? and then where does the ""a"" come from?" 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 4169.0 0.0 1.0 0.0
"17:30 that guy just gave a thumb down to the professor. Such disrespect." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 509.0 0.0 0.0 0.0
"49:35 I don't think this example language actually does require nondeterminism? If you just pop everything that matches the current input and push everything that doesn't, and accept if the stack is empty at the end, it should still work. For example, the stack for the sample input (011110) would go 0 -> 01 -> 0 -> 01 -> 0 -> empty. I would try and write out the mathematical notation but I don't have the best grasp on that yet..." m9eHViDPAJQ "4. Pushdown Automata, Conversion of CFG to PDA and Reverse Conversion" "MIT 18.404J Theory of Computation, Fall 2020" 1307.0 0.0 1.0 0.0
Bravo. MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2919.0 0.0 0.0 0.0
"Companion of this lecture, could be this video: https://www.youtube.com/watch?v=6avJHaC3C2U" N-_XmLanPYg "11. Recursion Theorem and Logic" "MIT 18.404J Theory of Computation, Fall 2020" 3175.0 0.0 0.0 0.0
"he teaches so fast that i would feel like a dumbass if i asked a question" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13116.0 0.0 0.0 0.0
"wowwwwwwwwwwww!!!u are amazing sir" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 15440.0 0.0 0.0 0.0
"DR. Strang, this is another fantastic lecture on the Convolution Rule and how it's applied in the real world. Fast Fourier Transform has play important role in convolution over time. Convolution is useful because of Fast Fourier Transform. Convolution is also very useful in Signal and Systems Theory, which is part of Electrical Engineering." hwDRfkPSXng "Lecture 32: ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3289.0 0.0 0.0 0.0
"That guy writes mad fast." Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9890.0 0.0 0.0 0.0
"23:54 lmfao" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 717.0 0.0 0.0 0.0
"He gives the lecture like the place isn't almost empty" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4484.0 0.0 0.0 0.0
"My left ear feels lonely...." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 7767.0 0.0 0.0 0.0
"What is the thinking or thought process of NOT doing operation on x in A*x =b . What is the reason behind it? every row operation i do on A is also done on B but not done on x . WHY?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11540.0 0.0 1.0 0.0
"Would I be wrong if I remark that one can think of the Gauss-Jordan as being Gauss applied once, the rows being flipped and Gauss then applied again?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12003.0 0.0 0.0 0.0
"Wow. 2:17, the chalk on the board is very pleasing to the eye." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12085.0 1.0 0.0 0.0
"And thus it became immortal" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2452.0 0.0 0.0 0.0
"I wish he was my teacher." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 6222.0 0.0 0.0 0.0
Nice! zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7868.0 0.0 0.0 0.0
"vay amk" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 14992.0 0.0 0.0 0.0
"Thanks so much for the lecture. Professor Strang is a teacher that devote his heart to educate people , thanks to him I have been progressing in the field of Linear Algebra." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 9789.0 0.0 0.0 0.0
"just tell me what i said ::))" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 13743.0 0.0 0.0 0.0
"Incredibly fascinating! Probably the best course I have seen on this channel." N-_XmLanPYg "11. Recursion Theorem and Logic" "MIT 18.404J Theory of Computation, Fall 2020" 6704.0 0.0 0.0 0.0
"Nice tie prof <3" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 7857.0 0.0 0.0 0.0
"He donesn't even need any notes! legend" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4477.0 0.0 0.0 0.0
"Any chance someone could help me out with this?  I posted this on a separate MIT conditional probability video where scenario was: ""1 blue marble 4 red in Cup A vs 3 blue 2 red in Cup B"" and conditional probability of picking from cup A given there is blue marbe was said to be 1/4"" because you add all of the blue marbles for denominator and add up those blue marbles in Cup A for the numerator.

But I'm wondering if let's say I have 1 and only 1 marble in cup A, and it's a blue marble, and say 5 out of 11 marbles in cup B are blue marbles.  It feels like if I know I picked a blue marble, then there should be more than a 1/6 chance of that marble coming from cup A.  I guess because since cup A i this case is 100 percent blue?  I don't know..." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 2467.0 0.0 1.0 0.0
"Feels like I know everything well in lecture, but as I sit to do the exercises I can't solve most of them. Is it worth continuing?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 3750.0 0.0 0.0 0.0
"The best thing I like in his teaching style is that he picks everything from very basic. I have attended many lectures and classes, and I personally feel that people lack this; they make things more complicated unnecessarily. Kudos to MIT for this beautiful series. I remember one famous quotation by one of the best teachers that ""Everything is simple and interesting if it is properly conveyed.""" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 10011.0 0.0 0.0 1.0
"This is another fantastic lecture by the grandfather of linear algebra. Symmetric and Positive definite matrices pops up in systems and control engineering." UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 10634.0 0.0 0.0 0.0
"No. Calculus is easy as long as your prerequisite algebra and geometry skills are tight.
Make sure you know how to solve equations, graph functions, know geometry theorems and have a good base in trigonometry and the calculus is a breeze." jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7904.0 0.0 0.0 0.0
"So mostly neurotic system that connect with machine that go with x at y high or lower" cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8774.0 0.0 0.0 0.0
"@achrispens 
Lack of humor ，isn't  he？" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1766.0 0.0 0.0 0.0
"14:37 so there's no way to even appx that?" XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 431.0 0.0 1.0 0.0
"Where is the video he was planning to post on Stellar for the statistical table?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 11694.0 0.0 1.0 0.0
"Excelente aula!!!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3623.0 0.0 0.0 0.0
"Ditto, an awesome professor." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 3404.0 0.0 0.0 0.0
"""I'm sure that 300 different students means 300 different ringtones, but I'm not eager to hear all of them."" and ON QUE my phone rings." 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 67.0 0.0 0.0 0.0
"I Really Like The Video Work, average value, probability From Your" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5003.0 0.0 0.0 0.0
"Yeah the result at 41:40 should be 5/32 or 15,6 %." R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12120.0 0.0 1.0 0.0
"In 17.03, Why UU transpose is symmetric?" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6589.0 0.0 1.0 0.0
"A counter example to what?" zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2105.0 0.0 0.0 0.0
"He reveals the beautiful face of Math. I am not only learning but also I am really enjoying it. Thank you" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4598.0 0.0 0.0 0.0
"people shouldn't at 46:39 it should be e^0 since the limit is equal to 0. If you use direct substitution you get that 1/any number approaching infiniti will always be equal to 0, and so 1+ that is 1. Therefore, 1 to any power=1, and so you get ln1. That is 0 since e^o=1. So where did I go wrong?" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14174.0 0.0 1.0 0.0
"You are the king Mr Strang! Thanks" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12184.0 0.0 0.0 0.0
"A good opportunity to burn calories would be to wipe the blackboard properly." WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 2116.0 1.0 0.0 0.0
"bookmark Least Squares Problem 23:00" ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12551.0 0.0 0.0 0.0
"God of LA" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 4096.0 0.0 0.0 0.0
"Amazing professor. He knows exactly where students may get confused and would take it slow at those moments. Fantastic teaching style and incredible passion and warmth. Thank you Prof Strang." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 2391.0 0.0 0.0 0.0
"you r right
" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15514.0 0.0 0.0 0.0
"I will never understand why MIT courseware produces videos that look 100 years old" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 6191.0 0.0 0.0 0.0
"BRavo...... excellent... live long" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 2806.0 0.0 0.0 0.0
"Is there any method that we can get their handout?" z3SmljnD_nQ "15. Matrices A(t) Depending on t, Derivative = dA/dt" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6834.0 0.0 0.0 0.0
"@EgoSumIndigentia 
You can't show a class of sixty students a graph on your laptop monitor -.-
" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1618.0 1.0 0.0 0.0
"extraordinary professor of maths" ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12836.0 0.0 0.0 0.0
"thanks a lot" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 14563.0 0.0 0.0 0.0
"What textbook is he referring in min. 8, anyone knows?" zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11555.0 0.0 1.0 0.0
"I Really Like The Video Integration by parts, reduction formulae From Your" aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4979.0 0.0 0.0 0.0
"Who dares to dislike this masterpiece of a lesson?" ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11729.0 0.0 0.0 0.0
"I've watched the whole course. Absolutely wonderful. Thank you so much, OCW and Professor Rodriguez." u4qQ1oIQcW8 "Lecture 25: Power Series and the Weierstrass Approximation Theorem" "MIT 18.100A Real Analysis, Fall 2020" 6440.0 0.0 0.0 0.0
"Congrats to everyone who has finished and didn't skip lecture 33 
Have a good day <3



Germany, 2020" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3197.0 0.0 0.0 0.0
"All those watching prof strang's lectures during quarantine, hit a like!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 2313.0 0.0 0.0 0.0
"The Master Yoda of Linear Algebra" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9971.0 0.0 0.0 0.0
"Wish you long life Prof Strang......the world will never forget your contribution..." t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11963.0 0.0 0.0 0.0
"This is truly a fun series of lectures.

Amusingly, every problem seems to boil down to a problem in Linear Algebra!" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 10760.0 0.0 0.0 0.0
"HE is back!! My favourite linear algebra prof of all time!!! 😍" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4400.0 0.0 0.0 0.0
"The lectures I've watched so far in this course ( 2 of 'em) have been just what I need to inspire me to take up maths again.  Wonderful resource!" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10171.0 0.0 0.0 0.0
"yeah,it's where i got confused too" z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15475.0 0.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8432.0 0.0 0.0 0.0
"fantastic lecturer" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12848.0 0.0 0.0 0.0
"His accent is wonderful!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4739.0 0.0 0.0 0.0
"Sadly didn't define the vertical --- x --- notation" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 8592.0 0.0 1.0 0.0
"thank you sir" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14506.0 0.0 0.0 0.0
"Great video! :)" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4352.0 0.0 0.0 0.0
"@39:00 NERDGASM!" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1547.0 0.0 0.0 0.0
"41:50 starts with a seemingly intuitive concept which we usually take as granted. That is- why orthonormal basis are the best basis? Professor Strang explained it beautifully." MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1162.0 0.0 0.0 0.0
"Sir you are a student from lalpani school shimla. You were the topper in +2. I am very happy for you. You have reached at a level where you truly belonged to. I wish you more and more success." k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8706.0 0.0 0.0 0.0
"Anybody here who could answer the question (at 42:42) ""If matrices A and B have same 4 subspaces, then _____fill_in_the_blank____.""" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 2477.0 0.0 1.0 0.0
"27：24，the subtitles is error, I think he means 'n' rather than 'an', it is important。" 3eiio3Tw7UQ "19. Weak Law of Large Numbers" "6.041 Probabilistic Systems Analysis and Applied Probability" 827.0 0.0 1.0 0.0
"mhömhömhö i am a french güy. Actually this is just the video i needed right now." phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13941.0 0.0 0.0 0.0
"Pray for the betterment of MIT and all of the universities there.
God bless you. God loves you always." cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 8237.0 0.0 0.0 0.0
"at 32:30 why is it possible to express dr as (dx dy) vector?
i wanna see proof" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12438.0 0.0 1.0 1.0
"This is great, I'm doing this and Linear algebra, and will be moving on to Multivariable Calc and differential equations. Its a privilege to be taught by one of the foremost institutions in the world. Hopefully MIT will upload their more advance maths courses in the future and share the knowledge with the world. Thank you." 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10667.0 0.0 0.0 0.0
"Beautiful lecture and amazing lecturer! Thank you Mr. Strang!" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 2820.0 0.0 0.0 0.0
"YEEEEEEEEEEEEAHHHHHHHHHHHHH"""" ! <3" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12106.0 0.0 0.0 0.0
"Is Linear Algebra an upper division class? I know that introduction to Linear algebra is lower division." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6750.0 0.0 1.0 0.0
"Good Job Professor" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4111.0 0.0 0.0 0.0
"Is Taylor really that unpopular? (@ 38:20)
We tend to use 'taylor' as a verb: ""Doesn't integrate? Just taylor that shit.""" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 6755.0 0.0 0.0 0.0
"Thanks MIT. #Grateful." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9618.0 0.0 0.0 0.0
"prof strang.. I m 21 ,till this age I did not saw a teacher like .u r awesome.. I started loving Linear algebra. I don't have money to give anything to this open courseware but I can only give blessings from my side.. u r genious.. I hope I could be 0.001 percentage of you!!.. I also want to become a teacher like you.. and will serve the nation by imparting beautiful knowledge like u.. thank you prof.. I will go mit for post doc once in my lyff.. love from india😊" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 14212.0 0.0 0.0 0.0
"I'm an economist, but if with this professor, I can also become an engineer in 6 months. I also wonder if these profs take any drawing lessons. His circles are good!" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6306.0 0.0 0.0 0.0
"My term 2 (semester 2) is about to start. There we have maths 2 and to prepare myself for that I am here.My Senior suggested me this.
I am in foundation level (1st year) of IIT MADRAS (India) BS in Data Science and Applications.
Seems good one!
Yet to explore more!
By the way Thanks to Respected Prof Gilbert and MIT." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7793.0 0.0 0.0 0.0
"I remember doing this in high school. It was interesting but so detached from the real world." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5943.0 0.0 0.0 0.0
"Really is an excellent lecture, helped a lot with my understanding of Bayesian Stats. In the Non-informative priors section, is the unbounded case actually where an improper prior needed?" k2inA31Gups "18. Bayesian Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 8524.0 0.0 1.0 0.0
"MiT students freaked out by Taylor Expansion! I am not alone xD" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7661.0 0.0 0.0 0.0
"what is the difference between Vector calculus and Tensor calculus ?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15165.0 0.0 1.0 0.0
"Well it's quite helpful!" mc1y8m9-hOM "22. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 11355.0 0.0 0.0 0.0
"I cannot possibly over-recommend watching the 3blue 1brown series on linear algebra _before_ (or while) watching this series.  It will really make Dr. Strang's material far more clearer." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5229.0 0.0 0.0 1.0
"thank you, im from germany and our professor sucks." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 14532.0 0.0 0.0 0.0
"Can anyone explain, at 31:39, how do we know that v = e^lambda t * v(0)? Where did the v(0) come from?" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 3034.0 0.0 1.0 0.0
"His hand writing is more clearer than my future" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4753.0 0.0 0.0 0.0
"I'm not even here for learning. I'm an Engineer. I learnt all this in class 12. I just love watching these Math lectures. And I'm trying to revise everything.

The professor here is like the American guy YouTube, for me, an Indian guy. Irony." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6353.0 0.0 0.0 0.0
"its insane that this video is 15+ years old and still so valuable to someone beginning to learn linear algebra like myself" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13712.0 0.0 0.0 0.0
"Where my IIIT Hyderabad people at" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 11696.0 0.0 0.0 0.0
"a great thanx for awesome lesson!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 12284.0 0.0 0.0 0.0
"I wonder if these videos are fair. I go a cheap college that charges me almost nothing. My multivariable teacher isn't very good. So I come here to learn for free. However, those MIT students pay a lot of money for the same education. Is that fair?" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6246.0 0.0 0.0 0.0
"at 28:10 why are we stuck using (*) to find y.
it seems easily solvable to me?" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12433.0 0.0 1.0 0.0
"it is so beautiful the way he explains..." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 13674.0 0.0 0.0 0.0
"Really? Vectors are one of the few things that was useful and didn't pose any problem to me. Examples:
It helped me construct my own the reasoning behind the ""domino effect"" (if a cloud moves ""forward"", and is diverted by a mm - vector addition - it will eventually end up in a different place then it should). And my friend used it to program a ball&pad game (ball has a vector, and wall has one two, and when the ball hits the wall, vectors subtract, changing vector=direction of the ball-bounce)." ZwpwmGP5ITM "Lec 34: Final review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8540.0 0.0 0.0 0.0
"And we are so thankful that you did re-record it! :D" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 2453.0 0.0 0.0 0.0
"Sir, we miss you so much. happy to see you again!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8714.0 0.0 0.0 0.0
"why is there a dislike -.-" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15344.0 0.0 0.0 0.0
"At 28:50 he says, this is a key fact we deduced from Mean Value Theorem (MVT). I don't see how it is so. Can someone explain?" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2634.0 0.0 1.0 0.0
"he really is a fine teacher,  mine just reads off from the book and i'am completely  blank in the end.
your lectures remind me the inspiration i had for choosing maths as my subject" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 13110.0 0.0 0.0 0.0
"Great lecturer . Thank you Dr. Strang" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 4298.0 0.0 0.0 0.0
"1.5x speed gang" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 327.0 0.0 0.0 0.0
"Big picture starts at 20:47" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2892.0 0.0 0.0 0.0
"MIT is doing a wonderful job. Keep it up" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7525.0 0.0 0.0 0.0
"amazing lecture! the best lecture so far" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 12346.0 0.0 0.0 0.0
"Thank you very much 
I think that there is a missing factor (1-P(0,2)) in the response to the questions d and f. Is this true?" XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 9428.0 0.0 1.0 0.0
"+MIT OpenCourseWare 
good day, how is that book called which they use for solving problems ? How could we get that books with theory and practics ? Is it possible? Could you share with us?
Thank you so much for these videos" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 253.0 0.0 1.0 0.0
"I don't why I am in Love with this Guy." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 5362.0 0.0 0.0 0.0
32:00 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 923.0 0.0 0.0 0.0
"What is a discontinuity like in that of the function y=1/(x^2) called?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11515.0 0.0 1.0 0.0
"on the pocket of his shirt, it look like a guy screaming!!! Once you see it, you cant unsee" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14149.0 1.0 0.0 0.0
"these free videos are well worth the price" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14773.0 0.0 0.0 0.0
"@turkeyburgerfries you probably solved it yourself by now, but in case you didn't:
y' is the derivative of the inner function of y with respect to x. So its d/dx (y^2) = (d/dy y^2) * dy/dx which is the same as 2yy' with y'=dy/dx." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2054.0 0.0 1.0 1.0
"why did he label the axes to weirdly? Why did he use z for the vertical axe when he could have just used y to avoid confusion?" zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15296.0 0.0 1.0 0.0
"hi teacher" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 13156.0 0.0 0.0 0.0
"""this is more than just a dead end; it's a crash, burn AND SELF DESTRUCT""" zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 182.0 0.0 0.0 0.0
"At 39:00

The cost of b is not EXACTLY n^2 operations like he says in the video. 
Yes there are n elements, and we assume that all the elements are non-zero from the beginning. But that doesn't mean that EVERY element are being changed. For this to be true(that we are using n^2 operations) we ALSO must assume that there is no 1's in the pivot positions from the beginning. For example if it were 1's in all the pivot positions from the beginning the cost of b would be n^2 - 100(unlikely, but as an example) So the cost of b is not exactly but CLOSE to n^2." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 2656.0 0.0 1.0 0.0
"At 30:00, Is it silly to consider the vector v as a matrix and to look for the rank ??? I get why the dimension of the subspace is 3, because the 4th component does not bring anything new to the space created by the first 3. BUT I cannot say why it would be wrong to take v as a matrix and say the rank is one !!!!!

It seems I am mixing the dimension of the image created by a single vector, with the dimension of the image created by combination of all vectors v of S. If someone can help :)" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 2637.0 0.0 1.0 0.0
"I just realized that (x, 1) as the dual number is x and the derivative of x as a linear function Ax where A=1." rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5614.0 0.0 0.0 0.0
"This was a topic that I found more difficult at University. Had to pause a few times to follow and understand correctly but it was worth it. Really good explanations here." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 10966.0 0.0 0.0 0.0
"thank you so much professor Gilbert Strang. You literally make my day." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 14516.0 0.0 0.0 0.0
"I've been using the terms ""Closed under..."" in two of my midterms now without caring of what it meant exactly graphically...its only now that I understand it. Thanks" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 6407.0 0.0 0.0 0.0
"@zazzolina Nice pants cost money, they don't have, because they spend it in research. So they buy cheap pants. Or something like that." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2081.0 0.0 0.0 0.0
"He pushed the floor instead of the board :))
36:13" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4591.0 1.0 0.0 0.0
"First of, a big thanks for helping me understand the math concepts so much better...Bur really, this could have been explained better by you Mr. professor...Thing is I have been following other MIT video lectures and been amazed at the quality of content presentation. But this particular is not so clearly explained as those other lecture do..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3818.0 0.0 0.0 0.0
"I'm very grateful to MIT for providing all of this for free. Big thanks from Russia!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6397.0 0.0 0.0 0.0
"I love maths ..... but this lecturer is why I hate maths.

You make it so boring" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5765.0 0.0 0.0 0.0
"Professor Strang @ 25:11: ""R2 is, we could say, the plane. The xy plane. That's what everybody thinks""
Me: TELL ME YOUR SECRETS!!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 8344.0 0.0 0.0 0.0
"Thanks for posting these lectures. They are serving as a nice refresher course for me. However, am I the only one who is surprised that this is an MIT course? I had a lot of this course content in AP calculus in high school and I was far and away NOT smart enough to be accepted into MIT." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9692.0 0.0 0.0 0.0
"This video gave me TREMENDOUS AMOUNT OF KNOWLEDGE!!! I liked it very much,but one thing:Why don’t they use dusters instead of keep on changing the Blackboards?(Just asking in a leisurly way)." phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10950.0 1.0 0.0 0.0
"I guess I will have to read the book" z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5453.0 0.0 0.0 0.0
"if S is displacement then dS/dt is velocity... but he defined S as distance so he is correct in saying that dS/dt is speed..." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13530.0 0.0 1.0 0.0
"so fast that even auto caption cannot catch up!" phbw9r1iUDI "7. Parametric Hypothesis Testing" "MIT 18.650 Statistics for Applications, Fall 2016" 14332.0 0.0 0.0 0.0
"Lewin draws his dotted lines so much faster" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7345.0 0.0 0.0 0.0
"Really happy at these lectures... Delivered by pro. Strange" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 8518.0 0.0 0.0 0.0
"this course must definitely absolutely go on edx.
" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14800.0 0.0 0.0 0.0
"Indeed, you are like a magnet Prof. Strang! I couldn't believe I finished all your lectures. Why doesn't it go on and on... Thank you!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 6706.0 0.0 0.0 0.0
"1/2261 I wanna say I feel a little smart. but I am not gonna lie. I am struggling abit lmao. I need to read a stat book after finish up the course." vMaKx9fmJHE "12. Testing Goodness of Fit (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 330.0 0.0 0.0 0.0
"Ive learnt this is school but we don't use delta x. we just say it very simply this just made it confusing." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7105.0 0.0 0.0 0.0
"The best professor! Thank you so much! Always watch your course to make me keep learning linear algebra!" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10006.0 0.0 0.0 0.0
"@amarenpdas1975 Analysis SUUUUCKS! Gosh..." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 1779.0 0.0 0.0 0.0
"Sir,
I have seen your linear algebra lectures, read your book on introduction to linear algebra and calculus and now this lecture series. I have learned a lot from you. I would like to express my deep gratitude towards you. Thank you for contributions." hwDRfkPSXng "Lecture 32: ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8709.0 0.0 0.0 0.0
"Finally reached the end of the course. I am pursuing a career in ML and these lessons have just made the journey a lot easier. There were many concepts I was unable to understand in ML texts. I knew something was missing and that was this course. Thank you MIT. Thank you professor Strang. You are a gift to the world. God bless you." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 3775.0 0.0 0.0 0.0
"Having a live audience might help with the occasional  mis-speaks." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 4452.0 0.0 0.0 0.0
"I kept listening chalk dots on 39:20" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5630.0 1.0 0.0 0.0
"Thank you very much for these lectures. Through your lectures, I truly understood what I was doing in my PhD three years after completing it." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9442.0 0.0 0.0 0.0
"I Really Like The Video Lecture 18: Properties of Determinants From Your" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 4984.0 0.0 0.0 0.0
? _HRTdXJgZ0Q "Lecture 23: Pointwise and Uniform Convergence of Sequences of Functions" "MIT 18.100A Real Analysis, Fall 2020" 1462.0 0.0 0.0 0.0
"I really like the video quality. Thank you so much" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5928.0 0.0 0.0 0.0
"I Really Like The Video Volumes by disks and shells From Your" ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5002.0 0.0 0.0 0.0
"@18:54 am I subtracting wrong or did he?   For 2*R2 - R3 I got (2*2) - 4, (-2 *2) - 1,(2*6) - 2 => R3 : x = 0, y = 0, z = -5 and 10 on the right side.....he got R3 = 0, 0, 5, -10 ??" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1503.0 0.0 1.0 0.0
"I am thoroughly enjoying this lecture! Thank you for uploading this." MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5148.0 0.0 0.0 0.0
"I think it great effort" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6027.0 0.0 0.0 0.0
"Can anyone explain in Example 1 how he got: y-y0 = (-1/x0^2)(x-x0)).  I understand the calculus part (-1/x0^2), but not the rest of the equation." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3023.0 0.0 1.0 0.0
"Duster ❤️" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3532.0 0.0 0.0 0.0
"man that kid who asked the question at 25:48 prob dropped the class..." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13898.0 0.0 0.0 0.0
"what accent is this ?" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15116.0 0.0 0.0 0.0
"It's making me dizzy when camera moves with the movement of professor" KlAjiDivJoQ "Lecture 5: Zorn’s Lemma and the Hahn-Banach Theorem" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 7058.0 1.0 0.0 0.0
"This is the best tutorial every on the subject" gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 10747.0 0.0 0.0 0.0
"This class sounds amazing, best of two mid terms damn" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 10479.0 0.0 0.0 0.0
"made the lecture entertaining. awesome wish i knew about this lecture earlier." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13894.0 0.0 0.0 0.0
"last min 10 yr challenge" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 13758.0 0.0 0.0 0.0
"""We need an example here..Let me create an example"", He totally doesn't need the text book. aha" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 130.0 0.0 0.0 1.0
"ok sambil ngantuk" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 14128.0 0.0 0.0 0.0
"If you just put the cut across the three final lines (5, 1 and 8) you also end up with 14. However, is there any reason why you would choose one or the other?" feb9j65Iz4w "24. Linear Programming and Two-Person Games" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6551.0 0.0 1.0 0.0
"Why did I not have a professor like this? It could’ve made my life so easier" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 11805.0 0.0 0.0 0.0
"Shouldn't at 13:57, the reflection of [1 0] be in second quadrant and not fourth quadrant" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8647.0 0.0 1.0 0.0
"To come at this from the other direction, it is easy to see that the vectors in the second ""basis"" also fail to _span_ R^3 (the other necessary condition to form a basis).  Any linear combination of the three vectors will be of the form (x,x,y), so the vector (1,2,3), for example, is not in the span of the set of vectors." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 11030.0 0.0 1.0 0.0
"Why did he dust the board like that
White chalk on white background looks bad
Mit can't afford marker boards 😠😠😠😠😠😠😠" 0Va2dOLqUfM "5. Maximum Likelihood Estimation (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 11809.0 1.0 0.0 0.0
"This lecture video is amazing! " RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10828.0 0.0 0.0 0.0
"what happened to lecture 8?" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15141.0 0.0 0.0 0.0
"This is one of the more difficult lectures for me so far. The fact that I didn't fully grasp parametric equations is coming back to bite me up the ass...." 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 10701.0 0.0 0.0 0.0
"Watching this on an iPad haha. Pretty sweet for sure." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11305.0 0.0 0.0 0.0
"Finally at https://youtu.be/WfEQabCGAqI?t=10m10s the professor has a moment of joy.  Interesting how he chooses to explain using either the phases <projection> or <shadow>" WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3767.0 0.0 0.0 0.0
"Makes my head hurt.  What is it good for?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7565.0 0.0 0.0 0.0
"25:06 So performing row eliminations doesn't change the row space but changes the column space?

So to get the basis for the column space, would you have to do column elimination for matrix [A]? Or could you take the transpose, do row elimination, and just use that row basis for [A] transpose as the column basis for [A]?" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 764.0 0.0 1.0 0.0
"Thank's MIT to share this type of documents with the worlds. Thank's..." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 9569.0 0.0 0.0 0.0
"28:27 null space" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 836.0 0.0 1.0 0.0
"Omg I just discovered this channel and I didn’t have idea that YouTube have this excellent content. It remember me when I was in college and dreaming about being at MIT 
¡Gracias por subir este tipo de contenido!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8059.0 0.0 0.0 0.0
"36:50 It is not p and lp, it is p(polynomial) and np(not polynomial). I think he misspoke about it." feb9j65Iz4w "24. Linear Programming and Two-Person Games" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1047.0 0.0 1.0 0.0
"Why do they keep laughing whenever the professor shows the intersection planes?" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11826.0 0.0 0.0 0.0
"After a couple of years away from these topics I felt in love again with them. You gave me the light to find them again. Thanks! (there are not enough words to explain you all my gratitude about this) :-), best wishes." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 2245.0 0.0 0.0 0.0
"That's what makes MIT ... MIT" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9947.0 0.0 0.0 0.0
"A lot of respect for Professor Gilbert Strang, even at the age of 86, he is still teaching the world and sharing knowledge for free to many students in the world.
I recently started taking Linear Algebra course to understand some topics because I was struggling with the theory for PCA taught in MIT 18.6501x and in 6.419x. And finally I was able to understand some of the topics. I hope to learn linear algebra this year, and start this course in 2022." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2137.0 0.0 0.0 0.0
"*applause* That was great.

I remember those rules as
""First d-second plus second d-first""
""Low d-high minus high d-low, all over low-squared""
""d-inside times d-outside.""" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 244.0 0.0 0.0 1.0
"Thank you for an excellent lecture! Give me a clear track for development." k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9246.0 0.0 0.0 0.0
"This professor is also a interesting programmer🤓" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10898.0 0.0 0.0 0.0
"I went to a community college and my instructors were at least as good as any of the instructors I've seen on this channel. Specifically my physics instructor, Dr. Lecuyer, my math instructors Dr. Madson and Mr. Young." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 6190.0 0.0 0.0 0.0
"Did he say
 toin coss??" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3376.0 0.0 1.0 0.0
"At 11:35, I can't believe that he made such an obvious mistake! Everybody knows that the correct end of the formula is I+U=<3 :-D" XhSk_Lw2X_U "14. Low Rank Changes in A and Its Inverse" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2586.0 0.0 1.0 0.0
"I would love to have this man as my teacher." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6265.0 0.0 0.0 0.0
"@iDiViNeXx  In fact he is French, his name is Denis Auroux." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1880.0 0.0 0.0 0.0
"At the integral at 30:39 does x depend on ""y"" or ""z""? Or maybe both?" zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2729.0 0.0 1.0 0.0
"This we call applied mathematics. I honestly think the only great thing about MIT is a few gifted students every year and the fact that they prob got a lotta resources compared to other universities around the world" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10977.0 0.0 0.0 0.0
"@LogicalFlawDetector That is logically impossible because i never came from papa New Guinea" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1663.0 0.0 0.0 0.0
"Do we ever use cofactors for anything else besides computing the determinants?" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 3417.0 0.0 1.0 0.0
Great. k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4376.0 0.0 0.0 0.0
"Great video great lecture great professor." lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 4350.0 0.0 0.0 0.0
"there are a number of fool students they don't deserves this much intelligent people around i believe from India" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14758.0 0.0 0.0 0.0
"have you watched the entire series? after you're through with the entire course, let us know if you feel like MIT students aren't learning calculus as thoroughly as you are..." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13067.0 0.0 0.0 0.0
"Its very interesting to see the interviewer who genuinely look up to the person who she is interviewing" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7094.0 0.0 0.0 0.0
"that totally made sense..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14642.0 0.0 0.0 0.0
"In 32.08, can anyone explain how does he derive v(t) and u(t)?" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 6599.0 0.0 1.0 0.0
"tnx for sharing this" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 14942.0 0.0 0.0 0.0
"24:40 ""We are executing a determinate formula here."" 🤣🤣🤣🤣🤣" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 744.0 0.0 0.0 0.0
"How could ""any element of S+any element of U""= ""all 3*3's""?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 4828.0 0.0 1.0 0.0
"is anyone student of him? ^^" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13627.0 0.0 0.0 0.0
wonderful!  RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15399.0 0.0 0.0 0.0
"In the section Row space orthogonal to null space, (time 25.40) do we need transpose for row. Because (row)*x is the scalar product, not (row)^T*x." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6685.0 0.0 1.0 0.0
"00:00 - 10:14
component of vector along a direction

10:15 - 24:25
Area of 2D pentagon, determinant of two vectors in 2D space

24:26 - 32:45
3D space: volume

32:46 - 47:06
cross product
3D space: area

47:07 
Volume without determinant" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 276.0 0.0 0.0 0.0
"This seems to be the best discussion of line integrals (as noted below, starts around 16:00) of the many on YouTube because most straightforward.
." xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10920.0 0.0 0.0 0.0
"Watchin' at 2x speed" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 11289.0 0.0 0.0 0.0
"I thought this was an excellent lecture - lectures10 and 11 were a real struggle to get through but this really cleared up a lot of the terminology and why the four  fundamental subspaces are so important. Thumbs up Professor Strang.

(Weird ironing creases on his blue shirt in the vicinity of his right nipple.)" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6101.0 0.0 0.0 0.0
"Jump to 10:00, that is where the fun begins." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 7144.0 0.0 0.0 0.0
"I Really Like The Video Exponential and log From Your" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4945.0 0.0 0.0 0.0
"It is amazing how he can do these lectures in front of no students and still be so engaging. In a way he is a great actor." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6932.0 0.0 0.0 0.0
"44:25 Isn't vectors right hand side weird? I think it must be V^T*W = W1*V1^(T)+... so it becomes Dot product" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 1236.0 0.0 1.0 0.0
"At 17:30, he says we have four equations with three unknowns. How does a logic Ax = b may not have a solution flow from that? For three variables, three equations are enough. A fourth equation would appear dependent, or make a solution impossible. Is that the point? While b could have been any thing had there been four variables, but constrained when there are only three variables.
Edited: I get it. b can not be any thing arbitrary. Unless it is in the column space of A, there can be no solution." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 2596.0 0.0 1.0 0.0
"I love the boards and the chalks so much that I can fly there and solve a tangent line problem on those boards with those lovely chalks. What a chalk to write with, and what a board to write on." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5774.0 1.0 0.0 0.0
"Eigenvalue lam=1.0 leads to a term exp(lam t) = exp(t) grows out of bound. Or am I missing the point. In the last lecture lam= 0 became the steady state value." UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 3555.0 0.0 1.0 0.0
"Denis Auroux is the epitome of cool." 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3346.0 0.0 0.0 0.0
"I think he is a chinese teacher" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 6013.0 0.0 0.0 0.0
"My algebra teacher uses his book to teach, while I learn from the author himself. 😂 Upgrades." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 7735.0 0.0 0.0 0.0
"where can I find such practice sets which contains many many such problems?" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15224.0 0.0 1.0 0.0
"Excellent teaching styles." mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 3677.0 0.0 0.0 0.0
"I think cancelling S at 38:05 is a mistake. Variance must decrease by increasing the number of samples!" z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6008.0 0.0 1.0 0.0
"What a wonderful proof" z3SmljnD_nQ "15. Matrices A(t) Depending on t, Derivative = dA/dt" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11439.0 0.0 0.0 0.0
"0:00 ~ vector subspace
11:38 ~ column space
28:12~ null space" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 301.0 0.0 0.0 0.0
"“Handy to have a pair of scissors with you” 28:10" l4NoMKEHQwM "11. Derived Distributions (ctd.); Covariance" "6.041 Probabilistic Systems Analysis and Applied Probability" 15587.0 0.0 0.0 0.0
"14:34 - if these formulae are explained graphically it would be much easier to understand and interesting." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 429.0 0.0 0.0 1.0
"Image compression may be applied in Maclintock's  cytogenetic jump over   chromosones  over by a screwing the chromosomes for every one degree producing super conductivity involving the solar light pressure acting on chrosomes  jump  over by the crygenetic effect as observed from matrics application in topology .
Sankatavelayudhan Nandakumar on behalf of Hubble Telescope Researrch commitee thanking Prof.Sprang ." 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 6580.0 0.0 0.0 0.0
"Man I love chalkboards n the sound the make :D" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7569.0 1.0 0.0 0.0
"@matanorland1 hehe that's true, " YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1939.0 0.0 0.0 0.0
"donde consigo informacion de universidades con clases en idioma español" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12772.0 0.0 0.0 0.0
Cool. 9_xG0AGRa-w "Lecture 2: Cantor's Theory of Cardinality (Size)" "MIT 18.100A Real Analysis, Fall 2020" 3213.0 0.0 0.0 0.0
"Can anyone explain me last graph 📈 thing" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 3024.0 0.0 1.0 0.0
"42:40 Hahah are complex numbers that bad? As a passerby (who still watched the whole thing) imaginary numbers don’t seem to bad, neither do eigenvalues/vectors but i’ll admit i can’t answer any example questions yet so maybe i’m just too confident for my own good lol" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 1184.0 0.0 0.0 0.0
"Professor mentioned a book named 'Mathematics for the Million' which he had read in childhood
However, the book is written by  'Lancelot Hogben', not by the guy named 'Bell'. =D
(If you are interested, check 'THE ALGEBRA OF THE CHESSBOARD' chapter of book https://archive.org/details/HogbenMathematicsForTheMillion/page/n527/mode/2up )" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 8399.0 0.0 0.0 0.0
"@felix10271 your teacher probably didn't know the actuall proof or derivation herself.  HS teachers are often dumb anyway" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1836.0 0.0 0.0 0.0
"33:30 logarithmic differentiation" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 960.0 0.0 1.0 0.0
"Really love Professor Strang. By the way, does this course take MIT18.06 as a prerequisite?" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8526.0 0.0 1.0 0.0
"Thanks to the camera guy" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9811.0 1.0 0.0 0.0
"Cheap charity. Dirty black boards, illegible writings. Video art of some amateur. Is MIT to poor to fund a good online course in statistics?" TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 3142.0 1.0 0.0 0.0
"I am prepping for Mathematical Methods at Udub by watching these amazing lectures," YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5131.0 0.0 0.0 0.0
Wow. gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 12084.0 0.0 0.0 0.0
"28:37 that was awkward. Looks like he actually left the class, poor guy." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 841.0 0.0 0.0 0.0
"Lecture 3
Vector addition ➕ properties of vector https://youtu.be/LX88tL7EoBs" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7288.0 0.0 0.0 0.0
"At 41:39 i think he meant A2 times conditional probability of B given A2 happened, right ? must be a slip of tongue" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 2662.0 0.0 1.0 0.0
"professor you have my deepest thanks for these wonderful lectures. you will always be remembered by your lovely lectures" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14222.0 0.0 0.0 0.0
"Excellent! Thank you Professor Strang." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 3688.0 0.0 0.0 0.0
"Oooo man very very good thanks professor😎♥" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 8126.0 0.0 0.0 0.0
"God bless you. That is what education should be like. Available to everyone!!!" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4091.0 0.0 0.0 0.0
18:50 tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 548.0 0.0 0.0 0.0
"Watched this 5 months ago but needed refresher as I've got sidetracked in my learning! It's very nice to be walked through the least-squares equations. The explanations are easy to understand. Thanks Prof Auroux and MIT." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11286.0 0.0 0.0 1.0
"nice video" gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 14054.0 0.0 0.0 0.0
"Professor Jerison is the goat" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8331.0 0.0 0.0 0.0
"Great... Its just a great lecture... :)" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 4377.0 0.0 0.0 0.0
"Good professor, nice explanation, but I don't see that much a difference with my professor here in Greece, he explains the matrices just as well. The odd part is my professor linked us to this video to understand matrices better, but to be honest he could as well linked us to his own video :)
" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4152.0 0.0 0.0 0.0
"This guy is in a need of a lesson on teaching really." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10536.0 0.0 0.0 0.0
"Its kind of cool and odd that someone who has taught this subject for so long can keep it so fresh...like he's stumbling across the Null Space Matrix for the first time.  Thank you Dr. Strang and thank you MITOCW." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 7087.0 0.0 0.0 0.0
"Thank you Professor Strang ! 

but I think 14:43 is in the nullspace of (A-I)^T rather than nullspace of A^T isn""t it ?" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 9214.0 0.0 1.0 0.0
"Thumbs up to the camera angle management team; great video audio editing." rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11002.0 1.0 0.0 0.0
"4:14: Okay let's take a vote, is it sin-sin or sin-cosine? Proof by popularity!" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1315.0 0.0 0.0 0.0
"wow he sure knows a great deal of physics!" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15413.0 0.0 0.0 0.0
"32:40 How do we write the expectation value as 1/2 and 3/2 ?" P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 937.0 0.0 1.0 0.0
OK yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 7972.0 0.0 0.0 0.0
"Good explanation but the convention for letters assigned to angles (phi, theta) is different to the more usual one . Theta,  usually is  used for the angle from z-axis" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4127.0 0.0 1.0 0.0
"47:40 Turing starts" IycOPFmEQk8 "5. CF Pumping Lemma, Turing Machines" "MIT 18.404J Theory of Computation, Fall 2020" 1285.0 0.0 0.0 0.0
"its incredible what 15 years does 🙌🏽" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 13711.0 0.0 0.0 0.0
"Dear Mr Strang sounds so much similar to Tom Hanks. You have to listen with your eyes closed to notice." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 3326.0 0.0 0.0 0.0
"He brought the actual chain!" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4462.0 1.0 0.0 0.0
"and because they're rich" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12367.0 0.0 0.0 0.0
"Those chalkboards blow my mind" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10993.0 1.0 0.0 0.0
"At around 26:50, why does the professor not mention anything about the case where the discriminant is zero and there is only one root?" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2705.0 0.0 1.0 0.0
"@Avatarass 
That's what I thought, and then I failed calculus1. I dind't make the same mistake again. Math and calculus, always evolve in a very streamlined fashion from the previous subject. That's why they make sure you DO know what a derivative/limit etc. is. I studyed IT in hs and saw allot of the same stuff in college too, by the end I had such a deep comprehension of IT I realized why you start with most of the basics again. You can learn how, but knowing why, that's the true knowledge." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1595.0 0.0 0.0 0.0
"1:00:24 Loudly crying face (copyrighted) Source Unknown" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 571.0 0.0 0.0 0.0
"The whole thing is mathematically un-provable and only rests on the heuristic/intuitive concept of curvilinear continuity." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10338.0 0.0 0.0 0.0
"such a good teacher" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14412.0 0.0 0.0 0.0
"The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be  7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?" XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 10027.0 0.0 1.0 0.0
"in the diffusion equation, if u=u(x,y,z,t), why when taking the gradient we only take the partial derivatives of x,y,z? (for F in the left hand equation min. 49:10). I suppose it's because they're spatial dimensions, but then you need more constraints to make the result in the right hand of eq. not depend on time.. Thanks." wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 13597.0 0.0 1.0 0.0
"28:43 I'm kinda confused, why we are getting zero vector here, shouldn't it be vector 3, -1  https://matrixcalc.org/en/#%7B%7B1,2%7D,%7B3,6%7D%7D%2A%7B%7B3%7D,%7B-1%7D%7D" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 843.0 0.0 1.0 0.0
"wow I watched many different sources , this is by far the best and most clearly explained video. It really help us that love mathematics and want to learn by ourselves." P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 15410.0 0.0 0.0 0.0
"About 2 years ago, I failed a college linear algebra exam, and not only that, but I got the lowest in the class by a whopping 2 standard deviations (if I remember correctly). Eventually I dropped the course--I was so bored and discouraged by the professor's way of writing the textbook on the board every lecture that I looked for other sources to prepare for when I would have to take it again. I came across Prof. Strang preaching the 4 fundamental subspaces one day at my custodial job at 5 am. To say that it completely changed everything is a bit of an understatement. Every day, I would rush to work (again, keep in mind this is at 5am!), beast through all my work in about 2 hours, and then watch Prof. Strang teach for another 2 while avoiding my supervisor! It was a full-on addiction to a subject I once hated (: I can't even begin to describe how much better my college experience has been because of this man. (:

Best professor ever. It would be an honor to meet him (:" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2192.0 0.0 0.0 0.0
"Thank you! This is so helpful, currently studying calculus I at the Australian National University and this is a very useful supplement :)" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9483.0 0.0 0.0 0.0
"super nice lecture" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 14419.0 0.0 0.0 0.0
"beside math, I love taekwondo as well. Can I join the tournament at 30.48 ? hahahaha" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12533.0 0.0 0.0 0.0
"now i am literally lost here...." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 14089.0 0.0 0.0 0.0
"0:45 - We have heard about them eigentimes! ;)" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 307.0 0.0 0.0 0.0
"i wish the cameraman wouldn't move around so much!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13502.0 1.0 0.0 0.0
"Thank you for great linear algebra course." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 9251.0 0.0 0.0 0.0
"GS: ""the determinant of an upper triangular matrix would be just (d1) times (d2) times ...*hands rotate* (dn).""
me: *writes (dnd)*" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 3978.0 0.0 0.0 0.0
"Traditional camera angles were WAY easier on the eye." or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11081.0 1.0 0.0 0.0
"Great teacher. His remarks were very helpful in clarifying some of the fundamental questions that were quite mirky. Thank you professor, thanks MIT!" 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4341.0 0.0 0.0 0.0
"I just clicked on this to feel how dumb I really am" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 5600.0 0.0 0.0 0.0
"This is so fun !! I love math I take precal and I'm in 10 grade" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 10717.0 0.0 0.0 0.0
"thank you Dr. am from kenya, university of nairobi doing econ, this is very helpful" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14476.0 0.0 0.0 0.0
"At 27:34, the professor squared the equation both sides, is this OK to decide the trajectory of the equation? E.g., x = y is a line, but x^2 = y^2 is two lines, they are different." BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2630.0 0.0 1.0 0.0
"what a crack liam neeson, apart from being an actor he also teaches" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 15104.0 0.0 0.0 0.0
"this type of calculus we do in high school in canada" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14919.0 0.0 0.0 0.0
"Thank you Sir" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9231.0 0.0 0.0 0.0
"36:10 shouldn't it be = -3, -3, -6 ?" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1032.0 0.0 1.0 0.0
"7:45 how is edge 1, 2 and 3 make a loop when loop 3 is pointing to the opposite direction to the flow of edge 1 and 2 ??" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1402.0 0.0 1.0 0.0
"My only problem with the MIT lectures is they spend to much time on theory, rather than working problems. Although I'm sure they do problems during the recitation." wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 7781.0 0.0 0.0 1.0
"why u(0)= [1,0].T, is it a dummy vector that help calcuate?" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 15372.0 0.0 1.0 0.0
"I think there was a bit of misunderstanding with the question a student asked around 17:30. The student asks why the right hand limit must exist. When the instructor wrote down ""right hand limit"" he didn't mean the limit from the right hand side (x->a+), he literally mean the limit he wrote on the right.

Technically, the right hand limit (x->a+) has to exist otherwise the full limit wouldn't exist, but that goes without saying." PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6069.0 0.0 1.0 0.0
"I love this lecture so much. Thank you a lot prof." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 5816.0 0.0 0.0 0.0
"@iDiViNeXx yeah he's french" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1887.0 0.0 0.0 0.0
"This is an amazing lecture for Linear Algebra. Thank you Prof. Strang!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10624.0 0.0 0.0 0.0
"Im from a Machine Learning background(masters at the moment) and you are really good and smoothly going from concept to concept, in my opinion. I hope to continue this series during the holiday season." uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 6569.0 0.0 0.0 0.0
"This guy is a great professor." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10517.0 0.0 0.0 0.0
"@Brotrr and a sweet ass chalkboard" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1604.0 1.0 0.0 0.0
"Oh did I just invent a negative one, Priceless" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8004.0 0.0 0.0 0.0
"You are the best maths professor i've come accross thankyou so much Dr Gilbert Strang you're a blessing for all the students who struggle with linear algebra" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 12179.0 0.0 0.0 0.0
"Who was the person that entered the room; and we always Prof. portraying his sense of humour, ""Whether the rest of the world realize that I was in danger!!"" Such a great mathematician with such great sense of humour!" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 11755.0 0.0 0.0 0.0
"Great teacher. Wish my instructor could explain the concepts like he does. Wasted some time wondering why we were doing those problems. The concepts are so important." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4344.0 0.0 0.0 0.0
"@LoquaciousApe How is this an unknowledgeable class? Everybody raised their hands when asked, if you watched the video. You don't have to take physics to take calculus classes, and a teacher cannot skip vector introduction because he feels like it. How is it that you assert that there is a lack of trigonometry knowledge here? Prerequisite calculus, and basic high school classes such as algebra and trig, were skipped by all of these students then? Simply trolling, let's be honest. A YouTube math" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1665.0 0.0 0.0 0.0
"that fourth way is absolutely beautiful 🎂" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14629.0 0.0 0.0 0.0
"This prof has a way of making the ideas make sense. I am grateful, because I always dread learning about anything related to stats." 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 10888.0 0.0 0.0 0.0
"Most math courses will tell you the mechanisms by which to calculate problems.
But what I always wish they would begin with is a little history and purpose. For example what was the original, real world problem that linear algebra was created to solve? Yes, it solves systems of linear equations, but in the real world, how am I going to get a system of linear equations? How will I recognize where to apply this?

All through college I've never had a class that started that way and so math was just about memorizing the mechanisms to solve the test problems. Why? I'm not a teacher but if I were I would try to teach it differently." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7699.0 0.0 0.0 0.0
"@17:30:00 he says we are 1/sqrt(n) away from the mean. How does the CLT say that? The CLT says sqrt(n)(theta-thetahat) converges in distribution to N(0,sigma^2), what part of that statement gives an indication that the distance of the estimated mean to true mean is approximately the inverse of the square root of the sample size? It looks like it says the distance is proportional to the square root of the sample size, not the inverse of the square root of the sample size." phbw9r1iUDI "7. Parametric Hypothesis Testing" "MIT 18.650 Statistics for Applications, Fall 2016" 1501.0 0.0 1.0 0.0
"2020 now, he did make it immortal" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 626.0 0.0 0.0 0.0
"After watching Prof. Strang classes, I have decided to become a lecturer or a teacher . He is a true definition of passion." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 2262.0 0.0 0.0 0.0
"such a charming fellow" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14409.0 0.0 0.0 0.0
"this camera man sucks" seO7-TwXH_I "Lec 30: Line integrals in space, curl, exactness... | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14795.0 1.0 0.0 0.0
"thank you" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14466.0 0.0 0.0 0.0
*Kirchhoff 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 235.0 0.0 0.0 0.0
"God! Am I in Heaven?" O0Tw47okZJM "Lecture 21: The Spectrum of Self-Adjoint Operators and the Eigenspaces of Compact Self-Adjoint..." "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 4097.0 0.0 0.0 0.0
"Well, i don't want to look like an assuming but i can't conceive math of any kind without demonstrations. And i see none in this video, i just see notions that seem to be confirmed by numeric examples. The risk is to give for granted lots of things. In the example of P U L he clearly said that it's never a vector subspace, that's not correct if you don't say that if L lays on P. P U L is a subspace too. So he should have said that P is a plane containing O , L is a line containing O but not on the plane P, in this Hyp then PUL is not a subspace, otherwise i't a subspace being equal to the plane P" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 11366.0 0.0 1.0 1.0
"there is a special place named hell for ppl who disliked this video" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14762.0 0.0 0.0 0.0
"I kind of got lost on this video" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 5631.0 0.0 0.0 0.0
"where can I read about the diagonalization technique he mentioned to prove the equivalence between infinite and finite forms" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 15226.0 0.0 1.0 0.0
"wait, he was 72 in this video, right?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 15051.0 0.0 0.0 0.0
老很多了 YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15650.0 0.0 0.0 0.0
"When I was born , 27/11/1998, he was celebrating his 64th birthday. This is Math problem I can do." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11607.0 0.0 0.0 0.0
老教授实在是太伟大了，如此高龄居然还奋战在一线，太难得了！ or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15651.0 0.0 0.0 0.0
"Pr. Strang seems pretty lost in this lecture :(" z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8235.0 0.0 0.0 0.0
"jag ska skriva min den 14e :P har dessa föreläsningar hjälpt?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13719.0 0.0 0.0 0.0
"this guys has a point. it's part of being educated, having seen important concepts. He didnt even say ""without having *memorized..*"" he said *seen.
it's not a matter of perfect SAT scores either– why bring that up? 
" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14845.0 0.0 0.0 0.0
"Excellent relationship between parabola and normal curve." mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 3672.0 0.0 0.0 0.0
"I always thought mathematician would write very properly." lZrIPRnoGQQ "27. Backpropagation: Find Partial Derivatives" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5044.0 0.0 0.0 0.0
"I love it" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5757.0 0.0 0.0 0.0
"If an entire row or dimension is zero, then it doesn’t have an answer for every b but only for the ones that are zero in that dimension. Right?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6491.0 0.0 1.0 0.0
"well done" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 15084.0 0.0 0.0 0.0
"yup.I agree.Lack of humor and lengthy and boring lecture.[Not all of them].I don't understand why they make it so complicated by elaborating a lot of simple concepts.Is it because they want to preserve MIT standards?" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15529.0 0.0 0.0 1.0
:-O -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1449.0 0.0 0.0 0.0
"Thank you,  Professor Strang" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9490.0 0.0 0.0 0.0
"This course only makes sense if you already know the content ahead of the time." RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 10494.0 0.0 0.0 0.0
"Hit the row space and don't you come back no more no more no more no more....:D" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4770.0 0.0 0.0 0.0
"I can't believe this class would come to the end so soon. Watched from lecture 1 to here" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 5207.0 0.0 0.0 0.0
"The next lecture can be....pure happiness.  :D" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 10202.0 0.0 0.0 0.0
"i dont know why it says spring 2005. this was recorded in 1999." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13370.0 0.0 0.0 0.0
"Simply the real life Hogwarts." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8671.0 0.0 0.0 0.0
"For the example starting at 16:39, shouldn't it be |sec(x)| out of the square root part  in the first substitution? I am confused why we assume the sec(x) is positive and thus drop the absolute sign. Any insights?" CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3887.0 0.0 1.0 0.0
"Im doing a masters at this" rLlZpnT02ZU "4. Parametric Inference (cont.) and Maximum Likelihood Estimation" "MIT 18.650 Statistics for Applications, Fall 2016" 6568.0 0.0 0.0 0.0
"Dat chalk." 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3316.0 1.0 0.0 0.0
"5:14 - label a non-zero point on x-axis as X0 is confusing." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1359.0 0.0 1.0 0.0
"At 1.5x he sounds just like Jordan Peterson" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2581.0 0.0 0.0 0.0
"Thanks, you are God for me." ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9853.0 0.0 0.0 0.0
ctmu vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 12698.0 0.0 0.0 0.0
"Is it just me who hears poof everytime he says proof" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6782.0 0.0 0.0 0.0
"Wish the best for you Professor Gilbert Strang, the first person who gave me an enthusiastic way to Linear Algebra!" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11960.0 0.0 0.0 0.0
"Fixed audio sync problem in the first minute of the video." Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3830.0 0.0 0.0 0.0
"Does this have solutions to assignments to compare solutions?" 78vN4sO7FVU "Lecture 2: Bounded Linear Operators" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 3464.0 0.0 0.0 0.0
"@xkeikoxsanxdesu quite alot besides the usual insanely high grades...just check out thier websites. These guys only select the best of the best! Thier acceptance rate is 10percent lol.ITS IS EXTREMLY DIFFICLUT to get into M.I.T" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2068.0 0.0 0.0 0.0
"I don't understand why do we not multiply E3,2 matrix with E3,1 and have started using inverse instead . Wouldn't multiplying be easier?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5353.0 0.0 1.0 0.0
"I'm surprised. I didn't know that I found math so fascinating when I'm not under tremendous pressure to know it so quickly. I'm studying vector calc over the break so that I can have an easy time with it this coming semester." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6386.0 0.0 0.0 0.0
"M I freaking T!!!!!" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 7493.0 0.0 0.0 0.0
"thanks a lot John Tsitsiklis
, you are great professor" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 14568.0 0.0 0.0 0.0
"All my Respect goes to Dr. Gilbert Strang Sir and Massachusetts Institute of Technology, they have a big heart" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2302.0 0.0 0.0 0.0
"I think there was a slight mistake in 24:40 where it's is stated that there is an inflection point at x iff f''(x) = 0. But this (as far as I know) is not true. Because what I know about inflection point is that f changes from concave up to down at that point, which means the second derivate must change sign. But in some cases f''(x) = 0 but nothing changes in concavity at x. (like y = x)" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6070.0 0.0 1.0 0.0
"Can someone help me understand why property 3b explains |det A| = volume could be extended beyond cubes and rectangles but to all angles?" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 3081.0 0.0 1.0 0.0
"@4.46, snow fall outside...the learning exp will be awesome" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1554.0 1.0 0.0 0.0
"wow this guys actually teaching. fuck my prof" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15420.0 0.0 0.0 0.0
"If you made it all the way through this course, congratulations!" rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 6552.0 0.0 0.0 0.0
"He is not just the great teacher, but also the great artist. He just teaches these things seamlessly, and this is an art." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4527.0 0.0 0.0 0.0
"@13Septem13 How do you play the video at double speed?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 1498.0 0.0 0.0 0.0
"4:17,   x[i] <256 , right?" 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 1316.0 0.0 1.0 0.0
"What textbook to follow after watching the lectures...??" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11556.0 0.0 1.0 0.0
"""Poor misbegotten fourth subspace""
-Gilbert Strang, 1999


Remember when Elizabeth Sobeck decided to give GAIA feelings? These guys gave math feelings. And I love him for that. I didn't even know that was possible." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 102.0 0.0 0.0 0.0
gesundheit 16:57 FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12916.0 0.0 0.0 0.0
"I have been trying hard to grasp on the concept of matrices and anywhere I started teachers would burden me with tons of formulas I do not know when or where to use, and then they say you practice some questions and you would get ""marks"" that resulting into I kept on failing math exams. Now when I understand this my teacher himself sits besides me to understand how I solve my questions and sometimes say I never taught you this. I can never thank you enough sir." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5520.0 0.0 0.0 0.0
"oh.
my.
god.
i'm taking multivariable in my senior year of high school right now and my final's next week. this is gold. THANK YOU MIT." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14120.0 0.0 0.0 0.0
"damn chalkboard ninja, youre smart" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12707.0 1.0 0.0 0.0
"Thanks! <3" TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 9829.0 0.0 0.0 0.0
"Sir!!!
We love you to the power of infinity!!
Have love^∞
❤🇧🇩" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8708.0 0.0 0.0 0.0
"Great Course! Thanks MIT!" XtNXQJkgkhI "22. Bayesian Statistical Inference II" "6.041 Probabilistic Systems Analysis and Applied Probability" 4198.0 0.0 0.0 0.0
"Take Caculus BC AP, Save money from this" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9005.0 0.0 0.0 0.0
"This is the best lecture for Linear Algebra." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10739.0 0.0 0.0 0.0
"What is understanding the concepts he's presenting in comparison to being able to explain them to someone else? It's not nothing, to use a double negative, but you get the idea. It's of course not the only difference between professors and students, but if you can find someone interested enough, try explaining it to them, and you'll never forget the lesson. If you're not a professor, one difficult task is finding someone who's interested, in order to practice. Normally, the way to do this on your own is to write proofs." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11543.0 0.0 0.0 1.0
"I did not understand how did we related the formula ( TAYLOR ) that is produced from a spesific type of function ( POLYNOMIAL )  to other types of functions such as trigonometric and exponantial. In other words how can we apply taylors formula to all types of functions, eventhough it is proven by polynomials ( at least in this video)." wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5260.0 0.0 1.0 0.0
"A lecture without Aurox's magical erasings 😔" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2130.0 0.0 0.0 0.0
"I had to take a stats class as a requirement for my Admin Justice major..after I took this class and achieved in it just by sheer trying hard and studying..I was able to get an A and decided to try science and engineering courses and I did pretty good because I got Fs in HS when I took them. So I thought I'd settle for a career with less education requirement after HS--20 years later I'm a software engineer for a major telahealth company. I'd never would expect this--I thought I'd be a cop" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 5477.0 0.0 0.0 0.0
"He kinda lost it at the end" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 4564.0 0.0 0.0 0.0
"How does he get 1 / δ x at 19:40?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4860.0 0.0 1.0 0.0
"I came looking for strippers and cocaine" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5183.0 0.0 0.0 0.0
"40min short lecture contain lots juicy stuff,   watch two times" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 1141.0 0.0 0.0 0.0
"Prof. Alex:  The world is Sylvester.
Tweety: Hey! How about me?" 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8287.0 0.0 0.0 0.0
"Sir voice is not good" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 8703.0 0.0 0.0 0.0
"Know what... Actually it's not just the guys sitting in the class who learnt this.... Students from different corners of the globe, from over a decade's gap learnt it... Truly amazing 👍 thanks sir" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 7219.0 0.0 0.0 0.0
Wow!!! XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 12058.0 0.0 0.0 0.0
"31:18 Why there is only two cases? Why not consider sigma < 0?" Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 905.0 0.0 1.0 0.0
"This video is damaged?" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10953.0 0.0 0.0 0.0
"34:30 You might want to search YouTube for time invariant diffusion. The diffusion equation can be simplified by noticing that it looks the same if time goes forward as when time goes backward and a situation like that you can reverse the dye dillution. There are fantastic videos about how it's done. Do not say that partial differential equations are boring." wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 982.0 0.0 0.0 0.0
"I was so nervous about taking multivariable calculus at my college, because I was failing to understand the vector calculus I was learning at the end of calculus 2. I now realize it's not really that hard because I understand it, and that math minor is mine!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6165.0 0.0 0.0 0.0
"One of the best calculus lectures!" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8088.0 0.0 0.0 0.0
"Why can't dx/dy be squared to become dx^2/dy^2 ? After all, dx/dy can be treated as two separate number when solving a separable differential equation. Aren't dx and dy just two very small number that shrink to as low as you want, so that they present no significant value - have so many zero's in them after the decimal point-  that each of them is near enough to zero to ignore, but their ratio remains the same so that the slope can be found." XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11797.0 0.0 1.0 0.0
"16:40 Let me bury that error and talk about the row space." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 485.0 0.0 0.0 0.0
"After watching this lecture, all I can say is how truly amazed I am. What a great video! Except for the fact that I couldn't understand one word he was saying( currently taking Tech Math at HS). I mean the camera was on point, his writing was nice, and the students were quite polite. Superb! MIT you surely do not disappoint :D" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2266.0 1.0 0.0 0.0
"Thank you I now know the limit" cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 9115.0 0.0 0.0 0.0
"great videos, these explanations help so much." YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13018.0 0.0 0.0 0.0
"idk wtf nobody answers his questions? why r they ignoring him?? sitting at home and watching his lectures, I was about to reply him when he was asking ;((((" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 13526.0 0.0 0.0 0.0
"I have seen this video many times overoverover&again." ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5555.0 0.0 0.0 0.0
"At 42:59, while deciding the height of rectangle in an interval with x varying from 0 to 1, shouldnt we add the height of rectangle above or below the x axis? Why did we subtract?" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2669.0 0.0 1.0 0.0
"Thank you sir." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 9337.0 0.0 0.0 0.0
"By the way, youtube is for some reason changing the ""less than"" sign into ""<"". Following up on my last comment (this feels like ""linear algebra 500 characters at a time!""), if the solution is not unique there are either no solutions or infinitely many. Since we know that b=[1, 0, 0] has no solution in Ax=b, it must mean it's the former case. To answer this question means reversing the reasoning here. Starting with the fact that b has no solution and deducing from there that r is less than m." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 2978.0 0.0 1.0 0.0
"This is the moment in time where I have to say thank you! In my opinion this lecture connects everything that happend until now beautifully and builds the foundation for solving most advanced engineering problems." lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 10751.0 0.0 0.0 0.0
"@Voltar143 But the professor is French! LOL" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1753.0 0.0 0.0 0.0
"Beautiful lecture" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2818.0 0.0 0.0 0.0
"I'm quite surprised at the silence of the class during lecture when he asks them pretty simple questions. Are these MIT undergrads just so ultra shy and polite that they refuse to speak at all during lecture, or are they really just not following what he's saying?" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 6364.0 0.0 0.0 0.0
"For any other class, following around the teacher would be fine, but not for Calculus or any other type of math!" CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3850.0 0.0 0.0 0.0
Awesome!! YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2782.0 0.0 0.0 0.0
"I am freestyle developer in Brazil and since started my career did never have contact with computer science academics lectures, but after some years of experience I am loving all the free lectures MIT is providing in youtube. I have watched almost the whole channel since then, and I loved this one too.  I would love now to set up a  goal to study in MIT personally, but don't even know how much is the financial and general requirements to get into CS grad program." uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 5090.0 0.0 0.0 0.0
"If angle is measured in radians then the formula for arc length=theta*radius, as radius=1, arc length=theta, Now as angle theta gets closer to 0, arc length and that straight line, i.e. sin(theta), sits on top of each other making sin(theta) = arc length, so that is why sin(theta)/theta=1, as value of both sin(theta) & theta becomes equal.  and NOW as those two quantities are equal, it makes cos(theta)= radius= 1. and when calculated (1-cos(theta)/theta)=(1-1/theta)=(0/theta). and 0/anything=0. Correct me if I m wrong." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6492.0 0.0 0.0 0.0
"@fuckooo I read it in the comments of another one of these videos. I don't remember the exact comment though." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1843.0 0.0 0.0 0.0
"I don't understand how the student in the audience thought that the u and v the professor drew looked similar." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5343.0 0.0 1.0 0.0
"I agree. Then again, most high schools don't have layers of cascading chalk boards..." MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5032.0 1.0 0.0 0.0
"Toughest lesson so far" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 11080.0 0.0 0.0 0.0
"According to the mit prerequisites, all that is necessary for this course is high school algebra and trigonometry. To answer your question, yes, it is the right way to begin" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2230.0 0.0 0.0 0.0
"Long may Professor strang live!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7413.0 0.0 0.0 0.0
"I have a question in 22:00 if x0 go to infinitive then the value would be bigger and bigger isn’t it? for example -1/1 < -1/1000" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5500.0 0.0 1.0 0.0
"who's still here in 2020 XDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD" EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 15270.0 0.0 0.0 0.0
"He makes things too complicated where they are not.The proof of the magic number M(a) was in my high school text book in a formal way.He mixed up the things." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4584.0 0.0 1.0 0.0
"Boy, there are some dumb students in MIT. These are really basic stuff." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2913.0 0.0 0.0 0.0
"I like calculus" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5661.0 0.0 0.0 0.0
"Finally three videos left, I am not an English native speaker but  appreciate myself for going this far. He's really amazing!" 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 3782.0 0.0 0.0 0.0
agreed eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12313.0 0.0 0.0 0.0
"Great lecture from one of the grandmasters...indeed a true honor to hear this" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4252.0 0.0 0.0 0.0
"Honey you should see him in a crown" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4783.0 0.0 0.0 0.0
"Thank you MIT for share this valuable lecture" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 9147.0 0.0 0.0 0.0
"Thanks for this!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 9737.0 0.0 0.0 0.0
"awesome! Thank you very much. :)" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12496.0 0.0 0.0 0.0
"When teaching is this solid, learning feels effortless and pleasant. Like eating good food one bite at a time. =P" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11634.0 0.0 0.0 0.0
"at    31:00  how  come  that  a  vector  u  in  any  direction  in the surface   graph  of  restriction   g= c  implies  that   df/ ds in  u  direction   is  zero ?  .....It  is  another  surface   !    ...the  graph  of   f   ....NOT   of  g." 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12407.0 0.0 1.0 0.0
"independence: a bunch of vectors are independent if there is no such combination among them that gives zero (other than all-zero combination).
reminder: pivots represent independent columns while free columns mean there is dependence.
a bunch of vectors C in a matrix A are independent when the nullspace of Ac =0 happens only when C is all zeros, a matrix of independent columns will have a rank = n (number of columns).
span: vectors v1...vl span a space when that space consists of combinations of those vectors.
basis of a space is a sequence of vectors v1...vd that are 1. independent 2. span that space
basis test:
n vectors of subspace Rn give basis if the matrix made from those vectors is invertible.
given a space (such as Rn) then every basis for that space has same number of vectors (n vectors), that is what we call ""Dimension"".
so for a space(n) we have a matrix A where rank(A) =  no. of pivot columns = dimension of space n" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 13606.0 0.0 0.0 0.0
"I want to adopt him as my grandpa." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6134.0 0.0 0.0 0.0
"this guy is my theta^ for the distribution of cool statisticians" rLlZpnT02ZU "4. Parametric Inference (cont.) and Maximum Likelihood Estimation" "MIT 18.650 Statistics for Applications, Fall 2016" 14829.0 0.0 0.0 0.0
"But adding an identity matrix plus upper triangular gives us again upper triangular so in this special case we obviously dont get  all 3×3 matrices or 9 dimensions? Or am i missing smthing?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 2957.0 0.0 1.0 0.0
"I had to rewind at 38:23... did I hear a flatulence?" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5475.0 0.0 0.0 0.0
"32:28 I think he missed..." WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 931.0 0.0 1.0 0.0
"Great video. Thanks Prof. Strang." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4361.0 0.0 0.0 0.0
"https://youtu.be/Ojtwh8XDF8M <- equation a reference" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13298.0 0.0 0.0 0.0
"He reminds me of Heisenberg. Yes you are goddamn right" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4594.0 0.0 0.0 0.0
"Nearly all Newtonian mechanics uses vectors." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7809.0 0.0 0.0 0.0
"Great 💔 i am from Bangladesh" ImHAGH_OEow "Lecture 20: Taylor's Theorem and the Definition of Riemann Sums" "MIT 18.100A Real Analysis, Fall 2020" 4366.0 0.0 0.0 0.0
"a wonderful human being and a legend! thank you Professor Strang." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 12296.0 0.0 0.0 0.0
"Nice lecture. Easy to see why solutions are exponential in t. But, I did not get why solution is exponential in lambda*t." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 7848.0 0.0 1.0 0.0
"@childkiller1500 obviously no professor at MIT lacks knowledge, but it looks like he's not ""in"" the whole lecture. he's just on another level than the students. Being a good teacher, one needs to be on the same level as the students. Btw i'm doing masters in mathematics so don't think im an inexperienced student" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1817.0 0.0 0.0 0.0
"why am i watching this before board exams??..." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 15279.0 0.0 0.0 0.0
"I learned this in 8th grade wtf??" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5653.0 0.0 0.0 0.0
"i love these lectures... but this episode has LITERALLY the worst cameraman ever..." nbENJ-Ce7Nc "Lecture 3: Cantor's Remarkable Theorem and the Rationals' Lack of the Least Upper Bound Property" "MIT 18.100A Real Analysis, Fall 2020" 13431.0 1.0 0.0 0.0
"in conditional PMF, what if the probability of each random variable is not same? Then how do we scale each probability?" -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 13582.0 0.0 1.0 0.0
"Thank you. I've just learned that a few days ago, and you helped me to understand it better." TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9558.0 0.0 0.0 0.0
"Very helpful, thanks! ✌️" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11198.0 0.0 0.0 0.0
"WTH,

first 2 min in. Kilowatt hour is NOT the same type of unit as calorie or ft-lbs. KwH is energy per unit time whereas the other 2 are just energy.

and why is he using those horrendous English units. Use the damn metric system." jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11253.0 0.0 1.0 0.0
"Awesomely done prof. XD." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 2792.0 0.0 0.0 0.0
"Is there a technology at MIT to effectively remove chalk from the chalkboard?" TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 6825.0 1.0 0.0 0.0
"at 26:52 why does he use a^t vs regular a" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12430.0 0.0 1.0 0.0
"The silence in the class is profound!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10278.0 0.0 0.0 0.0
"thank you prof Strang..... i'm really appreciate your series of lectures and its make me want to study more advance maths........... i really thank you soo much..." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 14503.0 0.0 0.0 0.0
"DID HE JUST DIS MR. SCHMIDT👀😂😂" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 3272.0 0.0 0.0 0.0
"Pa mi huevo jsjsjjss" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8153.0 0.0 0.0 0.0
"I think the prof. used too complicated of an example in this lecture, the students seemed confused and I had a hard time following it ... he went in 1,000 different directions" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6061.0 0.0 0.0 1.0
"Finally a professor who gets straight to the material.  No wasting half a lecture on philosophical gasbagging." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3765.0 0.0 0.0 0.0
"Disculpe no fue mi intención incomodar con mi comentario, al contrario estoy muy agradecido con los cursos. Bueno muchas gracias y espero que sigan colocando más videos. Saludos cordiales." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 3402.0 0.0 0.0 0.0
"whoooo!!, just lost in the wild. I have to watch it again." 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 15273.0 0.0 0.0 0.0
"Great series of Lectures. Thanks to Prof.Tsitsiklis and MIT." rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 4330.0 0.0 0.0 0.0
"If you want to see some cool expansions of these ideas, check out G. Strang in /watch?v=CgfkEUOFAj0" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 6560.0 0.0 0.0 0.0
"It snows in Boston at this time?" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6987.0 0.0 0.0 0.0
"i don't care, they still charge so much money they can offer these without asking for donations" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13362.0 0.0 0.0 0.0
"You can axpromiate almost every function under certain condition with a polynomial given by the Taylor rule, that's why :)" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12186.0 0.0 0.0 0.0
"thanks MIT and this professor is really great.
Thanks professor really appreciate your teaching" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14555.0 0.0 0.0 0.0
"thank u" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14457.0 0.0 0.0 0.0
"Beautiful lecture and amazing lecturer !!!" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2819.0 0.0 0.0 0.0
"I had never seen that ""stack the 2nd matrix on top"" visual aid for multiplication - very helpful visualization" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5466.0 0.0 0.0 1.0
"Im sorry but i think this is a very poor lecture compared to the others" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 6578.0 0.0 0.0 0.0
"A good video to supplement the gradient and rate of learning :-) : https://www.youtube.com/watch?v=NomUbVmmyro" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 2119.0 0.0 0.0 0.0
"thanks OCW :) for this wonderful series !!" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 14559.0 0.0 0.0 0.0
"please also write what is in the recitation of each video when you update the next time ." phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14186.0 0.0 0.0 0.0
"What is (ATA + d^2 I) ^-1? I think it cant be separated as (ATA )^-1 + (d^2 I)^-1." Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11511.0 0.0 1.0 0.0
"WE NEED MORE TEACHERS LIKE YOU Mr.Strang!!!!
Regards a fellow student you never met" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 11241.0 0.0 0.0 0.0
"Im in wierd part of youtube again. " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6573.0 0.0 0.0 0.0
"There is non.. I believe lec 8 is supposed to be for exam review, this is the start of unit 2" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10374.0 0.0 0.0 0.0
"I HATE MATH" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4923.0 0.0 0.0 0.0
"How strange is it that the student pointed out the exact mistake the concept of which the professor was gonna go ahead with. i.e the connection bw column space and row space." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4894.0 0.0 1.0 0.0
"Awesome lecture, thanks!" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2761.0 0.0 0.0 0.0
legend 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 13775.0 0.0 0.0 0.0
"does anybody know what the time limit is for this exams? Because I use 2 hours, but I'm thinking maybe I should be faster" BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12761.0 0.0 0.0 0.0
7:00 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1391.0 0.0 0.0 0.0
"looks like the best school needs some smart boards, or even white boards, lol" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13856.0 1.0 0.0 0.0
"Let me guess. This was the first video you ever watched in the realm of machine learning. Now you're an engineer." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7333.0 0.0 0.0 0.0
"Thanks (2 years after) because I didn't understand it. Now it's obvious :D ! 
" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 9581.0 0.0 0.0 0.0
"Professor Alan Edelman, thank you for a beautiful lecture and a power introduction to Julia. I watched and take notes from all 36 lectures and they are awesome. I learned  a tremendous amount of Linear Algebra from the Grandfather of all mathematics. Thanks to MIT and all the wonderful people behind the scenes for putting these lectures together." rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8321.0 0.0 0.0 0.0
"Glad to see these lectures. It would have been an honour being taught by this professor! A lot of things are making sense today, that didnt make sense when I took college a decade ago." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4059.0 0.0 0.0 0.0
"Its because people are in the middle of viewing the videos" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 7083.0 0.0 0.0 0.0
"Someone please give a medal to Prof. Auroux. Genius indeed how he closed the lecture with Divergence..." WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8839.0 0.0 0.0 0.0
"Really awesome!👏🏽" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8507.0 0.0 0.0 0.0
"what clean boards!!!, love them :)" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15129.0 1.0 0.0 0.0
"His accent makes this very hard to listen to at 2x speed..." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4740.0 0.0 0.0 0.0
amazing 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12343.0 0.0 0.0 0.0
"calculus is pointless. " bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12586.0 0.0 0.0 0.0
"""for like 48 different reasons, that determinant is zero. It's dead"" OMG I love this guy" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 151.0 0.0 0.0 0.0
"lex fridman brought me here." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13786.0 0.0 0.0 0.0
"mergin and splitting of the poisson process - > again the poisson process. 
Random Incidences of Poisson - > bus example for poisson process" XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 13940.0 0.0 0.0 0.0
"why did people cheer when he wiped the upper blackboards??" _CdoRiNSrqI "Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15381.0 1.0 0.0 0.0
"ich versteh es nich  Mein kopf macht BOOM!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13523.0 0.0 0.0 0.0
Legendary..! 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 7327.0 0.0 0.0 0.0
"""Predict how many iPods there will be in ten years""...
0 my friend. The answer is zero." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 103.0 0.0 0.0 0.0
"Where can I find lec8?" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11657.0 0.0 0.0 0.0
"The guy is million times more enthusiastic than my 26 yr old maths teacher... Hats off" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 10132.0 0.0 0.0 0.0
"I have been waiting for this since the day I was born ! I shall achieve the Buddhahood once OCW releases the ""Functional analysis"" series." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 5521.0 0.0 0.0 0.0
"1:39 <--- and there you go. This statement pretty much sums up EVERY video on YouTube that has to do with EigenSTUFF conceptually. Yes, clearly...there is SO much more, but if for someone learning this the first time, this is such a critical outcome that NO textbook that I read, other than his, clearly and succinctly states this simple cue. Even after getting degrees in math and physics, it took me a bit of time to figure this out eventually. Thank you, MIT, for sharing this." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 596.0 0.0 0.0 1.0
"Prof. Edelman, Are you saying that generic programming and support for types and operators (+,-,/,* etc.) results in these benefits? Or are there other language features in Julia that make this possible? Thank you for making the lecture available to the world." rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8293.0 0.0 0.0 0.0
"I thought that students that get into MIT take at LEAST 1 calculus course in high school. Apparently not. Or they could be refreshing. I'm not sure." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6096.0 0.0 0.0 0.0
"Very good video" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 11186.0 0.0 0.0 0.0
"buenas dias" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12566.0 0.0 0.0 0.0
"For anyone who is confusing why u[t] = exp(At)* u[0] is showed up here, a video made by @3Blue1Brown really explains it well:
Title: 'How (and why) to raise e to the power of a matrix | DE6'
Link: https://www.youtube.com/watch?v=O85OWBJ2ayo&list=PLZHQObOWTQDNPOjrT6KVlfJuKtYTftqH6&index=7&ab_channel=3Blue1Brown
Hope this could help you out~" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 3856.0 0.0 0.0 0.0
"great man!!!!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12994.0 0.0 0.0 0.0
"At around 8:57, professor says that only zero vector leads to zero in the inequality, which is wrong. Because as long as x is in the nullspace of A, the equal sign will be reached in the inequality" TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 2708.0 0.0 1.0 0.0
"Love for Prof Strang .😊. Real picture of Eigen value and eigen Vector ..AX parallel to X ...touched and fascinated  with real story behind Mathematics. Lucky students  of MIT who is quietly listening  the story interestingly." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 7436.0 0.0 0.0 0.0
"@OriakoPhi fuuuuck, I made the same mistake the person at 37:50 did XD" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1697.0 0.0 1.0 0.0
"Fantastic artwork." hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3728.0 0.0 0.0 0.0
"God I don't know if I am crazy, but when he goes around with a demonstration which takes hours and he pases over a figure such as saying :""the slope of a exp to x where x=0 and we know that a exp 0 is equal to 1. right there what could it be easier." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4067.0 0.0 0.0 0.0
"40:00 wait, doesn't the slope also approach zero as x approaches infinity?" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1122.0 0.0 1.0 0.0
"Very clear" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 11159.0 0.0 0.0 0.0
"Great Lecture!" KcI2_r51Eb8 "Lecture 17: Minimizers, Orthogonal Complements and the Riesz Representation Theorem" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 4201.0 0.0 0.0 0.0
"They could have mics for students to go up to when asking questions. I kind actually want to hear their questions" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10436.0 1.0 0.0 0.0
"I wish i was a student sitting over there and attending the class...." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 6225.0 0.0 0.0 0.0
"yeah he is right , of course, sorry teacher." YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15466.0 0.0 0.0 0.0
"MIT has 100s of millions of dollars in its Trust .... can't nail down quality audio pick-up ....  money ain't everything ...." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 7518.0 1.0 0.0 0.0
"Can anyone be awesome enough to explain how he gets (2/d) * (2/pi) as the density of X and theta respectively? He is saying it has to integrate to 1 which I kind of understand as the PDF but not sure how he gets there... @25:07" CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 3014.0 0.0 1.0 0.0
"Take another look at the list...the first time I feel glad at so many left unwatched." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9008.0 0.0 0.0 0.0
"Camera: I see you're leraning about Morkov Matric- (3:43)
Heyy nich shirt ma dude" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 3000.0 1.0 0.0 0.0
"I think this subject is pretty easy and there's not much of rules to follow by, but he took so much time to explain!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6077.0 0.0 0.0 0.0
"Such a shame education system in my country is as archaic as The Flintstones, although they have a better education than we do here, and well, what can we expect, Spanish invaders brought thieves, scum and crap to our continent.

Long live America." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8940.0 0.0 0.0 0.0
"32:44 I guessed 7 too 🤗 thank you auntie" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 939.0 0.0 0.0 0.0
"hahaha, this guy does not get ready for lectures hahah. so funny.." jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 13052.0 0.0 0.0 0.0
"Generally people from India, specially Bihar think that they are very smart in mathematics but that's of type ""Rattafication"" a/c my experience
Here's the actual mathematics !!!
Literally Loved this lecture, wish to complete whole calculus part from here, not for any entrance but just to make my understanding to next level!
Thanks MIT :)" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3992.0 0.0 0.0 0.0
"45:34 the other revolting stuff. 


oh, my motherfricking god. this guy is a genius." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 1256.0 0.0 0.0 0.0
"wonderful professor" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15396.0 0.0 0.0 0.0
"This instructor makes the subject over-complicated by burying the student in unnecessary details. The solution of the 2X2 example can be found in 3 to 5 minutes. The 3X3 example will take a little longer, but maybe the instructor needs to dazzle the students to justify making the class longer.
Take the first equation:                                     2x    - y = 0
Add the second equation multiplied by 2:    -2x + 4y = 6
Add them together:                                            0x + 3y = 6  dividing by 3, we get y = 2.
Inserting the value of y into the first equation:  2x  -2 = 0  and add 2 to both sides we get:  2x = 2
                                                                                                                                                            or  x = 1
For the second equation:                                    -x + 2y = 3, so:   -x + 2(2) = 3  or   -x + 4 = 3  
 Subtracting 4 from both sides, we get:                                                                      -x = -4 + 3  or -x = -1
So,                                                                                                                                      x = 1
Final solution:  y = 2, x = 1.  DONE.
Graphing left to the student." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10577.0 0.0 0.0 0.0
"33:22 creativity at its best" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 957.0 0.0 0.0 0.0
"este profesor no sabe explicar se traba mucho" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12799.0 0.0 0.0 0.0
"1:14:50 i have been thinking about this question for days which is related to pset2 #4 [projection of decidable iff T-recognizable].How can we be sure that proofs itself doesn't cause looping.In the sense of projection problem How can i be sure that recognizable T is trying new inputs and not wasting its time with a pointless circles in specific pair of (x,y)" N-_XmLanPYg "11. Recursion Theorem and Logic" "MIT 18.404J Theory of Computation, Fall 2020" 590.0 0.0 1.0 0.0
"Watching this to make me feel better about college algebra. lol" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11306.0 0.0 0.0 0.0
"When he plots the solutions x in R^4 at minute 23-24, he plots Xp, Xn and Xcomplete=X. Shouldn't Xn be drawn through the origin and Xcomplete be drawn away from the origin and at the 'plane' without going through the origin?" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 11618.0 0.0 1.0 0.0
"Can someone kindly compute y-intercept for me? Where x = 0 into the asterisk eqn. I would just like to prove that y = 2y0. Thanks!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3086.0 0.0 1.0 0.0
"Too bad I can't afford all his books 😩... I'll start with his linear algebra books 🧐" MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11056.0 0.0 0.0 0.0
"Thank you, Strang! It was _you_ who inspired me to pursue mathematics years ago! (I owe you a lot for that gift.)" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9518.0 0.0 0.0 0.0
"Perfect professor and perfect explanation, how strange" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8179.0 0.0 0.0 0.0
"Anyone in 2018?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2500.0 0.0 0.0 0.0
"Keep up the good work🙏" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 7210.0 0.0 0.0 0.0
"Respectable professor Dr. Casey your each lecture is brain storming" W2pw1JWc9k4 "Lecture 12: Lebesgue Integrable Functions, the Lebesgue Integral and the Dominated Convergence..." "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 8564.0 0.0 0.0 0.0
"The problem of that calculation is given eigenvalues, the choice of orthonormal eigenvector matrix is not unique (we can multiply -1!). If we choose U not as identical, but as [[1,0],[0,-1]], the calculation will be alright." TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 10237.0 0.0 1.0 0.0
"Why is it that if there are more unknowns than there are equations there exists a whole bunch of solutions?" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 11881.0 0.0 1.0 0.0
"Here i thought  this was a Linear Algebra course . And was I surprised>>>>????" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4675.0 0.0 0.0 0.0
"Dr. Strang thank for helping me to relearn linear algebra and it's important concepts. When I took this class at the University of Maryland Baltimore County the professor did not care if I learn it or not." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 3509.0 0.0 0.0 0.0
"One of the best teachers that I've ever seen. I'm from Brazil and I could understand all their classes. Congratulations to the teacher and the institute (MIT). A very good job." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8094.0 0.0 0.0 0.0
"Where can I solve problem related to this lecture" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11664.0 0.0 0.0 0.0
"Thank you for the lectures, could you please state what topics did Lectures 10 and 16 covered? So we can research them 
separately." V4xOdtqic3o "15. Regression (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 9268.0 0.0 1.0 0.0
"I am glad to see you again, Prof." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5095.0 0.0 0.0 0.0
"Y pensar que pocos son los que ven estos videos." 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12103.0 0.0 0.0 0.0
"x/lnx IS DEFINED at x=0.

ln(0+) approaches –infinite = -1/0
so if f(x) = x/(lnx)
f(0) = 0/(ln0) = x/(-1/0) = x*(-0/1) = 0
Despite popular belief here in the comments, x=0 need not be an open dot, but closed as displayed." twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15455.0 0.0 1.0 0.0
"let's take a little shot at thinking 9 dimensions lol" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13782.0 0.0 0.0 0.0
"so far this course is more like differential geometry. " 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14331.0 0.0 0.0 0.0
"Watch on speed x2. You're  welcome" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11283.0 0.0 0.0 0.0
"Does the B column (the solutions column represent something geometrically?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3458.0 0.0 1.0 0.0
如意算盘 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15623.0 0.0 0.0 0.0
"But lessons are great!!!! I'am enjoying from every class. Thank you Gilbert Strang" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2963.0 0.0 0.0 0.0
"Glad Philippe touched on the John Oliver p-hacking haha" 4HRhg4eUiMo "8. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 4053.0 0.0 0.0 0.0
"For the QR decomposition ( 47:00 )  you can use Q^t * Q = I. With this you get:
                         R = q1^t * a1 q1^t * a2
                                 q2^t * a1 q2^t * a2
but since we work in real numbers the internal product
                                 A^t. B = B^t. A
Using it, we are left with:
                        R =  a1^t * q1 a2^t * q1
                                 a1^t * q2 a2^t * q2" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 3881.0 0.0 1.0 0.0
もし、本当に一橋大学を不正に落とされてたら一流大学に行きますが嘘情報なら今の大学に残ります。当然だろう。不正な方法で大学に入れる訳ないだろう。 QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15615.0 0.0 0.0 0.0
"Gilbert, you are an extremely good lecturer plus a very pleasant person." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 4042.0 0.0 0.0 0.0
"i hate these types of professors that gives the most simplest examples then expect us to do the most complex problems like this guy" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 13389.0 0.0 0.0 0.0
"Just the exam and then 18.01 is done. Thank you MIT.
😊🇮🇳. 
INDIA.
24.11.2020." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7197.0 0.0 0.0 0.0
"What was so funny about the plane intersection?" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11566.0 0.0 0.0 0.0
"Only one example and prof strang  can explain work done by centuries" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 8121.0 0.0 0.0 0.0
"may I ask what the p mean?" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13924.0 0.0 1.0 0.0
"the best, thanks!
" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14669.0 0.0 0.0 0.0
"21:45, 29:10 - how to know whether f'(c) is PARALLEL to line 'a➡b'?
Exciting to listen to the real life problem solving examples and techniques." 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 683.0 0.0 1.0 0.0
"Very beneficial lectures. Thanks MIT  from 2020's (:" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11158.0 0.0 0.0 0.0
"15 years later still the best" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 441.0 0.0 0.0 0.0
"Sir Gilbert Stang is my inspiration for learning linear algebra" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 8690.0 0.0 0.0 0.0
"at what age do mit students study..... if anyone knows pls tell me" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12480.0 0.0 0.0 0.0
"where is the lecture 13?" asjAc90L8rE "12. Time Complexity" "MIT 18.404J Theory of Computation, Fall 2020" 15242.0 0.0 0.0 0.0
"in 30.41 he writes ""set u=Sv"" he says that S is the eigenvector Matrix but he does not say nothing for WHAT IS THIS ""v small"" ,and why did he do that trick..it is disheartening" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 13576.0 0.0 1.0 0.0
"haha so easy" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13041.0 0.0 0.0 0.0
"THATS ART" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8992.0 0.0 0.0 0.0
"Seems like a great instructor." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8619.0 0.0 0.0 0.0
"YouTube: You're taught the same things as MIT students, but potentially twice as fast!" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12259.0 0.0 0.0 0.0
"The students close the door so gently. Nice." nvXRJIBOREc "Lecture 21: Minimizing a Function Step by Step" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10288.0 0.0 0.0 0.0
"Finish at 21 March 2020" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3799.0 0.0 0.0 0.0
"well done!" XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 15085.0 0.0 0.0 0.0
"I had a question and was hoping somebody could help me out here. The two spaces (floor and wall) were not orthogonal because not all vectors were orthogonal. In fact, they intersect in a line and hence have equal vectors. But in general two planes will always intersect in a line and in that case can never be orthogonal. So how can the row space of a 4x4 matrix of rank two be orthogonal to the null space of that matrix? I really can't find where my reasoning is off." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5462.0 0.0 1.0 0.0
"very helpful videos..." ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 15018.0 0.0 0.0 0.0
"at 24.45 u explain cdf abt uniform continuous r.v the distribution goes linearly... what abt the case if it is non-uniform??" mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 12426.0 0.0 1.0 0.0
"i couldnt resist xD" PnPIqh7Frlw "Lec 24: Simply connected regions; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13353.0 0.0 0.0 0.0
"whats the point for me to paying for my host uni.. I cant understand what they were saying and i have to come up to attend lecture from other uni
" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15200.0 0.0 0.0 0.0
"The subtitles said ""Windowed financially bathroom"" 31:13

What the hell? " wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10292.0 0.0 0.0 0.0
"Can some one explain me what is the meaning of   'low and behold' ." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3062.0 0.0 0.0 0.0
"haha, they freaked out when he mentioned Taylor approximation. I love Taylor appr. it makes life so much easier ;)" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13049.0 0.0 0.0 0.0
"Is there a playlist where all of these lectures on Linear Algebra of 18.06 can be accessed?
For every course taught by Professor Strang?" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 6821.0 0.0 0.0 0.0
"I really fucking bombed the exam, damn." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5917.0 0.0 0.0 0.0
"Thanks! I prepared my high school final exam from this lecture. This really helped me!!" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9831.0 0.0 0.0 0.0
"Just one feedback from a student: It would be even better if the camera doesn't move too frequently following the lecturer. 
Thank you for all the camera works, just wanted to help make them even better. Thanks for great videos." k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7191.0 1.0 0.0 0.0
"This is absolutely incredible. The 'big formula' was thrown at us with absolutely no context and no mention of arithmetic with determinants; this cleared up so much for my university algebra course." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 10607.0 0.0 0.0 1.0
"This professor is awesome!" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 10901.0 0.0 0.0 0.0
"This  dude  is excellent! " XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10452.0 0.0 0.0 0.0
"but if we realy have to solve with cartesian co-ordinate what will we do?" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12572.0 0.0 1.0 0.0
"It's been over 10 years since I first learned this in high school. Now I think I finally understand the formula for the derivative after this guy lectured for 20 minutes." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7033.0 0.0 0.0 1.0
"I have no doubt this man is a linear algebra genius, but I have no idea what he is talking about.  His manner of speaking is not linear." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 5545.0 0.0 0.0 0.0
"Proving closures using NFAs feels like a cheat code" oNsscmUwjMU "2. Nondeterminism, Closure Properties, Conversion of Regular Expressions to FA" "MIT 18.404J Theory of Computation, Fall 2020" 8456.0 0.0 0.0 0.0
"Is there no interactive transcript on this one? I'm not seeing it..." RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6843.0 0.0 0.0 0.0
"there is a mistake ! area of square bottom equal 2(square of x) plus four(xy)" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14761.0 0.0 1.0 0.0
"@rax7 lol totally hope you're not serious....." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1984.0 0.0 0.0 0.0
"Seems teacher didn't do his homework. Seems his concepts were not very clear. Because the proofs of sinx/x and other one of cos can be done by other methods as well and they are very easy.  He did not explain well some statement left unexplained. MIT myth is busted. I guess he can't even solve problems of mathematics in Indian engineering college entrance exam i.e. JJE advanced." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8621.0 0.0 0.0 0.0
"why was M(e) equated to 1?" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15373.0 0.0 1.0 0.0
"Every thing is fine but why does professor repeats the  same shirt , tie and the pants ?😂" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3600.0 1.0 0.0 0.0
France PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3919.0 0.0 0.0 0.0
"All are going well in this course series. But Professor didn't cover Error Analysis very well." 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2293.0 0.0 0.0 0.0
"Thanks so much, Professor Strang!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9791.0 0.0 0.0 0.0
"The smelly dill pathogenetically list because decimal acutely warm onto a waggish windshield. alive, husky angle" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10281.0 0.0 0.0 0.0
"36:05 to sleep in front of 300k people... a fucking legend" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 1029.0 0.0 0.0 0.0
"Is this an intro to Calculus? I learned everything this guy is talking about my Freshman year of High School." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6854.0 0.0 0.0 0.0
"2013 or 2014?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 620.0 0.0 0.0 0.0
"You probably can't get into MIT." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12233.0 0.0 0.0 0.0
"lol. i like the way he says temperature. (hope i spelled it correctly)

he's awesome!" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 13843.0 0.0 0.0 0.0
"Ax=b,does not have solution,but how does
A'Ax'=A'b have a solution since 
when we multiply by A' ,we just take combinations of rows and create new rows 
So ,if x' satisfies 2nd eqn , it must satisfy 1st 
pls clear my doubt  
" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2797.0 0.0 1.0 0.0
"Professor is gift to the mankind. Thank you so much." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 8393.0 0.0 0.0 0.0
"Thank you heard my request" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 9296.0 0.0 0.0 0.0
"@redzor812 So you have a first calculus course and it doesn't include the basics of calculus? Sound strange." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1988.0 0.0 0.0 0.0
"Very very nice." 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11231.0 0.0 0.0 0.0
"@HackyTV It's a university (or college) like any other. They teach lesser mathematics too, this is also the first lecture which is very typically a review of the previous course work or a very basic overview of what it will cover. I'm pretty sure they will go very in depth into these topics. 

After watching a bit more, its very obviously a first year class, which are not very difficult, especially the first lecture. Try watching lectures from the end of the semester from this class." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1629.0 0.0 0.0 0.0
"didn't know multiplication could be this interesting" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12744.0 0.0 0.0 0.0
"long live gilbert strang" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13846.0 0.0 0.0 0.0
"after years and years of no well known university uploads a full course in this topic, it had to be MIT 

Thanks Again MIT from Bolivia!" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 12310.0 0.0 0.0 0.0
"beautiful, beautiful stuff" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12519.0 0.0 0.0 0.0
"upload courses taught on computer screen in a infographic way" os_XGBNPllM "Lecture 8: The Squeeze Theorem and Operations Involving Convergent Sequences" "MIT 18.100A Real Analysis, Fall 2020" 14981.0 0.0 0.0 0.0
"SO fantastic！！！THE Right way to open Linear Algebra!!! 我是来自中国的学生，当我认真学习线性代数的第一堂课后，我被深深的shocked到了！让我重新理解了维度！ N-D space is a combination of N-1-D sapce and non-N-1-D vector!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8582.0 0.0 0.0 0.0
"finished ...." rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 12863.0 0.0 0.0 0.0
"why do you just put the whole slide on the screen when he is pointing something on the slides? there is no way to see where he is pointing. just point the camera at the slide" OYcdw5vOgIc "23. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 15307.0 1.0 0.0 0.0
21:36 N28g_YBXY8Y "9. Reducibility" "MIT 18.404J Theory of Computation, Fall 2020" 681.0 0.0 0.0 0.0
"That was a beautiful ending. It made me cry" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9915.0 0.0 0.0 0.0
"Thank you, Professor Strang." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 9514.0 0.0 0.0 0.0
"I love this Man." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5801.0 0.0 0.0 0.0
"Great lectures! I just wanted to comment because I am learning a lot from all his lectures! And I already have a degree in physics!" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 4305.0 0.0 0.0 0.0
"I literally screamed why is this prof. so **** smart..
" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 5706.0 0.0 0.0 0.0
"Lecture timeline Links
Lecture 0:00
What are Vector spaces 1:05
Subspaces of R³ 2:33
Is the union of two subspaces a Subspace? 4:23
Column space 11:36
Features a Column space 14:46
How much smaller is the Column space? 15:48
Does every Ax=B have a solution for every B? 16:17
Which Bs allow the system of equations solved 19:39
Null space 28:12
Understand what's the point of a Vector space 40:24" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 7299.0 0.0 0.0 0.0
"Is there a link where I can find some exercises to practice the concepts of the lectures?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 6820.0 0.0 0.0 1.0
"We lived so long and we skipped the proof  39:40!!!!!!!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 11324.0 0.0 0.0 0.0
"That intro track tho" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9892.0 0.0 0.0 0.0
"This is fantastic, very clear explanations. I'm currently taking Calculus 3 in Summer session and  I work a full time (40 hours per week)   so I have no life... well Calc 3 is my currently life. But I love it" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 10662.0 0.0 0.0 0.0
"Such a great lecturer. Thank you!" wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8930.0 0.0 0.0 0.0
"yeah but once you have supposedly found the y intercept the x intercept doesnt exist. fuckin idiot" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15464.0 0.0 1.0 0.0
"This was either: the class was taken just for the video and hence no students were there OR the students just didn't show up...if it was the latter it is really a great thing that Prof Strang did take the class at all, even for the video...if something like this had happened in my college then we would have been in so much trouble.." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 10969.0 0.0 0.0 0.0
"math is cool but i want that chalk" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13915.0 1.0 0.0 0.0
"This man saved my GPA." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 10877.0 0.0 0.0 0.0
"Great Teacher!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4210.0 0.0 0.0 0.0
"8:28 so n fuck-torial" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 1420.0 0.0 0.0 0.0
"my teacher multiplied times 10 = this teacher...." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 14006.0 0.0 0.0 0.0
"Great lecture, but what is stated at 58:15 is quite incorrect. Estimating demand from price alone can be quite tricky due to endogeneity issues. That is, from price alone you cannot know whether you are actually estimating a demand or supply function since the points can go in either direction." yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 4280.0 0.0 1.0 0.0
"1:09:19 the subtitle error ""data"" should be ""theta"". Same for the next sentence. Thanks" QXkOaifVfW4 "9. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 582.0 0.0 1.0 0.0
"For the Complex Unit Circle part, watching this video (https://www.youtube.com/watch?v=0BcZjxKsVnY&ab_channel=Elucyda) prior helped me better understand it" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 3878.0 0.0 0.0 1.0
"woah this guy just singlehandedly saved this semester for me. and he does it so nonchalantly. i'm stunned" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 15388.0 0.0 0.0 0.0
"Thank you for the excellent lecture!" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 9263.0 0.0 0.0 0.0
"Thank you so much, I have learnt a lot with the course, greetings from México." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9393.0 0.0 0.0 0.0
"85 years old not a single white strand of hair in sight." 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 1411.0 0.0 0.0 0.0
Woah!😍😍💝🇧🇩 bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11976.0 0.0 0.0 0.0
"""...giving other self-learners in the world opportunities of learning from the best.""

True enough. Of course, it would also be nice if they would release a few more lecture series from other subjects. I'm spoiled now...  it is so frustrating walking into a course without already knowing it forward and back. 

;)" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 19.0 0.0 0.0 0.0
Wow UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 12020.0 0.0 0.0 0.0
"An Indian edition of this book is available only in India
http://www.wellesleypublishers.com/buy.html" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2426.0 0.0 0.0 0.0
"@gomefun2 it's at 38 minutes (if you didn't already notice)." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1853.0 0.0 0.0 0.0
"Thank you so much professor. I love you" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9377.0 0.0 0.0 0.0
"Could someone please explain why is the Archimedian property stated in that form at 16:10?
Edit: spelling." M2d4HsBsu8Y "Lecture 5: The Archimedian Property, Density of the Rationals, and Absolute Value" "MIT 18.100A Real Analysis, Fall 2020" 3238.0 0.0 1.0 0.0
"to not waste you're time
Lecture 1: Dot Product

 Lecture 2: Determinants
Lecture 2: Determinants

 Lecture 3: Matrices
Lecture 3: Matrices

 Lecture 4: Square Systems
Lecture 4: Square Systems

 Lecture 5: Parametric Equations
Lecture 5: Parametric Equations

 Lecture 6: Kepler's Second Law
Lecture 6: Kepler's Second Law

 Lecture 7: Exam Review
Lecture 7: Exam Review

 Lecture 8: Partial Derivatives
Lecture 8: Partial Derivatives

 Lecture 9: Max-Min and Least Squares
Lecture 9: Max-Min and Least Squares

 Lecture 10: Second Derivative Test
Lecture 10: Second Derivative Test

 Lecture 11: Chain Rule
Lecture 11: Chain Rule

 Lecture 12: Gradient
Lecture 12: Gradient

 Lecture 13: Lagrange Multipliers
Lecture 13: Lagrange Multipliers

 Lecture 14: Non-Independent Variables
Lecture 14: Non-Independent Variables

 Lecture 15: Partial Differential Equations
Lecture 15: Partial Differential Equations

 Lecture 16: Double Integrals
Lecture 16: Double Integrals

 Lecture 17: Polar Coordinates
Lecture 17: Polar Coordinates

 Lecture 18: Change of Variables
Lecture 18: Change of Variables

 Lecture 19: Vector Fields
Lecture 19: Vector Fields

 Lecture 20: Path Independence
Lecture 20: Path Independence

 Lecture 21: Gradient Fields
Lecture 21: Gradient Fields

 Lecture 22: Green's Theorem
Lecture 22: Green's Theorem

 Lecture 23: Flux
Lecture 23: Flux

 Lecture 24: Simply Connected Regions
Lecture 24: Simply Connected Regions

 Lecture 25: Triple Integrals
Lecture 25: Triple Integrals

 Lecture 26: Spherical Coordinates
Lecture 26: Spherical Coordinates

 Lecture 27: Vector Fields in 3D
Lecture 27: Vector Fields in 3D

 Lecture 28: Divergence Theorem
Lecture 28: Divergence Theorem

 Lecture 29: Divergence Theorem (cont.)
Lecture 29: Divergence Theorem (cont.)

 Lecture 30: Line Integrals
Lecture 30: Line Integrals

 Lecture 31: Stokes' Theorem
Lecture 31: Stokes' Theorem

 Lecture 32: Stokes' Theorem (cont.)
Lecture 32: Stokes' Theorem (cont.)

 Lecture 33: Maxwell's Equations
Lecture 33: Maxwell's Equations

 Lecture 34: Final Review
Lecture 34: Final Review

 Lecture 35: Final Review (cont.)
Lecture 35: Final Review (cont.)" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 14947.0 0.0 0.0 0.0
"Plz subscribe my channel https://youtu.be/0Bm4RFOmqlo" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8223.0 0.0 0.0 0.0
"In Spanish please 😞" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6620.0 0.0 0.0 0.0
"This is the most correct way to learn linear algebra.
Establish direct sense but not be buried by thousands of definition and proof." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 10752.0 0.0 0.0 0.0
"Totally true." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11077.0 0.0 0.0 0.0
"Magistral lecture!" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7562.0 0.0 0.0 0.0
"what undergraduate year is this course?" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15186.0 0.0 0.0 0.0
"Dr. Gilbert made these cofactor things are so obvious!" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 3500.0 0.0 0.0 0.0
"am i the only one watching the lectures in 1.5 or 1.25 playback speed?" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 12339.0 0.0 0.0 0.0
"Thank you MIT and Professor Strang for those fascinating lectures. In every lessons we reuse the things we have learned before and this makes a super connection between the topics. This lecture was a great example of that. Thank you again <3" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 9137.0 0.0 0.0 0.0
"@ 11:30, the question given is not the same one given on the OCW site." Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1465.0 0.0 0.0 0.0
"@inuyashalivesbaby 

There are boards like that at my school.

Not that special of a device. Common at large universities." dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 1893.0 0.0 0.0 0.0
"Your videos have been saviour for me. Thanks a ton dear prof ❤️" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 12264.0 0.0 0.0 0.0
"감사합니다, Thank you." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 15670.0 0.0 0.0 0.0
"that's pleasure for me to see all of your videos and i can't stop to do it because i've learnt much things" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14647.0 0.0 0.0 0.0
"We love Gilbert Strang!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11325.0 0.0 0.0 0.0
"Legend Sipser!" m9eHViDPAJQ "4. Pushdown Automata, Conversion of CFG to PDA and Reverse Conversion" "MIT 18.404J Theory of Computation, Fall 2020" 7319.0 0.0 0.0 0.0
"typo (error) in 33:08 A = 3*x^(2/3)*v^(2/3)" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14969.0 0.0 1.0 0.0
"wheres his blue shirt?
" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 15248.0 0.0 0.0 0.0
"Prof Strang, thank you so much for all your lectures." 1pFv7e9xtHo "31. Eigenvectors of Circulant Matrices: Fourier Matrix" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8276.0 0.0 0.0 0.0
"How did he get the equation x(s) = x(0) + as and similarly for y(s)??" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 4836.0 0.0 1.0 0.0
"Thank you, professor,
very intuitive, which is not have probability is usually taught but should be." 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 9526.0 0.0 0.0 0.0
"Selfeducation with such good teachers is the future! 
Thank you Professor Strang." 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 8625.0 0.0 0.0 0.0
"Thought there would be some Bj jokes 24:42 , but then again it's a MIT math class taught by Gilber Strang, maybe most are too absobed by his awsome lecture for that haha." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 10999.0 0.0 0.0 0.0
"So much love and respect for Prof. Strang! Thank you so much!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8779.0 0.0 0.0 0.0
"So... I didn't even know what a matrix was until 80 minutes ago... 
This guy rocks!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8813.0 0.0 0.0 0.0
"""Make Bases Orthonormal Again!""" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 81.0 0.0 0.0 0.0
"Shouldn’t delta x and delta f be dx and df since we’re talking the derivative." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8655.0 0.0 1.0 0.0
"The greatest lecturer I've ever seen" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10128.0 0.0 0.0 0.0
"Thank you!!! MIT!!!!" XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 9487.0 0.0 0.0 0.0
"I can't stress my thanks enough. Thanks for everything Prof Strang, MIT." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 5223.0 0.0 0.0 0.0
"what i dont understand is why teach such basic concepts again that were studied before and in depth in linear algebra?

Or take the law of cosinus: that is sth you'd need to know to get into almost any university. I mean you're attending multivariable calculus classes but you don't know how to sum two vectors?
Anyways, I'm not saying it's wrong, it's just a doubt that comes across when watching this video." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15144.0 0.0 0.0 1.0
"at 33:40, why is it only true for union of finite number of sets?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 12442.0 0.0 1.0 0.0
"So HEEERE. As you can see. Something is appearing that we would note that way. Approximatively. These variables. We don't want these variables. OK. You drop it. What we want here it makes appear, on the plan, the derivatives of quantum mechanic (.)" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 8728.0 0.0 0.0 0.0
"U.S. colleges offer a very wide variety of levels of mathematics.  Some majors require less math than others, and some students like to start college taking a certain level of math again as a refresher while they get used to college life." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11114.0 0.0 0.0 0.0
"Ι saw whales, SWAT, Ubuntu on the subs...

How come this lecture not have a correct subtitle like 1-8" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 15547.0 0.0 0.0 0.0
"Gotta respect Gilbert Strang." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 4174.0 0.0 0.0 0.0
"the man the myth the legend Gilbert Strang" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 14715.0 0.0 0.0 0.0
"Does it matter whether english is my first language or not? If it was would you feel proud or ashamed? or if its not would you feel disgusted? Just back trace your statements a bit, You are asking why a student is in MIT because you feel the student asked a trivial question.. did you forget that it was a student? and that mistakes are expected from students?.. from MIT or NOT?  Or is your brain too slow to use that rational?  " 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3457.0 0.0 0.0 0.0
"Thank you， Professor Strang." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9568.0 0.0 0.0 0.0
"38:38 I did not get what he meant. Y is a random variable indicating the time we have to wait. And for time, isn't it continuous? Then Y should also be a continuous RV. Why did he mention PMF rather than PDF?" gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 1084.0 0.0 1.0 0.0
"This is way too advanced for me. I can understand the calculus but when he starts talking about convergence in probability and distribution, i get really lost. Can anyone point me to a book where i can get a better understanding on these topics of inference and convergence?" JTbZP0yt9qc "6. Maximum Likelihood Estimation (cont.) and the Method of Moments" "MIT 18.650 Statistics for Applications, Fall 2016" 10766.0 0.0 0.0 0.0
"Thank you for uploading it. I'm very appreciate it~~ I'm going back to university after graduated for 3 years. it help me refresh my knowledge a lot. " kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9289.0 0.0 0.0 0.0
"that smooth camera work with the show of hands 😗👌" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14639.0 1.0 0.0 0.0
"@userisdosser OM MY GOSH, I thought I was the only one who thought this. Powerpoint just doesn't help me I really wish my lecturers would use a blackboard!
" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2056.0 1.0 0.0 0.0
"This man has infinite chalkboards" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 10851.0 1.0 0.0 0.0
"The discrepency from canadian universities to MIT is an order of magnitude w.r.t to quality.   I am so thankful M.I.T did this." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10077.0 0.0 0.0 0.0
"good professor, but no necessarily a clear one. respect him." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12949.0 0.0 0.0 0.0
"there are three kinds of mathematicians 1) who know how to count 2) who don't." wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 14760.0 0.0 0.0 0.0
27:35 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 822.0 0.0 0.0 0.0
Calculus<3 PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2989.0 0.0 0.0 0.0
"This assumes the earth is flat.

Actually, since the earth is not flat and roughly spherical, if the blocks stack up to high enough scales, the blocks would need to cover the arc length of the circle (along which the blocks are run on the earth) and that arc length increases linearly with the radius from the center of the Earth;

hence I think the real answer would probably be no if you don't assume the earth is flat. (Just a thought)" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10466.0 0.0 1.0 0.0
"good lecture" 0Va2dOLqUfM "5. Maximum Likelihood Estimation (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 12946.0 0.0 0.0 0.0
"Hi, I am just a beginner with not much knowledge.  Toward the End he is doing a proof stating that 
xTAT=(Ax)T.  I believe A is a square matrix and x is just a column vector.  To me this doesn't make sense.  I don't see how you can see can perform such an operation X Transpose A Transpose.  Can someone explain?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 4717.0 0.0 1.0 1.0
"I learned a new word ""timesing"" !" 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5650.0 0.0 0.0 0.0
"Hi guys! Can you please reupload this with the background static removed?" TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 4712.0 0.0 0.0 0.0
"I wish I went to an ivy league school where the lectures are actually comprehensible. Unlike my university |:" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6213.0 0.0 0.0 0.0
"Prof.Strang: ""If you can tell me whats in that block , I'm gonna be quiet for the rest of the day"" Wow !! 
 
This shows his passion. *Hats off* Sir ..." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8318.0 0.0 0.0 0.0
"thanks prof" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 14595.0 0.0 0.0 0.0
"Great lesson! just wondering how is the quadratic apporx. equation (the extra addend) come from? Like I know how the linear is proved to be but what about quadratic apporx equation proof?" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4312.0 0.0 1.0 0.0
nice UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14027.0 0.0 0.0 0.0
"@theRealCheeseCake uhh u have to be smart too" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2040.0 0.0 0.0 0.0
"Thanks sir" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9773.0 0.0 0.0 0.0
"khkhkh i guess that i'll get graduated from a school i've never been in before!" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13754.0 0.0 0.0 0.0
"Dang this is an amazing lecture" cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3313.0 0.0 0.0 0.0
"That's probably why I've found that many non-U.S. students can't solve non-standard problems or think of innovative solutions that require intuition and imagination." -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9934.0 0.0 0.0 0.0
"Please like subscribe and share" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8205.0 0.0 0.0 0.0
"At minute 23:48, I think the hypothesis of x>0 is in fact needed to be able to apply the Archimedean Property." M2d4HsBsu8Y "Lecture 5: The Archimedian Property, Density of the Rationals, and Absolute Value" "MIT 18.100A Real Analysis, Fall 2020" 2718.0 0.0 1.0 0.0
"Size of text on the blackboard is small, so no good visible." EBdgFFf54U0 "Lecture 14: Basic Hilbert Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 8718.0 1.0 0.0 0.0
"This is amazing! Just found out about this and I am so excited!!!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10616.0 0.0 0.0 0.0
"@inuyashalivesbaby 

Nah, just saying that my university isn't a great one (it's great by some standards, nobel prize winners have taught here), but it's easy to get into this one." dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 1891.0 0.0 0.0 0.0
"Se a ver te conseguir passar a algebra do maggy até que casava contigo" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8605.0 0.0 0.0 0.0
"Came here as some sort of review, end up learning something new, especially the fact that, derivative of an odd function is an even function... So, thanks for that 😅😁" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2991.0 0.0 0.0 0.0
"Thanks.That's gonna be interesting. I was wondering how the concepts such as curl(F) can be extended to high-dimensional scenarios and also whether all the geometrical interpretations remain. " tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9856.0 0.0 1.0 0.0
"If I had teachers like Gilbert Strang, I likely would've had a Ph.D in Math by now. No kidding! I love this guy! He made me fall in LOVE with Mathematics." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 6467.0 0.0 0.0 0.0
"This was made a bit after the iPhone" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10971.0 0.0 0.0 0.0
"The most interesting math video I've ever seen. Thank you very much!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10197.0 0.0 0.0 0.0
"Could someone explain why vector, lambda and 1 is a solution to the nullspace at 48:43? First component, (1-lambda)*lambda+1 is not 0 or different from lambda^2 - lambda -1." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 3235.0 0.0 1.0 0.0
"5:54, why is the reduced matrix 

u
0


instead of

Identity
0" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 1366.0 0.0 1.0 0.0
"11:19 I think the columns of C are combinations of the columns of B and the rows of C are combinations of the rows of A. If not can someone explain it to me, I am taking notes and I can share them on discord to see how I got to my conclusion" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 369.0 0.0 1.0 0.0
"أستاذ عبقري!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 15563.0 0.0 0.0 0.0
"this explains why most people will pick 7 when asked to pick number between like 1-10  or 1-12   hahaha seems our brain makes an automated computation we might not realize" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 14805.0 0.0 0.0 0.0
"I love the joke but I love the course more=]
Thx" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 5777.0 0.0 0.0 0.0
"Sorry I just meant to be specific. Note that I said the derivative is not JUST the slope of a line. If the function given is a slope.You're right. thats all." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8851.0 0.0 0.0 0.0
"what a great teacher" 3PzuSPQPEU4 "8. Undecidability" "MIT 18.404J Theory of Computation, Fall 2020" 15108.0 0.0 0.0 0.0
"@joeglimmix Only if the professor can clean off the second chalk board  while the 3rd is coming down." 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 1905.0 1.0 0.0 0.0
"Is this high school edition ? .. these students surely aren't undergraduates .." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6872.0 0.0 0.0 0.0
"28:37 did anyone notice the asian who realized he f'ed up by coming late to class?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 840.0 0.0 0.0 0.0
"@redrum41987 man, i wish i could think faster than i can talk" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1986.0 0.0 0.0 0.0
"7/5/21 ASE review" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1389.0 0.0 0.0 0.0
"I really recommend this course! there are a lot of in-depth comments that refresh your understanding about statistic." TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 5934.0 0.0 0.0 1.0
"then we basically have a bunch of rectangles. when n approaches infinity, the rectangles width gets infinity small, and the values for f(x) over that interval pretty much become equal, they differ very little. so we can multiple f(x) by the differential dx, the very small width, and get the anti derivtive of each one of the rectangles. the sum then becomes of a bunch of rectangles, and is now the following. [F(n)-F(n-1)] + [F(n-1) - F(n-2)] ...-[F(2) - F(1)]. THEN, the amazing part...." Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14756.0 0.0 0.0 0.0
"at 45:22 how can be moment of inertia  has dimension of [M*l^4]   i think it should be [M*l^2] right" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12455.0 0.0 1.0 0.0
"Prezado nobre amigo professor do  Canal Open Course Ware, interessante sua explanação e demonstração, simples e de fácil aprendizado aos alunos(as) aqui presente neste singelo canal, com meu respeito á todos aqui presente, que tal usar este pi que padronizei, foi reconhecido Cientificamente que ele é Racional e Irreversível, segue minha obra para sua apreciação, o autor Sr Sidney Silva, gratidão sempre.

: https://www.portaldoslivreiros.com.br/livro.asp?codigo=4410831&titulo=A+Ousadia+do+Pi++Ser+Racional

: https://www.estantevirtual.com.br/mod_perl/info.cgi?livro=2655536635

 https://aeditora.com.br/produto/a-ousadia-do-%cf%80-ser-racional/

 https://www.amazon.com.br/dp/655861281X?ref=myi_title_dp

https://aeditora.com.br/produto/a-ousadia-do-%cf%80-ser-racional/

Onde encontrar minha obra, segue os links acima em epígrafe, e adquirir uma obra onde sua leitura é bem simples e objetiva provando a Racionalidade de Pi, para saber se é Racional ou não, compre minha obra, gratidão sempre o autor Sr Sidney Silva." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8253.0 0.0 0.0 0.0
"Thanks MIT OCW and Prof. Gilbert for your hard work." Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 9607.0 0.0 0.0 0.0
"Can anyone tell why those three properties exist and why only and specifically them?" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 3053.0 0.0 1.0 0.0
"question: a f(x,y) with gradient y,x shouldn't be xy + c? (nothing changes in practice)" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14240.0 0.0 1.0 0.0
"thanks a lot Pro. Strang" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 14569.0 0.0 0.0 0.0
"One of the best and youngest professor ever...thanks very much Auroux and MIT" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8087.0 0.0 0.0 0.0
"Recorded in 1999, still relevant in 2021.  ""Comes back 40 years later"" - Yep still relevant" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 8541.0 0.0 0.0 0.0
"Thank🌹🌹🌹MIT
AND LOVE FROM India🇮🇳🇮🇳" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9875.0 0.0 0.0 0.0
"Why did they clap when we was moving the line through the vector field at around 10 mins? =D" _CdoRiNSrqI "Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11813.0 0.0 0.0 0.0
"thank you sir" rLlZpnT02ZU "4. Parametric Inference (cont.) and Maximum Likelihood Estimation" "MIT 18.650 Statistics for Applications, Fall 2016" 14507.0 0.0 0.0 0.0
"For people who deal with statistics, this lecture is probably the most important in the entire series.  This is so fucking good." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3871.0 0.0 0.0 0.0
"01:39 specially interested vectors - eigenvectors" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 288.0 0.0 0.0 0.0
"8-  Metal Foil Resistors . Sep 15, 2022  Thermal treatment TCR. 1 ,This movie describes the first part of the metal foil treatment.https://www.youtube.com/watch?v=_pVK6fHFWS0&t=36s" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 1408.0 0.0 0.0 0.0
"Harvard does have a series for Probability on Youtube
." P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 4430.0 0.0 0.0 0.0
"I love how everybody cheers when he erases the board faster than the pulley moves it : P" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5748.0 1.0 0.0 0.0
"this is the big stuff" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 14880.0 0.0 0.0 0.0
"And you have access to their videos for free :)" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2455.0 0.0 0.0 0.0
"Amazing prof" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 2386.0 0.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8428.0 0.0 0.0 0.0
"This guy is good in converting everything to shit, Sincere advice - stop this video and go to https://www.youtube.com/watch?v=L-pQtGm3VS8" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 10531.0 0.0 0.0 0.0
"Thank you professor once again been through differential though in much depth n passed to start integrals in same video .. Not been possible with everyone's hard work .." -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9324.0 0.0 0.0 0.0
"I barely encountered determinants until I reached multivariable." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5162.0 0.0 0.0 0.0
"Thanks Prof Strang, MIT!" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9628.0 0.0 0.0 0.0
"I love Prof. Gilbert Strang, he is a dedicated man to teach mathematics. Please receive a huge hug on my behalf." Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5721.0 0.0 0.0 0.0
"The best course of linear algebra. Thanks Prof. Strang!" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 9993.0 0.0 0.0 0.0
"Very good course, except the teacher's accent needs  a little bit time to accomadate" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 11175.0 0.0 0.0 0.0
"ok i am kinda lost in this lecture" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14125.0 0.0 0.0 0.0
"Thank you from the bottom of my Professor.
May Allah bless you." HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 9295.0 0.0 0.0 0.0
"I think the constraint made the system have only 2 degrees of freedom. Cause if Det=0 then the matrix is not Linearly Independent. Therefore: 
2x=λy, 2y=λx and xy=3 have only 2 L.I. equations. If Det=0.
This means if λ is a real unknown and x is an unknown, and y is an unknown, the equations is unsolvable if you only have 2 L.I. equations. 

3 unks with 2 L.I. equations, only becomes solvable when the constraint gave the system only 2 degrees of freedoms. Allowing you to solve for λ. This would also mean λ is not a real unknown." 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6051.0 0.0 1.0 0.0
"36:49 This paradox gave me a headache. In our school, we just solve dimensionless problems. This paradox opened my eyes to the subtlety of computations in calculus. Thank you, MIT." ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1044.0 0.0 0.0 0.0
"@Michciu0911 Because advanced students don't want to sit around why the slower students plod through a problem.  Do homework on your own time." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1675.0 0.0 0.0 0.0
"@MrSystemVI good thing you're sticking with math and not English =)" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1685.0 0.0 0.0 0.0
"Thank you Prof." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9187.0 0.0 0.0 0.0
"is the recitations and tutorials are available?" H_k1w3cfny8 "10. Continuous Bayes' Rule; Derived Distributions" "6.041 Probabilistic Systems Analysis and Applied Probability" 13647.0 0.0 0.0 0.0
"Can anyone give me an example of a 'real-symmetric' matrix whose eigen value and singular value are not same..." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 3036.0 0.0 1.0 0.0
"Love these lectures" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 7455.0 0.0 0.0 0.0
"One of the best lectures on Youtube, thanks Prof. Gilbert for explaining this beautifully." rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8090.0 0.0 0.0 0.0
"hes ""the substitute"", but i sure liked how he explained that chain rule! very helpful." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13144.0 0.0 0.0 1.0
"very easy" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 15002.0 0.0 0.0 0.0
"F
A
I
L" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3714.0 0.0 0.0 0.0
"my left ear feels lonely" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13988.0 0.0 0.0 0.0
"Amazing lecture. Thank you!@" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2375.0 0.0 0.0 0.0
"I don't get how you get to decide a particular matrix which when multiplied by the original matrix results in a desired matrix." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5304.0 0.0 1.0 0.0
"Property 2 wasn't needed as a fundamental property, since it follows from property 3." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 8418.0 0.0 1.0 0.0
"i have studied scalars and vectors in intermediate educations but its just on the black board and i wz unable to implement it in real life.Honestly i was never comfortable with mathematics." ZwpwmGP5ITM "Lec 34: Final review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13398.0 0.0 0.0 0.0
"His book is pretty terrible, but it's a bit more manageable with his lectures. I don't see where all the praise for him comes from, let's be honest he's an ok professor : 6.5/10" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 4741.0 0.0 0.0 0.0
"Hindustan zindabad!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4737.0 0.0 0.0 0.0
"Legend 👏👏😊👏😊" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7320.0 0.0 0.0 0.0
"What a stunning illustration of pure applied logic. Lecturer truly pays tribute to the theory." 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11431.0 0.0 0.0 0.0
"Look, your product rule argument is circular.  The proof of the product rule ""assumes"" two things:  1) That the limits exist.  2) that the functions are differentiable (at least around the limits).  Continuity can't be proven, if that is the assumption you are beginning with.  " ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7418.0 0.0 1.0 0.0
"thanks so much for your videos, you are one of a kind" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14608.0 0.0 0.0 0.0
"MIT u rock,pls upload the next lecture" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7548.0 0.0 0.0 0.0
"45:26 transform an exclamation mark into an M. Brilliant!" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1253.0 0.0 0.0 0.0
"Great lecture Dr. Tsitsiklis.   I have a question where you were applying divide and conquer to solve the Geometric example where A1: X=1 and A2: X>1.  You said that P(X>1) = (1-p).  But, this is the probability that the first toss is a T.  The case where the Head appears in the 5th toss for example also corresponds to P(X>1) and this probability is (1-p)^(4).q.  It seems to me that its the geometric sum of all the cases corresponding to X>1...  May be I am wrong in my thinking or just a little confused as to why you set P(X>1) to be the same as getting T in the first toss." -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 4247.0 0.0 1.0 0.0
"Colleges need to be removed, and all education will be online. We can visit labs for few month every year only for practicals. Current  education system is useless" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3163.0 0.0 0.0 0.0
"38:46 Professor: Did I tell you about product of the eigenvalues? No, but that's a good thing to know.
ps: He did tell about the product of the eigenvalues. do you remeber where he did? =D" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 1085.0 0.0 0.0 0.0
"I started studying math at the age of 40.
Professor Gilbert Strang
Do you think it is too late to learn?
If it is such an extensive and complex discipline" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5972.0 0.0 0.0 0.0
"Come and back to see again, you will get more than you thought." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3166.0 0.0 0.0 0.0
"thanks pro Strang, thanks MIT.  the best linear algebra course." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 14594.0 0.0 0.0 0.0
"Expressing something really complicated in an easy and fun way is not about teaching or communication skills. It can only be achieved by an extremely deep understanding of the subject. Some might say their teachers teach badly because they don't have the passion or don't care about students. The surprising truth is that they actually don't have a deep enough understanding of those seemingly easy topics." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 3710.0 0.0 0.0 0.0
"7:33 Surprise horn?" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 1400.0 0.0 0.0 0.0
"Lecture 1: Dot Product
Lecture 2: Determinants
Lecture 3: Matrices
Lecture 4: Square Systems
Lecture 5: Parametric Equations
Lecture 6: Kepler's Second Law
Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds)
Lecture 8: Partial Derivatives
Lecture 9: Max-Min and Least Squares
Lecture 10: Second Derivative Test
Lecture 11: Chain Rule
Lecture 12: Gradient
Lecture 13: Lagrange Multipliers
Lecture 14: Non-Independent Variables
Lecture 15: Partial Differential Equations
Lecture 16: Double Integrals
Lecture 17: Polar Coordinates
Lecture 18: Change of Variables
Lecture 19: Vector Fields
Lecture 20: Path Independence
Lecture 21: Gradient Fields
Lecture 22: Green's Theorem
Lecture 23: Flux
Lecture 24: Simply Connected Regions
Lecture 25: Triple Integrals
Lecture 26: Spherical Coordinates
Lecture 27: Vector Fields in 3D
Lecture 28: Divergence Theorem
Lecture 29: Divergence Theorem (cont.)
Lecture 30: Line Integrals
Lecture 31: Stokes' Theorem
Lecture 32: Stokes' Theorem (cont.)
Lecture 33: Maxwell's Equations
Lecture 34: Final Review
Lecture 35: Final Review (cont.)" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7272.0 0.0 0.0 0.0
"I don't think he went over the mean value theorem yet?" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5334.0 0.0 1.0 0.0
"Why can't Cornell professors be this good?" WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11796.0 0.0 0.0 0.0
26:28 Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 800.0 0.0 0.0 0.0
"MI who? :)" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 7498.0 0.0 0.0 0.0
"Why are we doing A transpose to fine the current? Any intuition?" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11787.0 0.0 1.0 0.0
"Geometrically I can see why the intersection of two subspaces of Rn is another subspace, but thinking purely algebraically (in terms of sets) this does not seem obvious.

Does anyone have a clear way to explain in terms of intersections of sets of vectors why the result is a subspace?

In particular, it doesn't to me follow that any combination of vectors in S^T is necessarily still in S^T when thinking just in terms of sets of vectors." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 4002.0 0.0 1.0 0.0
"YouTube algorithm making me feel stupid" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 12257.0 0.0 0.0 0.0
"in which College are you and what is ur class's number? I mean MAT115? MAT114????

thanks" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13602.0 0.0 1.0 0.0
"u substitution method" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14975.0 0.0 0.0 0.0
"What is S Pj in the denominator?" z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11513.0 0.0 1.0 0.0
"Thank you so much.👌" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 9418.0 0.0 0.0 0.0
"I'm curious why we should choose 1 and 0 as our free variables?  Choosing different values will produce different, but still numerically consistent results, so what makes 1 and 0 the appropriate choice?  Are other solutions valid?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 6316.0 0.0 1.0 0.0
"I would have failed this class if it wasn't for these lectures" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 6258.0 0.0 0.0 0.0
"Thank you very much." JTbZP0yt9qc "6. Maximum Likelihood Estimation (cont.) and the Method of Moments" "MIT 18.650 Statistics for Applications, Fall 2016" 9457.0 0.0 0.0 0.0
"I love this professor. Amazing explanation!" tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5834.0 0.0 0.0 0.0
"for such an important concept you would think Mit would've fixed this issue by now" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 12887.0 0.0 0.0 0.0
"Why are these people so excited? I thought that they are all IMO winners" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11784.0 0.0 0.0 0.0
🔝🔝 EBdgFFf54U0 "Lecture 14: Basic Hilbert Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 15728.0 0.0 0.0 0.0
"Done +++" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3483.0 0.0 0.0 0.0
"I can't thank MIT enough." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5224.0 0.0 0.0 0.0
"Ausome videos" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 2746.0 0.0 0.0 0.0
"I need the book where this information is" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 5877.0 0.0 0.0 0.0
"Only took you twenty minutes to finally get to the second theorem lol." Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8125.0 0.0 0.0 0.0
"Awesome to see a functional analysis series uploaded." uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 2772.0 0.0 0.0 0.0
"where would i get the exercies from like the homework on the board" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15247.0 1.0 1.0 0.0
"@DanEMO592 thanks very much!" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1612.0 0.0 0.0 0.0
"All at the American people's expense.  Anti-American globalists hard at work to destroy liberty and representative government." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2294.0 0.0 0.0 0.0
"I think intuitively (right - left) is due to the direction of the axis. Like top is always larger than bottom, the positive direction for the horizontal axis is set from left to the right, hence numbers on the right are larger. it might be an easier way to see this." _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6026.0 0.0 0.0 1.0
2021 PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 629.0 0.0 0.0 0.0
"the prof said ""u are easily amused""" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14727.0 0.0 0.0 0.0
"It was the last like I gave to him." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7001.0 0.0 0.0 0.0
"I made it! Thank you, professor for these great lectures. -From Korea" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5867.0 0.0 0.0 0.0
"Dont all speak at once:)" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 3485.0 0.0 0.0 0.0
"He teaches with rigor and yet manages to make it look easy!" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4615.0 0.0 0.0 0.0
"Support OCW!" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8969.0 0.0 0.0 0.0
"The volume is too low!" mc1y8m9-hOM "22. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 10318.0 0.0 0.0 0.0
"Again Prof. Gilbert Strang! Thank you very much!" L3-WFKCW-tY "33. Neural Nets and the Learning Function" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2270.0 0.0 0.0 0.0
"20:08 dang Prof flipped us off 😂" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 643.0 0.0 0.0 0.0
"Mit has done wonderful job to give us quality education for free veryyyyy thanks" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 7676.0 0.0 0.0 0.0
"I made it here, from Lec 1." sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5866.0 0.0 0.0 0.0
#endcalc 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 202.0 0.0 0.0 0.0
1.618..:D 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 328.0 0.0 0.0 0.0
"Dear Prof. Strang, you’re a great teacher" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3329.0 0.0 0.0 0.0
"Mmh I dont know, mathematicians can tell me what they want but I think their definition of infinity is fishy as hell! Using zero for both infinitely small as well as x=x' -->x-x'=0 seems irrational. Well I guess it's just a definition and phrase you have to get over... :X" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 7685.0 0.0 0.0 0.0
"OMG why did the -2 change into a minus -1 suddenly at 07:59" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7985.0 0.0 1.0 0.0
"I am a little bit confused so - why vectors (1,1,2) & (2,2,5) doesn't span the space R^3?? and why (1,1,2), (2,2,5) & (3,3,8) does span the space R^3?? 
I don't know why I am stuck here for days please if someone could explain a bit it would be a great help." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 5053.0 0.0 1.0 0.0
"These courses are the remedial courses of MIT, to get all students entering all fields up to some common level. Most students in america do this in a precalculus/trig course by 11th grade. The real MIT multivariable course for math/hard science majors is: 18.024" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10402.0 0.0 0.0 0.0
"s is used to represent distance, rather confusingly, but v is used for velocity which clears that one up.

So, v = ds/dt." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14271.0 0.0 0.0 0.0
"This guy says ""OK"" alot :D" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 10559.0 0.0 0.0 0.0
"The way he says the days of the week is perfect. ""Fridee""" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10331.0 0.0 0.0 0.0
"other colleges should be envious that MIT has a great of a professor as Dr. Strang" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14161.0 0.0 0.0 0.0
"maths practically awesome" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13919.0 0.0 0.0 0.0
"He implied that while graphs are discrete, there is something analogous to a graph which is continuous. What is that something?" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4493.0 0.0 1.0 0.0
"OMG I never knew that MLE has its theoretical basis. I always thought that it's based on common sense :-)" rLlZpnT02ZU "4. Parametric Inference (cont.) and Maximum Likelihood Estimation" "MIT 18.650 Statistics for Applications, Fall 2016" 7981.0 0.0 0.0 0.0
"yeah! the golden ratio!" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 15473.0 0.0 0.0 0.0
"LOL is this mathematics at an undergraduate level in the USA!?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7236.0 0.0 0.0 0.0
"I love his french accent, it makes the class more interesting" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5741.0 0.0 0.0 0.0
"My left ear is learning while my right ear is getting bored cause it already learned this." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7769.0 0.0 0.0 0.0
"the prof is awesome!!" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14726.0 0.0 0.0 0.0
"This makes me not miss school at all lol..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10844.0 0.0 0.0 0.0
"Really deep lectures, I learn something new every time I watch them again and again.  These lectures are gold." Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8509.0 0.0 0.0 0.0
"""what b turns out to be.. right."" LOL" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 192.0 0.0 0.0 0.0
"It's a weird feeling to be a sophomore in college and be nostalgic for college lecture halls..." mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 7024.0 0.0 0.0 0.0
"10:37 ""the queue is getting closer and closer to pee""" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 351.0 0.0 0.0 0.0
"> it's good that people are learning these things.

Why is that?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 1460.0 0.0 0.0 0.0
"i can actually understand this!woohoo!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 13346.0 0.0 0.0 0.0
"Wouldn't the fact that the king is actually a king lower the probability of the other sibling being a boy? Because if he were a boy and older, the current king would not be king, but his brother would be instead! Could someone please elucidate this?" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 12014.0 0.0 1.0 0.0
"30:55 Since the cofactor here is 0 coincidentally, it would be better to use a general tridiagonal matrix(n by n or at least 5 by 5) to show that the cofactor is Dn-2" QuZL5IKpO_U "24b. Quiz 2 Review" "MIT 18.06 Linear Algebra, Spring 2005" 898.0 0.0 0.0 0.0
"During these covid times, my lineare algebra teacher hasnt adapted to well to online courses, the material sucks. Started watching these half way through, only reason I passed the course. Online or offline, teachers should all take notes on Strang's method of teaching. In his words, THANKS." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 3530.0 0.0 0.0 0.0
"Would have loved to have Professor Strang 40 years ago when I first experienced Linear Algebra in Pre-Algebra 1 and 2; 30 years ago in Finite Math with Calculus." or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12009.0 0.0 0.0 0.0
"42:15 why can't solutions form a vector space?? Why can't solutions form a subspace?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 1175.0 0.0 1.0 0.0
"The rule for the dimensions of Symmetric and Upper Triangulars only apply to 3x3 matrices?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 10272.0 0.0 1.0 0.0
"Prof. Strang is a myth" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 8304.0 0.0 0.0 0.0
"i learned this in 6th grade in my country lol" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13412.0 0.0 0.0 0.0
"At 84 years of age, he continues to be a maverick in the world of math education. Inspiring, to say the least." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2698.0 0.0 0.0 0.0
"Staring at 22:00, should not we follow in the opposite of the gradient direction to reach minima? Gradient gives the steepest ascent directions as far as I know." xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8879.0 0.0 1.0 0.0
"Thanks Sir" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9644.0 0.0 0.0 0.0
"My teacher was a total failure in teaching prob and stat. He is making my worst nightmare in a pleasant discovery." IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 7790.0 0.0 0.0 0.0
"The professor brings the subject to life..Excellent teachers make excellent learning... Most of my past teachers ought to be shot!!" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10246.0 0.0 0.0 0.0
"He is making things more complicated than it is" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4523.0 0.0 0.0 0.0
"i think it's obviously seen that he is from france as he pronounce ""r"" with french pronunciation" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 13475.0 0.0 0.0 0.0
"Neat trick. Can we use this to find the circumference of an ellipse?" zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7810.0 0.0 1.0 0.0
"Hellow everyone. Please, Can someone tell me how the prof introduce the notion of transpose in the begining of video?" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4668.0 0.0 1.0 0.0
"my mind is crashed by that differential thing..." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 13992.0 0.0 0.0 0.0
"Great error at 36.15 both functions are continuous in R-{0},there are no descontinuity points anywhere in their domain. He made a mistake, this is noth a removable discontinuity at x=0. He just make a extension of the domain to include zero and make the value of the functions in x=0 to be 1 to equal the limit." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4222.0 0.0 1.0 0.0
"Yes, it's still immortal in 2020." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12150.0 0.0 0.0 0.0
"Tell me again how much research do they do? And how much financial aid do they give? =P Just remind me." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9027.0 0.0 0.0 0.0
"For this semester, I am counting on you professor." 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 3898.0 0.0 0.0 0.0
"God bless you!" HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 4085.0 0.0 0.0 0.0
"these kids are coming from high school with out hearing about vectors and determinants and they go to MIT?" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14775.0 0.0 0.0 0.0
"I can't believe how he simplifies all those concepts." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5205.0 0.0 0.0 0.0
"@Zidnihuda just mathematical" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1762.0 0.0 0.0 0.0
"I don't understand how vectors of N(A) can be in R^m ! If A is a m*n matrix, we need a R^n vector to have the 0 matrix, no ?" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5344.0 0.0 1.0 0.0
"I'm guessing it's included in required reading and the students will encounter it elsewhere." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6324.0 0.0 0.0 0.0
"my professor is useless, Dr. Strang is so much more helpful" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 13998.0 0.0 0.0 0.0
"This is such a wonderful intellectual lecture i really enjoy listening  your lectures.
Thanks very much. Education is the only way in my humble opinion to  reduce the ignorance that tend to dominate the world in with we living today. " 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 10727.0 0.0 0.0 0.0
"go figure" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12924.0 0.0 0.0 0.0
"I like how much reinforcement it took for the MIT students to comprehend the idea that (1-cosΘ)/Θ goes to 0 as Θ goes to 0 because 1-cosΘ heads there quicker while I understood it the first time around. Made me feel slightly smart for a moment there." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5667.0 0.0 0.0 1.0
"I was in the Sheldon Axler camp that linear algebra should be taught abstractly with focus given to linear transformations from an almost exclusively algebraic point of view and hold off on determinants until the last possible second. Strang's lectures change all of that, these are the best lectures on linear algebra taught from the angle of matrix algebra. Both approaches are valuable but Strang really nails it. Deriving the determinant from properties like this provides excellent motivation versus just jotting the nasty formula down, it also helps with mathematical maturity since it forces understanding by the student." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 6154.0 0.0 0.0 1.0
love 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13858.0 0.0 0.0 0.0
"p（n）is just like f(x),alright ?" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 14233.0 0.0 0.0 0.0
"The application was crazy confusing 😨" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9982.0 0.0 0.0 0.0
"Thank you Professor Strang
Thank you MIT OCW
2022/08/07" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9213.0 0.0 0.0 0.0
"Thank you so much....  :-)" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9416.0 0.0 0.0 0.0
ok cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 14122.0 0.0 0.0 0.0
"At least professor Strang appreciates the importance of taking things slowly." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 2716.0 0.0 0.0 0.0
"For anyone looking for some more visual intuition, 3blue1Brown has an amazing video on raising matrices to powers in his DE series." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 3854.0 0.0 0.0 1.0
"Calculus is one of the most important inventions of human history. It has allowed us to explain the world around us. I hate d, I mean HATED math until I got to Calculus!! Then it all made sense. Sometimes i still get obsessed with Calculus." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2988.0 0.0 0.0 0.0
"Statistic is fun because i have able finding much of porn in stats" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8890.0 0.0 0.0 0.0
"This professor is great! Thank you!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10903.0 0.0 0.0 0.0
"I think in general mathematicians are good at teaching. I guess professor Gilbert Strang is not a specialist on machine learning, but he can teach neural nets better than specialist on machine learning." sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6023.0 0.0 0.0 0.0
hwat? TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 13318.0 0.0 0.0 0.0
det(A)=aij*det(A-columni,rowj)*(-1)^n-1 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 12738.0 0.0 0.0 0.0
"Thank you very much to MIT and Prof. Jerison for this great public service. Are the backwards question marks he draws on the board something peculiar to MIT?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9447.0 0.0 0.0 0.0
"very nice lecture, much better than any that i can find in my  university, thanks a lot MIT :)" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15031.0 0.0 0.0 0.0
"""The key point is to think with them, not to just say here it is, listen up!  
I think the question all over again as they do. 
And you have to give time, you can't zip through a proof""." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 119.0 0.0 0.0 1.0
"00:00:00 to 00:02:50 : Introduction
00:02:51 to 00:13:45 : What is Orthogonality?
00:13:50 to 20:49:00 : What is Orthogonality for Subspaces?
00:20:50 to 26:00:00 : Why RS(A) ⊥ NS(A)?
26:01:00 to 34:00:00 : What is Orthogonal complement?
39:45:00 to End      : Properties of A^T.A ?" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 286.0 0.0 1.0 0.0
"U-sub FTW" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11113.0 0.0 0.0 0.0
"learn it when in 14 but never truly understand in till studying it in uni when lecturer goes thru the same things but with more in-depth explanation with other topic combined.
" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13764.0 0.0 0.0 0.0
"This is easy in comparing to our Math :p and with only one variable :D" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10658.0 0.0 0.0 0.0
"I got the best mental picture of convolution from here. Thanks for the cut and shift...It helped a lot. Thank you" l4NoMKEHQwM "11. Derived Distributions (ctd.); Covariance" "6.041 Probabilistic Systems Analysis and Applied Probability" 5450.0 0.0 0.0 1.0
"I wonder where the students in these videos are now, 16 years later." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 6250.0 0.0 0.0 0.0
"If you get lost with the overall intuition and understanding of the general concept (WHAT FOR?) of this course, then please check out 3Blue1Brown channel and his playlist about Linear Algebra. Love, Maria!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6544.0 0.0 0.0 1.0
"A good complimentary explanation to understand lnx > https://youtu.be/765X_PAxhAw" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2115.0 0.0 0.0 0.0
"I don't like to solve problems, please more lectures, Prof. Strang." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5329.0 0.0 0.0 0.0
9:12 nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1437.0 0.0 0.0 0.0
"After understanding and enjoying all the lecture videos (1-27), this one and Jordan form one (lecture 28) disappointed me." TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 2260.0 0.0 0.0 0.0
"We saw and able to proof that if a function is defferenciable, the it is continuous.  Does the same theorem goes to vice versa? that if a function is continuous, then it is defferenciable??" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11332.0 0.0 1.0 0.0
"Thanks MIT. Appreciate it" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 9619.0 0.0 0.0 0.0
"There is only so much blackboard energy 😆" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10378.0 1.0 0.0 0.0
"Gilbert Strang shows the art of the linear algebra." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4031.0 0.0 0.0 0.0
"""Using Math to Understand Art"" by Ingrid Daubechies | TEDxDuke: https://www.youtube.com/watch?v=jrF1SGPyF4g" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 128.0 0.0 0.0 0.0
"This professor is just amazing" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 10904.0 0.0 0.0 0.0
"Thank you so much." YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9407.0 0.0 0.0 0.0
"Thanks MIT for uploading these videos. I liked them a lot." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9610.0 0.0 0.0 0.0
"One thing i do know .... he's using lovely chalk." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8109.0 1.0 0.0 0.0
"people having trouble with the triangle can look at this video. It's the same instructor and same course just edX version of it. https://www.youtube.com/watch?v=aXFbBcabaQA" CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 14172.0 0.0 0.0 0.0
"Mathematics = lies about false identities perched over insanity & mortal delusions." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7614.0 0.0 0.0 0.0
"The key to understanding this lecture well is to follow along in a notebook.
The cameraman is not able to track the entire board for you to reference previous arguments." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10150.0 1.0 0.0 0.0
legend! 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 13779.0 0.0 0.0 0.0
"Are those empty seats??Please let me sit in one of those and I swear I ll attend everyday!!" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 2536.0 1.0 0.0 0.0
"what's the sample space of geometric distribution?" gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 15196.0 0.0 1.0 0.0
"I like your style man! I wish I had those blackboard oh man.. Thanks for the passion you put in" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 5701.0 1.0 0.0 0.0
"I Really Like The Video Column Space and Nullspace From Your" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 4937.0 0.0 0.0 0.0
"I opened this to study PDE but....." ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5894.0 0.0 0.0 0.0
"At 15:00, plugging in the vector <1,2,-1> into the equation is basically doing the dot product with the normal vector. This is because the plane equation IS a dot product of a known vector and an unknown. So if you plug in an unknown vector into x,y,z them that is basically the dot product." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2592.0 0.0 0.0 1.0
"you want to learn linear algebra? you GOT  THE WHOLE INTERNET to learn tricks n tips.
you want to understand it?YOU have to COME here........" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 15516.0 0.0 0.0 0.0
"Most people will know. But it's usually repeated just to make sure that everyone is on the same page. I mean different teachers and different classes sometimes uses different notations and perspectives so it's good to have a quick walk-through of everything before." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7706.0 0.0 0.0 1.0
"I'm studying exactly that at high school, which isn't  so complex at all..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6382.0 0.0 0.0 0.0
"It is mind blowing how elegant linear algebra really is" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 6957.0 0.0 0.0 0.0
"You can see the genius while watching this guy." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12194.0 0.0 0.0 0.0
Ts cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 11100.0 0.0 0.0 0.0
"do people do vector calculus just for fun?

well my friend says he enjoys it." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12755.0 0.0 0.0 0.0
"Linear Algebra is amazing" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 7371.0 0.0 0.0 0.0
"thank you SIR" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14490.0 0.0 0.0 0.0
"This is another awesome lecture that Minimize a Function Step by Step which includes Convex sets and  functions. DR. Strang also thank you for analyzing Newton/Raphson method from calculus." nvXRJIBOREc "Lecture 21: Minimizing a Function Step by Step" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10630.0 0.0 0.0 1.0
"Much easier to understand now that I have a second person explaining it, what a great professor! Also helps that I can rewind and listen however many times I want :p." dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 7720.0 0.0 0.0 1.0
"Independent means not related or connected or attached or involved." 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 6708.0 0.0 0.0 0.0
"I like this video" BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 5694.0 0.0 0.0 0.0
"Περίφανος που βλέπω κι άλλον Έλληνα να διδάσκει εδώ" jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 15549.0 0.0 0.0 0.0
"1-cos(theta) tends to zero faster than arc length (= theta), so it becomes  like -- 0 divided my any number so its zero" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 319.0 0.0 1.0 0.0
"Amazingly explained!" P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 2408.0 0.0 0.0 0.0
"Like if you watched It at 1.5x velocity" BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7357.0 0.0 0.0 0.0
"I had this in my bachelor of computer science in german. My prof was way worse and he was talking in my language. I understand more this in english than my prof. In my language. Huge compliment to Dr.strang" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5470.0 0.0 0.0 0.0
"Love you sir .love from India ." xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7469.0 0.0 0.0 0.0
"Great sir" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4332.0 0.0 0.0 0.0
"french accent" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12899.0 0.0 0.0 0.0
"pardon me for not being much bright ... but ... can anyone tell me how to calculate the probability of a change of state from 1 to 2 (suppose) if time step n is known with no existing states in between.


Any help is appreciated.
Thanks in advance." IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 14167.0 0.0 1.0 0.0
"He constantly stops and asks if theres questions, and he elaborates on subjects he feels are pretty trick to catch at first. good teacher.  not as sharp of a dresser as professor donald sadoway though :)" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4468.0 0.0 0.0 1.0
"memorylessness can be expressed as P(X > m+n | X > m) = P(X > n)" -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 13938.0 0.0 1.0 0.0
"@4:39 there is an error for those who are hard of hearing. Pho should be ""rho"" the Greek letter. The captions are absolutely greatly appreciated by myself and many others. Thank you to those who put in that work on this channel." phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1567.0 0.0 1.0 0.0
"@19:20 i think the E(X) sud be = b-a/2" mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 1504.0 0.0 1.0 0.0
👍👍👍👍👍 JBIz7UadY5M "14. Regression (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 15707.0 0.0 0.0 0.0
"At 9:50 that should read  a <=  x <= b not a<x<b" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2701.0 0.0 1.0 0.0
21:29 Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 680.0 0.0 0.0 0.0
"it seems good" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 13680.0 0.0 0.0 0.0
"At 40:42, when you said ""well let me explain this in a slightly different language"" it would be fun if you started to talk Chinese or something like that" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2660.0 0.0 0.0 0.0
"13:30 why is dimension 2? He wrote see 3 vectors" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 418.0 0.0 1.0 0.0
"thank u teacher u are the best ever <3" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14462.0 0.0 0.0 0.0
"He looks pretty linear to me. " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4572.0 0.0 0.0 0.0
"If MIT students couldn't understand these materials, I shouldn't blame myself for being too dumb." 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6480.0 0.0 0.0 0.0
"MIT 18.102 Introduction to Functional Analysis, Spring 2021
Instructor: Dr. Casey Rodriguez
View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/
YouTube Playlist: https://www.youtube.com/watch?v=uoL4lQxfgwg&list=PLUl4u3cNGP63micsJp_--fRAjZXPrQzW_&index=1" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 7502.0 0.0 0.0 0.0
"i wish i had a teacher like this. he clearly expresses a strong fundamental understanding of the field, and can explain it clearly to minds of all sorts." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13498.0 0.0 0.0 0.0
"Ever great lectures, thanks professor Strang and MIT.Merci la vie!" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 3595.0 0.0 0.0 0.0
"He means that as many the powers that many the ratios ex 1/x^4=  A/x^4 +B/x^3 +C/x^2  +D/x + all other dactors " HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4585.0 0.0 0.0 0.0
"33:46 Maximum Likelihood Estimation" rLlZpnT02ZU "4. Parametric Inference (cont.) and Maximum Likelihood Estimation" "MIT 18.650 Statistics for Applications, Fall 2016" 967.0 0.0 0.0 0.0
"@Wirrit You be surprised how ""perfect"" native speaker's grammars are." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1757.0 0.0 0.0 0.0
"Thank you
" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9088.0 0.0 0.0 0.0
"Thank you to whoever did the closed captioning (subtitles) on this - tedious work, but very appreciated." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9423.0 0.0 0.0 0.0
"How does this idea transfer to eigenvalues and eigenfunctions of differential operators? They don't quite look like matrices, do they?" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 4862.0 0.0 1.0 0.0
thanks. VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 14614.0 0.0 0.0 0.0
"Too bad this course is ruined by discontinuity... There seems to be a whole lecture missing, they should have added also the second lecture from 2017 at least. It's better to have some overlap than missing data." C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 11060.0 0.0 0.0 0.0
"Think of it this way. Let's say the wheel did not turn but was simply dragged. The curve describing the path of a point on the wheel would be equal to the displacement of the wheel. Similarly, if the wheel did not move but simply turned in place the arc length would be 2pi for each revolution. The cycloid includes both the revolution and the translation as part of its length." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10448.0 0.0 0.0 0.0
"I wish I had teachers like Prof Gilbert Strang when I studied linear algebra. What a difference makes to have someone dedicated to explaining the geometry of what is going on." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6201.0 0.0 0.0 1.0
"I am watching this lectures, I understand them, but when I go to solve the Psets, seems I dont know shit.... anyone having the same issue with the Psets?" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5155.0 0.0 0.0 0.0
"in greece, applied probability is a standard course in order to get accept to any economically oriented university." EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 13588.0 0.0 0.0 0.0
"So elegantly explained. You are a master, Professor Tsitsiklis" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 8751.0 0.0 0.0 0.0
"Hi, does the i in this video stand for imaginary number or i hat ?" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 4728.0 0.0 1.0 0.0
"In 2020 Gilly Strang woulda been #MeToo into oblivion for mentioning Monica" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 6593.0 0.0 0.0 0.0
"by 'all 3 by 3 matrix', does he mean matrix has 3 rows and 3 column?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 12579.0 0.0 1.0 0.0
"how come this one has more views than the last one (almost doubled)" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 13206.0 0.0 0.0 0.0
"Man, u know why since lecture 23 or sth the views sinks🤣: u have to read the book to clarify to yourself about the important points the Prof Strang has leave there purposely, which is actually elegant😀 now I go to read the book to find out why the sign of pivots are the same as the of EV.." UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 7589.0 0.0 0.0 1.0
"If I told younger me that I was going to be watching MIT videos to actually learn the content they are teaching, I would never believe it. yet here I am studying for an exam." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 6474.0 0.0 0.0 0.0
"Is it me or most of us, that it was a bit hard to catch up with previous LA classes of Prof. Strang. Now I know the reason, which was expressed by the professor himself in this video." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6791.0 0.0 0.0 0.0
"i would of though MIT would be able to afford a electronic board " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13508.0 1.0 0.0 0.0
"YEEEEEEEEEEEEEEEEEEEEEAHHHHHHHH!!! <3" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12107.0 0.0 0.0 0.0
"how can i find the number of  pivot in a matrix ?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 13199.0 0.0 1.0 0.0
"Outclass teaching skills! No queries in my mind whatsoever" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8138.0 0.0 0.0 0.0
"I am grade 9 in germany and I have understand a lot" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5098.0 0.0 0.0 0.0
"45:28 ""I'm very positive about positive definite matrices."" This is epic." TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 1254.0 0.0 0.0 0.0
"Thanks for the videos mit! I watch em everyday...
" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9723.0 0.0 0.0 0.0
"Thank you Professor Strang and MIT." 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 9215.0 0.0 0.0 0.0
"The passion for mathematics and teaching it, shines through you and it is really infectious. Forever grateful. <3" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 10221.0 0.0 0.0 0.0
"Thanks professor Strang." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9763.0 0.0 0.0 0.0
"Love this guy. I'm teaching a course like this, and am taking notes. These lectures are a pleasure to listen to! :)" mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 7459.0 0.0 0.0 0.0
"the why he says ""zero"" -- ziho ziho" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14753.0 0.0 0.0 0.0
"Great, then I assume you've at least browsed the mathematics courses MIT actually has to offer? This is a course which you may or may not have to take depending on individual circumstances and your field of interest. This material and 18.03 Differential Equations is sufficient for much of physics, so it really doesn't matter when you actually cover it as long as you end up knowing it." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4375.0 0.0 0.0 0.0
"Did not know he's this old. I wonder when the lecture videos were recorded.
Just so sad to see a brilliant mind like him has to age.
I love his  video lectures." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 3382.0 0.0 0.0 0.0
"Try studying in India. You finish this by 10th grade :/" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11096.0 0.0 0.0 0.0
"This would be much better had a noise-cancelling microphone been used." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 10980.0 1.0 0.0 0.0
"That was too good, "" poor misbegotten subspace"",...🤣🤣...He is too good...." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9925.0 0.0 0.0 0.0
"Excellent !" 0Va2dOLqUfM "5. Maximum Likelihood Estimation (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 3627.0 0.0 0.0 0.0
Excellent! UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 3685.0 0.0 0.0 0.0
"Absolutely well done and definitely keep it up!!! 👍👍👍👍👍" QXkOaifVfW4 "9. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 2210.0 0.0 0.0 0.0
"Just finished after 11 weeks of watching all the lectures, doing all the homeworks, and taking all the exams.  Cannot thank Prof. Strang and MIT enough for creating and posting this series of lectures.  It's so rare to find an obviously brilliant mathematician who actually seems to enjoy teaching introductory-level courses, and Prof. Strang was such a joy to spend ~30 hours with through these videos.  I've taken Linear Algebra before but needed a refresher after 10 years, and this course was perfect for walking me through the concepts." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 7167.0 0.0 0.0 1.0
"Question: the x-particular needs to have 0 corresponding to the free variables in A, and in order to find the free variables in A you need to row reduce it, but after you have done this, why can't you just arbitrarily select numbers for the pivot variables in x-particular? Why solve for them by setting some ""b"" when the vector is going to give some valid ""b"" anyways?" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 8480.0 0.0 1.0 0.0
"In the proof for ""E_TM is undecidable"" in the construction of M_w you don't even need to Check, whether x != w. You can Just Run M on w for all x. Then the language of M_w is either Sigma* or empty." N28g_YBXY8Y "9. Reducibility" "MIT 18.404J Theory of Computation, Fall 2020" 6681.0 0.0 1.0 0.0
"while listening to lecture, one has some general concerns, excellent part of the professor is he addresses most of my concerns without me asking!!" mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 15255.0 0.0 0.0 0.0
"Thank you." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 9544.0 0.0 0.0 0.0
"Lec 8 is missing !" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7261.0 0.0 0.0 0.0
"I thought why he was spending so much time on this particular case at the beginning, then at 38th minute... wow!!" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6104.0 0.0 0.0 0.0
"stfu you little troll" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14397.0 0.0 0.0 0.0
"Self note: 45, please future me remember what this means lol" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 8623.0 0.0 0.0 0.0
"Wow I learnt all these in high school during my jee preperation 😁😁🔥🔥" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12027.0 0.0 0.0 0.0
"This is truly remarkabe teaching. Greatly helps understanding and intuition of what SGD actually does. prof. Sra's proof of SGD convergence for non-convex optimization is in prof. Strang's excellent book ""Linear Algebra & Learning From Data"", p.365" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10762.0 0.0 0.0 1.0
"This is so helpful, thanks alot!" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10720.0 0.0 0.0 0.0
"Thank you very much Dr. Strang for making this intuitive and natural. I had only gone through SVD in bits and pieces and never had what I could consider a good enough understanding until I saw this lecture." rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9430.0 0.0 0.0 0.0
"@profardalan from their OCW website http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/1.-differentiation/part-b-implicit-differentiation-and-inverse-functions/session-20-hyperbolic-trig-functions/" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1981.0 0.0 0.0 0.0
"One of the best teacher for Matrix . What a legend sir . Huge respect" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8092.0 0.0 0.0 0.0
"To think that I have to do 2 more years of classes before I get to do this fun.  I can't wait :D" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11045.0 0.0 0.0 0.0
"Use headphones and set the sound mode to Mono Audio." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11134.0 0.0 0.0 0.0
"@ 44:00 why summation of both eigen values are 1?? have i missed any concept behind this?? : (" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 1478.0 0.0 1.0 0.0
"20:15 chatper 3 start" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 648.0 0.0 0.0 0.0
"Trump learned from Him how to wear a tie." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 11095.0 0.0 0.0 0.0
"At 42:15, how would I find the projection matrix, if the inverse of Atranspose*A doesn't exist, such as in this example?" QuZL5IKpO_U "24b. Quiz 2 Review" "MIT 18.06 Linear Algebra, Spring 2005" 2667.0 0.0 1.0 0.0
"Seriously MIT, chalk and a blackboard?......IT´S MIT!!! they should have had already a computer voice recognition software that can laser the command of the teacher into a screen..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8627.0 1.0 0.0 0.0
"Jesus man, I remember back before I started college when I checked out Prof Strang’s calculus series. 
He’s aged quite a lot since that series, but he’s always sharp as a tack. And I’m just astonished that even being so old he knows so much about machine learning, I didn’t think it was his field. 
Huge kudos Gilbert Strang, huge kudos." wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7136.0 0.0 0.0 0.0
"fuck scool" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12903.0 0.0 0.0 0.0
"Thanks for uploading this great video, MIT great professers" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9739.0 0.0 0.0 0.0
"Gilbert Strang is one of the most charming teachers that I know of." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4025.0 0.0 0.0 0.0
"nice post" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14048.0 0.0 0.0 0.0
"I have started a PhD and my research area is applied deep learning. I have to do multiple things in parallel. There is a lot of material available related to Deep learning on the internet and I am confused that which one is worthful for my research. So can anyone comment on this course that, how much this course is useful for me?" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5559.0 0.0 0.0 0.0
"Thanx a lot Mr.Strang and MIT" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9876.0 0.0 0.0 0.0
"All in all these lectures are great, but sadly it seems to be he doesn't really reply properly to the question the student asks @ around 20 min in - it seems to me the student is correct, and that the Venn Diagram is akward in explaining exactly what he asks about. Maybe because the event B with probability = 0 is poorly pictured using anything but a point, in a venn diagram.
Please comment on this to enlighten me of alternative views on the subject." 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 2297.0 0.0 1.0 1.0
"I can't continue the course anymore, the last 30 minutes of this lecture seems to be way too much for me. *after trying to understand the first 15 minutes of his last 30 minutes for an hour and I'm still confused. 
Appreciate your work Professor Strang. It's a great experience learning from you. 
Got this lecture bookmarked, I'll return to it one day" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 5210.0 0.0 0.0 0.0
"Is anyone else bothered by poor camera movement? It focuses on the professor while missing the board many times. " 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6761.0 1.0 0.0 0.0
"For those following along with the course:
Session 15: Equations of Lines 0:00
Session 16: Intersection of a Line and a Plane 11:00
Session 17: General Parametric Equations; the Cycloid 25:34
Session 18: Point (Cusp on Cycloid) 41:45" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3903.0 0.0 0.0 0.0
"29:51 that’s why electron clouds are drawn as balloons with really solid surface areas. We can draw the surface of the solid that the electron is in 95% of the time (or whatever P is if it is not 95%) because of “convergence in probability”." C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 861.0 0.0 0.0 0.0
"At t = 21:00, Strang covers the definition of inversion (and at 32:00 he gives an example): first suppose A is an n x m matrix. Then if you have a left inverse L that acts on A, it will produce an identity matrix, call it I_n; similarly, If you have a right inverse R, when A acts on R it will also produce an identity matrix, call it I_m. So a Matrix is non-singular (sometimes mistakenly called regular) only if  m = n, A is square, and det(A) (does not) = 0. In particular, if the matrix A have full rank = n, all its columns and rows would be independent, so A would be invertible." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2722.0 0.0 0.0 1.0
"We're down from 1.2mill views on the first video :D" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 11338.0 0.0 0.0 0.0
"It's a ""toin coss""!" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7013.0 0.0 0.0 0.0
"where does the logarithm come from?" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15231.0 0.0 1.0 0.0
"BRILLIANT !!!! MUCH BETTER THAN the SUCKed TEACHER IN MY UNIVERSITY!!!!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 2805.0 0.0 0.0 0.0
"Thank you prof for great lectures!" 8IxHMVf3jcA "Lecture 16: Fejer’s Theorem and Convergence of Fourier Series" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 9301.0 0.0 0.0 0.0
"In your first equation, the acceleration is divided by 2.

xf = x0 + v* t + a/2 * t²" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6699.0 0.0 1.0 0.0
"Thanks a lot, great understanding." gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 9669.0 0.0 0.0 0.0
"Iam from india I love your teaching" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 6454.0 0.0 0.0 0.0
"Calculus Previsited for me!! THanks for the lecture absolutel fantastic!!!!!! keka!!!!!!!!!1" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2985.0 0.0 0.0 0.0
"The audio is messed up on this one." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 9985.0 0.0 0.0 0.0
"please don't zoom the whole frame to the professor, I can't see the writings on the boards in that way..." d32WV1rKoVk "12. Computing Eigenvalues and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14187.0 1.0 0.0 0.0
"you can, because that law is rote memorization before you learn the proof, and mit regularly decline perfect SATs anyhow..they just don't care" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15500.0 0.0 0.0 0.0
"5/32 is the probability of x-1/2
(5/24)/(4/3) are the areas

Probability is so more interesting that the integration formulas (what I'm doing at school)" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1333.0 0.0 0.0 0.0
"Just finished this excellent course. Thank you Prof. Tsitsiklis for this masterclass and MIT for making it available to all of us." rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 7178.0 0.0 0.0 0.0
"Why does x[2 -1] col1 arrow goes down. I am thinking they are x co-ordinates so should only move across x-axis? Please let me know. Thank you!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11851.0 0.0 1.0 0.0
"his neatness makes me smile" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13167.0 0.0 0.0 0.0
"were they booing " YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15098.0 0.0 0.0 0.0
"Oh, this old-school projector is so nice)" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 8033.0 1.0 0.0 0.0
"Such clarity and elocuence! Great lecture" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 8948.0 0.0 0.0 0.0
"Why did we use condition probability for r21(n) @46:00. Why is r21(n) not 0.3 instead?" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 11815.0 0.0 1.0 0.0
"32:12 I do not understand why are the resulting vectors called u1 and u2. I expect Ax1 and Ax2 to be there as a result of A multiplication. If U multiplication is rotation, than u1 and u2 are just rotated unit vectors (exactly as v's, different rotation)... Can somebody prove me wrong please?" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 926.0 0.0 1.0 0.0
"18:20 no one asked the following question: we write dV/dt or dt/dh all the time, but what is this ""t"" variable is? Where did it come from?" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 534.0 0.0 1.0 0.0
"Audio channels fixed!" QuZL5IKpO_U "24b. Quiz 2 Review" "MIT 18.06 Linear Algebra, Spring 2005" 2736.0 0.0 0.0 0.0
"at 46:50 why is f(x) symmetric when powers are odd" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12458.0 0.0 1.0 0.0
"Such an amazing professor, great lecture!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8945.0 0.0 0.0 0.0
"this guy is a national treasure.  or would be in a civilised country..  [and sorry, but if you ""like"" this comment b/c you think i'm suggesting this country is un-civilised for having elected OMB, i have to tell you instead i meant something more like civilised as in no infanticide, kardashians, or cardi b.]" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 14813.0 0.0 0.0 0.0
"I thought that he was gonna start crying at 46:37 =/" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6093.0 0.0 0.0 0.0
"me, a south american that never have seen snow before: how people stand not to go out when it's so beatifully snowing!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13934.0 0.0 0.0 0.0
"@JuicyBoobies1 

These videos are great.  They are basically what you would get in any intro calc course. If your really want to excel in calc, you could read ahead (if you have the time and inclination).  Do lots of problems!  Without the heavy lifting on your part, these videos will not help you as much." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1647.0 0.0 0.0 1.0
"So Julia then?" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8734.0 0.0 0.0 0.0
"40:49 That's wonderful way of saying it" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1137.0 0.0 0.0 0.0
"You lost me half way on >:((. Shit ain't easy." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 12223.0 0.0 0.0 0.0
"MIT plz provides lecture of real analysis..." WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7538.0 0.0 0.0 0.0
"how is it that a row is a linear combination of two upper rows if we get all 0 from elimination Please explain" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 13237.0 0.0 1.0 0.0
"Are you talking about the x= sin(theta) sub?  I think anyone who's passed first year calc knows to do that.  " YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2543.0 0.0 1.0 0.0
"Play video MIT self study" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 8194.0 0.0 0.0 0.0
"what amadala" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15120.0 0.0 0.0 0.0
"MIT I think you sohuld pull off one of these videos, you have two of em." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7503.0 0.0 0.0 0.0
"35:01 show off!" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 997.0 0.0 0.0 0.0
"looks like moriarty is alive and well" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13855.0 0.0 0.0 0.0
"In case anyone is interested in the plot, here's a Wolfram Alpha link: http://www.wolframalpha.com/input/?i=plot+2x%5E2+%2B+12x*y+%2B+7*y%5E2" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 6627.0 0.0 0.0 0.0
"Poor dog I liked my own commet how sad." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8229.0 0.0 0.0 0.0
"What does he mean at @7.45 'these guys are much smaller than x and y when x and y are zero' ?" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11489.0 0.0 1.0 0.0
"MIT is really the hope of human !
spread education all over the world !" ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 7531.0 0.0 0.0 0.0
"can I think of the definition at 25:54 as exact match regarding regular expression?" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 12596.0 0.0 1.0 0.0
"What is the instructor's name? I really appreciate is educational method of teaching. I learned a lot about exponential functions from him. Thank you." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11528.0 0.0 0.0 0.0
"dang he even covers part of continuous distribution what an amazing lecture." R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12716.0 0.0 0.0 0.0
"At 53:30, you could just pick a orthonormal basis of Null(T)^\perp. Since the rank of T is finite, then the dim of  Null(T)^\perp is finite. The basis hence formed does the job." PBMyBVPRtKA "Lecture 19: Compact Subsets of a Hilbert Space and Finite-Rank Operators" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 2690.0 0.0 0.0 0.0
"This professor is amazing" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 10899.0 0.0 0.0 0.0
"https://youtu.be/m6ewJpbGfsE
3D vectrially" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13303.0 0.0 0.0 0.0
"Good informative knowledge 🙏🙏🙏" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 4128.0 0.0 0.0 0.0
"Le board.... It moves!!! =D" tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7253.0 1.0 0.0 0.0
"This helped so much!" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10575.0 0.0 0.0 0.0
"Umbilible I got it" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11119.0 0.0 0.0 0.0
"Thank you, sir. You are a great teacher." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9531.0 0.0 0.0 0.0
"Sooo love Prof. Strang!!" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8849.0 0.0 0.0 0.0
"The dart board problem. It turns out to be 1% and he says that's pretty high? Seems to me 1% is pretty low." jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10069.0 0.0 0.0 0.0
"I have to say that the quality of the hypothesis testing section is not as good as estimation section. And why the sample variance is not divided by n-1?" QXkOaifVfW4 "9. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 5563.0 0.0 1.0 0.0
"I am a little confused. It seems to me that u-axis and v-axis should not be perpendicular to each other. " UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5054.0 0.0 1.0 0.0
"something wrong with this lecture, 32:39, A^{100}u_0=SM^100c. Here I use M to substitute the eigenvalue diagonal matrix. The professor said A^{100}u_0=M^100Sc which is not correct." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 14365.0 0.0 1.0 0.0
観覧 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15658.0 0.0 0.0 0.0
"I pay 40k a year for my linalg professor to read through slides…" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5898.0 0.0 0.0 0.0
"Considering its MIT, many have already taken the course ahead of this one in high school. However, this is a much more rigorous version of the course. Obviously this is the first lecture so the lecturer is simply demonstrating the concepts." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3203.0 0.0 0.0 1.0
"WOW! i was expecting to see any answer, i saw the whole video just for that... But using 9 boards... jaja that's too much for me! i didn't understand anything though, i haven't seen maths since 2009... :( thx anyway!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11247.0 1.0 0.0 0.0
17:39 YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 512.0 0.0 0.0 0.0
"He hurts my brain!!!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 4492.0 0.0 0.0 0.0
"Is this MIT's university or MIT's high school?" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6846.0 0.0 0.0 0.0
"It's getting more and more interesting when differential equations are involved!" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 7044.0 0.0 0.0 0.0
"A quick note for those who are interested in the proof of orthogonal eigenvectors of matrix A, given the condition AA*＝A*A( 15:30 ) http://www.cs.uleth.ca/~holzmann/notes/eigen.pdf see page 2." HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 2151.0 0.0 1.0 1.0
"Gilbert 'steal yo girl' Strang preaching up in here" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 4010.0 0.0 0.0 0.0
"18:18 talk about LIMITS and CONTINUITY..." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 532.0 0.0 0.0 0.0
"Wonder what physic slass is like in MIT" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11980.0 0.0 0.0 0.0
"I had to rewind so many times" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5476.0 0.0 0.0 0.0
"I hate the camerawork" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5484.0 1.0 0.0 0.0
"37:44 ""JUST DO IT""" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1071.0 0.0 0.0 0.0
17:30 EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 508.0 0.0 0.0 0.0
"Thank you for this amazing journey. This project is really exceptional. And my calculus foundation is finally strong :) Excellent lecturers, clear recitation videos and plenty of exercises for practice. This cannot be better. MIT is leading the way. Thank you once more." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9276.0 0.0 0.0 1.0
"but chalk rocks (no pun intended of course)" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12568.0 1.0 0.0 0.0
"The video format for a lecture is super udnerrated... nothing like being able to control time. You can even pause mid lecture, complete exercises, and then resume." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 10312.0 0.0 0.0 1.0
"wonder why this lecture is cut so short" BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 15391.0 0.0 0.0 0.0
"Awesome series! However, starting at 31:00 he's using loose language and is not very precise with notation (or I am missing something). IMHO, it is not correct to write Y=g(X). Moreover, below that he is also writing g(x) (lower case ""x""). I think the correct ought to be Y=g o X (where ""o"" is function composition). Only then does g(x) (lowercase ""x"") make sense. Otherwise if what he is writing ""Y=g(X)"" is the correct form, what is the domain of g?" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 2767.0 0.0 1.0 0.0
"Professor Strang this is another great lecture on Backpropagation and finding partial derivatives from a computational graph. Calculus is still an important piece of all upper level  mathematics." lZrIPRnoGQQ "27. Backpropagation: Find Partial Derivatives" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8371.0 0.0 0.0 0.0
"@NothingPersonalTA Well technically yes if you exchange the 2nd and 3rd row. Pivot point on the 2nd row would then be 4, third row -2. Row echolon form is not unique (meaning how you solve it and what numbers will show up depend on the person). However, once you reduce it, RREF is unique (solution should be the same for everyone). " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1692.0 0.0 1.0 0.0
"22:29 it could be x2 = f(x^0)
isn´t it?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 698.0 0.0 1.0 0.0
"This is a great lecture, and Prof Jerison seems a very good teacher.
However, although I followed and understood this without any problems, this is only because *I am familiar with the notion of integral anyway*, having already covered it in my mathematical education up to this point.

If this lecture was my first exposure to this stuff, I think I'd have been pretty confused about what was going on, with the speed that Jerison went and the way in which he introduced the concepts and notations: the integral sign and the dx on the end just suddenly appearing out of nowhere.

On the MIT website, it says that no prior knowledge of calculus is required to take this course: although this is technically true, I think I'd struggle if I'd never seen any of this before." -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10592.0 0.0 0.0 1.0
"18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying ""above the unit disk"".  " WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 530.0 0.0 1.0 0.0
"no creo que consigas en español, es estados unidos, asi que triste y todo pero todo del MIT está en inglés!" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14064.0 0.0 0.0 0.0
"my probability professor skipped poisson distribution saying it is not so important." jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 13996.0 0.0 0.0 0.0
"At 6:25, df is defined to be an infinitesimal change in Δf, so shouldn't that be a number too. Like in 18.01, we considered it to be  one of the three dimensions while calculating volume of revolution. Can someone help??" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2695.0 0.0 1.0 1.0
"Dr. Strang & MIT open- you are a gift to entire field of engineering" Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3504.0 0.0 0.0 0.0
"while the professor may understand the math, his mistakes make the lectures overly confusing." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 15256.0 0.0 0.0 0.0
"I'm a freshman in college and I'm only taking BASIC algebra" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6296.0 0.0 0.0 0.0
"How valuable these lectures are !!! Kinda Addicted !!!! 🙏 Thank you very much Prof. Strang and MIT 🙏" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 4904.0 0.0 0.0 0.0
"What an inspiring teacher!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11459.0 0.0 0.0 0.0
"in 12:20, is it valid to say that the natural numbers has a least upper bound? does it even have an upper bound?" M2d4HsBsu8Y "Lecture 5: The Archimedian Property, Density of the Rationals, and Absolute Value" "MIT 18.100A Real Analysis, Fall 2020" 13574.0 0.0 1.0 0.0
"@ 10:55  If F'(x) = { 1/(1+x) }  then, F(x) = log(1 + x) , So, how F(0) = 1 ?" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1464.0 0.0 1.0 0.0
"Student: [INAUDIBLE]" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8917.0 0.0 0.0 0.0
"can somebody explain me the explanation in 25:49 I can understand what he says but I'm confused about the text." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12617.0 0.0 1.0 0.0
"Thank you." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 9545.0 0.0 0.0 0.0
"Is this equivalent to calculus 1 and 2? Derivatives, integrals, and sequences and series?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6867.0 0.0 1.0 0.0
"no offense but zzzzzzzzzzzz BORING" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14071.0 0.0 0.0 0.0
"""You get an A in the course."" Hahahahha. Not only does he give an amazing lecture, but nice sense of humor as well. 5/5." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 138.0 0.0 0.0 0.0
"first lecture, first day of introductory calculus" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12869.0 0.0 0.0 0.0
"I liked the 2nd (chain rule) method more." 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5702.0 0.0 0.0 0.0
"Don't you just feel his love and warmth! Gauss would have been so proud.


His 18.06 course are one of the greatest treasures of online education, just like Khan Academy Cardiology, Hans Bethe quantum mechanics lectures, Andrew Ng's machine learning course, Jeremy Howard's fast.ai course and Gerald Sussman's SICP computer science course.


Thank you so much MIT OCW....you have changed the world with your MOOCs!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 3482.0 0.0 0.0 0.0
"Whats the point of this" bBESL68iX6s "Lecture 14: Limits of Functions in Terms of Sequences and Continuity" "MIT 18.100A Real Analysis, Fall 2020" 11597.0 0.0 0.0 0.0
"NICE LECTURE....there is 1 doubt at 23:00....how was F(x)=root of pie divide by 2?? please reply" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7801.0 0.0 1.0 0.0
"Great work" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4365.0 0.0 0.0 0.0
"Also the most Abstract math seems like. " FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2325.0 0.0 0.0 0.0
"I found this lecture quite confusing.  His last example of computing (AB)C vs A(BC) is the key idea.  The blog article he talks about I think misses the main computational point because it focuses on the composition of 2 functions and there is little computational advantage between forward vs. backward with only two functions.  

In case it might help others, here is how I think about it: Say everything is linear but the variables have different dimensions:
F(x)=F3(F2(F1(x))
start with variable x (input layer)
h1=F1(x) = Cx (hidden layer 1)
h2=F2(h1)=B*h1  (hidden layer 2)
y=F3(h2)=A*h2 (output layer)
Then F(x)=A*B*C*x and jacobian(F)=A*B*C
Forward differentiation first computes derivatives of h2 wrt x by multiplying jacobians (JF2)*(JF1).  Then finds derivative of y wrt x by multiplying by JF3 --> so this is A*(B*C)
Backward differentiation first computes derivatives of y wrt h1 by multiplying jacobians (JF3)*(JF2).  Then finds derivative of y wrt x by multiplying by JF1 --> so this is (A*B)*C

In a neural network, you might have x very large N-dimensional input (pixels in an image), hidden layers h1 and h2 with a moderate n-number of dimensions, and output y a scalar (probability the network thinks image is a cat).
So forward differentiation computes A*(B*C) -> cost is 1*n*N + n^2*N
backward differenations computes (A*B)*C costs 1*n^2 + 1*n*N" lZrIPRnoGQQ "27. Backpropagation: Find Partial Derivatives" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5433.0 0.0 0.0 0.0
"You're a bit confused. He teaches 34 sections of 18.06, staggered so that each one starts the day after the last, and about 45 minutes later. This was just one continuous 24 hour period of teaching with the order reversed for our convenience. It's more efficient that way; just the kind of innovation we expect from MIT." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 12247.0 1.0 0.0 0.0
"this lecture made my night before the midterm" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14894.0 0.0 0.0 0.0
"Just awesome! My ass got saved!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 7157.0 0.0 0.0 0.0
"Good Job  Professor" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4109.0 0.0 0.0 0.0
"I'm attending to an statistics class at University of Buenos Aires because I'm following Economics, and I miraculously ran into this. Incredible lecture!!!" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 6307.0 0.0 0.0 0.0
"Watching this in Denmark for exam preb. Could just have seen this course first, an amazing job. Thank you very much!" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 11303.0 0.0 0.0 0.0
"Thank you for the lecture series!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9265.0 0.0 0.0 0.0
"@vaibhav1803 

hey, do you understand the first part when he stated that ( d/dx +x ) y = 0, translates to dy/dx +xy = 0? 

I'm a little confused about that. i see from the first equation that was a give that dy/dx = f(x) = y. Therefore y should equal dy/dx, so shouldn't the equation be (d/dx)(dy/dx) = -xy? 

" 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2057.0 0.0 1.0 0.0
"@6:50 ""no mathematics involved here, just making a vector stand up"" :'D" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1575.0 0.0 0.0 0.0
"he tells you that t is nx^(n-1) which is a way to find the deri\vative. there are other rules i dont know why he wouldnt go over it." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13117.0 0.0 0.0 1.0
"The number of paper clips that intersected the lines were 3. So the probability is 2/3 and hence pi therefore is 1.5." CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 10207.0 0.0 0.0 0.0
"Oh i love how this teacher sounds like a dupont or professor calculus in TIN TIN" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8010.0 0.0 0.0 0.0
"For everyone begining this lectures that have no notions of linear algebra, I reccomend you to watch 3Blue1Brown series before because he put a lot of image on the word. Sorry for the mistakes, I am not an english speaker." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3863.0 0.0 0.0 1.0
"me encanto!!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13933.0 0.0 0.0 0.0
"Wow, his humility at end of lecture made me tearful ... he is thanking us!?  I've lived my mathematical life with this man's first edition books since I was a twenty year old kid!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 12070.0 0.0 0.0 0.0
"Professor Strang, you are now  MIT grandfather of mathematics. Thank you  for this new experience in life's non-stop learning." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8388.0 0.0 0.0 0.0
"@3:20 Should not the area under the slope z be equals to:
1/2 * sqrt(z^2 - 1^2) = 1/2 * sqrt((y/z)^2 - 1^2)
?" l4NoMKEHQwM "11. Derived Distributions (ctd.); Covariance" "6.041 Probabilistic Systems Analysis and Applied Probability" 1550.0 0.0 1.0 0.0
"Best explanation ever I have seen" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 2857.0 0.0 0.0 0.0
":D understand this review and got his projection questions right so far at 8th grade. Pretty cool that we covered this in Saxon Geometry and by using common sense and a little luck you can expand so much furthur." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1453.0 0.0 0.0 0.0
"Thank you professor" rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 9306.0 0.0 0.0 0.0
"Stick to this course and your life will change," J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8898.0 0.0 0.0 0.0
"Why is the integral of f'(x)dx  the avg value of f '(x) rather than f (x)  help me i am stuck at it.." Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11887.0 0.0 1.0 0.0
"The solution to QR decomposition in HW - systolic arrays is a triangular Systolic array." d32WV1rKoVk "12. Computing Eigenvalues and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10283.0 0.0 0.0 0.0
"The slides are so easy on the eyes." 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 10280.0 0.0 0.0 0.0
"heyyy stop moving the  camera" 49Ro2zf9hAc "Lecture 7: Convergent Sequences of Real Numbers" "MIT 18.100A Real Analysis, Fall 2020" 13153.0 1.0 0.0 0.0
"Thank You" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 9044.0 0.0 0.0 0.0
"@3:57: ""And then I take ""u"" the way it is"" That is just so beautiful, everyone should just be taken as they are" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1553.0 0.0 0.0 0.0
"sadly i'm too stupid to understand this." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 14273.0 0.0 0.0 0.0
"Take the integral from 0meters to (a meters) if along the y axis and from 0 meters to the (square root of a meters) if along the x direction i.e. use UNITS. This helps ensure the units of the answer come out properly. Again, dont delete k in y=kx^2 because its numerically equal to one, the units are needed. k=1/(1 meter). k is exact so does not effect significant figures of your answer." ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9011.0 0.0 1.0 1.0
"Very sincere thank you for sharing these lectures." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11225.0 0.0 0.0 0.0
"I remember hating taylor series as much as them but for the life of me I can't understand why they're so easy now" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5945.0 0.0 0.0 0.0
"One word. Thanks!" gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 8116.0 0.0 0.0 0.0
"I think mexican pesos won't help a lot, but of course i wanna help bc u helping me even more gg." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6035.0 0.0 0.0 0.0
"very interesting every time i watch i learn thank you" 58B5dEJReQ8 "Lecture 3: Quotient Spaces, the Baire Category Theorem and the Uniform Boundedness Theorem" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 15022.0 0.0 0.0 0.0
"His derivation of the derivative of a power is understandably ""simplified"" but I found it a bit sloppy. The actual derivation uses sums of infinite series. It's weird, because he's using the properties of infinitesimals without explicitly saying so" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4747.0 0.0 1.0 1.0
"cc are crazy" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12646.0 0.0 0.0 0.0
"this guy is amazing, thank you from Spain!!" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14818.0 0.0 0.0 0.0
"can anyone explain what happened at 28:40?" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12604.0 0.0 1.0 0.0
"When the professor uses the term ""speed""; I believe he should be using the term ""velocity"". My understanding is that speed = |velocity|. That is speed (magnitude) is always positive, where velocity may be positive or negative (magnitude and direction). 

Nice lecture series... Thanks, MIT" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11635.0 0.0 1.0 0.0
"Professor Strang ,this is a really useful lecture that starts with classical topics in mathematics. Linear Programming and Two- Persons Games are large topics in applied mathematics." feb9j65Iz4w "24. Linear Programming and Two-Person Games" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8339.0 0.0 0.0 0.0
"dtan(x)/dx = 1+tan^2(x) so darctan(x)/dx = 1/(1+x^2) because dx/dy = 1/(dy/dx)." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12776.0 0.0 1.0 0.0
"why f is equal to (1/2)X(transpose)Sx where prof did not explain what is S. Does anyone know what is that?" wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15318.0 0.0 1.0 0.0
"Date : 16th May'20 - The world is dealing with COVID19 pandemic and somehow I want to understand the real world of linear algebra. 
Dropping a note for future Generation" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 3317.0 0.0 0.0 0.0
"beautiful chalk and blackboard, my school's blackboards and chalks are craps" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12516.0 1.0 0.0 0.0
"thank  a lot" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14447.0 0.0 0.0 0.0
"Love and appreciate Dr. Strang" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7435.0 0.0 0.0 0.0
"The black board trick never gets old...XD" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10020.0 1.0 0.0 0.0
"Thanks, Professor. You are a global treasure." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9843.0 0.0 0.0 0.0
"how AnB is 8??" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 13189.0 0.0 1.0 0.0
"These are great lectures! Is the autograder and programming assignment available somewhere?" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10395.0 0.0 0.0 0.0
"""I never drew a pi-e before..."" GOD I love this man!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 59.0 0.0 0.0 0.0
"Respected old man,his hair grow more white." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8565.0 0.0 0.0 0.0
"How come they did not applaude at the end? OMG you are awesome man!!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4824.0 0.0 0.0 0.0
"24:12 why Sir was standing like that???" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 728.0 1.0 0.0 0.0
"I want to tell all math enthusiasts out there to never give up, because maths is difficult for everyone... You can see even mr. Strang says sometimes he gets lost, and he teaches this stuff for years. (I felt this was missing in the comments) btw. *what a living legend!*" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6143.0 0.0 0.0 0.0
"This was too late for me 😂 But this is great for the others😍" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 10976.0 0.0 0.0 0.0
"Im really suprised how young, full of energy and smart this guy is.Thats what i call pure talent(or genias?)" jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6577.0 0.0 0.0 0.0
"This course gives me an intense urge to raise my hand with the answer to the professor's questions!! (Ofc, unlike the live audience, I have the benefit of the pause button :P)" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10487.0 0.0 0.0 0.0
"thank you MIT you are the best !" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14483.0 0.0 0.0 0.0
"what is alpah bita and gamama etc
answer me quick tomorrow i have paper
and  i don't know" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 15150.0 0.0 1.0 0.0
"I don't get it. So it's okay if we have a limit like 0/0, but a limit like 0/1 is wrong, is that right?" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5309.0 0.0 1.0 0.0
"HI guys am a student at BOTHO UNIVERSITY IN BOTSWANA STUDING COMPUTER SCIENCE.I realy like Proff John Tsitsiklis.PROBABILITY MODELS AND AXIOMS wish i attended at M.I.T   ....." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 4403.0 0.0 0.0 0.0
"Are there any lecture notes?" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 2531.0 0.0 0.0 0.0
"This is enlightening! thank you prof" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10659.0 0.0 0.0 0.0
"I really really do enjoy watching/learning this, my prof. isn't doing a good job." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5933.0 0.0 0.0 0.0
"At https://youtu.be/YzZUIYRCE38?t=615, Professor Strang applies FOIL to vectors.  I'm not clear on why you can do that." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2714.0 0.0 1.0 0.0
"@jkrobertson88 Massachusetts Institute of Technology. Big Difference." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1902.0 0.0 0.0 0.0
"What did he mean by the Dimensions?" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 11480.0 0.0 1.0 0.0
"To all those who didn't exactly got why dr/ds=(u hat), try understanding this way of explanation:
In the X-Y plane lets just take R(r vector) to be the position vector of a point in X-Y plane. Now if we move a length ds along u vector(U), the position vector of the point will change by amount dR. Thus, if you draw a picture of what I just said, you will understand this that,                                                                                                                                                             (R +dR) - (R) = (ds)(U hat). That is dR=(ds)(u hat). And thus dR/ds=(u hat)." 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 11022.0 0.0 0.0 1.0
"""You've taken linear algebra. You've taken calculus."" Buddy, not even close. But please, continue! >.<" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 141.0 0.0 0.0 0.0
"""Statistics is about replacing expectations with averages ... everytimes you see an expectation you replace it by an average""  this resume all this lecture." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 111.0 0.0 0.0 0.0
"you can also swap 1,2 and then 3 with one of them." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 15497.0 0.0 1.0 0.0
"Excellent explaination" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 3641.0 0.0 0.0 0.0
"what prerequisted  for this 18.06 ?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 15180.0 0.0 1.0 0.0
"nice
" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14029.0 0.0 0.0 0.0
"He could have answered the students question better by explaining that theta was tending to zero by the center moving out rather than the lines closing in.  He tried to say that but didn't explain it right.

If you view it this way, the top is tending towards zero while the bottom is a constant." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4469.0 0.0 1.0 0.0
"I love it how he does not even need to explain it carefully, but everyone was already interested in Linear Algebra taught by him. He really encourages students to brainstorm other insights based on strong background that he could provide them." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 5758.0 0.0 0.0 1.0
"THAT IS SEXY" tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8990.0 0.0 0.0 0.0
"Lessons are very clear and understandable, however the one who writes all the subtitles doesn't know anything about the lecture because there are too many mistakes at the subtitles." H_k1w3cfny8 "10. Continuous Bayes' Rule; Derived Distributions" "6.041 Probabilistic Systems Analysis and Applied Probability" 7330.0 0.0 0.0 0.0
"the explanation of the fondamental limit is quite.... sick" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14687.0 0.0 0.0 0.0
"31:23 ""One more time""... ""No""  GET ROASTED SON" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 910.0 0.0 0.0 0.0
"thank you so much MIT" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14511.0 0.0 0.0 0.0
"I think it would be better for someone who already have linear algebra background. I learned something from another perspective. The meaning behind it. 
For new learners, it is still hard." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6028.0 0.0 0.0 0.0
"That's generally what discussion or recitation sections are for, not lectures." Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9932.0 0.0 0.0 0.0
20:26 JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 651.0 0.0 0.0 0.0
"I was almost done with the lectures but then today I saw that there were suddenly 36 instead of 35 videos in this series. I was confused and started scrolling through the video playlist to see what I missed and stumbled upon this gem :) He looks different on the outside but he acts the same and is the same on the inside <3" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6150.0 0.0 0.0 0.0
"Linear Algebra has been my good old friend for several decades, but now I see a fresh look at my friend that looks much younger, all this thanks to the amazing profession Prof. Dr. Gilbert Strang. The essence of the timeless reverence Guru Brahma proved again. I shall be going through the entire series, even though, I wish I had this opportunity a decade and half ago. 🙏" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7370.0 0.0 0.0 0.0
"May God make this man eternal" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7629.0 0.0 0.0 0.0
"I love him!!! deeply!!!" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5734.0 0.0 0.0 0.0
"Maybe I don't have basic in Mathematics, but when I read Prof Strang books about linear algebra (all deep learning for my dream project in machine learning). And now I introduced to Prof Strang OpenCourse, I'm feeling blessed and inspired as Computer Programmer Learner. Thanks to MIT & Prof Strang from East Nusa Tenggara Province, Indonesia. 🙏🙏🙏" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7635.0 0.0 0.0 0.0
"Here, before GATE 2022" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 4680.0 0.0 0.0 0.0
"they always use easy examples in lecture, come the exam it takes 45 minutes to solve lol" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14783.0 0.0 0.0 1.0
"Wow, I really made it through (almost) :D" tBUHRpFZy0s "24. Classical Inference II" "6.041 Probabilistic Systems Analysis and Applied Probability" 12062.0 0.0 0.0 0.0
"out of curiosity, i did the math on e^(-3x)*(1+x)^(-1/2). it's a long and messy road but you'll end up with 1-(7/2)x." BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14162.0 0.0 1.0 0.0
"Why are the parameters of one of the normal distributions he describes identifiable and the others aren't?" TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 11778.0 0.0 1.0 0.0
"This lecture invoked me much inspiration!! 
교수님 연금 달달하십니까" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 10789.0 0.0 0.0 0.0
"Thanks for providing such a lecture" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9696.0 0.0 0.0 0.0
"35:00 
recap" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 993.0 0.0 0.0 0.0
"Whoa, I had a serious  aha moment here!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11759.0 0.0 0.0 0.0
"I wish I did watched it at 2000." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6196.0 0.0 0.0 0.0
"Well boys, future starts here." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11346.0 0.0 0.0 0.0
"A big thanks to MIT and YouTube to be able to share this valuable content with everyone around the world. I would've never imagined if I could ever learn from a MIT professor. Truly appreciate the opportunity. Stay safe and wish y'all the best." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 2098.0 0.0 0.0 0.0
"Is this course a prerequisite for machine learning?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 6859.0 0.0 0.0 0.0
"Great Lecture. Could anyone answer my question:
I understand that error vector (b-p) is smallest when e is orthogonal to column space. What I am confused at is the squared error portion. Using projection, I thought what was solved is the Xhat that could minimize the error vector instead of error square. Could anyone help me clarifying this?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 4205.0 0.0 1.0 0.0
"Hes a class lecturer. I envy anyone who had him in college." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4683.0 0.0 0.0 0.0
"Is it just me? Is that a mistake? He writes x=Wc at 37:11, where x represents vector in the old basis, and c the vector in the new basis, and W the columns of new basis vectors. Should it be c=Wx instead?" 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 6786.0 0.0 1.0 0.0
"You still have to admit...it is cool, common or not...it. is. epic." dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 12242.0 0.0 0.0 0.0
"Thank u sir" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 9076.0 0.0 0.0 0.0
"Just a litte typo that I came across throught out this perfect lecture is the ""confusion region"": min(a_i/b_i) and max (a_i/b_i) should be min(b_i/a_i) and max (b_i/a_i).

Generally speaking, this lecture is the best explanation on SGD I have ever seen. Again, thank you prof. Sra and thank you MITOpenCourseWare so so much 👍👏

P/s: Any other resources that I've read explained SGD so complicatedly 😔" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7154.0 0.0 1.0 0.0
"really well explained but may need to watch twice if you are completely new to conditional probability concept." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 14258.0 0.0 0.0 0.0
"Love his lectures but I think there's a little mistake in there, correct me if I'm wrong. Professor Strang said {(1,1,2),(2,2,5),(3,3,8)} makes a basis for R^3, but can't that set of vectors only produce vectors where x1 and x2 are equal? So you cant get (1,0,0) from the vectors and certainly not the entirety of R^3, right? The first and second row would even be the exact same written as a Matrix, so they should be linearly dependent for that reason as well. Again, maybe I'm overlooking something but it doesn't add up for me.

Edit: Should have sorted comments by new first, it seems a lot of people saw this too but it didn't make it to the top comments" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 7441.0 0.0 1.0 0.0
"In Romania we do this in high-school, 10th grade or something like that... and you're doing it at MIT? Great course(video) though" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 6618.0 0.0 0.0 0.0
"very clear !" ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 14998.0 0.0 0.0 0.0
"Are projection matrices always symmetric? Professor seems to say so. Is this correct?" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2525.0 0.0 1.0 0.0
"Gratitude from India." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4187.0 0.0 0.0 0.0
"the most interesting algebra ever. thank you professor!!" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 14718.0 0.0 0.0 0.0
"hey guys, i have a quesion to ask and i appreciate if someone can help answer my question.
When the prof tried the free column, he tried (x,1, x, 0) and (x, 0, x, 1), this is understandable. But can i try one more which is (x, 1, x, 1) ??!!
thank you with regards." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 13149.0 0.0 1.0 0.0
"Thanks Prof. Strang , I really liked your course very much. Thank you so much" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9633.0 0.0 0.0 0.0
"My high school teacher moves way faster than this guy and at 8:00 AM when I still am not awake. Someone should talk to her." 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7762.0 0.0 0.0 0.0
"OMG I was literally like didn't they fight in the revolutionary war? then he makes a joke about it 🤓" nvXRJIBOREc "Lecture 21: Minimizing a Function Step by Step" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7983.0 0.0 0.0 0.0
"At 1:05 he says ""What does a matrix do? It acts on vectors"". I just love the way he looks at the matrices. He is definitely a ""matrix"" artist.  Every time I watch his video, I get a feeling that I learnt something new. Absolutely brilliant sir!" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 2602.0 0.0 0.0 0.0
"oh sir thank you a lot !!!!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14111.0 0.0 0.0 0.0
"So if you had to boil the topic of this lecture down into 1 main idea, is it that the probability of a whole set is the sum of the probabilities of each individual set? 

Seems very simple, not sure if I missed anything" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 8772.0 0.0 1.0 0.0
"lecture 1: 60k views
lecture 2: 6k views
lecture 3: ..." 9_xG0AGRa-w "Lecture 2: Cantor's Theory of Cardinality (Size)" "MIT 18.100A Real Analysis, Fall 2020" 13771.0 0.0 0.0 0.0
"I have not watched this yet, although I am very excited to. Anyone that is struggling to get the big picture (or motivation in general) of functional analysis can check out the book Functional Analysis for Physics and Engineering by Hiroyuki Shima." uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 5546.0 0.0 0.0 0.0
"hmm it seems the person that who truly appears dumb is yourself haha according to the person on the bottum" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13175.0 0.0 0.0 0.0
"I m guessing I am the smallest guy who watched this lecture" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5861.0 0.0 0.0 0.0
"The best determinant lecture I had!" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 9995.0 0.0 0.0 0.0
"I know this is a stupid question but can some explain why r=2acos theta as opposed to 2asec theta?" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5642.0 0.0 1.0 0.0
"Interesting proof: showing  probability of two separate coincidental events being larger than  the probability of a single event occurring in the universe of events by saying that they are not coincidental events, however,  but 1 single event with a larger probability than a single event occurring in the specific universe. Very clever." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 6730.0 0.0 0.0 0.0
"Now all the learners of this course know what happened about Monica LOL. I think at the end of 2010s many of unis students do not know these 1990s things." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 7957.0 0.0 0.0 0.0
"What an inspiring lecture" 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11458.0 0.0 0.0 0.0
"DR. Strang, from looking at your pass quizzes at MIT  they seem very challenging to me. There are many twist and turns in your quizzes. I hope that the MIT students are learning linear algebra that stays with them forever. These students are supposed to be the world's brightest." QuZL5IKpO_U "24b. Quiz 2 Review" "MIT 18.06 Linear Algebra, Spring 2005" 3286.0 0.0 0.0 0.0
"SEXUAL Harassment!" X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 8578.0 0.0 0.0 0.0
"31:53 what is this ""natural notation""? 
I wish he derived that form from u(t) = c1e^(λt)x1" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 917.0 0.0 1.0 0.0
"Thank you for posting !" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 9255.0 0.0 0.0 0.0
"Why the number of operation is equal to n^2 ? Can anyone ?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 11919.0 0.0 1.0 0.0
"Oh my cheese sticks!!! I actually understood (some of) what he was saying. Kudos to the professor!!!" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8015.0 0.0 0.0 0.0
"did this guy do the voice for the T-rex in toy story?" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 12740.0 0.0 0.0 0.0
"If the rows of a matrix are dependent, does it mean that the columns must be dependent too?" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 6524.0 0.0 1.0 0.0
"Can you share your slide please?" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 3121.0 0.0 0.0 0.0
"LOL.. I wonder if he brought the chain especially for explaining why that derivative called a chain derivative ! It was a wrong explanation anyway!" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7240.0 0.0 1.0 0.0
"Teachers does not represent the school. It's students who absorb the subject and learned from it. It is not school but the learned knowledge. Oftentimes graduates felt they knew anything about the science they learned ending up looking for genetically common financial aspects. Recovery of education invested.Where is this knowledge dumped these days?Facilties uses this knowhow?What are they doing now?Labor expensive. Application minimal. R&D?Always money matters 4 survival. Survival exploits." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9017.0 0.0 0.0 0.0
"Is there Any Course on Basic Electronics" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6817.0 0.0 0.0 0.0
"in minute  10:34   the last right matrix  the last pivot element should be -3 because we multiply the previous one by 2 in 2nd row and add to 3rd row so, the element (3,3) should be -3 otherwise it will be 3 if we multiply by -2 and subtract" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13592.0 0.0 1.0 0.0
"Absolute legend. Every time I hear him is an education!" MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2198.0 0.0 0.0 0.0
"great professor ... amazing teaching method and he clearly has developed an astonishing intuition over the concepts, Bit Thumbs up from me!" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 12997.0 0.0 0.0 0.0
"Thank you Sir" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9232.0 0.0 0.0 0.0
"I see that they jump right into max and min, the hessian, etc after this...


do they cover this topics on this class??

limit and continuity for multiple variable functions
diferential calculus of multiple variable functions(things like, directional derivatives, supirior order partial derivatives C1 class, c2 class, etc...,Scharwz theorem,chain rule)
inverse and implicit theorems of multiple variable functions


beacouse in my multiple variable calculus class.  firts I had the review of vectors, parametrics ecuations and all of that, then I had topology and then the list of the thing I listed above(where I am currently in) and after that I´m going the have max and min, lagrange and with that I finish half of my calculus class, after I will see multiple variable integral calculus and after that to finish the course vectorial calculus(green, stokes and all of that)

so do this course cover that??? and if not wath should I be looking for?" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5959.0 0.0 0.0 0.0
"Yea but if you use an errorfunction constricted to a higher power function then that function will go to zero when x goes to zero. Use ordo. 
So in that case you just need to use the second order maclaurin term to solve the problem and ofcourse the ordo term constricted to x^4. Then you get the a really easy problem." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12117.0 0.0 1.0 0.0
"I watched this lecture maybe three times. and still screaming. thank you Prof. Gilbert Strang" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 6185.0 0.0 0.0 0.0
"“Well don’t speak all at once” 👍 gotta love his sense of humor !" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 15599.0 0.0 0.0 0.0
"at 17:10 answer: y = -1/2g(t*t)  + v(start)t + y(start) [equation for a free falling body]

the body is at 80 feet and gravity(g) = 10 and v(start) = 0
hence y= -5(t*t) + 80  " ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12416.0 0.0 1.0 0.0
">Calclulus BC AP exam tomorrow

IT'S HAPPENING" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1461.0 0.0 0.0 0.0
"Usually this guy is great when teaching linear algebra, but I think he got thrown into this course for couple days and was unprepared. I mean that discussion when off track quick." lZrIPRnoGQQ "27. Backpropagation: Find Partial Derivatives" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11141.0 0.0 0.0 0.0
"44:15 <--- ¿ inverted question mark! the teacher maybe speaks spanish." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1230.0 0.0 0.0 0.0
"48:14 that guy totally knew he was blocking the camera" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1292.0 1.0 0.0 0.0
"According to the course calendar, Assignment 1 is due on the same day as Lecture 2, i.e. this lecture. But this lecture contains material that is needed to be able to work on Assignment 1. In fact, towards the end of the lecture, the prof gives a sketch of how to solve Exercise 6 of Assignment 1. Why is this?" 9_xG0AGRa-w "Lecture 2: Cantor's Theory of Cardinality (Size)" "MIT 18.100A Real Analysis, Fall 2020" 2228.0 0.0 1.0 1.0
"równowaznosc wierszowa i klumnowa; amerykanie ..." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14270.0 0.0 1.0 0.0
"I think the main point of this lecture is not to find the solution at all, but to know when you can find it. So you can watch in perspective and answer when you can and when you cannot to find it. That's the reason for what he did'nt begun by putting numbers as results of the equations, but with literals, meaning they can be any number and the answer to that system just can be found if those numbers meet the condition of beeing a mix of every column in the matrix." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 6058.0 0.0 0.0 0.0
"8:00 isn't it the integration of the area of semicircle 🤔" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1413.0 0.0 1.0 0.0
"You’re a wonderful teacher" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 12266.0 0.0 0.0 0.0
"Very clear and natural to follow the lesson. Thank Professor Strang so much. Btw, his books are also very wonderful." AeRwohPuUHQ "22. Gradient Descent: Downhill to a Minimum" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11161.0 0.0 0.0 0.0
"Counting means adding." 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 3251.0 0.0 0.0 0.0
"thanks MIT" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14554.0 0.0 0.0 0.0
"intuition behind  linear regression is awesome.." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 13622.0 0.0 0.0 0.0
"Lec6 done." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 7262.0 0.0 0.0 0.0
"Some of the questions made were very naive." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8822.0 0.0 0.0 0.0
"I've studied linear algebra from another online source, and that's given me a great foundation, but this lecture has really helped me to SEE the matrix multiplication from a higher level. Before this video, I hadn't considered that the left multiplication can be thought of as applying row operations." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6431.0 0.0 0.0 1.0
"Awesome stuff, thanks MIT!" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2769.0 0.0 0.0 0.0
"They don't ""need"" donations. They don't need to give away content for free either but they still do." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10437.0 0.0 0.0 0.0
"It is not rate of change it is variation with respect to one variable to another variable.whenever you say rate of change only time factor is involved in it.it refers to variable changes with time." 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6962.0 0.0 1.0 0.0
"can't L'Hopital's rule be explained geometricly? what about the functions curves' tangancy ?" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12640.0 0.0 1.0 1.0
"his teaching is rigorous, precise, strict and concise, to the point, helps me clarifying the cloudy understanding in statistics." 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 13171.0 0.0 0.0 0.0
"No offense but you should be studying English instead of Linear Algebra." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 7880.0 0.0 0.0 0.0
"Watch in 1.5 speed, makes it far more bearable" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11282.0 0.0 0.0 0.0
"Hey, so will ((d^a)/(dx)^a) * x^n be equal to (n!/(n-a)!) * n^(x-a)" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4700.0 0.0 1.0 0.0
"@aritrayou then you can use rectangular coordinates. cylindrical method is good when there is a circle (projection) on xy-plane" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1785.0 0.0 1.0 0.0
"""Some make simple things complex and Some make complex things simple""
Thank you, Sir Sipser❤️
Thank you, MIT
Thank you, YouTube" KAySmSEGc9U "3. Regular Pumping Lemma, Conversion of FA to Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 108.0 0.0 0.0 0.0
"Yeah, his handwriting is good. I noticed that early on." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12127.0 0.0 0.0 0.0
Cospiover4=cospiover4 RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3222.0 0.0 0.0 0.0
"I keep answering his questions, then laugh about it. He is a great engaging professor :)
Like if you are doing the same thing" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 5629.0 0.0 0.0 0.0
"Rather watch one of the lectures on PCA by Prof Ali Ghodsi." WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 8495.0 0.0 0.0 0.0
"Some things require only a textbook." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 8828.0 0.0 0.0 0.0
"Personally, for the limit around 30 minutes, I used the fact that the hundredth derivative of x^100 is 100! and factored it out along with p^100." PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8184.0 0.0 0.0 0.0
"At 14:20 the dimension formula is more intuitive if stated as dim(S) + dim(U) - dim(S∩U) = dim(S+U)    i.e. "" the dimension of S added to the dimension of U minus the dimention of the interscetion of  S and U is the dimension of S+U""  ... so much easier to visualize stated that way n'est-ce pas?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 2591.0 0.0 0.0 1.0
"If a teacher makes it complicated then he is not a good teacher. If he makes it super easy then only he is a good teacher. :-)" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 6489.0 0.0 0.0 0.0
"12:06 book recommended" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 386.0 0.0 0.0 0.0
"Where is the follow-up lecture on PCA it seems to be missing from the following lectures?" Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11691.0 0.0 0.0 0.0
"watch this for better explanation:
https://www.youtube.com/watch?v=l27xKSNad2Y" zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15066.0 0.0 0.0 0.0
"@Shmling stop wishing and do something about it" BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1728.0 0.0 0.0 0.0
"is W1=T(V1) W2=T(V2)...? because the transformation output doesnt always have to be a base for the space, it only happens to be when the transformation is an isomorphism between the two spaces." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13624.0 0.0 1.0 0.0
"I'd say if you play this video at speed 1.5, it's even more awesome!" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 6282.0 0.0 0.0 0.0
"Cramer's Rule starts at 20:00" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 3257.0 0.0 0.0 0.0
"thanks Prof and MIT" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14560.0 0.0 0.0 0.0
"Momentum forsenCD" wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7688.0 0.0 0.0 0.0
"My lecturer shared this link in online classes saying this link will direct to free NordVPN. Now I've became software engineer and I regret" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7765.0 0.0 0.0 0.0
"Wouldn't the z-axis be orthogonal to the entire x-y plane?  It kind of goes against one of his remarks in the 20-21 minute part of the video." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12016.0 0.0 1.0 0.0
"thank you" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14467.0 0.0 0.0 0.0
"This is another great lecture by MIT Professor DR. Gilbert Strang. Least Squares put linear algebra into another world by itself." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 10637.0 0.0 0.0 0.0
"my doubt  in this lecture: sir told dA' is the area of the square in uv coordinates,but acc. to the diagram it dA' is the area of a parallelogram whose sides are not parallel to uv axes,how can that be possible" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13976.0 0.0 1.0 0.0
"Good content, but it sure does seem to move a little slow.  Maybe it'll pick up pace; I'm only half an hour into lecture 1." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4124.0 0.0 0.0 0.0
"Very good content to understand Bayesian inference. Thanks prof." bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 11173.0 0.0 0.0 0.0
"That is True" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 9893.0 0.0 0.0 0.0
"I know the definition of a Limit and watch this courses for pure enjoyment, don't get me wrong, he is great explaining, but nither of those two things you say is the point. First, anybody can probably find many places that explain the definition of a Limit, and second, even if he talks about limits more as lecures go on, he should've defined it before using it in the first place. Limit and its definition usually go first in most Calculus courses." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5640.0 0.0 0.0 1.0
"Not to be weird or anything, but I swear I can hear his heartbeat. 😂" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7932.0 0.0 0.0 0.0
"I'll prefer a discussion of a practicl cases...Physics Electrical" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6288.0 0.0 0.0 0.0
"Thanks a lol way much clearer" gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 9648.0 0.0 0.0 0.0
"@Santakingkong i don't get what ur saying but Thnx.
Anyway, i think i may have found the solution. 
When he was talking about line L, i thought L was a subspace of P (also his diagram of L kind of looks like L is inside P) . If it was, than P U L=P & P itself is a subspace of P.So P U L is a subspace of P.
But if he was talking about L that passes through orgin but doesn't lies in plane P (so L penetrates P), than ofcourse P U L will not be subspace of P. 
So my interpretation of L was wrong.lol" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 1717.0 0.0 1.0 0.0
"so the goal or purpose of this lecture was to achieve Minimizing _x_ Subject to Ax = b is my assessment accurate?" MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14346.0 0.0 1.0 0.0
"Next time, please put the main topic of each lecture in the video title." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7830.0 0.0 0.0 0.0
"thats cool chalk." UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14650.0 0.0 0.0 0.0
"because knowledge is more important for them than their appearance" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12526.0 0.0 0.0 0.0
"i still get confused with derivative notations sometimes. when he differentiated x^2+y^2=1 why did the differentiated form of y have y' on it?? i see that happen when we differentiate y but why do i have y' included and not just 2y." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13461.0 0.0 1.0 0.0
"Finally it is making sense that learning is made simple by method it is taught to us" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3774.0 0.0 0.0 0.0
"there is always someone who is unhappy as he said!" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 14763.0 0.0 0.0 0.0
"where is the proof of 39b) for the paralellopipe?" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 15244.0 0.0 1.0 0.0
"Should he add x hat at 12:58?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 8641.0 0.0 1.0 0.0
"Simple most, step by step, taking all kinds of examples with not a single extra word ! So, everybody praises MIT . Thanks MIT for the OCW for the whole world .♥️🙏" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 8661.0 0.0 0.0 1.0
"Superb lectures" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 8963.0 0.0 0.0 0.0
"I only new from his books and lectures of him i watched online. 
What a brilliant man.

MIT folks who had a chance with knowing in person are extremely lucky." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5893.0 0.0 0.0 0.0
"I am a statistician that watching this video :)))" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 5056.0 0.0 0.0 0.0
"@28:50:00 why would there be a square root 2 pi there, I don't get the significance of what he is saying when there are no fudge factors and this is the true asymptotic variance. Why would there be any of that?" JTbZP0yt9qc "6. Maximum Likelihood Estimation (cont.) and the Method of Moments" "MIT 18.650 Statistics for Applications, Fall 2016" 1528.0 0.0 1.0 0.0
"The professor was very humble." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10251.0 0.0 0.0 0.0
"I really like how the final result can be interpreted intuitively with some geometry. It shows how a bit of human intuition can transcend a lot of mechanistic elaborate calculations." Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5924.0 0.0 0.0 1.0
"I LOVE MIT LECTURES" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 4926.0 0.0 0.0 0.0
"Just a phenomenal professor and course. I looked at a couple lectures to help one of my kids in her calc course and ended up doing the whole class because it was so enjoyable. ENJOYABLE! Great job MIT. The effort you put into these OCW courses is really appreciated." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7155.0 0.0 0.0 0.0
"43:25 I think he meant electrical potential difference is voltage, electrical potential itself is not the same as voltage." z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1206.0 0.0 1.0 0.0
"I've looked at a lot of  explanations for Eiganvectors and eiganvalues but this is the first one to clearly identify the vectors in R3. and to show how  zero lambdas represent vectors in the null space." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 6422.0 0.0 0.0 1.0
"@IIAOPSW can you explain to me how it is incorrect? please brush up on your metric units before criticizing a professor at MIT :)" jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1638.0 0.0 0.0 0.0
"Only determinant is the topic that’s does catch my interest." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 8118.0 0.0 0.0 0.0
"He should have groupies." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4605.0 0.0 0.0 0.0
"So pancakes follow vectors? 


I promise you they do. ;)" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8785.0 0.0 0.0 0.0
"Why did we include the x=c in the continuity part ( |x-c|<delta), while the definition of limits does not include x=c (0<|x-c|<delta)?" smIcuRZybsA "Lecture 15: The Continuity of Sine and Cosine and the Many Discontinuities of Dirichlet's Function" "MIT 18.100A Real Analysis, Fall 2020" 11814.0 0.0 1.0 0.0
"colourful box changes all! " sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12662.0 0.0 0.0 0.0
"Love you sir from Kashmir" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7470.0 0.0 0.0 0.0
"Instead of writing ""Eg"" he writes ""Example"" 
.
DEDICATION LEVEL" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 6717.0 0.0 0.0 0.0
"auroux is great." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12483.0 0.0 0.0 0.0
"how did i end up here and why am i still watching it?
" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13216.0 0.0 0.0 0.0
"on 07:08, he doesn't seem to care about the dx. While there is an absence of dx is in the discrete setting, there is dx for every sum in our continuum. Does that not make the difference, becuase rather than have a continuum sum of infinitisemal f(x) we have a continuum sum of f(x)dx?  so it should be Ave(F'(x))(dx)(delta_X). Can anyone Clarify?" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14146.0 0.0 1.0 0.0
"It was fun watching this lecture. Thank you for posting this." sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6999.0 0.0 0.0 0.0
"@hellomate639 

I made that comment two years ago. Can you imagine me saying that aloud in a MIT classroom?? lmao. That's why I don't go there...

Believe it or not, I'm not that shallow. Don't judge my character based on that one comment. I'm teacher's assistant for a calculus lab at my university now. I have 23 students. lol." dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 1865.0 0.0 0.0 0.0
"uuuu the quality in this video is better than the another on the previous playlist" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 14988.0 0.0 0.0 0.0
"GUYS HOW DO I KNOW THE HOMEWORK?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 3979.0 0.0 0.0 0.0
"The benefits of learning from the person who wrote textbooks on the subject 🤔😀Awesome!!!!!!! He’s math lab—Awesome again😀😀😀 Where was this guy when I was taking Pre-Calculus 1 and 2!!!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 9990.0 0.0 0.0 0.0
"Thank you MIT OpenCourseWare..Prof. Strang is God, Not only MIT students the whole World deserves a great teacher like him.
A student from India" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 9133.0 0.0 0.0 0.0
"all of a sudden i'm heavily interested in linear algebra and math" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 12323.0 0.0 0.0 0.0
"An Indian edition of this book is available only in India
http://www.wellesleypublishers.com/buy.html" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 2424.0 0.0 0.0 0.0
"You still have that strong voice!!!! 
And WHY ARE YOU AGING????" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 12241.0 0.0 0.0 0.0
"Come to India and these things are taught in school 😁😁😁" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3169.0 0.0 0.0 0.0
"Believe me . Please upload all of the lecture you teach on campus. You are smarter when you do that because you will get the feedback and learn a lot" cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 2844.0 0.0 0.0 0.0
"i pay 1000€/year and need to learn a lot more than they teach on these videos... at least 1 thing is great in Portugal =) " YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13450.0 0.0 0.0 0.0
"@pedroissler This is fascinating, but can you elaborate on this further? Quantity and quality of what? Instruction? Research? Both? What human resources are they using or importing to make this happen and from where are they getting it? This is a great reply by the way." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1965.0 0.0 0.0 0.0
"The problem here is that he's using ""delta"" which they've already been thought to call the ""average"" in place of the ""d"" which they know as ""instantaneous"" rate of change." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10236.0 0.0 1.0 0.0
"I don't understand how some of these students still haven't learned determinants if they're MIT students taking multivariable calculus........" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5342.0 0.0 0.0 0.0
"38:46 not anymore ;)" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 1086.0 0.0 0.0 0.0
"Power series starts at 22:45" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8233.0 0.0 1.0 0.0
"If the speed were non-unity say w, the relation would have come out to be root(2-2cos wt)...no biggie" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6525.0 0.0 1.0 0.0
"En el minuto 3:08, dentro de la integral doble no debe decir ""curl F"" solamente (de ser así, esa sería una integral de flujo). Lo correcto es ""(curl F)·n"" donde n=(0,0,1) o ""(curl F)·k"", es decir, hacer el producto punto del rotacional del campo F con el vector normal al plano. Esa notación es mejor, puesto que es la que se usa después en el teorema de Stokes.

Mi punto es, no se realiza una integral de una función vectorial (Integral de flujo) sobre la superficie R, sino una integral de una función escalar, misma que proviene del producto punto del rotacional del campo (curl F) y el vector normal al plano: k.

Fuente: ""Cálculo de varias variables"", George Thomas.

https://www.dropbox.com/s/8b2bhta48jv34s3/Teorema%20de%20Green.png?dl=0" tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3565.0 0.0 1.0 0.0
"Is this his first time?" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 6874.0 0.0 0.0 0.0
"Awesome! I could watch the lectures over and over and each time, I gain a different and extra insight into the results and the process. Linear Algebra could turn into magic after you apply it’s theory—-the once dull computations of rows and columns. The most fascinating aspect of linear Algebra is when the entire matrix details unfold into a single effect, one that resembles the effect of simple scalars used in simple math formulas. Thanks to the fundamental concept of the Eigenvectors and Eigenvalues. Understanding the very essence of a matrix and what it does to any vector quantity (change in magnitude and direction) is the key concept to appreciating the underlying concept of various matrix decompositions. It all boils down to how many ways we could see the workings of a matrix in terms of its decomposed forms. The SVD composition is one of those decompositions of a matrix that allows a matrix to be seen as a sequential transformation of direction and magnitude in terms of some orthonormal basis characteristic of such matrix and its Eigenspace. Such a beauty!" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2781.0 0.0 0.0 0.0
"Best teacher I have ever seen." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2877.0 0.0 0.0 0.0
"Your work is appreciated Prof. Thank you very much." HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12265.0 0.0 0.0 0.0
"Great lecture!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 4259.0 0.0 0.0 0.0
"@phurt89 
im in victoria, school started last monday
" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1973.0 0.0 0.0 0.0
"He made a monica lewensky joke in there, that cracked me up." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 4575.0 0.0 0.0 0.0
"What a smart and humble person! Long live Prof. Strang!" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11430.0 0.0 0.0 0.0
"You can NOT define the derivative as the slope of the tangent line.  You have got it backwards.  The slope of the tangent line is equal to the value of the derivative, which value is defined by calculation." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12185.0 0.0 1.0 0.0
"I make the perfect brain" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5868.0 0.0 0.0 0.0
"Always got something great to listen to" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2330.0 0.0 0.0 0.0
"at 14:18, the energy can also so be EQUAL to 0 (not JUST bigger than 0)! Then does this not mean that the matrix is positive SEMI definite as opposed to positive definite?" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12414.0 0.0 1.0 0.0
"Splendid lecture." WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8871.0 0.0 0.0 0.0
"Although the lecture on determinants are great, in the beginning of math 18.06, DR. string seems disinterested in determinants. Determinants play an important part in solving linear equations." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 2329.0 0.0 0.0 0.0
"these lectures are excellent for indian students who learnt entire caclulus by byhearting formulas and now need to understand how everything works" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14779.0 0.0 0.0 0.0
"I agree, lovely teacher" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5027.0 0.0 0.0 0.0
"Wow, watching the expected payout be equal for both x and y was exhilarating. Fantastic lecture" feb9j65Iz4w "24. Linear Programming and Two-Person Games" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12079.0 0.0 0.0 0.0
FRONZ! PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3722.0 0.0 0.0 0.0
"Free physics preview! My favorite!" BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 3922.0 0.0 0.0 0.0
"Genius lecture ." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3995.0 0.0 0.0 0.0
"being a maths major student, and lucky enough this course we are taking this semester, this is really helping me Dr." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 12530.0 0.0 0.0 0.0
"thanks mit" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14592.0 0.0 0.0 0.0
"Very good explication !
Thanks from Italy 😊" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 11176.0 0.0 0.0 0.0
"The most amazing teacher" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10192.0 0.0 0.0 0.0
"Professor Strang said that the span of any vectors is the smallest subspace, I didnt quite get that. Would appreciate if anyone helps me on that regard, but nonetheless, this is a gem of a lecture, Thanks professor Strang." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 8362.0 0.0 1.0 0.0
"i am 17 i and know hat the porf just all said hahah :P" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13325.0 0.0 0.0 0.0
"david jerison" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12726.0 0.0 0.0 0.0
"This guy has figured out how to access the 12 dimension. Infinite chalkboards; some crazy wizardry shit." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 10511.0 1.0 0.0 0.0
"I would have applauded him at the end" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6257.0 0.0 0.0 0.0
"Thanks MIT you are doing a great job in  educating those who can't afford." 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9612.0 0.0 0.0 0.0
"at the end he says that the limit is equal ""1"" so how that equials to e^1 !? doesn't it supposed to be e^0 ?" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12476.0 0.0 1.0 0.0
35:50 vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 1019.0 0.0 0.0 0.0
"HAPPY  BDAY!" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4396.0 0.0 0.0 0.0
"GOAT Lectures as first course in probability" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 3971.0 0.0 0.0 0.0
"I am preparing to start an accelerated 1 month online single variable calculus class. Wish me luck." YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5130.0 0.0 0.0 0.0
"2) I felt (and again, this is my opinion), that he went too much into the intuition of the problem and not enough into the mechanics. I personally prefer to see the number crunching that goes on behind the scenes, and from there proceed to understand the holistic, intuitive story that's going on. Buzz words like ""combination of columns"" is too vague for me.

That being said, the lecture is freely distributed so I cannot complain. Thank you MIT for taking the time to make these videos." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 611.0 0.0 0.0 1.0
"44:40 the probability of x falling into the a interval is the integral of the density over this set" rLlZpnT02ZU "4. Parametric Inference (cont.) and Maximum Likelihood Estimation" "MIT 18.650 Statistics for Applications, Fall 2016" 1241.0 0.0 0.0 0.0
"this vdos made me laugh when I reviewed" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14920.0 0.0 0.0 0.0
"living legend  :-)" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13813.0 0.0 0.0 0.0
"Why dont mit upload more new videos?" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11857.0 0.0 0.0 0.0
"English ❤️" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3570.0 0.0 0.0 0.0
"@markkerollos I know that, chief.  But the rest of the country calls it ""Calc 1"" or ""Calc 2"", and people pretty much know what it is." aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1935.0 0.0 0.0 0.0
"Is this a lesson for the faculty of mathematics? " 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6851.0 0.0 0.0 0.0
"Love the Gilbert Strang ability to make linear algebra very illustrative and theorems so simple. One more time, thank you! )" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 7450.0 0.0 0.0 0.0
"the number of people watching this series decreases as the lecture progresses" mc1y8m9-hOM "22. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 14722.0 0.0 0.0 0.0
"The needle example is a great one that illustrates the usefulness of Statistics well :)" CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 10200.0 0.0 0.0 1.0
"Thanks to dear Prof Denis and of course MIT, wow I have completed another course for MIT" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9809.0 0.0 0.0 0.0
"The educational lead up to 40:07 ""We really have discussed the most fundamental algorithm for a system of equations.""" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 10082.0 0.0 0.0 0.0
"at 5:50 or so the student's question is why isn't [1/(b-a) * [integral from a to b] f(x)dx ] the average of F, not f, which is a good question.  Then he goes on to explain what an average is?  

Ironically I think the difference between a brilliantly effective professor and a very poor professor is minimal at MIT where the students are smart, because a brilliant professor challenges them legitimately and a poor professor requires them to self learn which ultimately are the same thing." Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12465.0 0.0 1.0 0.0
"Could you add Lecture 10 and 16 from this year (2017)?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3244.0 0.0 0.0 0.0
"tangent line? more like tangent lie" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14437.0 0.0 0.0 0.0
"@KanzakiGNT You mean (x^2 + ax + b)^3?
The easiest way would be to factor it (which will always work if you know complex numbers).

Without factoring, you'll probably get a great mess." HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1649.0 0.0 1.0 0.0
"Can anyone give me an example of a 'real-symmetric' matrix whose eigen value and singular value are not same..." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 3035.0 0.0 1.0 0.0
. 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 258.0 0.0 0.0 0.0
"My puny mind can't handle this matrix exponential thing." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 7783.0 0.0 0.0 0.0
"am i right that the 2nd row should be (right at the beginning)
0 -2 2
and not
0 2 -2
and consequently the 2nd multiplier is -2 not 2 (or we can add instead of subtract) which leads to
0 0 -5
?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12337.0 0.0 1.0 0.0
"Its good they still use blackboards, significantly better and easier to follow than the bland powerpoints we seem to get at my uni.." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7086.0 1.0 0.0 1.0
"damn it‘s hard" JTbZP0yt9qc "6. Maximum Likelihood Estimation (cont.) and the Method of Moments" "MIT 18.650 Statistics for Applications, Fall 2016" 12712.0 0.0 0.0 0.0
"Very nice of world class." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11211.0 0.0 0.0 0.0
"The point is that the parabola has an intrinsic length specified by its shape.
This length is the diameter of the horizontal slice containing the focus of the parabola.
The formula for the volume of the paraboloid is actually:
(Pi a^2 k)/2
where k is the length in the parabola, therefore a volume is obtained and the units match up.
The slim cauldron has k=1cm and the fat cauldron has k=1m.
This is why the volume of the fat cauldron is 100 times bigger." ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10229.0 0.0 0.0 0.0
"Wow, brilliant explanation of Moment of Inertia, far better than I got in physics." 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12067.0 0.0 0.0 0.0
"Thank you so much MIT and to both professors who taught me Calc 1! I can't even put a price tag on what these videos will help me achieve." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9352.0 0.0 0.0 0.0
Wow 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12017.0 0.0 0.0 0.0
"Question is..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8476.0 0.0 1.0 0.0
👏 yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 15717.0 0.0 0.0 0.0
"Learning the exact same thing as a high school senior" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7256.0 0.0 0.0 0.0
"I was with him right up until ""Hi, this is the first lecture...""" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6175.0 0.0 0.0 0.0
"learning linear algebra with you is like watching movies. it's fascinating, exciting, convincing and fun. thank you so much Professor Strang! Im so lucky to be learning this subject with you!" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 13766.0 0.0 0.0 0.0
"im a high school senior and i've known this =D" XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13563.0 0.0 0.0 0.0
"ALL of the terms between N and 1, which I substituted for the endpoints b and a, sorry tht was confusing. anyway, all the terms between there cancel out. and were left with just the terms at the end. " Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2178.0 0.0 0.0 0.0
"Most glaring thing about raising trigfunctions in powers is that the reciprocal (-1) is used as showing arcus-functions eg. inverse trigs, not reciprocal." XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7697.0 0.0 1.0 0.0
"@Voltar143 Not just the United States:  there's at least one very good maths lecturer - Dr Chris Tisdell - operating out of University of New South Wales in Australia, and there are plenty from elsewhere, but the US does indeed have quite a nice slab of teaching vids out there." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1755.0 0.0 0.0 0.0
"Who the hell is down-voting these videos? 😠" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11754.0 0.0 0.0 0.0
"@thePENANCE ha ha :)" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2037.0 0.0 0.0 0.0
"This is my favorite professor" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10694.0 0.0 0.0 0.0
"He is explaining as though he is discovering the answers for the questions for the very first time. If that’s not intuitive, then I don’t know what is. In the future when I become a professor I want to teach like him." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4513.0 0.0 0.0 0.0
"I was wondering if a semicircle is differentiable at x=+1. I would say no, since it becomes minus infinity." TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6176.0 0.0 1.0 0.0
"when finding an orthogonal vector, are there specific steps to find it, or do we have to find a vector (through inspection) which when multiplied by another vector through dot product is zero?" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 15203.0 0.0 1.0 0.0
"Statistics is replacing expectation with averages: frame it, get a tattoo, I don't care...
I'm sold." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8894.0 0.0 0.0 0.0
"sort of like solving sudoku, like it." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 14381.0 0.0 0.0 0.0
"Good observation, In Portugal we learned it using the proof ot the squezze theorem, and that is the correct way. I am actually a mathematician. the intuitive aproach used in the lesson only had the benefit of spare the students the intrincacy of point set topology in its basic sense.
" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4147.0 0.0 0.0 1.0
"Saludos desde México! Excellent lectures" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 8595.0 0.0 0.0 0.0
"That's really helpful!! Thanks!!" HIMxdWDLEK8 "18. Markov Chains III" "6.041 Probabilistic Systems Analysis and Applied Probability" 9935.0 0.0 0.0 0.0
"Thank you so much!!" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9389.0 0.0 0.0 0.0
"@SynthMelody The union is not a subspace. The union is bigger than P or L so it definitely can't be a subspace of either of them. and by adding a vector from P with a vector from U you can get to a point that is neither in P nor in U or in other words by adding two points from P∪L you can get to points outside of P∪L (somewhere in R³). But to form a subspace you have to be able to add any vectors from that subspace and the result has to be in that subspace." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 1735.0 0.0 1.0 0.0
"Eulers law is just beautiful ...." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 3580.0 0.0 0.0 0.0
"Guys i am just confused guy from india
Is this video old or what i mean is this upto time?
I have studied all these during my jee preparation even i didn't get into IIT but remembered all these
Look anybody please" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4390.0 0.0 0.0 0.0
"Gilbert is really good at teasing the next lecture. I have to force myself to stop watching so I can sleep." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 4039.0 0.0 0.0 0.0
"he is the best professor i know" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13102.0 0.0 0.0 0.0
"Looks like Thomas Gore and Stephen Colbert merged into a mathematician." -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7422.0 0.0 0.0 0.0
"Cover up method is common way that evaluate 2 constants and spent about 5 minutes long. But I use half cover up method to evaluate one constant and another constant by analysis, so it just spent about 10 seconds only. If professor interested it, I'd like share with you. I created many SC of PF, that let many PF from complicated getting to easier and simple." HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3254.0 0.0 0.0 0.0
"Thank you so much for your hard work." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9376.0 0.0 0.0 0.0
"For the acceptance problem for CFGs, why can't we make Da-cfg simulate the equivalent pushdown automaton of the CFG?" 4MgN6uxd4i4 "7. Decision Problems for Automata and Grammars" "MIT 18.404J Theory of Computation, Fall 2020" 3882.0 0.0 1.0 0.0
"At 20:29, why does x0-(x0+deltaX) simplify to -deltaX? Shouldn't x0 - x0 equal 0, and adding 0 to deltaX = deltaX?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2605.0 0.0 1.0 0.0
"well explained, thank you very much professor" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15088.0 0.0 0.0 0.0
"""A random variable is not random. It's not a variable. It's just a function from the sample space to the real numbers."" Good stuff!" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 24.0 0.0 0.0 0.0
"This is for those people who don't know why the Permutations is 6 or 24 at the end. You should check out the Discrete Math 1 playlist on the youtube. 

You can also see my explanation if it helps you. Let's say there are 3 seats and 3 people. How many ways  of Permutations we can have. For the 1st person, there are 3 ways to letting him choose because there are three seats. After, the 1st person seated on of the 3 seats, there are two seats for the second person. so on... it will be 3 factor, which 3!. 3x2x1=6. You have 3 rows and 3 row operations, and this is just like the Permutations of 3 seats for 3 people." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 10664.0 0.0 1.0 1.0
"Or five 9:32" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 8134.0 0.0 0.0 0.0
"is this for 1st year undergrad? O.o" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13662.0 0.0 0.0 0.0
"I don't understund the laught at the end of the lecture. Seems like have appeared something in the board. I don't know. Perhaps is for my english. XD" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5359.0 1.0 0.0 0.0
"Amazing professor'e last minutes made its count" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2390.0 0.0 0.0 0.0
"I'm a student in Ariel University at Israel. I'm studying computer science and math, and I just want to say that you are a terrific teacher!
I will recommend your lectures to my friends for sure!
Thank you a lot." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6302.0 0.0 0.0 0.0
"easy. All they have to do is to have three lectures per week over perhaps 13 weeks (3 months) plus a bit more and you have 40. Yes that generally means that a freshman will have many hours of lectures per week across all subjects. Heavy workload." BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12790.0 0.0 0.0 0.0
"A work of art." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2169.0 0.0 0.0 0.0
"My godness, stop moving the camera :<" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 7756.0 1.0 0.0 0.0
"Agreed, you will need some background in statistics and calculus to follow. But if you have the pre-requisites this is excellent" TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 2275.0 0.0 0.0 0.0
"Thank you MIT and Gilbert Strang for the course. Very useful" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9134.0 0.0 0.0 0.0
"Only dummies will dislike this video" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 8119.0 0.0 0.0 0.0
"Pauli Spin Matrices
http://mathworld.wolfram.com/PauliMatrices.html

These are fun." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 8158.0 0.0 0.0 0.0
"Thank you sir for your lecture, why are we going to matrix form in order to solve equations" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9332.0 0.0 1.0 0.0
"The biggest takeaway from this class, besides how to guess the vector that makes the equations equal, is how to do math. Out of all of my math teachers, only Prof. Strang taught me this." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 10016.0 0.0 0.0 0.0
"Everything ok sir it is being thought during my school but where to use or apply this maths in sceintific or commuter making softwares." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 3616.0 0.0 0.0 0.0
"Great video. Must view video to understand Counting.. Thank you guys" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 4360.0 0.0 0.0 0.0
"Pretty easy material but I think the professor makes it harder than it really is. " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8248.0 0.0 0.0 0.0
"So much better than my prof" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 8775.0 0.0 0.0 0.0
"Love Story starts Just before General Strategy." twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7433.0 0.0 0.0 0.0
"Someone said they didn't know the law of cosines, then there is another question, ""how did they get into MIT?""" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8840.0 0.0 0.0 0.0
"If you guys don't understand why ds/dt = |v|  i.e. the arc length thing, go watch the arc length videos from 18.01 Prof. Jerison explains it much much better." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6545.0 0.0 0.0 1.0
"Great thnx from India!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4348.0 0.0 0.0 0.0
"This is my favorite lecture" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 10693.0 0.0 0.0 0.0
"Thank you very much MIT for these free lectures." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9431.0 0.0 0.0 0.0
"....a huge lecture hall..but the instructor has to use chalkboard to write notes!!!" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 266.0 1.0 0.0 0.0
"12:38 is it because regular language also CFL?" IycOPFmEQk8 "5. CF Pumping Lemma, Turing Machines" "MIT 18.404J Theory of Computation, Fall 2020" 397.0 0.0 1.0 0.0
"A query, when Dr Strang, l assuming he has a PhD, expalains the row multiplication, isn't the resultant matrix a 1x3, so that its 1x row1, 2xrow2, 7xrow.. could someone clarify please." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2148.0 0.0 1.0 0.0
"my left ear is pleased now" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13989.0 0.0 0.0 0.0
"My left ear is finally being educated" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7768.0 0.0 0.0 0.0
"Dont have money for book on amazon, how can i download it to solve the part 1 problem sets?" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3486.0 0.0 1.0 0.0
"Is matrix mean different from E[estimator]? Because i didnt know you had to multiply by the number of samples" z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6799.0 0.0 1.0 0.0
"I Really Like The Video Multiplication and Inverse Matrices From Your" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4989.0 0.0 0.0 0.0
"Very clear lecture. Awesome job.
" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 11164.0 0.0 0.0 0.0
"thank you" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 14470.0 0.0 0.0 0.0
38:30 eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1078.0 0.0 0.0 0.0
28:18 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 834.0 0.0 0.0 0.0
"48:06  How does he know that the transformation matrix A must be a 2x3 matrix?" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1290.0 0.0 1.0 0.0
"Gilbert Strang is too complicated.  Simply graph out the lines by the slope and y intercept method and see where they cross if they do." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 4028.0 0.0 0.0 0.0
"I have some small issue about the Jacobian. Why do we even need to take the absolute value of the determinant? In single variable case, the derivative can similarly be thought of as the ""exchange rate"" for the dx to du if we change variables and in the sense similar to the Jacobian but in there even if the detivative is negative we don't take absolute values. But why should we take absolute values in the Jacobian determinant case?" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5558.0 0.0 1.0 0.0
"I switched from engineering to math/physics during college, and so was taught linear algebra with and without coordinates.  One course, entirely with matrices.  Another course almost entirely without matrices.  What a beautiful topic." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5987.0 0.0 0.0 1.0
"47:20 see you mondy :)" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1280.0 0.0 0.0 0.0
"I'm so excited for this!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6372.0 0.0 0.0 0.0
"i enjoyed this seminar very much. from the very beginning there was a crescendo building towards the end where the climax had arrived and the meaning of e and ln were understood." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13372.0 0.0 0.0 0.0
"Check out math for computer science fall 2010 MIT operncourseware. Reading number 9, its gives a detailed explanation of this concept. As an aside ""trust me i solved this problem in my physics class"" isn't a proof :)." wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3145.0 0.0 0.0 0.0
"where is note? i cannot find. is it in https://ocw.mit.edu/18-065S18 ? he keeps mentioning about note that things he passed is in there" Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15239.0 0.0 0.0 0.0
"Is the answer in the probability task 5/32 ?" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6808.0 0.0 1.0 0.0
"Thx  Gilbert Strang and MIT for share this. Ok, ready for the trip! Lets goo" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11004.0 0.0 0.0 0.0
"IF { he continues to write letters that big     AS he gives the lecture

THEN he's not gonna fit very much onto that blackboard." MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6445.0 1.0 0.0 0.0
"very helpful for self-study also." tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15016.0 0.0 0.0 0.0
"what is his name `?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15156.0 0.0 0.0 0.0
"Sir Gilbert Strang just blew my mind!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8691.0 0.0 0.0 0.0
"Second best part about watching these lectures is the comment section" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 8608.0 0.0 0.0 0.0
"25:10 it is NOT a toin coss" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 767.0 0.0 1.0 0.0
"5:26, he said he is going to subtract, how is 3(2) - 8 = 2 and how is 3(1) - 1 = -2?? 

It should be -2 and 2 respectively " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1362.0 0.0 1.0 0.0
"It must be something students learn during their first year... the MIT is prestigious, it can't be that basic.. " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6979.0 0.0 0.0 0.0
"he is 70 here and has that hair" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13084.0 0.0 0.0 0.0
"At 25:03 the row rank of the matrix can be found by converting the matrix A in echolon form. The reduced matrix will look like this
 1 0 1
 0 1 1
 0 0 0" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2623.0 0.0 1.0 0.0
"When he uses those glasses he looks so kawai :3" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 11627.0 0.0 0.0 0.0
"16:35 — timestamp for beginning of Work and Line Integrals" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 483.0 0.0 0.0 0.0
"Amazing. This man is  a real genius. Thanks MIT." 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 2407.0 0.0 0.0 0.0
"https://www.youtube.com/channel/UCkuYW-AoSOiZ6pvQOwrCKQQ
Please subscribe my channel" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13268.0 0.0 0.0 0.0
"Wish I'd seen this earlier. Guess this is what I'll be doing with my summer!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11958.0 0.0 0.0 0.0
"Thank you !!!!" P3tGiT72APw "14. Graph limits I: introduction" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 9091.0 0.0 0.0 0.0
"I think he's actually not very sympathetic with students but he masters the subject and I find his explanations very enlightening, and hear him increases my knowledge and understanding a lot." TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6020.0 0.0 0.0 0.0
"Simply excellent this professor is" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8665.0 0.0 0.0 0.0
"This cameraman... Stop zooming and show me the whole board instead." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10471.0 1.0 0.0 0.0
"Good Job professor" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4120.0 0.0 0.0 0.0
"Thank you 💞💞💞💞💞 ocw ocw" 3PzuSPQPEU4 "8. Undecidability" "MIT 18.404J Theory of Computation, Fall 2020" 9460.0 0.0 0.0 0.0
"The example is totally wrong. If the blocks are not stuck together the bottom block has not to be considered, as for the center of mass, and the max distance that can be reached is twice the length of a block." wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10095.0 0.0 1.0 0.0
"now doubt sir you are the blessing for mathematicians and also for related to this field,i often enjoy your lectures  in my vocations" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 14088.0 0.0 0.0 0.0
"""vectors from the space formed by independent eigen vectors of original matrix A == eigen  vectors themselves for some similar matrices to A (with same eigen values)""? Is this statement true or false? 42:24" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 187.0 0.0 1.0 0.0
"F will have the same number of rows as I, but maybe not the same number of columns. So to make N, you just put -F on top and fill in the bottom with the identity matrix of the correct size (the number of columns of F). So say I is m by m and F is m by n, then N will have (m + n) rows and R will have (m + n) columns, so it works out. And each block multiplication (I * -F and F * I) also work out." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 3717.0 0.0 0.0 0.0
"perhaps prof jerison is dyslexic? he's a brilliant professor either way." HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14180.0 0.0 0.0 0.0
"Let's take out a moment of Appreciation for the camera man👏👏" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7339.0 1.0 0.0 0.0
coughing dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 12683.0 0.0 0.0 0.0
"Truly awesome instructor. Fantastic!" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11093.0 0.0 0.0 0.0
"@PlushChronicles calling the students ""those idiots"" is pushing it. You have to know a little bit more than just ""getting a first intro lecture"" to get into MIT. :)" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1703.0 0.0 0.0 0.0
"I can see in the class of this excellent professor and mathematician what the real problem in mathematical education is: our obsession to cover the topics always skips the necessity of the students to form the proper intuition of a topic. Intuition takes time, but above all takes proper activities to develop it. His talk is basically about the generation of spaces through linear combinations, but honestly could anyone sitting down there and listening reproduce those ideas without the help of proper representations, say, software, or at least good pictures? In mathematics, physics etc, intuition is the most important, but scholastic education has always tortured them with logic. That is totally unfair and a waste of talented students." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5197.0 0.0 0.0 1.0
"Thank you MIT" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9118.0 0.0 0.0 0.0
"I think B_j should be A transpose replaced by b 24:16" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 5993.0 0.0 1.0 0.0
"18:22 felt like teleportation :D" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 535.0 0.0 0.0 0.0
"It's like I have learned the philosophy of linear algebra, and now my conscience is at a higher state. I had such a great time. Thank you sir 🙏. Thank you ocw👍." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 7056.0 0.0 0.0 0.0
"1:49 Sometimes I watch his classes several times to make things settle in my mind, but sometimes just because I want to enjoy the humor." UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 602.0 0.0 0.0 1.0
"11:26 Thinking back to last lecture
if the first pivot was a 0
then the first and 3rd equations would be on the same plane 
and then there wouldnt be a b value for every point on the Row graph?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 374.0 0.0 1.0 0.0
"His book seams very good as well." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4742.0 0.0 0.0 0.0
"Thank you Professor Gilbert Strang for your awesome presentation ,  got inspired to be faculty." or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9209.0 0.0 0.0 0.0
"Hope we become neighbors in heaven Mr Strang." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 4788.0 0.0 0.0 0.0
"Hats off!! thanks prof. Strang." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4443.0 0.0 0.0 0.0
"Why the Total Variation distance between P theta and P theta prime is one half of the sum? Where this one half comes from? (Min 42:32)" rLlZpnT02ZU "4. Parametric Inference (cont.) and Maximum Likelihood Estimation" "MIT 18.650 Statistics for Applications, Fall 2016" 11916.0 0.0 1.0 0.0
"At 49:30 can someone please explain me how in matrix -b and -k came, I tried hard but couldn't understood, or am I missing some sort of pre requisite here?" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 2686.0 0.0 1.0 0.0
"Professor is great... Camera man sucks. I need to watch the chalk board.. Not the professor." CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8394.0 1.0 0.0 0.0
"this man is great teacher every lecture he did is really a great piece of Art" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 14903.0 0.0 0.0 0.0
"INDIANS 🇮🇳 🇮🇳 🇮🇳   OP😎" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6449.0 0.0 0.0 0.0
"r serious ? you love math?!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14242.0 0.0 0.0 0.0
"I'm so happy to see you here. I only trust you when it comes to lecture" wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6377.0 0.0 0.0 0.0
"I've noticed them since I've watched the 4th lecture ..I think its some sort of computer generated comments someone at MIT is using. But to whaat end m not sure. Creepy shit" XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6427.0 0.0 0.0 0.0
"confusing name of the lecture." ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12668.0 0.0 0.0 0.0
"As an avid Rick and Morty fan (200 IQ.) i thought id visit calculus videos to see if the profs were doing a good job." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2568.0 0.0 0.0 0.0
"51:46 he probably meant ""this plus that"" instead of ""this plus that""." jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 1344.0 0.0 1.0 0.0
"great lecture" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12975.0 0.0 0.0 0.0
"@Alyosha Karamazov lol you are so right lol" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1582.0 0.0 0.0 0.0
"could I go through this course without watching the linear algebra course?
Or should I start with linear algebra first?" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12684.0 0.0 0.0 0.0
"25:56  ""I'm a happier person now."" I love his interludes. Thank you, professor, a lot." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 790.0 0.0 0.0 0.0
"It is very nice activity to learn from an old man as Strang. Thank very much Prof. Strang for  all services such as your physical energy, your smartbrain  and sacrifice. By  watching these videos, I learn a lot things and I decide to follow Prof. Strang." 2K7CvGnebO0 "19. Saddle Points Continued, Maxmin Principle" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6971.0 0.0 0.0 0.0
"People from all around the globe is covering the intellectual need of USA.
  " bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8168.0 0.0 0.0 0.0
"der bass muss ficken" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 12734.0 0.0 0.0 0.0
"37:40 Wrong assumption, one of the lengths of the vectors can be 0, in which case angle isn't defined and even though it's perpendicular(by definition of euclidean spaces if I remember correctly) you can't deduce cos theta is 0 from that." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1069.0 0.0 1.0 0.0
"What took MIT so long to post past Lecture 12. Thank for the recent uploads MIT, but don't slack on us now, please post the other Single Variable Courses IMMEDIATELY. I love these videos." sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11563.0 0.0 0.0 0.0
"I feel that Khan Academy's way of explaining double integral seems clearer to me" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5402.0 0.0 0.0 0.0
"37:18   
That's what she said" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1061.0 0.0 0.0 0.0
"well I don't think A' has an inverse. so you can't backtrack from eq 2 to eq 1" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 15083.0 0.0 1.0 0.0
"
Excelent!! :P" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4.0 0.0 0.0 0.0
Excelent... J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3622.0 0.0 0.0 0.0
"An abbreviation is a shortening of a word or a phrase. An acronym is an abbreviation that forms a word. An initialism is an abbreviation that uses the first letter of each word in the phrase (thus, some but not all initialisms are acronyms)." OHiu2F18dFA "Lecture 7: Sigma Algebras" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 2432.0 0.0 0.0 0.0
"professor was wrong on solving function (3x-x exp 3) at time 38 and above" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14221.0 0.0 1.0 0.0
"8:35 isn't this wrong? the graphs doesn't match, so it can't be equal. 
Graph for  (1 + 1/ x) /  (1 + 2 / x) https://www.google.com/search?q=grah+%281+%2B+1%2F+x%29%2F++%281+%2B+2+%2F+x%29&sxsrf=ALeKk00LvcAzRnSK-mywIEQGsNryImE0zg%3A1618115267380&ei=w3pyYMLEFviJ9u8PivSKkAE&oq=grah+%281+%2B+1%2F+x%29%2F++%281+%2B+2+%2F+x%29&gs_lcp=Cgdnd3Mtd2l6EAM6BwgAEEcQsANQ5uoKWObqCmCd7ApoAXABeACAAWWIAa0BkgEDMS4xmAEAoAEBqgEHZ3dzLXdpesgBCMABAQ&sclient=gws-wiz&ved=0ahUKEwiCst6NrfXvAhX4hP0HHQq6AhIQ4dUDCA0&uact=5

Graph for 1 + x / 2 + x https://www.google.com/search?q=grah+x+%2B+1%2F+x+%2B+2&oq=grah+x+%2B+1%2F+x+%2B+2&aqs=chrome..69i57j0i22i30l7j0i8i13i30l2.4521j1j7&sourceid=chrome&ie=UTF-8" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1422.0 0.0 1.0 0.0
"I'm new to math but isn't Euler's formula e^ix = cosx + isinx,
I can't see how the equations with nodes and edges relate to the formula.." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6349.0 0.0 0.0 0.0
"A healthy society uses the generated wealth to improve itself, to improve the living standards, the education people gets, etc.. but your society is a sick one, and sadly that sickness is spreading everywhere as mcdonalds did, stop being such fools and wake up, you don't have middle class anymore, middle class is by definition people who can afford a more or less normal life WITHOUT being heavily indebted and being slaves of that debt. " YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2125.0 0.0 0.0 0.0
"he has very neat hand writing." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13083.0 0.0 0.0 0.0
"its at 15:25 actually" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13704.0 0.0 0.0 0.0
"@shuffledream nope, maybe a bit too late but he did mean tangent. take a look at the first example he did ~18mins. The vector field is parallel to the normal but the answer isn't zero.
and any 2 perpendicular vector dot each other would give zero, so that should explain 14:27 as well" phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2013.0 0.0 1.0 0.0
Test C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 9032.0 0.0 0.0 0.0
21:52 FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 687.0 0.0 0.0 0.0
"I like how well he is trying to give us those intuitions" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 5673.0 0.0 0.0 1.0
"Beautiful lecture, just beautiful. Prof. Strang is drawing the beauty of Linear Algebra on a blackboard." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 2821.0 1.0 0.0 0.0
"if the gods give everyone a boost of 10cm... lolll we have a true champ here." 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 13541.0 0.0 0.0 0.0
"Just I have wondered. Are they student of MIT? Why are they so silent??????" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7152.0 0.0 0.0 0.0
"True I remember learning this in 9th grade in algebra 2. Didn't learn cross product or having to compute det/inv of 3x3 matrix" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11087.0 0.0 0.0 0.0
"I used Professor Strang's Linear Algebra book in 1981.  I wish there a way to ask the questions I have about the material.  There's one question in particular that I have that keeps bugging me.  If anyone knows how and where I can ask my question, please let me know." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6125.0 0.0 0.0 0.0
"""unless you have one of those fancy cars with the GPS"" - this lecture will be funny in some years" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 186.0 0.0 0.0 0.0
"Just finished 18.01. Thank you so much, Prof. Jerison and MIT OCW for this gift to the world. Manila, Philippines (2020/03/08)" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7164.0 0.0 0.0 0.0
"Is the sound echoing because the prof is teaching in god mode?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6815.0 0.0 0.0 0.0
"I laughed out loud at the corn field metaphor" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5645.0 0.0 0.0 0.0
"I know that chalk..." bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 5638.0 0.0 0.0 0.0
"@IntegrateUs dude it doesn't matter, most likely if you go to MIT, you're going to be making a ton of money.
A ton of money=Unlimited women" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1642.0 0.0 0.0 0.0
Brilliant 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 2920.0 0.0 0.0 0.0
"I think you ment restricting f(x) = sin(x)/x between f(x) = cos(x) and f(x) = 1." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6083.0 0.0 1.0 0.0
25:48 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 788.0 0.0 0.0 0.0
"I love youuuuuuuuu ❤️❤️❤️❤️❤️❤️🙏🙏🙏🙏🙏🙏" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5855.0 0.0 0.0 0.0
"What’s going on here?" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 11598.0 0.0 0.0 0.0
"Can the ideas of linear approximation be extended infinitely to develop the taylor series for e^x and sin(x) and cos(x)?" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3107.0 0.0 1.0 0.0
"Is it me or lectures are getting tougher day by day" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 6790.0 0.0 0.0 0.0
"O wold like to know the MIT’S Building o the buildin school." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7967.0 0.0 0.0 0.0
"Thank you Professor Auroux for your teaching, and MIT OCW for making this available! I really enjoyed this class. Now I'm ready for 18.03, 8.01, and 8.02 :)." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9205.0 0.0 0.0 0.0
"This guy can teach. He is not pretentious, and is not afraid to explain the algebra behind the calculations. I remember my freshman calculus course. If you forgot any of the algebra basics there was a lot of uncomfortable silence." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10506.0 0.0 0.0 1.0
"what's the diference between this course and 6.041? if i try to understand 18.650 wich of them should i see?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 15193.0 0.0 0.0 0.0
"People like Gilbert Strang are a gift for the entire world. They advance the progress of civilizatio by hundreds of years in their lifetime through sheer dedication and genius, while being humble enough to impart that vast amount of knowledge to students in a lingo that they understand." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8169.0 0.0 0.0 0.0
"Thank you sir" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9329.0 0.0 0.0 0.0
"@supertincho18 in italy we do that in highschool...and i did that in highschool too while i was in the US... i guess it just depends... but if it's a beginning class..maybe it's better to start from the beginning." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2031.0 0.0 0.0 0.0
"That dora cake tho.." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9882.0 0.0 0.0 0.0
"is he french? his accent is so funny" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 13631.0 0.0 0.0 0.0
"Where did he use in the proof of the calculation formula for directional derivative that u must be unit vector? Thank you" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 11673.0 0.0 1.0 0.0
"Is this really MIT? sin (a + b) = sin a . cos b.... REALLY????" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6878.0 0.0 1.0 0.0
"""I'm coming"" - Mr. Cognitive Decline
""Not today"" - Dr. Strang" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 65.0 0.0 0.0 0.0
"When taping a lecture, keep the camera on the board, not the professor. Lesson of the day.
" CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11633.0 1.0 0.0 0.0
"Thank you Gilbert Strang. I remember when I was an undergraduate in 2010 and studying linear algebra. I didn't understand anything going on, and found your videos on MIT open courseware. Not only did you get me to understand linear algebra, but your lectures sparked my interest in math. I decided to become a math major after the course. Now it is 12 years later and I am again taking a matrix theory course for my part time graduate degree and again are using your videos. Thank you again for everything you have done for us, people who never stepped foot on MIT. Your impact on the world is enormous and your contributions should be appreciated!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9112.0 0.0 0.0 0.0
"close packing order with density as a function of particle in 3 dimensional space is my forte. nice example" ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12659.0 0.0 0.0 0.0
"Exellent work by the Prof... for those like ME who are LOST...This can help clarify a bit : https://youtu.be/KsqmAJ7Qyf8" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3702.0 0.0 0.0 0.0
"Thanks a million professor Strang and thank you MIT for your generosity. God bless. I'll be taking this course in July and i'm confident of passing." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9671.0 0.0 0.0 0.0
"Linear Algebra = Useless fake math in the dream world.
Pre-calc + Calc = real life math. " 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 7369.0 0.0 0.0 0.0
"Great lecture! Thx" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4272.0 0.0 0.0 0.0
"ƒ'(x) isn't Newton's notation. It's Lagrange's." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15542.0 0.0 1.0 0.0
"Very good lecture, thanks professor" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11180.0 0.0 0.0 0.0
33:28 mlPLLXHZ8_U "Lecture 4: The Characterization of the Real Numbers" "MIT 18.100A Real Analysis, Fall 2020" 959.0 0.0 0.0 0.0
"MIT OCW, I believe there are a couple typos in the copy of the Unit 4 Exam included on the course website, as the problems given differ from those to which the answer is given in the solutions sheet, specifically for problems #3 and #6a on aforementioned Unit 4 examination." PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7506.0 0.0 0.0 0.0
"Yay! I just finished this in school holiday! (my single most productive holiday ever) But ouch I havent taken the final exam yet :s" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12114.0 0.0 0.0 0.0
"@AnimeASK nvm it was in the next lesson :p 
sry about that" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1584.0 0.0 0.0 0.0
"Excellent Prof!!! ElGrecoProf++" Tx7zzD4aeiA "20. Central Limit Theorem" "6.041 Probabilistic Systems Analysis and Applied Probability" 3631.0 0.0 0.0 0.0
"I think I am too lazy to use this. Probably will just use mv calculus. Great subject anyway and a very nice intuition to have." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 5995.0 0.0 0.0 0.0
"God bless him, he is amazing really" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4080.0 0.0 0.0 0.0
"한 걸음 내딛을 때마다 지식만이 아니라 흥미까지 차오르는 강의였습니다. 한 학기 동안 정말 감사했습니다, 스트랭 교수님.

Not only were these lectures intellectually pleasing, but they also showed me the beauty of linear algebra itself. Thank you again, Professor Strang." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 15692.0 0.0 0.0 0.0
"Can t understand the binomial expansion" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3105.0 0.0 1.0 0.0
"Wow, super clear! Really enjoy the lecture" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 12073.0 0.0 0.0 0.0
"This is just an introductory course to make sure everyone has the exact same foundation for more difficult courses later on. Keep in mind that this is also known as Calculus I and every university, from the smallest to biggest, teaches the same basics as everyone else." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10682.0 0.0 0.0 0.0
"can anyone provide me notes" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 12611.0 0.0 0.0 0.0
"How is it possible that some people were taking this course on MIT and still didn't know about the law of cossines or even vector addition???" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4870.0 0.0 0.0 0.0
"Damn his handwriting is very pretty" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3295.0 0.0 0.0 0.0
".' .░░░💕*so much thankful to M.I.T and you all kindness; beautiful courses.'" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 259.0 0.0 0.0 0.0
"what a smart camera man!" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15113.0 1.0 0.0 0.0
"A toin coss😂" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 2161.0 0.0 0.0 0.0
"which books do they follow??" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 15251.0 0.0 1.0 0.0
"@rinwhr He subtracted 3 x row 1 ""from ""row 2. That is 8 - 3(2)  = 2; 1 - 3(1) = -2. 

An easier way to think about it instead is multiply row 1 by -3 and add it to row 2. People find it easier to add instead of subtract when negative numbers come haha. " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1990.0 0.0 0.0 1.0
"@KatherineRogers Second: If we take “a” as the height of the figure, then the equation would be V= (pi/2)h*a, (remember that height is NOT unit squared). We could also write “a” as “x”(or radius) squared, so the final equation would be V=(pi/2)h*r^2 which won’t have any problem with units. I hope I made myself clear." ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1652.0 0.0 0.0 0.0
"Thank you MIT for enabling us enjoy these treats.. And Prof. Strang is just pure genius" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9142.0 0.0 0.0 0.0
"I love these lectures" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5795.0 0.0 0.0 0.0
"Love you Professor. You are such an adorable person and a great great teacher!" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 7465.0 0.0 0.0 0.0
"@EssexPN This is just my guess, but I imagine this course is geared towards engineering and science majors at MIT, not math majors. Or at least I hope! Because I goto a small liberal arts college no one has ever heard of, and my linear algebra course was much more rigorous than this. All theory and proofs. No applications. Which I didn't mind. :)" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 1619.0 0.0 0.0 1.0
"18:30 is the time when they should applaud. They didn't!" PnPIqh7Frlw "Lec 24: Simply connected regions; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 540.0 0.0 0.0 0.0
"oh.my.god. he is just TOO PRECIOUS!!!!!
every time he starts with his way too excited ""OK!"" I actually get excited too :)
Thanks Dr. Strang!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 14121.0 0.0 0.0 0.0
"44:18 ""¿"" xD" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1232.0 0.0 0.0 0.0
"I am very happy wondering why people keep being happy about the video - Inderminate forms - L'Hospital's rule" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5152.0 0.0 0.0 0.0
"Who is the professor?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11742.0 0.0 0.0 0.0
"In math doesn't exist a geometric proof" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6642.0 0.0 0.0 0.0
"tq MIT and  G.Strang" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 14957.0 0.0 0.0 0.0
"I bought the book Linear Algebra and Learning from Data, it is used as the course notes for the course series . I could borrow it from my university library for free, but I really think it is a book worth keeping and I want to show my respect to Dr. Strang for sharing his wisdom selflessly, thank you professor." sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5178.0 0.0 0.0 0.0
"I think we can assume the probability of individual points in continuous sample space as epsilon which is infinitely small but when add it turns out to be 1 without sacrificing the math/probability" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 6080.0 0.0 0.0 0.0
"at 47:53 omg left bottom corner: hooded ""A"" taking a class at MIT! that explains everything!" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 12459.0 1.0 0.0 0.0
"Thank you very much prof Strang. (Respectful greetings from Guatemala (Central America))" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9445.0 0.0 0.0 0.0
"and Why they are writing so big? :-P" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12365.0 0.0 0.0 0.0
"Funnily I am watching this on a 4:3 monitor and I love it." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 3955.0 0.0 0.0 0.0
"Was lecture 34 a test? Is that why it is missing?" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11276.0 0.0 0.0 0.0
"God bless MIT!" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4076.0 0.0 0.0 0.0
"Kinda sucks they couldn't film an actual class with students" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 7216.0 1.0 0.0 0.0
"Nice shirt!" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7855.0 0.0 0.0 0.0
"Thanks MIT. Really useful for me, my team of teachers and students. We are not only learning calculus but also how to teach it to our kids. Prof is down to earth, humble and going to great length explaining the topic. I have a new perspective on teaching after viewing these five lectures. Thanks again!!!!!! You're transforming lives." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9620.0 0.0 0.0 1.0
"Arre kehna kya chahte ho" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 2559.0 0.0 0.0 0.0
"Hi friends,

Can someone please clarify below 2 doubts, please 

1. What does those junk terms exactly look like? One example string would be good

2. Why did prof didn’t substitute with x0 in last calculation 

Thank You very much in advance 🙏🏻" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4710.0 0.0 1.0 0.0
"Great lecture! I have enjoyed it; thanks." C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 4266.0 0.0 0.0 0.0
"19:00 Proof by mathematical induction.
41:41 Pumping lemma." KAySmSEGc9U "3. Regular Pumping Lemma, Conversion of FA to Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 550.0 0.0 0.0 0.0
"This was a fantastic course! Thank you very much!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 10962.0 0.0 0.0 0.0
"how is 27:55 2 dimesional ?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 13231.0 0.0 1.0 0.0
"Awesome........Thanks MIT :)" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2789.0 0.0 0.0 0.0
"21:25 Why are people laughing?" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 678.0 0.0 0.0 0.0
"If I wasn't doing his 18.085/ 18.086 course I'd be doing this." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6475.0 0.0 0.0 0.0
"9:00: ""That's what to remember from this lecture...""
Me: ""Ight boys n gals. We can skip to the next lecture""" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 1434.0 0.0 0.0 0.0
"42:13 Did someone just applaud? Lol" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1174.0 0.0 0.0 0.0
"Prof. Strang is such a good teacher.  Awesome." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8308.0 0.0 0.0 0.0
"I am in 8 standard but i learn whole calculus through mit lectures" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5107.0 0.0 0.0 0.0
"I Really Like The Video From Your Final review." ZwpwmGP5ITM "Lec 34: Final review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4956.0 0.0 0.0 0.0
"What textbook do they use for MIT calculus?" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 11553.0 0.0 1.0 0.0
"This is great. This guy is soo much better than my teacher and much more enthusiastic." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10669.0 0.0 0.0 0.0
👍👏👍👏👍 cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 15716.0 0.0 0.0 0.0
"@HD4WG This is Calc 2. Your argument is invalid." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1627.0 0.0 0.0 0.0
"Will we have later in the course any explanation of the 9 dimensions example? I didn't get it well although he's a master, a great Professor really." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11953.0 0.0 1.0 0.0
"MIT, thanks you!" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 7555.0 0.0 0.0 0.0
"Does anyone realise that he sometimes try to add humour to his lectures?" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3448.0 0.0 0.0 0.0
"Every time he says 'i claim' I say thanks MIT for such beautiful lectures from a great teacher " BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3605.0 0.0 0.0 0.0
"I can not admit he is a good teacher." PnDtMfyZSIE "Lecture 6: The Uncountability of the Real Numbers" "MIT 18.100A Real Analysis, Fall 2020" 5193.0 0.0 0.0 0.0
"i don't know... i only just now finished week 6. and i'm like fuck, 35 weeks, it's going to take me months to finish this." eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13365.0 0.0 0.0 0.0
"There are 10 types of people in the world: those who understand hexadecimal and F... the rest." wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 10344.0 0.0 0.0 0.0
"its a pitty that he didnt explained what happens above two (independent) variables, since you cant use the second derivatives test there.

there's a method involving taylor polynomial but i didnt get it well from the book

thanks anyways, these videos are REALLY usefull for donkeys reading math books like me." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13702.0 0.0 1.0 1.0
"you have changed my life Dr. Strang!" Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15506.0 0.0 0.0 0.0
"so the apple dose fall farther from  the tree''s  original point  ,lol " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14345.0 0.0 0.0 0.0
"Amazing professor" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2387.0 0.0 0.0 0.0
"Two methods can be used to calculate the total resistance of the parallel circuit. They are the Product Over Sum equation or the Reciprocal Formula. Sumequation as we only have two parallel resistors. Theparallel resistors must be reduced to a single series value before being added to the series resistor." Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11104.0 0.0 1.0 0.0
"when this lecture was recorded?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15214.0 0.0 0.0 0.0
"HE JUST MADE ME TO GO IN INEPTION OG THOUGHTS WHILE TALKING ABOUT HYPOTHETICAL NINE DIMENSIONS THEN IN THE END HE JUST MADE IT PUFFF GO AWAY" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 4398.0 0.0 0.0 0.0
"I wish i knew this lectures before my midterm 1. I hope I will be recover my grades for mt2 and final. Thanks a lot!!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 6224.0 0.0 0.0 0.0
"Perfect revision after almost 30 years ! thank you ." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8180.0 0.0 0.0 0.0
"Professor Strang!! Wooow, no wonder that MIT is the best, this guy is the best teacher ever found... 
I wish we had more of Professor Strang!!!!
Thank you very much Sir, your the best :)) " RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 8376.0 0.0 0.0 0.0
"The class is empty, but Gilbert Strang's passion is full..." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 10044.0 0.0 0.0 0.0
"Thanks prof. John Tsitsiklis and mit to share the knowledge to the whole world 
Sorry about my language, not native speaker." 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 9757.0 0.0 0.0 0.0
"Mr strang is the  best thing ever happened to humanity!!!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 7711.0 0.0 0.0 0.0
Thanks! nvXRJIBOREc "Lecture 21: Minimizing a Function Step by Step" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9826.0 0.0 0.0 0.0
"I'm studying in McGill and this man is saving lives. Ofc, cramming before the finals :D God bless this man. Watched his videos on 1.25x speed" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6383.0 0.0 0.0 0.0
"Went thru it one time, today thru the couse again and take my own notes. Prof Strang is a sooooo great!!!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 11378.0 0.0 0.0 0.0
"Los subtítulos en inglés son muy útiles para los que tenemos un dominio parcial de su idioma =)" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 7425.0 0.0 0.0 0.0
"I got a little bit confused about the definition of Taylor Formula. It seems that what Prof. Jerison has written is Maclaurin Series, which is a special case of the Taylor Series. And is there any difference between Taylor formula and Taylor Series? If you translate them directly to Chinese (My mother tongue:P) there are some differences. I got stuck in this point, hope someone can help me out, tks:)." wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5442.0 0.0 1.0 0.0
"Is there a practical use to matrix diagonalization, or is it just a cool trick like 3 balls Mill's mess or sword swallowing ?" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 6822.0 0.0 0.0 0.0
"Gilbert Strang lecture: ""and this is a matrix...""
Gilbert Strang textbook: ""Find the corners of a square in n dimensions and whether vectors a, s, d,e w,wieidwdjdkdk are contained in the cube....""" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 4029.0 0.0 0.0 0.0
"5:00 I would definitely use Support Vector Machine" 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 1354.0 0.0 0.0 0.0
"The Lecture has become immortal, sir! Thank you!
(Ref - first sentence of Prof. Strang in the lecture)" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9969.0 0.0 0.0 0.0
"The natural log explanation (21-27:~) was absolutely fantastic!!!
" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10198.0 0.0 0.0 0.0
"Oops. At 7:45 he said prime without referring to ribs. What part of YouTube did I just end up in?? I'll keep watching but there better not be a jump scare later.  jk." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8130.0 0.0 0.0 0.0
"Going to MIT has been a dream of mine for a long time and thanks to these videos I can fulfill these dreams. 
I'm incredibly greatful for all the open courseware MIT offers me and the whole world.
Thank you." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4103.0 0.0 0.0 0.0
"Very nice board work and excellent lecture." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11205.0 1.0 0.0 0.0
"@Anonymiusen This course is great. But there are also khanacademy calculus videos, they are great too." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1589.0 0.0 0.0 1.0
"im using this as prep for my real analysis class next quarter at UCLA. Using winter break to my advantage ;)
I will learn all of real analysis before the class even starts lol" M2d4HsBsu8Y "Lecture 5: The Archimedian Property, Density of the Rationals, and Absolute Value" "MIT 18.100A Real Analysis, Fall 2020" 13572.0 0.0 0.0 0.0
"Upto 19:00 Row operation elimination and back substituton(row eschelon form)" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11130.0 0.0 0.0 0.0
"This class is brighter than calculus class" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10473.0 0.0 0.0 0.0
"An excellent lecturer. I'm growing less fond of the students in the audience, who seem easily amused by random occurrences, are obsessed with whether a concept is going to be on the exam rather than being interested in learning for its own sake, and they repeatedly joke/complain about the difficulty of Taylor's series, even though for someone who got into MIT that should be elementary." 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2439.0 0.0 0.0 0.0
"This is best lecture everrr" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10649.0 0.0 0.0 0.0
"This is the best explanation of the projection formula that I have ever seen. Prof. Strang not only provides a mathematical basis of the formula by deriving it, but also provides clear intuition and motivation. He also takes the time to go through the simpler case of projecting onto a line first, which allows building up the understanding of the content gradually. What a great lecture!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10735.0 0.0 0.0 1.0
🤔🇺🇳🗣️🇺🇳🗣️🇺🇳🗣️🇺🇳🗣️🇺🇳🗣️🇺🇳🗣️🇺🇳🗣️🇺🇳🗣️🇺🇳🏋️🇺🇳🗣️🏋️🗣️🇺🇳🗣️🏋️🗣️🏋️🗣️🏋️🇺🇳🗣️🗣️🗣️🏋️🇺🇳🗣️🏋️💅💅💅💅💅🇺🇳🗣️🏋️💅🏋️🏋️💅🧠🇺🇳🏋️🏋️💅🧠🇺🇳🗣️🏋️💅🧠🏄🏄🏄🏄🏄🏄🏄🏄🇺🇳🗣️🏋️🏄💅🇺🇳🗣️🏋️💅🧠🗣️🏋️💅🧠🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🇺🇳🗣️🏋️💅🏄🎃🎃🎃🎃🎃🎃🎃🎃🎃🎃🎃🎃🎃🎃🎃🎃👽🎃👽👽💩👽💩👽💩👽💩🤖💩👽💩👽💩👽👽💩👽💩👽💩👽💩👽💩👽💩👽💩😵😵😵😵😵😵😵😵😵😵😵😵😵😵🤯🤯🤯🤯🤯😵😵😵🤯🤯🤯🤯🤯🤯🤯🤕🤮🤕🤮🤕🤮🤕🤮🤕🤮🤕🤮🤕🤮🤡🤡🤡🤡🤡🤡🤡🤡🤡🤡🤡🤡🤡🤡🤡🤡☠️☠️☠️☠️☠️☠️☠️☠️☠️☠️☠️☠️☠️☠️☠️☠️☠️☠️☠️☠️☠️☠️☠️☠️☠️☠️☠️ 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15744.0 0.0 0.0 0.0
"can you sign my book?" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 12639.0 0.0 0.0 0.0
"An Indian edition of this book is available only in India
http://www.wellesleypublishers.com/buy.html" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2422.0 0.0 0.0 0.0
"What is F?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 11512.0 0.0 0.0 0.0
"Anyone have the proof he didn't have time for regarding stochastic gradient in non-convex case." k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2497.0 0.0 1.0 0.0
"Find Uk...
Easy, it's in Europe!" QuZL5IKpO_U "24b. Quiz 2 Review" "MIT 18.06 Linear Algebra, Spring 2005" 3796.0 0.0 1.0 0.0
"These lectures deserve higher IMDB score than most netflix series." sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10416.0 0.0 0.0 0.0
"It is my pleasure to learn from this lecture thanks a lot sir" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 6960.0 0.0 0.0 0.0
"This is another brilliant lecture  on column and row space. These topics are very important in linear algebra for current and future learning." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 10632.0 0.0 0.0 0.0
"Dude needs better erasers" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 3523.0 1.0 0.0 0.0
"@savvasik21 the lectures that are uploaded from MIT are pretty informing (and helpful) whether you think professors are idiots or not. And an advice , being arrogant is not a bad thing , being arrogant with nothing extraordinary to prove extraordinary claims gives other people a good reason to think that you are also an idiot. 

@dfszinho02 you say you are both smart , but your conversation was not intellectual at all

have a nice day :)" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2001.0 0.0 0.0 0.0
"ty for lectures" _CdoRiNSrqI "Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14966.0 0.0 0.0 0.0
"I am confused...  For R²  subspaces are
1 origin
2 line itself... Alright upto here
But last one is it's any line through origin or something else" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 5077.0 0.0 1.0 0.0
"Just finished the course - what a wonderful series of lectures! Thank you so much Professor Auroux and MIT OCW!" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7170.0 0.0 0.0 0.0
"Which algebra course do you think is better, this one or the one Gilbert took in 2005?
PS: Of course both must be great. 
Thank you" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11705.0 0.0 0.0 0.0
"I love the nerdy comments on youtube... make me feel like home" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5780.0 0.0 0.0 0.0
"Today I have finished this course. I just wanna say Prof. David Jerison is an excellent and extraordinary teacher.  
Bundle of thanks for those who have made this possible to bring this course online and make it available to everyone for free.
Thank you very much MIT..." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11052.0 0.0 0.0 0.0
"I don't get the final table he made. What is (sqrt(5) - Xn) ?


P.S It's the error analysis. I got from the next lecture." sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5311.0 0.0 1.0 0.0
"We love you" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 11326.0 0.0 0.0 0.0
"This guy must drink a lot of coffee before class lol " kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10555.0 0.0 0.0 0.0
"Seemed sooo difficult in class today......now i understand why they are so good at MIT. Such a great teacher....Make it look easy. " tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8618.0 0.0 0.0 0.0
"Protect him at all costs! 🥺" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8451.0 0.0 0.0 0.0
"""don't all speak at once"" is he joking, or trying to hide the fact that the class is empty? not sure yet :)" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 149.0 0.0 0.0 0.0
"At 43:22 why did we not consider the bigger loops?" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2671.0 0.0 1.0 0.0
"i was completely lost for 2 whole days trying to make intuitive sense of it after my college professor taught us this. I mean i only got taught the algorithm for finding the jacobian but not what it actually is but after watching this, it finally clicked and i am so happy lmao" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13489.0 0.0 0.0 1.0
Wow QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12019.0 0.0 0.0 0.0
"10:18 Peek A BOO!" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 344.0 0.0 0.0 0.0
"Wow , Wow ! What an amazing explanation ... i felt like Multivariate Calculus is very easy as opposite of usual" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 12024.0 0.0 0.0 0.0
"It is a silly question, but making me curious. How does the chalk board always remain clean for the professors to write. I love chalk boards, but thought it is messy to clean !! ? His writing is excellent, and his presentation is SUPER ! Thanks a lot." _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6927.0 1.0 0.0 0.0
"Khan gives a shallow explanation and explains rather easy problems...He's pretty good at helping with some intuition, but these courses are WAY more complete. " bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7212.0 0.0 0.0 1.0
"His proof on sine theta/theta is classical. Love it!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4763.0 0.0 0.0 1.0
"35:17 Fourier Series" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 1004.0 0.0 0.0 0.0
"why is the slope of the pyramid 1/2" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15342.0 0.0 1.0 0.0
"sometimes they are extremely hard, we had one that was almost unsolvable in our exam" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14367.0 0.0 0.0 0.0
"you'd think MIT would have invented an automatic board erasing device by then." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15520.0 1.0 0.0 0.0
"At around the 21 minute mark, he says that it’s too much to hope for to reduce the matrix A0 to an upper triangular matrix. He immediately follows up with a statement that it’s impossible to solve a 5x5 system with simple steps. And this is why you instead reduce A0 to an upper Hessenberg matrix instead.

I got lost trying to follow this argument, so I did a bit of research.  Can someone tell me if I've got it right:
1) The eigenvalues of a triangular matrix are just its diagonal elements.
2) The Abel-Ruffini theorem says that's impossible, using radicals, to find the roots of a 5th order polynomial.
3) If you were to try to solve det(A - lambda I) = 0 for a  5x5 triangular matrix, you'd be trying to find the roots of a 5th order polynomial. Though doesn't it automatically come perfectly factored for you to read off the eigenvalues?

Combining all of these, does the Abel-Ruffini theorem imply that you can't transform a 5x5 matrix into triangular form via orthogonal transformations (e.g. Householder reflections) which preserve the eigenvalues?  This doesn't sit right with me, so I'm thinking that can't be it." d32WV1rKoVk "12. Computing Eigenvalues and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2709.0 0.0 1.0 0.0
"The way he arrived at the Identity Matrix.. So ingenius !!
Never thought of it that way

Edit: And he explained inverses BEAUTIFULLY !!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10322.0 0.0 0.0 0.0
"Why wouldn't the error be the perpendicular distance to the line? in the video, the prof said it to be the vertical distance to the line." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 11937.0 0.0 1.0 0.0
"This lecture is such a sad story for those who never understood electrical engineering basics like me. It could have gotten a lot better if he stuck to those friendships and Internet applications he mentioned in the last lecture." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10811.0 0.0 0.0 1.0
"That moment you need to learn math to play ff14..." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9908.0 0.0 0.0 0.0
"4:03 ""then you will either enjoy yourself"" did I hear what I thought I hear? /facepalm" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1312.0 0.0 0.0 0.0
"wow hes old now...." xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15414.0 0.0 0.0 0.0
"I love this prof. Thank you" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5832.0 0.0 0.0 0.0
"I like more the A(i,j)*-1^(i+j)*C(i,j) form" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 5678.0 0.0 0.0 0.0
"no white boards there?" 9_xG0AGRa-w "Lecture 2: Cantor's Theory of Cardinality (Size)" "MIT 18.100A Real Analysis, Fall 2020" 14074.0 1.0 0.0 0.0
"Mathematics has to be the most boring subject, idk why im watchin this but MrdeathMental's comment is fuckin hilarious" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7615.0 0.0 0.0 0.0
"Is it just me or is the quality of the video progressively getting worse?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 6781.0 0.0 0.0 0.0
"Finally i know what determinants is . i want to cry" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 3773.0 0.0 0.0 0.0
"I thought that the projection of the points onto the line (""error"") was meant to be perpendicular to the line, and not a projection in the y-axis." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 6097.0 0.0 1.0 0.0
"There are no students sitting there, but the lecture is still so good." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10350.0 1.0 0.0 0.0
"Holy shit! The legendary Michael Sipser is teaching it in video!!!!" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 4779.0 0.0 0.0 0.0
"How do i integrate , (Cos√x)/Sinx" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4847.0 0.0 1.0 0.0
"22:00

25:20" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 692.0 0.0 0.0 0.0
"This discussion has an application for the quantum sciences.  The quantum Hall spin-polarized effect has subatomic particles translations through crystalline structures in arbitrary space.  This has an epic important for finding new medical, electronics, energy, and other devices that will change our world." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 10498.0 0.0 0.0 0.0
"Somehow I have the feeling Professor is making it very difficult in this lecture and assume students to have already done some deep courses on Linear Aljebra!" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 8831.0 0.0 0.0 0.0
"so substitute infinity  minus one and chart the resultant here and now on the time line relax allow the unknown as infinite as well same graph pulse the fibronchi generator chart for rms the rms positive on sine only so return to chart and now condense the univariable into quantum  zero" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14343.0 0.0 0.0 0.0
"IT FINALLY MAKES SENSE my god i feel like crying what an incredible teacher" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 6451.0 0.0 0.0 0.0
"I'm not fighting anything. The comment you replied to here itself refers to a comment that a) was removed b) a syntactical failure c) needlessly abrasive and d) factually incorrect." jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6354.0 0.0 0.0 0.0
"The comments are edu canned laughter,not as smart as they need!!" phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10053.0 0.0 0.0 0.0
"Thank You Sir" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 9054.0 0.0 0.0 0.0
"I think that's because he's calculating how many blocks you need to have hanging over the edge of the first one. That would let him not count it in the calculation." wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6046.0 0.0 0.0 0.0
"today i completed the course!!
my last 34 days were like i was in heaven!!! 
i had tears in my eyes at the last moment. i want to study all my life.
thank you for inspiring me.
I'll work hard . you have ignited me thank you for providing acceleration to my life.
can't describe the feeling in the words." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 14952.0 0.0 0.0 0.0
"why is d/dx ln(x)=x'/x?" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15328.0 0.0 1.0 0.0
"Watching this after learning my times 6 times table 😂" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 11297.0 0.0 0.0 0.0
"Conclusion: Four fundamental subspaces of A(m*n), including 1. The column space means spanning the column vectors, which is in R to m, notation as C(A)
2. The nullspace of A means the free variables corresponding vector span the null space, which is in R to n, notation as N(A)
3. The row space means spanning the row vectors, which is in R to n, notation as C(A') equal to n-r
4. The left nullspace of A means the A' free variables corresponding vector span the null space, which is in R to m, notation as N(A') equal to m-r.
other conclusions: The sum of dim(C(A')) and N(A) is equal to n, the sum of dim(C(A)) and N(A') is equal to m." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3196.0 0.0 0.0 0.0
"Should i already have experience with proof writing?" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 8642.0 0.0 0.0 0.0
"Why everyone clapped at 43:25?" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11859.0 0.0 0.0 0.0
"Why I-P at 8:22?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 11767.0 0.0 1.0 0.0
"Why do we have e = b - p and not, e = sqrt(b^2 - p^2) ?" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 11829.0 0.0 1.0 0.0
"I've been watching all the lectures till know and I intend to watch the rest,

thanks to the professor and to the sponsor for making such wonderful world-class education available to anyone." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6409.0 0.0 0.0 0.0
"I'm in the UK and i've taken this not even in my final year of high school, but bear in mind, this class is for people NOT taking maths, it's for other majors who have to take it. Also i really doubt you covered it at the pace of these lectures (the whole of elementary single variable calculus in a term).

Great video" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6333.0 0.0 0.0 0.0
"Just finished Single Variable Calculus course. 
Thanks to MIT for this opportunity. Prof. David Jerison is the best math teacher I ever had.
Kazakhstan, 2022" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7165.0 0.0 0.0 0.0
"@hmpcon you have kassabov?" WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1869.0 0.0 0.0 0.0
"His sniffling is making me sniffle" 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 4764.0 0.0 0.0 0.0
"(In such texts, students also are told that that they MUST NOT say that a matrix A is equal to a matrix B when B does not have exactly the same number of columns as A.)  The use of the notation ""R^3"" for the space of real (3x1) matrices (aka (3x1) column vectors) requires one to accept a conflation of three DIFFERENT KINDS of real vectors with three entries, 3-tuples of real numbers, row vectors with exactly three real entries, and column vectors with exactly three real entries.  (2 B continued)" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 222.0 0.0 1.0 0.0
"After so many years of using linear algebra, until today I finally understand the meaning of matrix multiplication.  matrix*vector is linear combination of the columns of the matrix, and vector*matrix is linear combination of the row of the matrix. Then from this standpoint, the meaning of permutation matrix becomes so obvious. Thank you Prof. Strang." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2255.0 0.0 0.0 0.0
"At first i thought his book was meant to be cryptic, now it makes sense..." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 2711.0 0.0 0.0 0.0
"ignorance is bliss. at least for me it is." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13557.0 0.0 0.0 0.0
"Ideally, do you learn multivariable calculus first or linear algebra? A lot of stuff here seems to be based on 18.06." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6456.0 0.0 1.0 0.0
"i am currently engineering first year . after i get a job i will definetely donate to mit ocw" phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13328.0 0.0 0.0 0.0
"No matter how artificial and ""strange"" matrices look, they are always derived from very simple reasonings.
In fact, you can quite easily derive the technicalities behind the determinant matrix operations, cofactor expansions etc simply by playing around with row reductions etc and experiment a bit.
I managed to derive the cross product even before I read the definition behind it, because I love figuring things out like that.

One major advantage in knowing the theory behind these things is that you don't need to ""look it up"", because since you know how it works you can simply derive it on the spot." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7876.0 0.0 0.0 1.0
"Where can we find the notes professor Strang mentions in the videos? ( 45:17 )" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11668.0 0.0 0.0 0.0
"Stanford also posts its lectures on YouTube" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8876.0 0.0 0.0 0.0
"Thank God for the student at 38:58. I thought I was losing my mind for a minute there." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9042.0 0.0 0.0 0.0
"for a good start into calculus, this might help you..... just take a look here : Big Picture of Calculus [Gilbert Strang]
watch?v=UcWsDwg1XwM&list=SPBE9407EA64E2C318" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12878.0 0.0 0.0 0.0
"wtf is going on with the cc at 3:08?" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 15444.0 0.0 0.0 0.0
"Honourable MIT, COULD YOU PLEASE ALSO TELL US THE TIME FOR EXAM 1(LEC 8)?

THANKS" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4784.0 0.0 0.0 0.0
"@santiagogcastro 

Computers are one of the main reasons people don't understand how to do arithmatic." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2000.0 0.0 0.0 0.0
"Possibly, but not necessarily. It could be positive, zero, and then back to positive like in y=x^3." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8232.0 0.0 1.0 0.0
"Hey in defining slope why we should take delta x tends to zero because for the point Q to be P it is both delta x and y both should be zero right??" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4693.0 0.0 1.0 0.0
"How can he compare sum of areas to volume? Its better if we use n*(n+1)*(2n+1)/6 to represent the sum of n^2 terms and compare it with other two terms." hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4812.0 0.0 1.0 0.0
"""Keep the matrices in their Gauss-given order""" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 75.0 0.0 0.0 0.0
"Gilbert strang rocks" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4041.0 0.0 0.0 0.0
"which is why you were reviewing your calculas just a year ago." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15252.0 0.0 0.0 0.0
"i highly recommend this video for those who have an idea of calculus" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13402.0 0.0 0.0 0.0
"at 26:13  I dont get how he can switch column 2 and column 3 to get the identity matrix in the first block of [ I F] ? You cant chage the order of pivot columns just like that ? PLEASE answer this for me someone! 1love" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 12429.0 0.0 1.0 0.0
"Salute and pranam to this great legend...I hope he lives till eternity" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8596.0 0.0 0.0 0.0
"Aw come on, the sound is bad!!" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 2749.0 1.0 0.0 0.0
"Greeks. Russians. No difference.

Just like with Nuclear Physics and Music Theory!" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 4381.0 0.0 0.0 0.0
"τσιτσικλη αλανι αναψε ντουμανι" gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 15551.0 0.0 0.0 0.0
"gilbert strang sir is the best mathematics teacher in the world" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12920.0 0.0 0.0 0.0
"@xkeikoxsanxdesu if you can't google and find the site of MIT they probably won't accept you there :P" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2067.0 0.0 0.0 0.0
"Steve Jobs should've watched (23:25). At the dawn of new phone era, it is destined to use iPhone." HIMxdWDLEK8 "18. Markov Chains III" "6.041 Probabilistic Systems Analysis and Applied Probability" 8897.0 0.0 0.0 0.0
"Kkkkk professor n dormiu mt bem na noite anterior" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7218.0 0.0 0.0 0.0
"F R E N C H B O I" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3715.0 0.0 0.0 0.0
"@redrum41987 sorry but that's what most ppl can do :)" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1987.0 0.0 0.0 0.0
"6 more lectures to go, let's finish strong. 

for those interested in following the course or learning the material more deeply, I've personally just been doing problems from the book rather than the OCW page (most of the problem sets are from the book anyway, not sure about the exams). I recommend looking through the problems because I find that they show different ways of applying the concepts and help develop problem-solving intuition. If you're like me and coming from a very non-mathematical background, I think putting in a lot of time (10+ h/week) to learn the material well is a very worthwhile endeavour, if you can afford it." 3eiio3Tw7UQ "19. Weak Law of Large Numbers" "6.041 Probabilistic Systems Analysis and Applied Probability" 1370.0 0.0 0.0 1.0
"In case you are wondering: the third root of 64.1 is about 4.0020822." -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6630.0 0.0 1.0 0.0
"Brilliant, brilliant lecturer." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2944.0 0.0 0.0 0.0
"Before I went to grad school in the summer of 2015 I watched Dr. Strang's entire 18.06 course to make sure I was prepared. Now, five years later, PhD in hand, I still learn something every time I watch him speak." or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2835.0 0.0 0.0 0.0
"@boblelan or Quebec or Ontario.." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1803.0 0.0 0.0 0.0
"After thirty years of 3D computing high education is still done manually all over the world. Ironically, universities are the most opposed to change. It's embarrassing." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 2258.0 0.0 0.0 0.0
"Best question at 26:30." 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2875.0 0.0 1.0 0.0
Opurem 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8132.0 0.0 0.0 0.0
"I enjoyed this lecture on Similar Matrices and Jordan Form as part of linear algebra. Once again DR. Strang  showed the application of both topics with examples." TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 5383.0 0.0 0.0 1.0
"for 2 by 2 systems the normal method at school is fine but it's too long and it's much quicker to write it in a matrix and the pivots and words like that are just terms to describe what he is doing" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12876.0 0.0 0.0 1.0
"모든 MIT 강의가 이럴 것이라고 생각하지는 않지만 연세가 80 가량인 노교수가 자신의 머리 속 생각을 투명하게 펼쳐보이며 수백 번은 이미 강의하셨을 내용을 생생하고도 열정적으로 학생들에게 마치 처음 설명하시는 것처럼 전달하시는 것을 보며 충격을 받습니다. 과잉 일반화하는 것일 수 있고 혹자에게는 편협하고도 부당한 평가로 폄하될 수 있을 말이지만 용기내 볼멘 소리를 하자면 한국 대학은 과연 대학이라는 정의에 포섭이라도 되고 있는 것일까 회의를 하게 된다는 것입니다. 60만 넘어도 무슨 대가라도 되서 강의조차 초탈하게 대해버리며 정부나 삼성만을 바라는, 학생들에게 많은 고통을 주는 많은 이 땅의 학자연하는 자들에게 이 강의를 보여주고 싶습니다." TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 15676.0 0.0 0.0 0.0
"Funnily enough, my linear algebra courses drilled the column picture into my head so hard that I completely forgot about the row picture. I kept wondering how we did all this fancy geometry with planes in school when solutions obviously represent vectors that get mapped to a certain vector, and matrices represent transformations of space. I hope the row picture comes up sometimes so I can redevelop that intuition." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3956.0 0.0 0.0 1.0
"I just love math. ^-^" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5610.0 0.0 0.0 0.0
"4:49
CFG : 1:00:00" KAySmSEGc9U "3. Regular Pumping Lemma, Conversion of FA to Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 1326.0 0.0 0.0 0.0
"11:25 19:03 21:03 24:42 36:00 40:34 44:44 48:58" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 373.0 0.0 0.0 0.0
"the quality is so low" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 14736.0 0.0 0.0 0.0
"i recommend first than 3Blue1Brown and this classes try to take a zoom into C.Lay book... that visión can understand much better this video" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13453.0 0.0 0.0 0.0
"Could someone give me a clue why use A(T)AX(hat)=A(T)b to solve [C,D] at 21:05 ? To my understanding, AX(hat) cannot be b if we fit a line which points are P1, P2, P3 instead of b1, b2, b3 or [1 2 2]_t?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 3236.0 0.0 1.0 0.0
"great professor, He is really teaching something compared with my professor who only knows repeating the textbook." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 12998.0 0.0 0.0 0.0
"Awesome video. Using it to get ahead for fall!  Thank you for providing this to the public. In the age of the internet, knowledge is as cheap as the wifi!" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 2776.0   
"Where can I find the detail solutions of other problem set ???" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11659.0 0.0 1.0 0.0
"What happens when the eigenvalues are complex?  It doesn't seem like the QR method would converge as all the numbers resulting from this method would be real." d32WV1rKoVk "12. Computing Eigenvalues and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11500.0 0.0 1.0 0.0
"Thank you so much ! But what if x and y (the observation) are continuous ?" H_k1w3cfny8 "10. Continuous Bayes' Rule; Derived Distributions" "6.041 Probabilistic Systems Analysis and Applied Probability" 9343.0 0.0 1.0 0.0
"I saw something, that i have never seen before ." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5956.0 0.0 0.0 0.0
"""the apparition just wanted to be sure that we got the right answer..""  MIT is super cool XD" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 177.0 0.0 0.0 0.0
"I hope that'll help me pass my linear algebra exam" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5590.0 0.0 0.0 0.0
"What kind of chalk is being used?     And what is the stick diameter? " ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11548.0 1.0 0.0 0.0
"I'm not sure why I'm even watching this, but in the beginning, the professor dotted an e. :P" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6358.0 0.0 0.0 0.0
"He is a legend!" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 4502.0 0.0 0.0 0.0
"This course helps me a lot. Thank you, MIT!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10489.0 0.0 0.0 0.0
"Complete waste of time" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 3178.0 0.0 0.0 0.0
"A question: Did you guys study this in your highschool too?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2149.0 0.0 0.0 0.0
"I'm a physics student and we take a lot of linear algebra classes. The lectures and the literature we get is, for me, just gibberish because our professor rarely dares to step out of the comfort zone and teach linear algebra in such an intuitive way like Prof. Gilbert Strang does. These lectures helped me so much and they're an underlying reason why I can not only understand the basics of linear algebra now, but appreciate the beauty of it too. Thank you, Professor. " RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 6300.0 0.0 0.0 1.0
Genius! M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 3999.0 0.0 0.0 0.0
"why did he plug the values of Qo in the equation (x+2y+4z) it does not make  any sense !" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15298.0 0.0 1.0 0.0
"god but change g to j and d to hn" 3eiio3Tw7UQ "19. Weak Law of Large Numbers" "6.041 Probabilistic Systems Analysis and Applied Probability" 12930.0 0.0 0.0 0.0
"Awesome explanations!" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2758.0 0.0 0.0 0.0
"40:50 
is the best plot twist awesomee" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1138.0 0.0 0.0 0.0
"should be the legend" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 14295.0 0.0 0.0 0.0
Check! J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3146.0 0.0 0.0 0.0
"Least square approximation" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 7257.0 0.0 0.0 0.0
"He says 'This guy' when referring to a vector. God help his students......" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 4601.0 0.0 0.0 0.0
"Im just gonna write this for ppl like me 

if you are like me(didn't finish high school yet(first year)) you will have to put some effort in studying this u gotta search for some basics u may not have been taught yet and it will take a lot of time to search alot but just try and take the reason you are studying this that early as a motivation cuaze some stuff will be so frustrating and hard to understand cuaze u haven't mastered some basics yet but ik for sure it's worth 

for me Im studying this to learn machine learning and some stuff i wanna also do physics engines and stuff like that to help people and i found that everything i wanna do is related to linear algebra and once i get it and get deep into it i can do whatever i want just by some basic research 

Trust me it's hard but worth❤" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6574.0 0.0 0.0 0.0
"A mathematician with Great sense of Humour. Mr. Strang !" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2140.0 0.0 0.0 0.0
"Can anyone tell me what was the purpose of giving '0' and '1' to free variables in order? Thank you!" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 3046.0 0.0 1.0 0.0
"cool lecture!!" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 12677.0 0.0 0.0 0.0
"because to use the 2nd der. test you need a critical point. In the types of problems with constraints, min/max is not necessarily a critical point." 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12527.0 0.0 1.0 0.0
"I Really Like The Video From Your Exam 3 review" zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4955.0 0.0 0.0 0.0
"I studied this and used it all my life, but I never learned the “column” view." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5977.0 0.0 0.0 0.0
"What book is Gilbert sir following? Can anyone give the name? I am from India about to pursue my masters and I need this course" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11470.0 0.0 0.0 0.0
"Best teacher" TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 2876.0 0.0 0.0 0.0
"Started this course on OCW and it is just brilliant, it gives an intuitive sense to concepts I learned a long time ago but which were conveyed in a much drier way. thanks !!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8883.0 0.0 0.0 0.0
"can someone suggest to me a lecture series that is mended for beginners I want to start calculus" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12632.0 0.0 0.0 0.0
"I have huge respect for this lecture series and Professor Strang. This exact syllabus is what we have to learn in 2020 as one of our core courses in  CSE MS in AI/Robotics and ML. It is going to take multiple revisions to really internalize all that this lecture series has to offer. Professor, I hope to build some good things and help usher in the AI revolution that is happening. Thank you for sharing your knowledge to us, the next generation to push things a little bit more into the future." Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 5530.0 0.0 0.0 0.0
"Very nice explanation. From now I am a big fan of him" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11206.0 0.0 0.0 0.0
"Mr. Strang! Ahahaha so nice at 43:10" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 7716.0 0.0 0.0 0.0
"2 months and nobody comments! D:" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 609.0 0.0 0.0 0.0
"An Excellent lecture thank you" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2414.0 0.0 0.0 0.0
"@someonep93 Well the people who came into the lecture late said they were from physics...." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2022.0 0.0 0.0 0.0
"very nice!" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15032.0 0.0 0.0 0.0
"my teacher made me think i hated linear algebra ..... but i dont think i do anymore ... i want this guy around in the physics lounge to teach me his ways  " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14005.0 0.0 0.0 0.0
"At 39:55, the professor multiply [A  S-1] to the left side of [S  AT; A  0] to get [S  AT; 0  -A*S-1*AT]. Can anybody please explain the purpose of this calculation ? Thanks in advance!" xaSL8yFgqig "Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2657.0 0.0 1.0 1.0
"No, I don't think so." wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 7898.0 0.0 0.0 0.0
"39:52 Gauss would quit, but Jordan says keep going." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1105.0 0.0 0.0 0.0
"when the love child of mr rogers and bill nye decides to teach algebra" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15212.0 0.0 0.0 0.0
"The first two eigenvalues are 0 and 2 which correspond to the eigenvectors (1,1,1,1), (0,0,-1,1). He says some of the components in this second eigenvectors are positive and some are negative which tells you which cluster each node is in. But he never carries it out and explain the 0 components? See wolfram-alpha https://tinyurl.com/y7vdkhua for decomposition." cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10112.0 0.0 1.0 0.0
"Taking notes on this class using mostly screen captures!  Very useable boardwork" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9014.0 1.0 0.0 0.0
"Salute this man, he has taught more students linear algebra than anyone in history, and is likely to continue to do so eternally!" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8597.0 0.0 0.0 0.0
"The logic behind his teaching is pretty coherent and well - organized." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10180.0 0.0 0.0 0.0
"Why this bullshit bicycle in the classroom?" phbw9r1iUDI "7. Parametric Hypothesis Testing" "MIT 18.650 Statistics for Applications, Fall 2016" 11927.0 1.0 0.0 0.0
"So big chalk.." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8742.0 1.0 0.0 0.0
"Wonder why do we need to differentiate a function just to find the slope between two x values
whereby x is acted as parameter to the function f(x)..
We can find gradient by simply do
f(x)-f(x-1)
so this guarentee over one unit of x you get gradient..
Also it does not make sense to find gradient between two units of x..
For example consider f(x)=x²
to find gradient simply do
f(5)-f(4)
or anything like that as long it is f(x)-f(x-1)..
In this example we will get 25-16=9
So the gradient of the tangent line that intersects x=4 and x=5 is 9..
If you use differentiation f'(x)=2x+c
Let say you neglect c for a second..
And plug into the formula
At f'(5)=2(5)
Which is equivalent to 10
But this is incorrect..the correct value is 9
so now we know c=-dx
So if you want to find gradient between two units of x you get c=-2
which means f'(x)=2x-2
So I don't think finding the gradient between two units of x is relevant and so why not just use f(x)-f(x-1)
to find the gradient when x only incremented by one unit not more and not less" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11981.0 0.0 1.0 0.0
"47:09, what would the sample space in terms of area look like for the coin flip of heads for the first time? How would you present an infinite area?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 1278.0 0.0 1.0 0.0
"I love the quirky teaching style of Prof. Strang, especially how he feigns to encounter something surprising, whereas in fact it is well-rehearsed." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5782.0 0.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8433.0 0.0 0.0 0.0
"For some of us this isnt enough =/. I actually have to sit in the library for hours to figure things out not all of us have it made ... Sadly" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3874.0 0.0 0.0 0.0
"So 0^1 = 0, yet 0^0 = 1. How's that for a head scratcher?" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8727.0 0.0 1.0 0.0
"27:37 ""favorte""" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 824.0 0.0 0.0 0.0
"should be A inverse plus ... for the S-M-W formula at the end ?" XhSk_Lw2X_U "14. Low Rank Changes in A and Its Inverse" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14294.0 0.0 1.0 0.0
心中永远的男神！ Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15627.0 0.0 0.0 0.0
"these lectures are enlightening. thank you Professor Tsitsiklis!" l4NoMKEHQwM "11. Derived Distributions (ctd.); Covariance" "6.041 Probabilistic Systems Analysis and Applied Probability" 14778.0 0.0 0.0 0.0
"10:20 prerequisites
14:50 explanation of the scientific process a bit before this. On the collection of data --> hypothesis, which will then be proven or disproven by more data" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 345.0 0.0 0.0 0.0
"Great improvement on video quality compared with 18.06" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4232.0 0.0 0.0 0.0
"I live in Hilbert Space." EBdgFFf54U0 "Lecture 14: Basic Hilbert Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 5709.0 0.0 0.0 0.0
❤️ 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 15606.0 0.0 0.0 0.0
"pumping 🅿️" KAySmSEGc9U "3. Regular Pumping Lemma, Conversion of FA to Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 14231.0 0.0 0.0 0.0
"This is optimization, not related rates." YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10703.0 0.0 1.0 0.0
"I bet 90% of those students are Asian ! Deadly boring quiet like Dead Sea! Numb faces!" a1ZCeFpeW0o "20. Principal Component Analysis (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 5175.0 0.0 0.0 0.0
"Thanks a million times!
" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 9672.0 0.0 0.0 0.0
"Input letters are a and b, then what is the regular expressions no two a's come together (string may be any length) can anyone plz help plz!!!!!!!" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 6711.0 0.0 1.0 0.0
"08•48 can anyone express this integration without using geometry" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 297.0 0.0 1.0 0.0
"Best explanation for the exponential family" X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 2858.0 0.0 0.0 0.0
"I thought retards who played music in the class only existed in shitty colleges like mine in third world countries. Guess these retards are everywhere unfortunately..." 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6092.0 0.0 0.0 0.0
"I don't get the point of A = LU.  You need to know U to solve for x in Ax=b.  You need E to find U, you can't get U from L.  Once you have U, you're basically done.  What do you need L for?

I understand the point that L is less costly than E -- but what use is L if you don't know U yet?    What am I missing?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 5312.0 0.0 1.0 0.0
"logs minus the natural" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13816.0 0.0 0.0 0.0
"It's been a long day without you my friend. I will tell you all about it when I see you again." sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7031.0 0.0 0.0 0.0
"Are you kidding me that this university is at the top of the ranking of all the universities around the world considering mathematics and my university doesn't even appear there? We learned many more things, we did very strict definitions, theorems, proofs (one proof could have taken an hour!), our lectures lasted for one and a half hour twice a week and we did three parts of Calculus during one and a half year! And yes, we did it from the first semester of the first year - undergraduate. This is what you teach future mathematicians at ""the best university of the world""? Here, where I live, such courses are destined for future chemists or engineers but surely not for mathematicians... How's it possible that you're at the first place and we even don't appear in topuniversities?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2540.0 0.0 0.0 0.0
"wow, this lecture has opened my eyes. Thank you, professor Strang!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 15429.0 0.0 0.0 0.0
"thanks for this lectures" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14588.0 0.0 0.0 0.0
"W. O. W. Nuff said." TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11239.0 0.0 0.0 0.0
"Professor Strang is one of the best out there, you can have all the knowledge and skills for mathematics but some teachers, no matter how passionate or smart, are really bad. There is something about the way Professor Strang explains things which makes everything more understandable and interesting. 
I'm using Howard Anton's book at school + my teacher is THE WORST. Linear Algebra had been a nightmare up to the point where i found these videos.
 If i ever meet Professor Strang I'll hug him and wouldn't be able to thank him enough." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 8352.0 0.0 0.0 0.0
"The girl who raised her hand in the first row when he asked what the name of the matrix is... :'( 
College is just a high level Dora the Explorer where the teacher asks a question, stares at you for 15 seconds, then answers it himself" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10120.0 1.0 0.0 0.0
"Great lesson. I just did not understand one part towards the end that if we rotate the arms of the angle O for ninety degrees, QPR would approximately be equal to O. (45:00) 
If it is just happen to be like that, is not the proof sort of incomplete?
Could anyone explain this part to me?" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4313.0 0.0 1.0 0.0
"Awesome lecture. Thanks for uploading.
" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 2763.0 0.0 0.0 0.0
"At 20:50  This is why studying at MIT is worth the tuition. Great teacher!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 2608.0 0.0 0.0 0.0
"Good Job Professor" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4116.0 0.0 0.0 0.0
"When your life depends on a p-hacked binary colour coded value on a spreadsheet..." 4HRhg4eUiMo "8. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 11649.0 0.0 0.0 0.0
"Such a good lecture" X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 8925.0 0.0 0.0 0.0
"Thanks mit for providing high quality education" G3mAXHuoDSw "Lecture 4: The Open Mapping Theorem and the Closed Graph Theorem" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 9752.0 0.0 0.0 0.0
"at 18:30, it clicked!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12419.0 0.0 0.0 0.0
"Thanks for sharing." 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 9703.0 0.0 0.0 0.0
"Can someone help me with an example of why the first state can't be the accepting state, in closure under *?" oNsscmUwjMU "2. Nondeterminism, Closure Properties, Conversion of Regular Expressions to FA" "MIT 18.404J Theory of Computation, Fall 2020" 3083.0 0.0 1.0 0.0
"when he does the fibonacci example, why does he add in the line F(k+1) = F(k+1)...i understand he is a god to everybody but me but he does many many things without explaining why or how.  i'm baffled how he is considered god when he leaves so many things out of the lecture." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 15204.0 0.0 1.0 0.0
"Yay professor Auroux. He's at Berkeley now HA go Bears." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12113.0 0.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8442.0 0.0 0.0 0.0
"This man hates Schmidt. XD" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 10854.0 0.0 0.0 0.0
"i feel like an asshole im not even able to underdstand what gilbert teaches i feel depressed that when whole world is undertanding who not me :-((" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13375.0 0.0 0.0 0.0
"Are those chalks hagoromo ?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2535.0 1.0 0.0 0.0
"he chose the numbers based on convienence...note 4 squared is 16, and 16*5 is 80.  and 80/4 is 20.  he planned out his numbers, he wasnt trying to be exact...but you are right, 9.81 m/s is the gravitational acc for earth.." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13070.0 0.0 0.0 0.0
"05:50 If the sizes don't match, can't we just extend them to their correct sizes and fill the extension with zeros? (well, except the main diagonal, where we need ones to keep the corresponding rows/columns untouched)" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 294.0 0.0 1.0 0.0
"Excellent clarity in preparing material and samples." gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 3636.0 0.0 0.0 0.0
"Thank you MIT opencourseware, it helps a lot!" ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 9149.0 0.0 0.0 0.0
Insightful! Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 6714.0 0.0 0.0 0.0
"if z=r is a cylinder then how z=ar is a cone,can someone help me resolve this." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13556.0 0.0 1.0 0.0
"@GretneRebirth hmmm, I skipped past the easy vector parts lol. 

but she kinda looks golden brown, not typical paris hilton blonde colour. it could be the lighting making her blonde. " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1626.0 0.0 0.0 0.0
"Did my A level and had just enough of this math stuff...can some maybe explain for dummies wherefore you would need this math stuff in reallity?" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3381.0 0.0 0.0 0.0
"probability or possibility of hitting dart in a area which tends to be very small or nearly zero will have a probability of it been hit by dart tending to zero not exactly zero :-)" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 14206.0 0.0 1.0 0.0
"It’s quite confusing to me that the variance sometimes is a vector/matrix, but sometime is a number. So is it a number or vector?

Also I don’t get the multiply by 2 for two samples. Initial definition is avg of 2 samples, not sum of two samples." z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7101.0 0.0 1.0 0.0
"I like how he sometimes reverts to french accent adn then goes back to american" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 5666.0 0.0 0.0 0.0
"What is the name of the textbook for this class?" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 11530.0 0.0 0.0 0.0
"41:32 recap point for A.t * Ax = A.t * b" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1155.0 0.0 1.0 0.0
"Thank you all in MIT for sharing this class with the world. I like it, a lot. Mathematics rock!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9245.0 0.0 0.0 0.0
"Everyone here is blessed by MITocw" P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 3609.0 0.0 0.0 0.0
"so i'm a sophmore in high school n i was wondering if i took all these lectures, will it give me enough information to take the ap calc ab exam??

and i'm finding these lectures really hard....is tht cause i'm only a sophmore??" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14333.0 0.0 1.0 0.0
"Prof Tsitsilis is just awesome! I have never come across such an witty scholar. Thanks MIT for making these lectures available in open." 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 8278.0 0.0 0.0 0.0
"Great lecture, anyone noticing that the chalk is getting worse than in 18.06? :D" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4278.0 1.0 0.0 0.0
"There is a mistake in lecture notes, example 71. Example in the lecture notes picks epsilon_0=1/2 and then proceeds with 1=|(-1)^M-(-1)^(M+1)|. This is wrong. Epsilon should be 1; and the expression with absolute values evaluates to 2. The lecture video is correct, the lecture notes are not." 49Ro2zf9hAc "Lecture 7: Convergent Sequences of Real Numbers" "MIT 18.100A Real Analysis, Fall 2020" 10365.0 0.0 1.0 0.0
"Absolutely well done and definitely keep it up!!! 👍👍👍👍👍👍👍" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 2222.0 0.0 0.0 0.0
"00:00 comments about approximation
31:50 don't abandon your common sense" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 282.0 0.0 0.0 0.0
"Great lec. I liked his explanation of the binomial theorem. 
moving forward to lec 2.

Watch out calculus! 
 HERE I COME!  XD" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4239.0 0.0 0.0 0.0
"I wish you had this before last term" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 6236.0 0.0 0.0 0.0
"45:00
in the case r = m < n,  then  
rref (A)  = [  Id.  F ] , if we allow permutation of columns." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 1247.0 0.0 1.0 0.0
"He explain with heart and soul. Thanks for sharing. Big love" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4478.0 0.0 0.0 0.0
"Ok but whats the actually difference between path and surface independence. Can a Field be path independent yet  not surface independent.... and 25:50 the divergence of curl of a vector Feild is always 0. Does it imply for all Vector Fields irrespective whether it has scalar potential or not.?" sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8043.0 0.0 1.0 0.0
"Can I find some slides for these lesson?" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 3005.0 0.0 0.0 0.0
"go to start 
search mono
enable mono....now enjoy equal sound on both ears....you are welcome..." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 12926.0 0.0 0.0 0.0
"This course would have been much better if the course site actually has solution for us to compare our answer with." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 10496.0 0.0 0.0 0.0
"@schwarzegarde This is the second semester in math mit has. Their first semester is Calculus 1 and 2 put together and their second shown here is calculus 3." z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2004.0 0.0 0.0 0.0
"This video is very helpful, i appreciate the help." YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10956.0 0.0 0.0 0.0
"@pelemanov You should enable htnl5 player: youtube com/html5
it has speed option" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 1968.0 0.0 0.0 0.0
"very good teacher" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15009.0 0.0 0.0 0.0
"pls anybody help me out! At @48:10 the sum given-->integrate 1/(xlnx). It''s possible by substitution method but not possible by integration by parts method." -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14193.0 0.0 1.0 0.0
"what is  the program the professor used to illustrate the plots ?" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15147.0 0.0 0.0 0.0
"Mister John our respect from Greece!! Pretty helpful courseware.. :)" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 7674.0 0.0 0.0 0.0
"There are two ways of solving for e^xarctanx. Anyone?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10358.0 0.0 1.0 0.0
"jimmy dore?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 13723.0 0.0 0.0 0.0
"I barely mastered long division, flunked high school algebra and everything he is doing looks like impossible to understand gibberish!  The fault is my own of course." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5163.0 0.0 0.0 0.0
"I can't figure out how A could ever be a negative number when it's given as e^c and e is a positive number." 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5213.0 0.0 1.0 0.0
"Newton's  method: this is a good example to see how mankind gets lost in particular problems, if you check the answer for square root of five you can see that it takes him a very long time to solve the equations and the fractions, while for me to solve manually (without calculator) could have an acurate answer  to the -4 exp in a couple of minutes the most. what it is nice is to see the interpretacion of the root in geometrical partabole." 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7826.0 0.0 0.0 0.0
"Calculus is not that difficult if you like it, you should understand the sequence of steps and functions, but in general is rather difficult." MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2987.0 0.0 0.0 0.0
"I saw this video fours years ago when I was an undergraduate student having linear algebra class, and now I saw it again when I am a graduate student, He is just a legend!, No one teacher I have ever seen can be compared to him." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5958.0 0.0 0.0 0.0
"20220530 簽" Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 638.0 0.0 0.0 0.0
"I don't have much time left for my final exams, but here I am watching all the lectures of the playlist.
Dr. Gil strang is a legend." 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 5315.0 0.0 0.0 0.0
"Use a digital board meh.. MIT" V3Wg_jrMSQY "Lecture 19: Differentiation Rules, Rolle's Theorem, and the Mean Value Theorem" "MIT 18.100A Real Analysis, Fall 2020" 11132.0 1.0 0.0 0.0
"Respect to MIT." ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 8560.0 0.0 0.0 0.0
"Great lecture" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 4243.0 0.0 0.0 0.0
"LOL. Looks like he didn't want his 'little brother' to look like a *big* brother - if you know what I mean." jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7239.0 0.0 0.0 0.0
"I have just completed the course!

Realy nice and a good Teacher, one with the capital T." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5531.0 0.0 0.0 0.0
"Professor Strang thank you for great lecture that involves Norms, Ranks and Least Squares. All three topics are very  important for solid linear algebra development." Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8369.0 0.0 0.0 0.0
"""very appropriate for me as a substitute teacher to tell you about substitution""XD" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 188.0 0.0 0.0 0.0
"The corresponding lecture form 18.03 by MIT OCW that bridges this module is Lecture 25. 
https://www.youtube.com/watch?v=heBvViSi9xQ" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 10061.0 0.0 0.0 0.0
"thankyou sir" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14618.0 0.0 0.0 0.0
"why is the prof so toxic at 10:28 uff" 0Va2dOLqUfM "5. Maximum Likelihood Estimation (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 15340.0 0.0 0.0 0.0
"He’s more effective with that one HUGE piece of chalk than my professor with her ipad and Zoom. She should just assign this as the lectures and be done with it." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 4703.0 1.0 0.0 0.0
"Sir , Thanks a lot Sir.. ! .." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 8688.0 0.0 0.0 0.0
legend Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13776.0 0.0 0.0 0.0
"A new course...
THANKS MIT 
:D" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 2144.0 0.0 0.0 0.0
"Econometrics is in the air ... :)))))))" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3549.0 0.0 0.0 0.0
"I do make this statement, after understanding Polynominal Crystal Agebra IV with the X-Axis,Y-Axis,& Z-Axis Polynominal Cyrstals revolving around""TIME""= 4D Algebriac, & Calculus Limit Questionaires using Newtonian Physics,WHY Don't you run that""STUPID FREEMASON U.S.A. IDIOT Government ,Now that you Fully Understand the Mathematics of Our UNIVERSE,you certainly can adapt it to""SCIENCE SOCIALISM of ELECTRIFICATION-Photons of Physics Calculus-Algebriac I,II,III & Algebriac IV Polynominal Graphing!!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5287.0 0.0 0.0 0.0
"limits are used as a tool in a proof... we call things such as these ""givens.""    you use givens to prove more complex algorithms.  this is how math progresses to more complex heights.

by the way, you should be doing limits at 15 or 14...that is when pre-calc is generally introduced. " ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13797.0 0.0 0.0 1.0
"Near 23 min in, how did he ignore the i, but remember it in his next example with n = 4?" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 7808.0 0.0 1.0 0.0
"@pattttttrick You see the gradient is a sort of operator, when you apply it to a scalar field, it gives a vector field. The gradient it self is not the vector." 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 1962.0 0.0 1.0 0.0
"Such an intelligent, yet nice professor -- taking time to answer all questions patiently..." jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8947.0 0.0 0.0 0.0
"why did he use the third derivative of x(theta) but only the second derivative for y(theta) in the taylor approx?" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15302.0 0.0 1.0 0.0
"d (S (fdx)) / dx = f .... S is sign for integral ..
It's obvious, but I don't know what he didn't say explicitly." Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12701.0 0.0 1.0 0.0
"Prof seems a bit disorganized otherwise a good lecture series" TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 8283.0 0.0 0.0 0.0
"Compared to courses in my collage, MIT’s courses are just feels better in many ways, dk why, feels relax even on math courses, which I would consider ‘hardcore’ before. Really enjoy it." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3176.0 0.0 0.0 0.0
"He is soooo goood at explaining. Amazing" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4542.0 0.0 0.0 0.0
"Determinant has been determined. Thank you MIT!" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 3360.0 0.0 0.0 0.0
"I learned mathematics from the best teacher and started to like it ever since. Great thanks to you, Prof. Gilbert Strang." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5651.0 0.0 0.0 0.0
"33:16, 40:50, I think it's incorrect to claim capital sigma is EigenValues. I think for square symmetric matrix it still has singular decomposition, U equals V, but capital sigma here is actually Eigenvalue square. Because SVD is based A'A and AA', not A itself. Can anyone help clarify? Thanks!" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 955.0 0.0 1.0 0.0
"hoah this lecture is tough but very interesting at the same time :3" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13179.0 0.0 0.0 0.0
"Thank you so much for sharing these beautiful information with the whole world." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9368.0 0.0 0.0 0.0
"Can anyone direct me to a good proof for 19:36?" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 3017.0 0.0 1.0 1.0
"This professor is not the best I've seen on youtube. Not that he doesnt understand what he explains but his methodology is not essentialising the obscure concepts. First, he should have discribed the slope as delta x on delta y....( why f(x))?...or the obscure equation y-yo= m (x-xo)... could have been easyer as m= delta x/delta y...." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10905.0 0.0 1.0 0.0
"muito obrigado." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13965.0 0.0 0.0 0.0
"Wow, MIT is awesome for putting these up on Youtube." tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12064.0 0.0 0.0 0.0
"From this great lecture, I am finally learning the full meaning and understanding of eigenvalues and eigenvectors in linear and system theory. DR. Strang is the  leading commentator on this subject." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 3935.0 0.0 0.0 0.0
"Please look up to ""The Venus Project"" it offers solution to most of the problems we face today.War, poverty, hunger, starvation, illnesses,unemployment, crime, deprivation, human suffering can be solved with THE VENUS PROJECT. It offers method to achieve better world." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8206.0 0.0 0.0 0.0
"Brilliant. He needs to be recorded. His every sentence clarifies some linear algebra confusion that I had. Even though I have done this corse in my university, I still find it useful to watch his lectures. Even the most introductory ones, like this. Truly amazing job." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2945.0 0.0 0.0 0.0
"10/10/2019: Just finished 18.01. David jerison is just amazing." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 335.0 0.0 0.0 0.0
"Excuse me, I'm new to LA, and I'm wondering why we can be sure that [-1,-1,1,0] and [-1,0,0,1] at ""47:53"" are the only two particular solutions. I mean, could it be two or more?" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 3697.0 0.0 1.0 0.0
"So this is like algebra and geometry combined... with a bit of grammar thrown in..." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8796.0 0.0 0.0 0.0
"Gilbert Strang, thank you very much for everything you have done for us. You are the best teacher I have ever met" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4034.0 0.0 0.0 0.0
"Poor Schmidt. He didn't deserve the shade" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 8227.0 0.0 0.0 0.0
"much easier than the first lecture imo" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13963.0 0.0 0.0 0.0
"I love this lectures. I refresh my math knowledge with them. Thank you!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5817.0 0.0 0.0 0.0
Excellent!! ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3689.0 0.0 0.0 0.0
"Mmore Olympic erasing by Denis Auroux!!" WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7687.0 0.0 0.0 0.0
"For 48 differet reasons, I love prof. Strang" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 3836.0 0.0 0.0 0.0
"Why can't zero be in the pivot position?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11800.0 0.0 1.0 0.0
"in every lecture of this teacher, why the students are laughing and coughing very much. that's kinda very disrespectful. the teacher seems very nice and sweet but the students are just making fun. they should respect him, atleast for mit when their lectures are on internet." tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13584.0 0.0 0.0 0.0
"what an epic!!!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 15123.0 0.0 0.0 0.0
"god bless u man,nice clear  lectures" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 12929.0 0.0 0.0 0.0
"thanks so much for pointing this out!!!!!!!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14607.0 0.0 0.0 0.0
"Prerequisites please??" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 8242.0 0.0 0.0 0.0
"He actually brought a chain, lol" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4458.0 1.0 0.0 0.0
"Professor Strang just pulls out numbers out of thin air without explaining where they come from. How does he come up with the solutions at 31:27?" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 8356.0 0.0 1.0 0.0
"Thank you MIT, I now understand green's theorem!" tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9154.0 0.0 0.0 0.0
"@32:20 me directing my gf on how to suck on deez nuts" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 1538.0 0.0 0.0 0.0
"The opening remark was just wonderful to listen to!" 3eiio3Tw7UQ "19. Weak Law of Large Numbers" "6.041 Probabilistic Systems Analysis and Applied Probability" 10216.0 0.0 0.0 0.0
"Great, super clear. I like his accent now" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 4374.0 0.0 0.0 0.0
"Is Guass-Jordan elimination is only work for square matrices? What about rectangular matrices?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6748.0 0.0 1.0 0.0
"I Really Like The Video From Your Spherical coordinates surface area." RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4970.0 0.0 0.0 0.0
"sir,can we think of matrices as complex numbers in argand plane" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 14315.0 0.0 1.0 0.0
"thanks a lot for these amazing lectures. Who's the author of the textbook?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 14571.0 0.0 0.0 0.0
"11:50 guy on left is watching other lectures" CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 381.0 0.0 0.0 0.0
"Very clear concept (Ce qui n'est pas clair n'est pas français (""What is not clear is not French"").)" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11163.0 0.0 0.0 0.0
"Great lecture series" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4255.0 0.0 0.0 0.0
"Professor Strang is an absolute legend!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8349.0 0.0 0.0 0.0
"Lol the most annoying camera man ever" YAo1sd4kuOQ "2. Forbidding a subgraph I: Mantel's theorem and Turán's theorem" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 7399.0 1.0 0.0 0.0
"this man is mad funny" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14904.0 0.0 0.0 0.0
"Excellent stuff." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3674.0 0.0 0.0 0.0
"Sir You are wonderful and  beautiful mathematician Thank you so much for teaching us for being with us" Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8694.0 0.0 0.0 0.0
"@24:38 When the professor mentions that the system is singular, why does he say it is because  (0,0,..0) is a solution of the system. Doesn’t a non-trivial nullspace of matrix A make the equation Ax=0 singular?" ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 1516.0 0.0 1.0 0.0
"To do column operation the matrix multiplies on the right. To do row operation the matrix multiplies on the left." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11032.0 0.0 0.0 0.0
"Awesome style of teaching...Thanks a lot !!!" EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 2770.0 0.0 0.0 0.0
"nice keplers law stuff. that part of physics got cut off because of covid for me" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14039.0 0.0 0.0 0.0
"Excellent , I was amazed to see the one to one correspondence between solving Ax=b when b is not in the column space of A and least squares fitting by a line when all the points doesn't exactly fit in a straight line" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 3628.0 0.0 0.0 0.0
"@valterlorran Sim, e acho uma boa ideia esse negócio de ensino superior grátis. Pois quem busca conhecimento é o aluno, escola é só para o professor corrigir os exercícios, aplicar provas, passar o tempo e dar diploma.  

=)" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2058.0 0.0 0.0 0.0
"Beautiful lecture, professor. I really appreciate this contribution." 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 2822.0 0.0 0.0 0.0
"Thank you so much!" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 9382.0 0.0 0.0 0.0
20:58 YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 664.0 0.0 0.0 0.0
"Gilbert Strang is the Noam Chomsky of Linear Algebra...... <3 <3" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4027.0 0.0 0.0 0.0
"That was an error, it should be -2, he corrected." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 9920.0 0.0 1.0 0.0
"""hm I don't know if I've done this too brilliantly""
I also say that after my algebra exams !" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 156.0 0.0 0.0 0.0
"What a wonderful man! Just wonderful!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11437.0 0.0 0.0 0.0
"Course complete. Prof. Strang is a master of his craft." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 3252.0 0.0 0.0 0.0
Thankyou lZrIPRnoGQQ "27. Backpropagation: Find Partial Derivatives" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9863.0 0.0 0.0 0.0
"the thing about one family hit me hard" TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 14745.0 0.0 0.0 0.0
"The real part of the lecture starts at 9:55" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 10269.0 0.0 0.0 0.0
"Penerbangan adalah jalur tercepat mencapai tujuan menggunakan pilot dan copilot utk menerbangkan pesawat bermesin jet dan berpenumpang banyak dgn jarak yg jauh dan melewati daratan lautan yg dinamis dapat lebih cepat sampai di banding melalui lautan dan daratan, mengatur arah angin melihat kondisi cuaca,dan mempersiakan semuanya...mesin yg digunkan bisa mesin sama dgn.kendaraan biasa bisa juga jet dgn aftur bahan bakar....standart pembuatan mesin sudah ada patent....hanya pembuatan teknologi baru itu ygvmasih di kembangkan teknologi matahari,listrik,plasma,laser,cahaya......itu perlu risert......utk buat mesin harus lansung ke lokasi supaya bisa buat mesinnya..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8161.0 0.0 0.0 0.0
"Jackpot unearthed....blessed" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 7123.0 0.0 0.0 0.0
"very good teacher, love it!!" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15010.0 0.0 0.0 0.0
"Have about this subject at the moment, don't understand anything about it - low selfconfidence. but watching this lecutre - I understand everything again." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4446.0 0.0 0.0 0.0
"just saw a funny way to write ""8"" lol" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 13740.0 0.0 0.0 0.0
"Wow! Sure wish I'd had this professor for linear algebra!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12051.0 0.0 0.0 0.0
"The conjugate transpose is written with H for Hermitian. In quantum mechanics, we use the ""dagger"" symbol which looks like a cross." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 10056.0 0.0 0.0 0.0
"this was in an otome game" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 14923.0 0.0 0.0 0.0
"I wish this guy would eat something" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6232.0 0.0 0.0 0.0
"Thank you Professor Strang! I am going to get up early tomorrow morning and watch this video with the best part of my day!

I also need to buy a super expensive notebook only for Professor Strang's class!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9222.0 0.0 0.0 0.0
"In the ex 1. on derived distributions y should be in (0, 8] not in [0, 8] to avoid division by zero in PDF for Y." H_k1w3cfny8 "10. Continuous Bayes' Rule; Derived Distributions" "6.041 Probabilistic Systems Analysis and Applied Probability" 6663.0 0.0 1.0 0.0
"I don't get a thing" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5302.0 0.0 0.0 0.0
"""But now for the most important step: WHY..."" This is what sets apart a math teacher from a great educator. 90% of people teaching GJ elimination wouldn't bother to show you why it works, thus creating a legion of students who act more like computers than mathematicians. What Strang does should be considered the standard, and its deeply satisfying to learn from him because of his standard of decency; that is, to respect students' intelligence and curiosity." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 36.0 0.0 0.0 1.0
"Prof claimed that A+b give the same result as ATA-1b in 40:39 if matrix ATA is invertable . But if it is not invertable ,what is geometric meaning of A+b? Is it still projection of b onto the column space of A?" ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8280.0 0.0 1.0 0.0
"Aah so that's how SVM works - chooses the vectors. I.e. the probabilities are highest proportional to norm squared." z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2190.0 0.0 0.0 0.0
"The best Probality Theory course I've seen." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 9992.0 0.0 0.0 0.0
20220517簽 xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 634.0 0.0 0.0 0.0
"Even though I'm in 5th grade this is educational!" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3588.0 0.0 0.0 0.0
"I started on 18th December, 2020, and today, I have reached it. I noted down every single thing, along with hundred of papers that manifest the thoughts of my own. I brainstormed, I suffered, but above all, I was enlightened. 18.06 is brilliant. MIT is brilliant. And Professor Gilbert Strang is spectacular. Thank you, MIT. Thank you, Professor Gilbert Strang." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5971.0 0.0 0.0 0.0
"My observation is not a comment about the quality of instruction. I really enjoyed these lectures, and I really appreciate Strang's instruction. I thought it was interesting that there was no one there, I wasn't implying anything." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 7779.0 0.0 0.0 0.0
"Thankyou prof. Strang and MIT ocw for making it all possible. i just cant express my feeling in words..... Thankyou" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9870.0 0.0 0.0 0.0
"19:01 ?" mc1y8m9-hOM "22. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 552.0 0.0 0.0 0.0
"Make the whole class an exercise and be done." ZWzCHjN3_3s "Lecture 11: The Lebesgue Integral of a Nonnegative Function and Convergence Theorems" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 7564.0 0.0 0.0 0.0
e^(ix)=cos(x)+i*sin(x) wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12783.0 0.0 0.0 0.0
"In the pyramid example, why is the height equal to n?" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6683.0 0.0 1.0 0.0
"Yo that last example kinda woke" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12157.0 0.0 0.0 0.0
EZ RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 3543.0 0.0 0.0 0.0
"Thank you Prof but I would like to find a video about apllied mathematics especially focused on power system thank you" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 9186.0 0.0 0.0 0.0
"weren't whiteboards invented before 2005?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 15099.0 0.0 0.0 0.0
"https://www.youtube.com/watch?v=dD60vgirt8g
How to Create a New Admin !User Account in Windows-10" ImHAGH_OEow "Lecture 20: Taylor's Theorem and the Definition of Riemann Sums" "MIT 18.100A Real Analysis, Fall 2020" 13279.0 0.0 0.0 0.0
"Thank you for this class. The teacher is very good." 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 9279.0 0.0 0.0 0.0
"Sir please explain how determiner use to find the equation has a unique sol.or not" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 8701.0 0.0 1.0 0.0
"Thank you, MIT, for posting these." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9503.0 0.0 0.0 0.0
"@bud389 lol" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 1808.0 0.0 0.0 0.0
"Sorry if this has been asked, but is there a textbook, handout resource ?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8855.0 0.0 0.0 0.0
"Amazing lecture😍😍" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2379.0 0.0 0.0 0.0
"Thx Professor" 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 11007.0 0.0 0.0 0.0
"what is difference between practice exam and exam on this page? https://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/exams/" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15153.0 0.0 0.0 0.0
"@Andrei Krishkevich there is no connection between e and e'. the notation is just somewhat misleading." 3eiio3Tw7UQ "19. Weak Law of Large Numbers" "6.041 Probabilistic Systems Analysis and Applied Probability" 1583.0 0.0 1.0 0.0
"https://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/ax-b-and-the-four-subspaces/transposes-permutations-vector-spaces/ lecture webpage" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 13264.0 0.0 0.0 0.0
"What is the text used for this class?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11538.0 0.0 0.0 0.0
"so MIT students don't even need to know vectors to get in?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14324.0 0.0 0.0 0.0
"12:27 did he just put a question mark at the beginning? I though that was only in Spanish..." sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 396.0 0.0 0.0 0.0
"Thank u mit" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 9072.0 0.0 0.0 0.0
"God, I love the way you teach!" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 4098.0 0.0 0.0 0.0
"Brilliant, better insight than the original 18.06" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2943.0 0.0 0.0 0.0
"I got goosebumps the first time I saw this lecture. He is an incredible teacher." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5446.0 0.0 0.0 0.0
"really great! much better than my professor." IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 14250.0 0.0 0.0 0.0
"Shouldn't we calculate dy/dx to find out the slope at the bottom point? Though y/x and dy/dx give the same result in this problem, is it the correct approach to calculate y/x instead of dy/dx?" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8654.0 0.0 1.0 0.0
"His choice of words are excellent and he makes the whole lecture so fluid. Thank you MIT" mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 4743.0 0.0 0.0 0.0
"Excellent lecture" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 3648.0 0.0 0.0 0.0
"Prof. Strang, happy birthday!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8312.0 0.0 0.0 0.0
"Thank you Prof. Strang for changing the way to study maths rather than cramming now we not only just study matrices but can visualize itbecaue of you. Never seen a wonderful teacher like you.I hope I will meet you somday to show my gratitude. Highly recommended for everyone." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 9196.0 0.0 0.0 1.0
"I have decided to comment on every lecture from here on. So far I have fallen in love with Maths. It is incredible." ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5522.0 0.0 0.0 0.0
"You find one angle, then what?" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12206.0 0.0 0.0 0.0
"Why they don't used the pointpoint slides for lectures? Though it feels quite cool~~" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11925.0 0.0 0.0 0.0
"wow this helps with my advanced proficiency calculus class in my high school." MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15421.0 0.0 0.0 0.0
"This is art ! Thank you Prof. Strang" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10639.0 0.0 0.0 0.0
"I loved the kindness and the clarity with which he teaches linear algebra in a playlist from the 90s. Now it touches me to see how much the passing of time has changed him (and not changed him at all at the same time!) after so long. Thank you prof Strang" 2K7CvGnebO0 "19. Saddle Points Continued, Maxmin Principle" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5858.0 0.0 0.0 0.0
"Amazing Lectures. If you think its taking too much time - Watch it at 2X speed. 2X Speed still sounds very clear." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 2351.0 0.0 0.0 0.0
"you can install the volume boost extension for chrome to increase the sound volume" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 15498.0 0.0 0.0 0.0
"I got 70 out of 75 in my final linear algebra exam thanks MIT..." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 5441.0 0.0 0.0 0.0
"Didn’t attend even a single lecture at this course on my university. Spend two weeks with this channel and went on to do past papers for two other weeks and eventually got the highest grade on this course all that thanks to this man. This channel deserves Nobel price someday. Thanks 🙏" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3397.0 0.0 0.0 0.0
"Loved that you captured your audience with the ""kissing Statue"" in relation to stats..... very engaging :) since statistics in a Phd program is so painful lol" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7477.0 0.0 0.0 0.0
"You have to do some elementary statistics course to understand these lectures, but when you actually manage to understand this, it transforms all you learned in elementary statistics course. Everything suddenly makes so much more sense" QXkOaifVfW4 "9. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 12212.0 0.0 0.0 0.0
amazing!!!! JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 12358.0 0.0 0.0 0.0
"skip till 10:00 to jump r8 into the lecture" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 14317.0 0.0 0.0 0.0
26:50 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 809.0 0.0 0.0 0.0
"Single Variable Calculus finished. 2021, China" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8683.0 0.0 0.0 0.0
"I just finished all my homework, now I'm watching this. Smh..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5603.0 0.0 0.0 0.0
"40:10 F norm" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1126.0 0.0 1.0 0.0
"I bet that the mistake was deliberate. It was a mathematical genius stunt , just to connect previous lecture to present." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5176.0 0.0 0.0 0.0
"El límite de mi agradecimiento tiende a infinito :)

The limit of my gratefulness tends to infinite :)" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3559.0 0.0 0.0 0.0
"I get what he means, but shouldn't dy actually be chopping in horizontal segments?" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5436.0 0.0 1.0 0.0
"Is there any prerequisite required?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6838.0 0.0 1.0 0.0
"What is everyone using these concepts for?" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 11517.0 0.0 0.0 0.0
"If you don't like this professors explanations I recommend you to watch the Thinkwell calculus videos. Unfortunately they are not free, but I have never seen such a intuitive, simple and funny explanation of calculus that will help you to really understand the concepts =)" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6541.0 0.0 0.0 0.0
"Thank you MIT OCW for sharing knowledge." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9130.0 0.0 0.0 0.0
"Gotta hand it to Dr. Strang! He's still going strong and loves doing it. Those students and all viewers of these videos should consider themselves lucky..." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4170.0 0.0 0.0 0.0
"for the people saying they did this in high school:  have you ever been to college?  are you aware that the people who go to college are all from different high schools?  are you aware that all high schools do not provide a good background in calculus?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12889.0 0.0 0.0 0.0
"Excellent video" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3678.0 0.0 0.0 0.0
"44:32 ""I'm pausing on that proof for a minute..."" doesn't complete it in the end :(" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 1238.0 0.0 0.0 1.0
"30:30 why is professor saying that random variable L cannot be 0 by definition? Is it because the string of days is infinite and there is always a possibility of at least having one losing day?" gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 890.0 0.0 1.0 0.0
"What book is used for this class?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 11471.0 0.0 0.0 0.0
"37:19
“Independence: that looks at combinations not being zero,
Spanning: that looks at all the combinations,
Basis: the one that combines independence and spanning,
Dimension of a space: number of vectors in any basis ( cause all bases have the same number)“" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 1062.0 0.0 0.0 0.0
"7:15 affirmative action and quotas yay!" TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1396.0 0.0 0.0 0.0
"Please correct me if I am wrong.
While subtracting 2*row 2 from row 3, the value at position 3,3 should be -5.
Also in b,  it should have been 10 not -10.
Please check 😅" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8201.0 0.0 1.0 0.0
"who didn't understand the transformation of variables I recommend you to watch wildberger  linear algebra series on you tube it is very helpful, he will take step by step with a wonderful journey of linear algebra." UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15258.0 0.0 0.0 1.0
"Do they provide certificate for the courses?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3415.0 0.0 0.0 0.0
"It's awesome" TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7030.0 0.0 0.0 0.0
"I actually have one more question at 24:19. Can I write the determinant of two vectors in columns instead of rows? Are these two the same mathematically? (Because the calculated results seem to be the same.)" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5016.0 0.0 1.0 0.0
"MIT course doesn't have any ads" z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7516.0 0.0 0.0 0.0
"38:54 very important" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1087.0 0.0 0.0 0.0
"@bmwills8993 Yes but nobody actually pays that (unless both their parents are doctors...)" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1799.0 0.0 0.0 0.0
"Every university has Linear Algebra some time in the begining because everyone don't have this in high school. I promise you, within 6 month if you study engineering you will be a bit humbled.

It's an introduction class man.. ^^" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3607.0 0.0 0.0 0.0
"Great lectures and problem sets. But is it possible to get related solutions? Or is any one working with problem sets? Plz contact me!" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 4303.0 0.0 0.0 1.0
"He looks he is french from accent" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4567.0 0.0 0.0 0.0
"i didnt understand how he got the third raw of E32 matrix" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13360.0 0.0 1.0 0.0
"He is such a sweet man and a genius teacher at the same time" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4543.0 0.0 0.0 0.0
"If we have any x,y,z to power greater than 1 then we it cannot be solved using linear algebra? If so, what is field that solves it?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6532.0 0.0 1.0 0.0
"He’s the best." Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4706.0 0.0 0.0 0.0
"thanks for such a great content" Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14581.0 0.0 0.0 0.0
"Thanks MIT" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9596.0 0.0 0.0 0.0
"Math - this is how you do it.

Oh, and I lol'd at 22:48 when they clapped for him." dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 7603.0 0.0 0.0 0.0
"Every lecture is mind blowing" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3597.0 0.0 0.0 0.0
"deepest thanks to u MIT" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12731.0 0.0 0.0 0.0
"What a waste of time of students. Nothing meaningful is learned in here!" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 11434.0 0.0 0.0 0.0
"You are a star, dear lecturer." jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 12165.0 0.0 0.0 0.0
"this professor is just amazing; I guess the guys attending are watching in absolute awe, melting in their seats, and that's why they remain in silence" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 14914.0 0.0 0.0 0.0
"With the avant-garde camera angles... film majors 10000%" nbENJ-Ce7Nc "Lecture 3: Cantor's Remarkable Theorem and the Rationals' Lack of the Least Upper Bound Property" "MIT 18.100A Real Analysis, Fall 2020" 11970.0 1.0 0.0 0.0
"@IIAOPSW LOL please look lower down. you removed them and are incorrect:)" jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1637.0 0.0 0.0 0.0
"1:18:14 good question" MGqoLm2aAgc "10. Computation History Method" "MIT 18.404J Theory of Computation, Fall 2020" 592.0 0.0 0.0 0.0
"He is great!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 4517.0 0.0 0.0 0.0
"I could not help smiling when he just so smoothly introduced the concept of Basis Vectors. I was never able to understand it and now it seems that it was always so easy. The pauses he takes during explanations really builds you up and makes you think. Do not fast forward. If he is speaking slow. There is a reason. I am sure he is experienced enough to technically garble all the information and leave. But he does not. Please respect that and you will actually start learning." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 5248.0 0.0 0.0 1.0
"""In mathematics all the key equations have zero in the right hand side""" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 72.0 0.0 0.0 0.0
"for now let us stay with the nice case where matrices work  😮
                                                                                           - sir gilbert strang" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12885.0 0.0 0.0 0.0
"lecture starts at 5:18" ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13773.0 0.0 0.0 0.0
"this man is such a good professor. in comparison to the professors of the University of Ghent..." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14905.0 0.0 0.0 0.0
"WOw, Unbelievable and incredible handwriting! So clear, concise, and elegant!!" 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11250.0 0.0 0.0 0.0
"Thanks for helping my insomnia" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9684.0 0.0 0.0 0.0
"such an awesome professor. MI,T could you also upload single variable calculus lectures from him. The one you have, right now,  is very confusing." dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 14415.0 0.0 0.0 0.0
"I do not know how to say thank you. I started loving and understanding linear algebra from when i started watching your lectures. Thank you so much. I really appreciate  it. wish you the best." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 5290.0 0.0 0.0 0.0
https://youtu.be/CssSU-jjb9c J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13290.0 0.0 0.0 0.0
"i don't think they're current, they're just the ones that are on the OCW website" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13366.0 0.0 0.0 0.0
"Finished (07/04/22). To the exam! Thank you MIT OCW!" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3801.0 0.0 0.0 0.0
"i agree, it's better for the environment and progresses science and math" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13323.0 0.0 0.0 0.0
"love this russian lecturer
" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 13884.0 0.0 0.0 0.0
"Thank you prof." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9302.0 0.0 0.0 0.0
"Thanks Michael, very cool!" oNsscmUwjMU "2. Nondeterminism, Closure Properties, Conversion of Regular Expressions to FA" "MIT 18.404J Theory of Computation, Fall 2020" 9623.0 0.0 0.0 0.0
"7:50 Lucky that the points got quite thick." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 1403.0 0.0 0.0 0.0
"Very good contribution to the student community, but not if I could put the
transcript of 18.01 Single Variable Calculus, thanks" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11174.0 0.0 0.0 0.0
"Всю школу прошили?" vMaKx9fmJHE "12. Testing Goodness of Fit (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 15552.0 0.0 0.0 0.0
"Wow, can't believe he was only 30 years old here." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12068.0 0.0 0.0 0.0
"Is Saying: ""the Square Root of Two"", Redundant?" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6754.0 0.0 1.0 0.0
"What is the professor's name ?" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11532.0 0.0 0.0 0.0
sorry VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 14371.0 0.0 0.0 0.0
"In the king example, the question is ambiguous. ""What is the probability of a child being a girl?"" vs ""Given two children of unknown gender, if one is a boy, what is the probability the other is a girl?"" It's not immediately clear which of these questions to answer from the verbiage in the presentation, and given the fact that the latter interpretation would probably not be asked in normal conversation, I don't think it's naive to answer the former interpretation. Apparently semantics is very important in probability and statistics." 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 6669.0 0.0 1.0 0.0
"non-trivial solutions doesn't exist for nxn matrix if their columns are linearly independent" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 14077.0 0.0 1.0 0.0
Psinphisintheta. RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8458.0 0.0 0.0 0.0
"The professor reminds me of Stuart from Big Bang Theory :)" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10250.0 0.0 0.0 0.0
"I was just watching his 2005 video lectures of Linear Algebra and I suddenly got to this lecture. I don't know why but it broke my heart to see Prof. Strang aged so much. Such a lovely human!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6155.0 0.0 0.0 0.0
"Thank you so much!!" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9392.0 0.0 0.0 0.0
"key lecture, love it!" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 13750.0 0.0 0.0 0.0
"Why they asking about how to solve a det ( )? I learned before that Mult Calculus…" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11924.0 0.0 0.0 0.0
"So.. line integrals over scalar valued functions are not covered in this course?? How dare u!!" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8812.0 0.0 1.0 0.0
"3:30 plot the points where the function is not defined, with new notation
19:20 general strategy for sketching
47:20 key idea to find max/min" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1114.0 0.0 0.0 0.0
"@fprecoiil math is easy if you have a good professor" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1840.0 0.0 0.0 0.0
"I honestly don't know what I would have done without this course. It has been a real joy listening to Professor Strang. Thank you" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5579.0 0.0 0.0 0.0
"Rather, Theft is wrong, even if you give some of your proceeds to the poor.  I think that's quite a bit closer don't you?" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8496.0 0.0 0.0 0.0
"How would something like a Bayes factor relate to a prior distribution?" bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 4908.0 0.0 1.0 0.0
"I learn it from lec 1 to the last one! Thank you, Prof. Auroux and MIT!" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5646.0 0.0 0.0 0.0
"Thanks! Will definitely donate after each time I finish one of your courses!" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9836.0 0.0 0.0 0.0
"at 36:20 i was yelling ""MOVE THE FUCKING CAMERA""" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12445.0 1.0 0.0 0.0
"In difference equation in 11:00 it is better to compare differential equation with v_t+1 - v_t =A* v_t." k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6632.0 0.0 1.0 0.0
"Now we need  a course on Complex analysis, Partial differential equations and differential geometry" 9_xG0AGRa-w "Lecture 2: Cantor's Theory of Cardinality (Size)" "MIT 18.100A Real Analysis, Fall 2020" 7961.0 0.0 0.0 0.0
"I think the regular professor is better! Well, I liked the way he taught the chain rule, but I didn't like the way he proved the product rule and the quocient rule. " 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6063.0 0.0 0.0 1.0
"the double integral is pi / 8 = 0,392699082
" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14684.0 0.0 1.0 0.0
+ J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 248.0 0.0 0.0 0.0
"This is the problem with my teachers, they just rush throughout everything." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 10754.0 0.0 0.0 0.0
"21:00 wow, I finally understood it!" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 670.0 0.0 0.0 0.0
"I want in MIT ! Please take me there :)" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6133.0 0.0 0.0 0.0
"I understand his argument for A and B, but I wouldn't really call it a proof. More like a persuasive description. There seems to be a magic moment where he says use your imagination as things go to the limit and you see that it does not blow up it just continues its trend. I can see that but it does not seem to pbe proven, just plausible. The other proofs he has shown cancellations that leave only real definite quantities behind. I know what he says is true, but I would not call his proof tight." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6118.0 0.0 0.0 1.0
"So remember here what actually are complex numbers. As we saw previously. And NOOOW as we've seen in order to ""IN-TRI-CATE"" in a manner of speaking the complete programme of this year... we gonna use the *vector real*.
Which is as you know how complex numbers in electricity are philosophically related to physic and so on. Here taking the shape of *real numbers*
#WTF 😑" 0_w-R_g5lRA "Lecture 10: The Completeness of the Real Numbers and Basic Properties of Infinite Series" "MIT 18.100A Real Analysis, Fall 2020" 8786.0 0.0 0.0 0.0
"@TheDareDevil2510 
+1" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 1739.0 0.0 0.0 0.0
"why are students shouting at the end? " 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15283.0 0.0 0.0 0.0
"Chalk boards drive me crazy." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3135.0 1.0 0.0 0.0
"A true informative lecture by a brilliant professor! Can't say how much I enjoy the way he explains every concept; so simple, so elegant!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 2164.0 0.0 0.0 0.0
"Strang goes hard." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 8902.0 0.0 0.0 0.0
"39:35，The cost of columns is about n^2 or 1/2n^2？I think it should be about 1/2n^2." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 1099.0 0.0 1.0 0.0
"48:22 let's do statistics" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 1294.0 0.0 0.0 0.0
"At 23:00 why would reusing data for different questions lead to wrongful  conclusion ?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 2614.0 0.0 1.0 0.0
"The way he explained the Buffon Needle Experiment. 
Wish I knew about this before.
Thanks MIT opencourseware for these lectures" CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 10326.0 0.0 0.0 1.0
"nerd fight." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14016.0 0.0 0.0 0.0
"Very nice.painstakingly explaining things nice." UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11222.0 0.0 0.0 0.0
"Strang is immensely passionate about his subject matter; a master of his domain — a caring, objective, and gifted communicator, never an arrogant showoff.  He intuitively knows how to pump life into seemingly dry material, shows everything by example without skipping critical steps, follows a clear and logical roadmap that leads to a strong framework for envisioning and dealing with practical applications, enables you to learn the myriad of technologies without losing sight of the interconnections and the big picture; and above all, he puts himself in the students’ shoes and patiently works through the maze of potential challenges that they might face in absorbing the material." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8907.0 0.0 0.0 0.0
"$40  and You are not welcome'" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 205.0 0.0 0.0 0.0
"This man is simply amazing and awakes the love to mathematics in everyone ♥" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 10873.0 0.0 0.0 0.0
"Even which students' have less idea in vector , they can properly understand watching these lectures...........
TQ so much sir 💐🇮🇳" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3593.0 0.0 0.0 0.0
"One of the most important lecturer" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8099.0 0.0 0.0 0.0
"Remember that so long as you do not change length or direction, you can place that vector anywhere. So, take your result somewhere in the top left and move it down and you will see that it aligns with his vector c. He did not explain this well, or he expected it to be review maybe." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8549.0 0.0 0.0 0.0
"This is the best probability course I have come across online. Checked out several courses but it has been simplified here that makes it very clear for us who graduated from school for a while. The teaching style is outstanding. Thank you MIT and Professor John Tsitsiklis" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 10743.0 0.0 0.0 0.0
"Thanks Sir ! I m so glad i ve had the chance to listen to your lecture its so clear and it made me advance in short time" ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 9645.0 0.0 0.0 0.0
" شرح جيد لا بأس به" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13.0 0.0 0.0 0.0
"i think it should be available online. " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13474.0 0.0 0.0 0.0
"Its professor from futurama irl! Haha strang is a living legend. " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7089.0 0.0 0.0 0.0
"suppose I'm in 3D if nullspace is a plane can we not simply write nullspace as an equation of that plane and every x,y,z be the possible values that give b of zeroes similarly if column space is plane and vice versa for row space and null space of A^t?
p.s I do understand we can't write any of four subspace as a line in 3D because there is no equation of a line in 3D it's just the equation of the plane" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14424.0 0.0 1.0 0.0
"this lecture take me 5 hours believe it or not. lmaoooo. let's go! we moving forward." JTbZP0yt9qc "6. Maximum Likelihood Estimation (cont.) and the Method of Moments" "MIT 18.650 Statistics for Applications, Fall 2016" 14898.0 0.0 0.0 0.0
"Meh, good video but his lectures are not much better than lecture from my college. Most outstanding teacher from MIT is Walter Lewin :D" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 7654.0 0.0 0.0 0.0
"quiz tomorrow woo
" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 14241.0 0.0 0.0 0.0
"""god gives everybody a bonus of extra 10 cm""" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 154.0 0.0 0.0 0.0
"Hats off for professor Gil Strang and MIT for this amazing classes.
One question: I may missing something, the last part, where he says that you can obtain the matrix G from D with this formula, I think that is not correct. You don't have the squared norms of the vectors and professor Strang assumes that you have it on the diagonal of D but diagonal of D is all zeros, am I right? Or am I misunderstanding anything?
Again thank you very much!" L3-WFKCW-tY "33. Neural Nets and the Learning Function" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4439.0 0.0 1.0 0.0
"Did ya notice that the limit as x approaches x zero of (x-x zero) IS zero only when your multiplying by it, but not when you are dividing by it? That is seriously sloppy. We need another math symbol to say that the (x-x zero) in the numerator approaches zero as opposed to equals zero. If it was EXACTLY zero, then dividing by the same term would be illegal." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3390.0 0.0 1.0 0.0
"""had better be more than 18"" was the correct answer" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 155.0 0.0 0.0 0.0
"beautiful method. he even risks seeming stupid during the lecture but his method is so beautiful, so effective. He is a REAL TEACHER." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 12518.0 0.0 0.0 0.0
"Are the whites the native americans?" BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 2528.0 0.0 0.0 0.0
"Many thanks to professor Jerison, Joel Lewis, Christine Breiner, professor Miller and the MIT for this excellent free course. Good education has never been so accessible. Off to 18.02!" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7595.0 0.0 0.0 0.0
"No, he didn't." PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7901.0 0.0 0.0 0.0
"I wish this was available when I was an undergrad. I would have came to OCW for every single friggin course. But glad its available now, certainly helps with grad school." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 6233.0 0.0 0.0 0.0
https://bookerystore.com/downloads/linear-algebra-and-optimization-for-machine-learning/ Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13256.0 0.0 0.0 0.0
"قناه جميله تستحق المتابعه اليوميه 👍👍🌹👍👍🌹👍 بالتوفيق والقبول الدائم ياارب العالمين" cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 15574.0 0.0 0.0 0.0
"What a privilege it must be to have such a marvelous professor.
Thanks MIT for these 35 lectures!" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11429.0 0.0 0.0 0.0
"Why is it Delta F instead of Delta Q?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11874.0 0.0 1.0 0.0
18.06 YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 522.0 0.0 0.0 0.0
"Such a mess, I don't get it." lZrIPRnoGQQ "27. Backpropagation: Find Partial Derivatives" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8936.0 0.0 0.0 0.0
"With this awesome tutorial and maybe one of the most passionate professors I've ever seen, even the snow outside the window seems to show some Christmas feelings." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11971.0 0.0 0.0 0.0
"Thank you! Prof.   I guess it is many of ""yous"" who make MIT the MIT!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9480.0 0.0 0.0 0.0
"very interesting" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 15021.0 0.0 0.0 0.0
"Did he ever define what a limit is ? where ?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3370.0 0.0 1.0 0.0
"that was some really badly cleaned blackboard at the 0:33" phbw9r1iUDI "7. Parametric Hypothesis Testing" "MIT 18.650 Statistics for Applications, Fall 2016" 14644.0 1.0 0.0 0.0
"I was taught that the inverse of matrix A can be found as ->   (1/ |A| ) * adj(A) ...... is this ok for me to skip these methods... coz I'm kinda frequent with that" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 6168.0 0.0 1.0 0.0
"what is c-cell ?" bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 15152.0 0.0 1.0 0.0
"superb lecture 👌" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 14421.0 0.0 0.0 0.0
"i appreciate this guys 3D drawing skills" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 13341.0 0.0 0.0 0.0
"some students drop at the portion.
But you can review this or others any times as you want." sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14361.0 0.0 0.0 0.0
"Love this guy. I did get a bit lost on the Taylor stuff but I need to review it and was here mainly for the parametric representation part." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7458.0 0.0 0.0 0.0
"Ahhh, ""deserving"" MIT students. Sleeping through the lecture. Noone to point out fast to the professor that he accidentally wrote 3 instead of 2 as the third coordinate of b. To professor Strang, my eternal gratitude for this wonderful series of gems and for showing us true beauty of linear algebra and math. Thank you so much." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 2289.0 0.0 1.0 0.0
"Google article mentioned at 4:33 [Why Swift for TensorFlow?](https://github.com/tensorflow/swift/blob/master/docs/WhySwiftForTensorFlow.md )" rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4164.0 0.0 0.0 0.0
"Yeah ... he was talking about (3,3,7) wich is the sum of the first 2 ...  in the next lecture he is correcting the error you are talking about : ) 
" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 12119.0 0.0 1.0 0.0
https://www.youtube.com/watch?v=PfSfjUuKnoU J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13276.0 0.0 0.0 0.0
"I don't get why people were laughing at around 19:54" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5313.0 0.0 0.0 0.0
"I didn't quite understand how (x+∆x).....(x+∆x) got us the term nx^n-1∆x. Won't ∆x be multiplied n-1 times instead of n?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5275.0 0.0 1.0 0.0
"Gilbert Strang is a gift to humanity!! This dude single-handedly made me love one of my most hated classes from college.
Cheers from Brazil 🇧🇷🇧🇷" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 4018.0 0.0 0.0 0.0
"Prof Gilbert Strang explanation is clear and definitely keeping student like myself learning Mathematics at 50 years of age motivated to learn more. Thanks a lot Prof. Gilbert Strang for your contribution in the field of Mathematics." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8262.0 0.0 0.0 0.0
"I'm confusion at  19:25. yTx = 1 which is the imposition,  but how to get YTX  =  identity (the matrix form below) ?  how to prove that  (yTi xj = 0) when i is unequal to j ?" z3SmljnD_nQ "15. Matrices A(t) Depending on t, Derivative = dA/dt" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6314.0 0.0 1.0 0.0
"Cool so good!!! I love it" z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3209.0 0.0 0.0 0.0
"Decided to watch this for ummm... fun and boredom and all I can say is... OWWWWW MY BRAIN D=" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3337.0 0.0 0.0 0.0
"This made my brain hurt." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10842.0 0.0 0.0 0.0
"17/3/20 Quarantine with calculus and David Jerison it's fun." YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 498.0 0.0 0.0 0.0
"How about adding
[a Q_accept b #]
[#]
and
[##]
[#]
Domino's to end things up.
Where we have possible permutations of the upper string with Q_accept states." MGqoLm2aAgc "10. Computation History Method" "MIT 18.404J Theory of Computation, Fall 2020" 4798.0 0.0 1.0 0.0
"Beautiful , so beautiful" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 2814.0 0.0 0.0 0.0
"6:23 ""that long, infinite series"" hmmm...." k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1383.0 0.0 0.0 0.0
"The textbook part of bayesian statistics is noticeably harder than other parts of the book." XtNXQJkgkhI "22. Bayesian Statistical Inference II" "6.041 Probabilistic Systems Analysis and Applied Probability" 10298.0 0.0 0.0 0.0
"12:10 the review is over." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 387.0 0.0 0.0 0.0
"another one for vectors..good" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12377.0 0.0 0.0 0.0
💡 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 15726.0 0.0 0.0 0.0
"I love this!!!!!" rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5839.0 0.0 0.0 0.0
"This is actually a shitty lecture, he doesn't even explain what it means to integrate both sides" 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10608.0 0.0 0.0 0.0
"22:50 What b turns out to be, or b? To be or not to b?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 704.0 0.0 1.0 0.0
"Is there a sequel? Like Linear algebra 2?" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 6823.0 0.0 1.0 0.0
"This is a masterpiece of explaining the basis of Linear Algebra, although it does not cover the advanced topics, such as derivative, used in ML and DL. Strongly suggest to follow the OCW full course instead of only watching the videos." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 10600.0 0.0 0.0 0.0
"This is high school stuff in my country." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10673.0 0.0 0.0 0.0
"Why you give as an examples about the hight , in min 40 , if we know that it is continuous variable and we talk about discrete variables ? Plz correct my ideas If I miss understand some thing" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 11939.0 0.0 1.0 0.0
"?? I understood everything except my pivots are 2, 3, 4 :(
I love that last bit. Kind of like SVD." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 1463.0 0.0 0.0 0.0
"Plz explain fubini's theorem proof" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8222.0 0.0 1.0 0.0
37:13 QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1056.0 0.0 0.0 0.0
"im surprised MIT offers high school math....such an expensive prestigious school and they take in students who barely passed high school lol. scored  a 5 on bc calc exam straight A's throughout all of highschool and got denied. its just pure luck boys. so much wasted time getting all A's i couldve just partied all highschool and had the same odds of getting into MIT" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13571.0 0.0 0.0 0.0
"Lagrange is not a french name. Lagrange was from Italy and settled in france later in his life. His real name was Lagrangia." 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7245.0 0.0 0.0 0.0
"Good Job Professor" TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4115.0 0.0 0.0 0.0
"Wow what an amazing professor. If only every math professor was as clear as him!

THANK YOU MIT!! 
" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12045.0 0.0 0.0 0.0
"sound is sadly really bad :/" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14383.0 0.0 0.0 0.0
"You are the best professor ever....Great great I want to keep saying great" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 12180.0 0.0 0.0 0.0
"@OCW @MIT OpenCourseWare, would it be possible to add the lab instruction sheets to the course material? It's not included unfortunately. References in this lecture, e.g. @31:22" 2K7CvGnebO0 "19. Saddle Points Continued, Maxmin Principle" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1694.0 0.0 0.0 0.0
"@45:36 If you don't remember that, please take immediate remedy :))))" rLlZpnT02ZU "4. Parametric Inference (cont.) and Maximum Likelihood Estimation" "MIT 18.650 Statistics for Applications, Fall 2016" 1562.0 0.0 0.0 0.0
"@22:30 there is a 3rd meaning: the boy saw (as cut in half with a saw) the girl..." m9eHViDPAJQ "4. Pushdown Automata, Conversion of CFG to PDA and Reverse Conversion" "MIT 18.404J Theory of Computation, Fall 2020" 1514.0 0.0 0.0 0.0
"reis 85 yaşında kafa zehir." wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14260.0 0.0 0.0 0.0
"Thank you MIT. #Grateful." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9163.0 0.0 0.0 0.0
"39:36. haha... this guy is a genius" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 1100.0 0.0 0.0 0.0
"Dr Jerison is one of the best teacher i have ever met in MIT. thanks so much for your work." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3492.0 0.0 0.0 0.0
"my right ear feels more educated than the left ear" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14000.0 0.0 0.0 0.0
"Hey could anyone help me to get homework. I REALLY WANT TO DO ALL THOSE QUESTIONS" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4692.0 0.0 0.0 0.0
"Lol I know how to do computations with eigenstuff and thought I didn't need this lecture. Then within the first 5 minutes or so, he starts discussing eigenvectors in terms of projection matrices (if you're already in a subspace of the projection matrix, your direction doesn't change). This kind of esoteric insight is why I've followed this lecture series from lecture 1. He gets my head turning every time.

Professor Strang, you are a gift to humanity, I wish you well! And many thanks to MIT OCW for making these teachings available to people everywhere ☺️ A lot of good will come of this

Anyways, back to the lecture." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 7396.0 0.0 0.0 1.0
"Very good lecture.  Very simple to understand.  Thanks for sharing." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11181.0 0.0 0.0 0.0
"16:15 why interior of Japan flag (second matrix) has rank 1?  Maybe it's 2?" 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 470.0 0.0 1.0 0.0
"Best linear algebra lectures" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 2866.0 0.0 0.0 0.0
"Please stop taking the camera off the equations!!" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8214.0 1.0 0.0 0.0
"What does he actually mean when he says ""it's inverse is going to be big"" .. he says it 2 times..  when talking about columns in bad condition and nearly singular matrix.. please help . And also, please tell what problems could a ""big"" inverse cause ?" Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11487.0 0.0 1.0 0.0
"I have a doubt, in projection we are considering the orthogonal distance and in lease squares approach it is the vertical distance.. how both become same. somebody please help me.." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5489.0 0.0 1.0 0.0
"videonun youtube kapak fotosu çok anlamlı.çalişmazsaniź nah geçersiniz şeklindeki hocanın hareketi çok manidar" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 15045.0 0.0 0.0 0.0
"shouldn't it be 8/(10 choose 3)?????????? wtf?? Does he correct it later in the video?" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 14297.0 0.0 1.0 0.0
"This makes me sad..I'll miss him and his lessons" ZwpwmGP5ITM "Lec 34: Final review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10845.0 0.0 0.0 0.0
"He got an A.B. from Harvard in 1975. Suppose he entered Harvard with 18 and got his degree 4 years later with 21. Then 1975-21 = 1954.
So he probably was born around 1954 and is 55 today." 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4486.0 0.0 0.0 0.0
"@ t = 8:45 If you transform the full rank Scottish flag i.e. turn it 45 degrees you get the rank 2 English flag. In other words, you can send the English flag with the instruction to turn it 45 degrees to avoid a full rank transmission." 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1489.0 0.0 0.0 0.0
"I would like to see the rest of these lecture" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6262.0 0.0 0.0 0.0
"ear
" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12787.0 0.0 0.0 0.0
"where is lec8" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15235.0 0.0 0.0 0.0
"all these comments have me scared, I havnt watched this lecture yet but the last one was pretty confusing" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 12327.0 0.0 0.0 0.0
"All students should start out with a course in Group Theory
(& a *rigorous* treatment of Limits) 
BEFORE taking Calculus." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2308.0 0.0 0.0 0.0
"Great lecture! But was the memorylessness property correctly formulated? I think it should be P(X+2|X>2). Or maybe I understood his notation incorrectly." -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 4264.0 0.0 1.0 0.0
"Can someone share a drive link of pdf of Gilbert strang Sir...if any...." d32WV1rKoVk "12. Computing Eigenvalues and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3099.0 0.0 0.0 0.0
"THAAAAAAANKKKK YOUUUUU!" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8979.0 0.0 0.0 0.0
"Real life sheldon cooper" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8498.0 0.0 0.0 0.0
"Pr. Tsitsiklis finds two envelopes with money notes, in every student's hat.
Changes the notes to coins, and tosses each coin.

What's the expectation that :
1- Pr. Tsitsiklis does something more exciting than tossing coins?
2- At most one hat, is available for Pr. Tsitsiklis by the Final Lecture (L=25)?" EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 8236.0 0.0 0.0 0.0
"sorry im confused how mc^2 disappear?" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 14377.0 0.0 0.0 0.0
"Wow,  YOU totally fail!   That is the standard equation for a free fall object, with eighty meters as the height.  

Integrate the equation to get Velocity.  V = -10(m/s^2)*t.  Get it?  He is rounding gravity to 10 m/s^2 for simplicity.  So at t=4 sec, the velocity is -40 m/s.

There are units  in his distance equation which are not usually shown

S = 80 (m) - 5 (m/s^2) * t^2

I hope that this helps you understand a little better." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12059.0 0.0 1.0 0.0
"I spent my years as a student. To teach something to someone, you firstly should motivate them by showing the point they will reach if they grasp taught. This is why firstly you should solve a lot of different real life example. In this course, students cant see the outlet of tunnel." C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 5968.0 0.0 0.0 1.0
"I couldn't clearly understand about vector spaces and subspaces..." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 5249.0 0.0 0.0 0.0
"is this who kevin spacy was supposed to be in 21? haha" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 13667.0 0.0 0.0 0.0
"@BYMYSYD so f'(x) is actually supposed to be something but he doesn't place it because it's long and anyway it gets multiplied by zero?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1597.0 0.0 1.0 0.0
"Anyone looking for an intuitive explanation of L'Hospital's rule: https://www.youtube.com/watch?v=Hu0z-sFfF8Y (Courtesy: Derek Owens)" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2509.0 0.0 0.0 0.0
難しいyo Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 15668.0 0.0 0.0 0.0
"Thanks! Now is time for 18.03. Long live MIT !" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9832.0 0.0 0.0 0.0
"excellent question." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 12825.0 0.0 0.0 0.0
"Professor Gilbert Strang is a great educator and teacher, I am watching his videos from many years now. I really love this guy. Professor it is my deepest , humblest and kindest request to you to make  a video lecture series on a convex optimization . Thanks for your effort , May Allah give you long age, health , wealth and Prosperity." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8326.0 0.0 0.0 0.0
"At 31:50 , why do A2 and A6 have a little c on top  to make it look like A2 complement, A6 complement ?" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 2643.0 0.0 1.0 0.0
"I didn't get the diagonalization trick for the finitary Schur theorem, do someone know what ""phi_N(k) stabilizes along the subsequence"" mean?" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 5267.0 0.0 1.0 0.0
"Everything in multivariable calculus makes perfect sense (especially when explained by a good teacher/professor like prof. Denis Auroux), until you are in the final exam with a million relatively new bits of information in your head." sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3614.0 0.0 0.0 1.0
"Wait ten years education will be free.." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11258.0 0.0 0.0 0.0
"wow, who the hell still uses a chalk board. L2 Powerpoint." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15431.0 1.0 0.0 0.0
"It is so satisfying when you struggle with linear algebra for a whole semester and then you watch these lectures and it all makes click. I bet it would be a bit harder to understand if this was the first time I heard about all these concepts because it's a lot to remember, but Gilbert Strang can explain why the rules we read in the textbooks are true very intuitively. Before I was able to solve exercises, now I am able to understand them." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 6967.0 0.0 0.0 1.0
"@eligray wow get a life " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1830.0 0.0 0.0 0.0
"master piece of video" jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 13913.0 0.0 0.0 0.0
"check out great books at fmafocus.com" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12652.0 0.0 0.0 0.0
"15th jan 2022" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 462.0 0.0 0.0 0.0
"@ Dr. Strang: OUTSTANDING!" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 1485.0 0.0 0.0 0.0
"so much love to him!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 14341.0 0.0 0.0 0.0
"But what if the first Eigen value found was wrong, based on addition and equality the othe will also be wrong" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 2966.0 0.0 1.0 0.0
"tosco??
se mas especifico de tu concepto de tosco" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14955.0 0.0 0.0 0.0
"insonmia solved" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13611.0 0.0 0.0 0.0
"@6:25 there are space robots that are starting to be able to self-replicate. it's able to mine asteroid and make spare robot parts, it's only a matter of time until it can fully self-replicate" N-_XmLanPYg "11. Recursion Theorem and Logic" "MIT 18.404J Theory of Computation, Fall 2020" 1573.0 0.0 0.0 0.0
"Very good sir" P3tGiT72APw "14. Graph limits I: introduction" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 11184.0 0.0 0.0 0.0
"Hes really good at explaining, not like my professor :<" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 4684.0 0.0 0.0 0.0
"How can you possibly go to MIT without having seen the law of cosines?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4817.0 0.0 0.0 0.0
"...what b turns out to b - lol" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 270.0 0.0 0.0 0.0
"Where is continuation? It must have been on Friday as Prof announced. But lecture 8 is not that lecture. Right?" Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11681.0 0.0 1.0 0.0
"I just finished his linear algebra 18.06 from year 2005...Good Heavens! I've studied in university for 10 years and I haven't come across a better math lecturer. Superb teaching!!! I finished the course and I can comfortably do some matrix operations without writing them down. Wishing you many more happy years and good health prof. Strang." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5604.0 0.0 0.0 0.0
"gauss jordan BIG BRAINSSSSS. Thank you Professor." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12915.0 0.0 0.0 0.0
"I have seen a lot of videos on the internet mostly through YouTube regarding random variables,  binominal, polinominal and multinominal random distributions.  I've seen several vids of this teacher and considering myself a guru on this particular subject, all I can say is that his approach, when it comes to teaching, is not the most adequate. To much theory and very few practical and clear examples. Being myself a college graduate and having the experience of knowing all lot of teachers, normally these kind of theorists are the ones who know less. They hide themselves in all this theory to try to disguise there lack of teaching capacity. Don't get me wrong, as theorists they're very good. Their lecture is very detailed and well studied. It's almost like you're hearing a recorder or a machine repeating the same thing over and over and over. Normally these kind of teachers won't even admit any sort of questions while the ""recording"" isn't finished playing (these are the worst kind). Even if you try to ask a question, anything out of the norm would cause discomfort, almost causing the ""machine"" to short-circuit. It's noticeable that he has a foreign accent. Maybe he doesn't feel very comfortable with his English and that's why he gives his lectures/classes the way he does. I don't know. I think I actually saw a video of this teacher in mutinominal distribution video where he actually says something like ""the multinominal distribution is a NICE generalization of the binominal distribution""?!?!? ""Nice generalization""?!?!?!?  When your teaching or talking about maths there is no place for words like ""NICE"". When you're teaching mathematics try to be OBJECTIVE . No wonder I have seen several videos of this guy and almost not a single practical case with a final answer. There are a lot of good videos on the internet that actually give clear examples and with final results like this one  https://www.youtube.com/watch?v=WWv0RUxDfbs&t=35s" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 5553.0 0.0 0.0 0.0
"From his lectures, I know for the first time the true beauty of Linear Algebra. It's so happy to see him again." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3930.0 0.0 0.0 0.0
"purrrr the accent..." U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14232.0 0.0 0.0 0.0
"Those 9 guys are probably from caltech.

MIT pwns." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10987.0 0.0 0.0 0.0
"Yes! Yes! I understood some of these words!" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 12143.0 0.0 0.0 0.0
"thanks , very helpful, thanks to this i dont have to suck my teachers dick anymore" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 14549.0 0.0 0.0 0.0
"one third of the way through! So glad I found OCW, I thought pivoting field for postgrad studies would be a chore, but it's turning out very smoothly. Only another 6 or 7 modules after this one, ahah." YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14153.0 0.0 0.0 0.0
"Thx,absolutely extraordinary lecture." EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 11009.0 0.0 0.0 0.0
"MIT 
course on writing" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7500.0 0.0 0.0 0.0
"his proofs are not rigorous at all.Like what is this pyramid stuff , it's just a series of squares of natural numbers , it takes like 2 lines to prove what it adds up to.I'm guessing he probably does not aim on rigor , due to this being a calc I course , but honestly a lot of times rigorous proofs are easier to understand than what he does.I feel like he tries to simplify things to a degree that they become questionable" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13170.0 0.0 0.0 1.0
"really hope teacher has a good health.he helps me a lot" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14251.0 0.0 0.0 0.0
"No real proof of the multivariable chain rule: I miss it at 20:27. Does anyone know where to find one on the internet? Thanks." 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7889.0 0.0 1.0 0.0
"Some smart people moved from CA to MA, and some stayed in CA and made a billion.  If only the probabilities had gone more my way." lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 8826.0 0.0 0.0 0.0
"hard to follow...." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 13059.0 0.0 0.0 0.0
"For the last question in 45:48, I think the other explanation should be, if the null space is [1,2,3], the first column will be the free variable,which is quite impossible, Am I right?" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 3892.0 0.0 1.0 0.0
"*This is 2019 and videos made 15 years ago, so what still top resource for linear algebra on the internet*" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 242.0 0.0 0.0 0.0
"Try:

h t t p://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/

(You have to do URL editing at the beginning because YouTube doesn’t allow links in comments.)

Lecture 28 is: “Similar matrices and Jordan form.”
" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 11097.0 0.0 0.0 0.0
"the integral on the witch's cauldron example simply gives the total energy inside the cauldron right? loved this lecture!" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14701.0 0.0 0.0 0.0
"i wish my university had that blackboard... it's awesome especiallty cause im SO SLOW " 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13501.0 1.0 0.0 0.0
"There is nothing wrong with chalk boards. If any school could afford white boards it would be MIT. Personally I find reading white chalk on a blackboard easier then those damn white boards." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10375.0 1.0 0.0 0.0
"Lecture timeline Links
Lecture 0:00
What's the Inverse of a Product 0:25
Inverse of a Transposed Matrix 4:02
How's A related to U 7:51
3x3 LU Decomposition (without Row Exchange) 13:53
L is product of inverses 16:45
How expensive is Elimination 26:05
LU Decomposition (with Row exchange) 40:18
Permutations for Row exchanges 41:15" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 7300.0 0.0 0.0 0.0
"@frade001 yea i know i'm a student at uofm and we cover the same book in the same amount of time... our exam questions are more difficult but most of our exams are curved, i'm guessing there's isn't.... MIT definitely has better lectures and the students probably have a better understanding of the material at the end of the year" PnPIqh7Frlw "Lec 24: Simply connected regions; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1841.0 0.0 0.0 0.0
"Props to the person at 36:12... I was thinking the same question !! Now it makes me think I am actually there" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8450.0 0.0 1.0 0.0
"(20:10) alternatively one can mutliply 2x = λy and 2y = λx to get 4xy = λ²xy, and use xy = 3 to get 12 = 3λ² or λ² = 4." 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 217.0 0.0 0.0 0.0
"47:34 A = Q*(Q^T*A) and obviously Q^T*A is an upper triangular matrix." 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 1284.0 0.0 0.0 0.0
"wait... this is the dude that wrote the textbook!!!???" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15053.0 0.0 0.0 0.0
"Dr. Stang --Thank U sir for making MCU great🤎" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3502.0 0.0 0.0 0.0
"@tautologicalnickname yeah, and seniors are picking on freshguys " ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2035.0 0.0 0.0 0.0
https://youtu.be/1TdZy5xYNXQ VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 13284.0 0.0 0.0 0.0
"I understand that this course is supposed to be for engineers/undergrads, but this level of math is unacceptable. The whole proof is inconsistent, lacking plausibility and even the  conclusions under the given simplifications are false. I like this series, but this lecture is a joke." wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 6121.0 0.0 0.0 0.0
"thank you al lot prof. Denis Auroux... you are a great lecturer" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14492.0 0.0 0.0 0.0
"my computer is so smart" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 13974.0 0.0 0.0 0.0
"Can anyone tell me why the professor says A repeated lambda is the source of all troubles in 1806 ? What happened?" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 3052.0 0.0 1.0 0.0
"""Maybe I'll leave the author to do that."" See, it's funny because he wrote the textbook. :)" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 84.0 0.0 0.0 0.0
"Age is just a number." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2273.0 0.0 0.0 0.0
"Professor: ""So it's -1 here. Is it right?""
Comment: ""(-1) should be (+1)""
Professor: ""Yep. That's right""
Now this is hilarious
P/s: I know he made a correction afterwards, I just wanna have some fun" aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8408.0 0.0 1.0 0.0
"I have just completed your 18.01 course and am now starting Multivariable Calculus. This is just as clear and well taught as the previous course. I think we have entered a new age of higher education where institutions such as MIT take the lead to post entire courses online free for all of whom are willing to learn. I look forward to seeing more advance courses in Mathematics, Physics and indeed all other disciplines uploaded in the future. From the bottom of my heart, thank you MIT." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5532.0 0.0 0.0 0.0
"too much information to grasp in one go.. woah nice lecture!" jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 14953.0 0.0 0.0 0.0
"20 minutes in, I am lost in information. I had to go back to understand everything bit by bit again" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 615.0 0.0 0.0 0.0
"I love Gil so much, his voice reminds me of gil from the simpsons" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5714.0 0.0 0.0 0.0
"Newton only did one iteration.. Raphson added the idea of using x1 for a new tangent… therefore Newton-Raphson Method" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7824.0 0.0 1.0 0.0
"very nice lecture, THANK YOU!!!!" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15030.0 0.0 0.0 0.0
"How are you doing" RzSp9nIFnbo "Lecture 11: Absolute Convergence and the Comparison Test for Series" "MIT 18.100A Real Analysis, Fall 2020" 4805.0 0.0 0.0 0.0
"""Real part of the lecture"" starts at 9:55" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 106.0 0.0 0.0 0.0
"I don't get why rank(P) is 1 .. anyone helps me please." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5314.0 0.0 1.0 0.0
"at one point in the 19th century vectors were controversial but they have overall proved to be easier and better than other methods. Quaternions can be used to do things  ONE DOES WITH VECTORS.  These days many people study both altho vectors are more well known." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12473.0 0.0 0.0 0.0
"This is the best MIT lecture on probability" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 10732.0 0.0 0.0 0.0
"Absolutely beautiful stuff ..." ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 2202.0 0.0 0.0 0.0
😵😵😵😵🚬🚬🚬🚬📵🕗🕣🕘👾 ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15740.0 0.0 0.0 0.0
"You don't have to memorize precisely how to start the addition rule for sin. You just have to remember to include the two possible pairings of cos and sin with a and b, and add them up. The order does not matter because of the symmetry." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12203.0 0.0 0.0 0.0
"A living master of linear algebra who is not intimidated by spontaneous insights as he articulates the deeper meanings hidden in the mysterious mathematical creature called matrices." UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 2134.0 0.0 0.0 0.0
#ERICKSONLectures VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 201.0 0.0 0.0 0.0
Nice hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7835.0 0.0 0.0 0.0
"Fantastic lecture!" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 3730.0 0.0 0.0 0.0
"i am sinful" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 13338.0 0.0 0.0 0.0
"I Really Like The Video Vector fields in 3D; surface integrals and flux From Your" phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5001.0 0.0 0.0 0.0
"Abstract
A growing lattice with a label system of growth in every direction from the centre to infinity 
whole numbers for measuring size in connection to the size of the lattice label to size and size 
of the knot so that you can solve a measure from the knot size and size from the label in three 
dimensions to help solve Euler Brick problem?

remember the difference between a label and a size.

I will show each three slices of the lattice.
slice one centre is 0L0 this is the middle of space x,y,z
0L0 is a label and it has size as well its size is the knot size.
L is not just a label knot it has size as well.


rule for this lattice
A=B
pick size of gaps in lattice 20mm
pick size of knots L in my lattice is a squares diaginal = 10mm
example
-----------------------------------------------------------------------------------
example of lattice

slice 0 centre 0L0 and centre of lattice

 2L0  2L0  2L0  2L0  2L0
 1L0  1L0  1L0  1L0  1L0
 0L0  0L0 (0L0) 0L0  0L0
-1L0 -1L0 -1L0 -1L0 -1L0
-2L0 -2L0 -2L0 -2L0 -2L0

slice 1 centre 0L1 but not centre of whole lattice

 2L1  2L1  2L1  2L1  2L1
 1L1  1L1  1L1  1L1  1L1
 0L1  0L1 (0L1) 0L1  0L1
-1L1 -1L1 -1L1 -1L1 -1L1
-2L1 -2L1 -2L1 -2L1 -2L1

slice -1 centre 0L-1 but not centre of whole lattice

 2L-1  2L-1  2L-1  2L-1  2L-1
 1L-1  1L-1  1L-1  1L-1  1L-1
 0L-1  0L-1 (0L-1) 0L-1  0L-1
-1L-1 -1L-1 -1L-1 -1L-1 -1L-1
-2L-1 -2L-1 -2L-1 -2L-1 -2L-1

------------------------------------------------------------------------------------


so a point on the lattice
example = 0L0 

so the lattice is infinite in every way so a line will look like this.

example y = 0L0 + 0L0 + 0L0 = 20mm*3 = y this line on the lattice
so a 60mm line.

example x = 0L0 + 1L0 + -1L0 = 20mm*3 = x this on the lattice so a 60mm line.

the hard point is a diagonal line 
example = 0L0 + -1L0 + 1L0 + (Knot=1 whole and 2 halves of a knot)
so 60mm because A=B so (0L0 + -1L0 + 1L0) = 60mm + knots

now a square
example =  1L0  1L0  
                    0L0  0L0  
                     
 
example =       1L0   1L0   1L0
                         0L0   0L0   0L0
                        -1L0  -1LO  -1L0  



now a cube

   1L1   1L1   1L1          1L0   1L0   1L0           1L-1     1L-1     1L-1
   0L1   0L1   0L1          0L0   0L0   0L0           0L-1     0L-1     0L-1
  -1L1  -1L1  -1L1         -1L0  -1LO  -1L0          -1L-1    -1L-1    -1L-1

By Aaron Cattell" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 2224.0 0.0 0.0 0.0
"Great lecture on linear algebra." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4254.0 0.0 0.0 0.0
"great quality" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13001.0 0.0 0.0 0.0
"You go to school to get an extremely expensive piece of paper which confirms that you know the things that others can learn for free :)" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 12207.0 0.0 0.0 0.0
"started : day 1" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 14394.0 0.0 0.0 0.0
"Thinking back, I want to thank my statistics professor. God forbid this guy teaching at my alma mater. Just mentioning standard deviation without any explanation -- no." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 10451.0 0.0 0.0 0.0
"His passion at this age is 100 times more than what I have right now and I'm in my early 20s.Lol" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4762.0 0.0 0.0 0.0
"Very nice." 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 11218.0 0.0 0.0 0.0
"This is probably a 4am mind-melted question... but why is a quarter of a circle with radius 1 end up as area pi/8? Wouldn't the full circle be area pi, so the quarter circle is pi/4? Or is this somehow suggesting the radius is sqrt(2)/2, which would be required to justify the area?" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10705.0 0.0 1.0 0.0
"He does not teach Linear Algebra, He teach us to see the MATH as an art form and tells us how to draw math, and admire its beauty." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 4473.0 0.0 0.0 1.0
"31:19 Is it correct to say that the sequence approaches 0 exponentially fast because we keep on multiplying by x, which is how exponentiation works?" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 906.0 0.0 1.0 0.0
"I feel honored to have been able to watch your classes, it was a completely privilege. Thank you so much." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5390.0 0.0 0.0 0.0
"So apparently MIT professors can teach as well as they are smart.  There are few professors I've ever had that teach as well as him." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8740.0 0.0 0.0 0.0
"Lecture 1: Dot Product
Lecture 2: Determinants
Lecture 3: Matrices
Lecture 4: Square Systems
Lecture 5: Parametric Equations
Lecture 6: Kepler's Second Law
Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds)
Lecture 8: Partial Derivatives
Lecture 9: Max-Min and Least Squares
Lecture 10: Second Derivative Test
Lecture 11: Chain Rule
Lecture 12: Gradient
Lecture 13: Lagrange Multipliers
Lecture 14: Non-Independent Variables
Lecture 15: Partial Differential Equations
Lecture 16: Double Integrals
Lecture 17: Polar Coordinates
Lecture 18: Change of Variables
Lecture 19: Vector Fields
Lecture 20: Path Independence
Lecture 21: Gradient Fields and Curl Of Vector Fields
Lecture 22: Green's Theorem
Lecture 23: Flux
Lecture 24: Simply Connected Regions
Lecture 25: Triple Integrals
Lecture 26: Spherical Coordinates
Lecture 27: Vector Fields in 3D
Lecture 28: Divergence Theorem
Lecture 29: Divergence Theorem (cont.)
Lecture 30: Line Integrals
Lecture 31: Stokes' Theorem
Lecture 32: Stokes' Theorem (cont.)
Lecture 33: Maxwell's Equations
Lecture 34: Final Review
Lecture 35: Final Review (cont.)" tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7284.0 0.0 0.0 0.0
14:41 J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 435.0 0.0 0.0 0.0
"https://youtu.be/BChhAS1sFvA?t=1599
26:39 I wonder that why he said if div(B)=0, we don't need worry about surface independent in Faraday law?  i only can figure out that  div(B)=0 means a magnetic field always is a closed loop." BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 13288.0 0.0 1.0 0.0
"Love and Respect." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7434.0 0.0 0.0 0.0
"I love this legend" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5818.0 0.0 0.0 0.0
"Don't you have to have taken calculus prior to attending MIT?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3481.0 0.0 0.0 0.0
"Inverse start at 21:28" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6740.0 0.0 0.0 0.0
"Yo shoutout to the camera guy zooming in to help us see better" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12154.0 1.0 0.0 0.0
"Sir....could we have any solution book of your book linear algebra and its applications fourth addition." 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 8717.0 0.0 0.0 0.0
"lets be real here....those first ten minutes, the ten I could bear, were extremely ordinary. Taking a plane projection matrix was a dreadful example to start topic." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 13783.0 0.0 0.0 1.0
"Reply to a question below on why we care about the 4 fundamental subspaces in the study of Ax=b: 

In professor Strang words (not in this lecture) ""understanding the four fundamental subspaces elevates the understanding of Ax=b to a vector space point of view, specifically, to to a vector subspace level of understanding""

It will pay off when learning different types of matrix factorizations, for ex, Single Value decomposition, SVD, where A=U∑V^T.  Where U is composed of orthonormal vectors in the row space, V of orthonormal vectors in the Column Space,  ∑ by the diagonal matrix of the squares of the singular values.

Similarly,  all other matrix factorizations QR, Q(LAMBDA)Q^T, etc benefit from their description in terms of subspaces.
This understanding/insight is super powerful, even critical, in Optimization,Machine Learning,  ill posed problems, etc 

Plz don't disregard this Vector Subspace approach, it's only apparently that it doesn't seem to shine when being learnt for the first time, but believe me, it's pure gold, and the clarity with which  Professor Strang explains it is invaluable
...he said it himself, it bends your mind when extended to sets of matrices, and to sets of functions (the differential equation example, a prelude to Fast Fourier Transform) but the dividends you gain are huge" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 8553.0 0.0 0.0 0.0
"I was waiting for the question that the student asked." 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6174.0 0.0 0.0 0.0
"Come on, don't be such a hairsplitter. All this stuff anyway was not invented by Americans." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3168.0 0.0 0.0 0.0
"He keeps talking about ""subspaces"". Now I want to play Subspace Emissary is Smash Brothers Brawl." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4563.0 0.0 0.0 0.0
"I have to say: his explanation is so god damn clear!" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5565.0 0.0 0.0 0.0
"I m in serior high school and watching this vid for about 10 min i realised that my coaching teacher is much better than him.....at this time i 've only one que to ask..if mit teachers are like this why this is one of the top universities in world.Well I guess this theory has got spread somehow by one of these kinda professors of mit..don't mind mit guyz...." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5864.0 0.0 0.0 0.0
"DR. Strang , this is an awesome lecture that demonstrates the power of numerical linear algebra. Control Theory/ Engineering uses  a tremendous amount of linear algebra to solve satellite type problems. Robotic systems, which is part of Control Engineering also uses a heavy dose of linear algebra." XhSk_Lw2X_U "14. Low Rank Changes in A and Its Inverse" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3275.0 0.0 0.0 0.0
"awesome lecture! Thank you very much!" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 12491.0 0.0 0.0 0.0
Best yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 2849.0 0.0 0.0 0.0
"*Student: Professor, can you write a little bigger so we can see?

*Professor: It might be the board. Let me just change this blackboard to a whiteboard really quick. This eraser should help." bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 238.0 1.0 0.0 0.0
"why doesn't you guys upload the latest versions of lectures???" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 15314.0 0.0 0.0 0.0
"16:35 To be honest, you did wake me up" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 481.0 0.0 0.0 0.0
"I would put my two degrees up against a guy who can't find the shift key, anytime.

Do you recognize this as one of the motion equations in the vertical direction?

y = y0 + Vy0*t + (1/2)*a*t^2

y0 = 80 m, the height of the building
Vyo = 0 m/s, the pumpkin starts at rest.
a = g = -10 m/s^2
y = h,  final pumpkin height 
Substitute into your eq
h = 80 m + 0 /ms * t + (1/2) (-10 m/s^2) * t^2
h = 80 m -5 m/s^2 * t^2
dh/dt = -10 m/s^2 * t
Now at t=4 sec
dh/dt = -40 m/s, not 80 m/s as you stated." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6268.0 0.0 0.0 0.0
"14:40 but which formula I have to use to find the centre of mass ?" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 434.0 0.0 1.0 0.0
Marvellous!!! k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7599.0 0.0 0.0 0.0
"Does this make sense if I just know basic math?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3465.0 0.0 0.0 0.0
"Why were the previous 2 videos “not available in your country”?" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11931.0 0.0 0.0 0.0
"If A and B have same 4 subspaces.  
Then their ranks must be same. 
Their dimensions must be same. 
Hence their RREFs must be same." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 6461.0 0.0 1.0 0.0
"Absolutely an exceptionally perfect course! Thank you MIT!" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 2201.0 0.0 0.0 0.0
"tbh, I cried." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14441.0 0.0 0.0 0.0
"Excellent video. Off to the next..." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 3680.0 0.0 0.0 0.0
"the result of the kepler's second law was the best explanation iv ever seen." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14741.0 0.0 0.0 0.0
"maybe they use those new dustless chalk 
dunno" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13930.0 1.0 0.0 0.0
"thats why we gona fail...because we give to much attention on bullshit in order to get highpayed jobs whitch the wold dont need...the function to say that is easy: PROVIT UP-PLANET DOWN" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14656.0 0.0 0.0 0.0
"This is one of the most beautiful lectures on Gaussian elimination." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10702.0 0.0 0.0 0.0
"Amazing lecture, everything clear even though it's mathematical, thanks for sharing" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 2371.0 0.0 0.0 0.0
"@iDiViNeXx sounds french, or from some francophone country " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1886.0 0.0 0.0 0.0
"Just blessing for students who couldn't go in mit" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 7160.0 0.0 0.0 0.0
"@junior1984able there angles of triangles
" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1910.0 0.0 1.0 0.0
"@poyanator 

USA education is shit. I live in Europe, studying Economics, and I had this in far more superior level. Proves again that even so-called higher level universities still are shit :) Imagine a public university in USA, equal to primary school in Europe I presume :D" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1977.0 0.0 0.0 0.0
"41:00 that was epic" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1144.0 0.0 0.0 0.0
"I fell asleep to this...
" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5403.0 0.0 0.0 0.0
"Watching here" cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 11295.0 0.0 0.0 0.0
"dear JL,its finding humour in every part of life,this makes life simpler" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12730.0 0.0 0.0 0.0
"Probably not one of the best professors I've ever seen. He's scatter brained, lacks method, and is a bit nervous. Calculus isn't hard to learn - this guy is hard to learn from. I remember my Algebra teach hastling us to ""SHOW YOUR WORK!""  - apperently this guy never learned that....  His simplifying and shortcuts make things way too complicated - he really thinks 50+ students are going to know what he is thinking?? I would have failed his class if I relyed on his lectures... TO MUCH CHALK!

" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8256.0 1.0 0.0 0.0
"For the FFT, there's another truth to be noticed.    $$w_{64}^k = -1.0 * w_{64}^{k+32}$$  Also for this reason,   -D appears here." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 3880.0 0.0 0.0 0.0
"If you start your day with one of the lecture of Gilbert Strang, your day will be perfect! :-)" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 6555.0 0.0 0.0 0.0
Monica?? 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 7690.0 0.0 0.0 0.0
"Started it for Machine Learning. started loving linear algebra." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 8882.0 0.0 0.0 0.0
"32:50 cleaning" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 941.0 0.0 0.0 0.0
"Going to differentiate sec x. ""Never mind, we'll do that in a sec"". Pun intended?" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4104.0 0.0 0.0 0.0
"Cameraman would have become Pro in Linear Algebra by absorbing such a high level of teaching." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3001.0 0.0 0.0 0.0
"""our little matrix"" - a Gilbert Strang production" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 168.0 0.0 0.0 0.0
"What a great lecturer. Very clear." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11412.0 0.0 0.0 0.0
"I Love how he seems to discover things as he is about to write them on the board. But he is literally the who wrote the book on the subject. What a good teacher!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4933.0 0.0 0.0 0.0
"I think vector is in high school education , isn't it?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6079.0 0.0 0.0 0.0
"@TheMaskShow777 xDDDD" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1741.0 0.0 0.0 0.0
"Damn, what a good teacher." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 3309.0 0.0 0.0 0.0
"one thing that's funny though is... why in the US all the men wear that type of pants? Seriously! :D" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14152.0 0.0 0.0 0.0
"I really want a chalkboard" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5936.0 1.0 0.0 0.0
"question, the vertical error of e1,e2,e3 does not represent the distance between b1,b2,b3 's projection on the line." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 14237.0 0.0 1.0 0.0
"Thank you!" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 9476.0 0.0 0.0 0.0
"Thank you Professor David Jerison and MIT. 
Completed 18.01 on 8 August 2022. It helped a lot. Thanks a lot again." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9207.0 0.0 0.0 0.0
"I saw example 2 which shifts (moves?) the whole plane. Does this mean that Translation is not a linear transformation? If not what is it? I thought it was a linear one..." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5955.0 0.0 1.0 0.0
"Bravo! Makes my UC professor look like a chump!" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2917.0 0.0 0.0 0.0
"The most greatest lecturer who I meet in my life.
" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10194.0 0.0 0.0 0.0
"Thank you to the guy who made the question at 24:28" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9422.0 0.0 0.0 0.0
"It's so important to develop a geometric view of linear algebra." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7069.0 0.0 0.0 0.0
"Thank you very much" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 9426.0 0.0 0.0 0.0
"PIVOT!!!!! PIVOT!!!!!!!!!!!!! PPPIIIIIIVVVVOOOOOTTTTTTT!!!!
*like if you get the reference* 😂😂😂😂" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8151.0 0.0 0.0 0.0
"Gracias Dr .Strang ,yo estudie algebra lineal con su libro ,pero  verlo a Ud ,explicando en ingles , me llena de emoción , desearóa estar en su clase ,es un genio ,en persona es mas de lo que pueda decir su libro ,Mi admiración y respeto , Que calidad magistral para explicar algo tan ABstracto ,lo hace ver facil y sencillo,tanto que hasta mi hija de 12 años que esta en primaria lo entiende ,es un superhiperExplicador" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 4177.0 0.0 0.0 0.0
16:36 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 484.0 0.0 0.0 0.0
"Construct NDPDA for the language of all non-palindrome.
Construct DPDA for the language of all those strings in which the no. of a’s twice the no. of b’s.
anybody help me please" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 3204.0 0.0 1.0 0.0
THANKS! srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 8988.0 0.0 0.0 0.0
" You can even derive the law of cosines purely from elementary geometry and the mere definition of the sine and cosine. Just use Pythagoras and you'l get there." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8.0 0.0 0.0 0.0
"he emphasizes everything so good so that even the most idiots can understand... Great man !!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 13075.0 0.0 0.0 0.0
"@MikeDunn That's good and all for people in the US, but you must realise that as an online thing it will be accessed from people outside the US such as myself to who ""calc 1"" has no meaning." aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1678.0 0.0 0.0 0.0
"khanexercises . appspot . com/   <--- this guy is the only person who's actually gotten the idea of how limits work for derivatives and what derivatives actually are across to me, ever, in the abstract mathematic principle. 

I now understand that derivatives are, among other things, functions of changing features of a function and that 2nd derivatives are functions of changing features of the derivative curve of the original. (e.g. slope)

Why is that so hard for people to get across?." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13753.0 0.0 0.0 0.0
confusing osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 12667.0 0.0 0.0 0.0
" " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 0.0 0.0 0.0 0.0
"Independence, Basis, and Dimension. Hmmm, sounds like a Robert Nozick title.    Thank you Dr. Strang !" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 6707.0 0.0 0.0 0.0
"Bahut Bahut Dhanyawaad Professor saab." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 2808.0 0.0 0.0 0.0
"The prof is quite funny." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 10241.0 0.0 0.0 0.0
"Class is crowded these days, no worries. Don't know why no one is attending back in 2005! " nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3151.0 0.0 0.0 0.0
"Can anyone clarify my question....!
At 32.01 it was told that r12(n) = 1- r11(n)... it is correct intuitively but if i calculate r12(n) using normal method i got it as r11(n-1)0.5+r12(n-1)0.8 which is not same as 1- r11(n) (Here r11(n)  = r11(n-1)0.2+r12(n-1)0.5)" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 3015.0 0.0 1.0 0.0
"Professor Strang, after a wonderful treatment of the Krylov subspace you leave us hanging with the question how to solve Ax=b. Luckily, it's in your book: GMRES and x=Qy and y=inv(Ht' H)H'b*" MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8382.0 0.0 0.0 0.0
"This lecture is amazingly put together. It feels like I am watching a well written movie, where all the pieces seem to fall into place. All this is thanks to the professor." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 10796.0 0.0 0.0 0.0
31:25 N-_XmLanPYg "11. Recursion Theorem and Logic" "MIT 18.404J Theory of Computation, Fall 2020" 911.0 0.0 0.0 0.0
"was he always old? :P" L3-WFKCW-tY "33. Neural Nets and the Learning Function" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15055.0 0.0 0.0 0.0
"This is by far the most convoluted way I've ever seen an introduction to integration presented.
He makes it many times harder to follow than it is." hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10653.0 0.0 0.0 0.0
"Where is lecture 8?" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11687.0 0.0 0.0 0.0
"2007 technology brings nostalgia :)" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 618.0 0.0 0.0 0.0
"Why are MIT students having class in a David Lynch movie??" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 11775.0 0.0 0.0 0.0
"long live professor strang!" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 13848.0 0.0 0.0 0.0
"An Indian edition of this book is available only in India
http://www.wellesleypublishers.com/buy.html" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 2425.0 0.0 0.0 0.0
"There are nonzero solutions to Ax = 0 if m < n 1:17
Definition of linear independence of vectors 4:36
Examples of linear independence and dependence of vectors 7:05
Linear independence of columns of a matrix 13:18
Vectors that span a (vector) space 18:05
Definition of basis of a vector space 21:26
Examples of basis of vector spaces 24:12
(Error referenced in next lecture 27:43)
Definition of dimension of a vector space 33:17
Examples of dimension of a vector space 37:44" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 10353.0 0.0 1.0 0.0
"This is his favourite shirt colour, all lectures, except 7th" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 10674.0 0.0 0.0 0.0
"34:17 - screaming into the screen of my phone: Multiply the Es! 😂 Magical lecture, great Professor!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 979.0 0.0 0.0 0.0
"@37 Doesn't rotation in 3d space require two angles only, theta(zenith) and phi(azimuth)?" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1545.0 0.0 1.0 0.0
"At 22:48 the professor makes a minor mistake, I think ""the expected value squared"". I think he meant ""the expected value of the square""." 4UJc0S8APm4 "23. Classical Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 2613.0 0.0 1.0 0.0
"Where is lecture 8." BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11686.0 0.0 0.0 0.0
"You know, at first you start a new course, and it's kinda cool and chill, and you like it. And then, you go like *WAIT I BLINKED WWW..... WTF IS THIS THING???*

*LINEAR ALGEBRA INTENSIFIES*" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 12221.0 0.0 0.0 0.0
"he explains it well, shame i haven't picked on him earlier" sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13076.0 0.0 0.0 0.0
"He’s not talking to an empty classroom. He’s talking to us." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4704.0 0.0 0.0 0.0
"hmmm... this is interesting.I never had it in school that you cannot integrate the function exp(-x^2) analytically .
And then I solved some similar integral, of  exp(-x^3/3)... and got an answer and wondered why everybody told me this cannot be solved. Nope. You actually can.  Here is the solution of  the integral of exp(-x^2) :
https://www.wolframalpha.com/input/?i=integral+of+exp%28-t%5E2%29+from+-inf+to+x
the integral is 1/2*sqrt(pi)*(erf(x)+1)
which you actually can get by yourself also with the definition of incomplete gamma functions and integration by parts. You just have to know the incomplete gamma functions. and substitute -x^2 by -t. If you do that you get and integral that is almost the very definition of the incomplete gamma function. 
https://en.wikipedia.org/wiki/Incomplete_gamma_function


It seems you have to be precise what you mean with analytic. analytic is all trigonometric functions and exp plus some sqrt and all their possible combinations....
Gamma functions and all kind of other integrals not included.

So no need to integrate this one numerically if you have incgamma or erf at hand. And I guess there is a reason why you call it error function. And neither do you need tables anymore

This is one example where analytic math has sort of stopped before the incomplete gamma funciton and other integral defined functions and a like have been invented. I guess this is actually a case where people would vigorously disagree just because they learned it otherwise without defining precisely what means actually analytic in this case.

I always wondered why on earth people think it until I came across this video by a german prof actually shading a little light on it. It seems this is only due to the historic definition of analytic
https://www.youtube.com/watch?v=l6w868U8C-M
https://en.wikipedia.org/wiki/Liouville%27s_theorem_(differential_algebra)

 For an enghineer I would say this statement doesnt really make sense. Anyhow calculating gammas and gammainc functions, also hypergeometric functions is another story in itself, especially when multiplying special functions like exp and erf with each other to get them, that much I remember from calculating something also called F1.

Anyway... incomplete gamma functions are already seriously cool. Since you can calculate them within standard math libraries and they are the general case of many other special funcitons like error function, exponential integral, I think even airy. For many solutions of variable coefficient second order odes it was useful in many cases. And wolfram alpha knows how to handle it pretty well ^ (try for example integral of exp(-1/3*x^3))" mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 13178.0 0.0 0.0 0.0
"Shouldn't all the bases equal to b/n since they all have the same base? I'm lost.." hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8646.0 0.0 1.0 0.0
"He is Frenchy!!!!!" TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 4496.0 0.0 0.0 0.0
"Why where limit were not defined in terms of u and v in respect of x and y" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11933.0 0.0 1.0 0.0
"I am so happy that i finished this course but much more than that i grateful to you for being the amazing person you are .You have inspired me so much through this course Thank you professor .Love you" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5142.0 0.0 0.0 0.0
"The questions they ask just leave me speechless. Like how do you make it into MIT but don't understand [ x and x.y/y] are the same thing?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10265.0 0.0 1.0 0.0
"Thumb up if you made it to this lecture of the course on youtube!" rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 11000.0 0.0 0.0 0.0
"Thank you, amazing learning experience." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9519.0 0.0 0.0 0.0
"This lecture could just as well have appeared in the beginning, as the very first one, to introduce the meaning of a matrix (except for the part about using eigenvectors as a basis, of course)." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10787.0 0.0 0.0 0.0
"My thanks go to Mr. Strang" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7795.0 0.0 0.0 0.0
"Yes, he did botch up the R3 bases.  Sometimes even us Mathematicians make errors. Far as the proof oriented courses versus the application/conceptualization they both have importance. Unfortunately U tube doesn't allow me enough charachters to explain it. Let's just say they both have great validity depending on your goals." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 12147.0 0.0 1.0 1.0
"My only issue is that the camera should have focused more on what he wrote (and pointed/referred to) on the board during his explanations instead of zooming in on him....." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7780.0 1.0 0.0 0.0
"29:14 , freeeeeee" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 852.0 0.0 0.0 0.0
"He should have chosen another number instead of 7 to determine the inverse, since it appears too simple when 7 is chosen..." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4604.0 0.0 1.0 0.0
"40:32 hahauahaha he really hit the nail with saying some mysterious function ahhwuauaHWWUWHWHAA" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1129.0 0.0 0.0 0.0
"That white chalk on the chalk board is so satisfying." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9926.0 1.0 0.0 0.0
"I feel like the construction of the clique graph makes more intuitive sense if a reduction to a graph for the independent set problem is explained first. Because the graph constructed for the Clique problem is the complement of the graph constructed for the independent set problem. It would explain the for forbidden edges a bit better" iZPzBHGDsWI "15. NP-Completeness" "MIT 18.404J Theory of Computation, Fall 2020" 5395.0 0.0 0.0 1.0
"Very clear and nice, to the point." k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11162.0 0.0 0.0 0.0
"53:24 I guess that's what everyone feels after talking so quick for a long time :D" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 1346.0 0.0 0.0 0.0
"Good morning, Dr. Strang. It is always a pleasure to listen to your classes. I wish all classes were as well organized and thorough as yours. It is always a joy to listen to your classes." k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4146.0 0.0 0.0 0.0
"@chesteronline2010 $20 unit huh here in Sacramento city college I pay $30 a unit its a shame that the cost of going to school is getting more expensive l" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1815.0 0.0 0.0 0.0
"04:02 What does the professor mean by *enjoying yourself*? Is it what I think it is? Given the context of folding your hands? Well, I mean those people are still humans, aren't they?" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 292.0 0.0 0.0 0.0
"Linear Algebra is much bigger than you think.
You listen musics in mp3 and play games in 3D just because of linear algebra." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 7372.0 0.0 0.0 0.0
"Great! But why there is no one audience to listen. Bad time they have missed the Vector Spaces introduction." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4368.0 0.0 0.0 0.0
"Thank you. What a good lecturer 
" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9562.0 0.0 0.0 0.0
"could anyone respond: can a 10th grader from india watch these? like is this a beginner course on calculus?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12686.0 0.0 0.0 0.0
"Oops, I meant differentiate, of course, not integrate." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8129.0 0.0 1.0 0.0
"haha :) ""as long as it is not periodic"" 25:00 very mathematical comment" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 13036.0 0.0 0.0 0.0
"Quite a bad habit not using the decimal system for science. That apart, nice course." sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8482.0 0.0 0.0 0.0
"Best Teacher in the World. I have viewed many lectures in machine learning but,  Nobody explains better than Prof. Strang. Salute" Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2853.0 0.0 0.0 0.0
"For the Cantor's proof, why do we assume that we can construct such a B? Also, couldn't such a B be constructed for a bijection from A to A and thus we could disprove that |A| = |A|?" nbENJ-Ce7Nc "Lecture 3: Cantor's Remarkable Theorem and the Rationals' Lack of the Least Upper Bound Property" "MIT 18.100A Real Analysis, Fall 2020" 3877.0 0.0 1.0 0.0
"I'm confused about why multiplying on the left by Atranspose gives 0. When he turns the equation into At (b - Ax) = 0. Can anyone help me?" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6311.0 0.0 1.0 0.0
"for A and B it can be used another geometrical proof using the f(theta) function's graphic, taking its tangent at theta equals zero and comparing to the tangent of y=theta . The graphic of y=1-cos(theta) shows a minimun in theta=zero and the graphic of Y=sin(theta) shows the same tangent than y=theta (the relation between arclenght and angle)" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12877.0 0.0 0.0 1.0
"Thank you so much!!" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9391.0 0.0 0.0 0.0
https://youtu.be/tvivOczRcM0 VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 13307.0 0.0 0.0 0.0
"The guy is a legend. It's so clear. Thanks MIT." p-bXJIa7QVI "Lecture 30: Completing a Rank-One Matrix, Circulants!" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10130.0 0.0 0.0 0.0
"That'll explain why just after 19:12 they didn't all speak at once :)
 
Seriously though, thanks for re-recording it!!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9928.0 1.0 0.0 0.0
"Thank you, professor." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9527.0 0.0 0.0 0.0
Nice RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 7833.0 0.0 0.0 0.0
"I absolutely hate Taylor Approximations. I just spent an hour obsessing over how he did the calculations in the last five minutes or so. My mistake was that I thought he was approximating the entire X and Y functions while he was just approximating sine and cosine. I got the same result either way but I hated to see my numbers not match his.

Anyway, I think I'm finally beginning to feel the effect of not actually being in the classroom with him. I bet he assigns homework and the students get lots of practice with the concepts we don't actually see. I'm not complaining because they're being generous just making this much open source. But it really comes out. He asks the questions on the board and gives them some time to come up with answers and the amount of time he gives them is not enough time for me to solve it. (But I've got a handy dandy pause button). 

I never thought I'd say this, but I'm actually missing the homework problems. With calculus, the more times you try it, the quicker you are at it and the students obviously have more practice then those of us hanging out here." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5008.0 0.0 1.0 1.0
"what does 1 over lambda represent in the fishing example?" XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 15135.0 0.0 1.0 0.0
"@43:00 I laughed like crazy. I just felt like he was saying : '' Please God let these kids understand the one most basic thign of all this linear algebra. This is about to be on tape! ''. Mr Strang is a great professor I wish I had him as teacher. Learnign alot from this linear algebra onlien course. Thank you MIT for creating open courseware" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 1557.0 0.0 0.0 0.0
"These tutorials arent congruent with the course." EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 10429.0 0.0 0.0 0.0
"@bobdagangster 
Coz I said so! Isnt that enough sweetums?" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1801.0 0.0 0.0 0.0
"The instructor got Confused? with the cos term, C dot C has an angle of zero so, cos (0) is 1, this is why no cos appears in C dot C, has nothing to do with going back to definition of dot product, (so simple!)" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10139.0 0.0 1.0 0.0
"love this lecture" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 13883.0 0.0 0.0 0.0
"wouldnt it be called maclaurin series if the taylor series is centered at 0?" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15406.0 0.0 1.0 0.0
"I just want to say thank you so much for your life's work in mathematics education. I improved my exam scores with the aid of your videos and textbooks. You're a real champion and we are the blessed people for having people like yourself educating us" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5624.0 0.0 0.0 0.0
"Clearly Explained. Thank you Professor and MIT." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3155.0 0.0 0.0 0.0
"Petty arguments between an Aerospace Engineering graduate student at Caltech and an international olympiad participant at the level of Grade 4 playground insults. You would think that being educated mathematically/physically translates to higher level cognition when communicating with other people? Think again." 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8187.0 0.0 0.0 0.0
"why did he sum them to obtain OP?" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15301.0 0.0 1.0 0.0
"not really" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14081.0 0.0 0.0 0.0
Yes PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12134.0 0.0 0.0 0.0
"https://youtu.be/8o5Cmfpeo6g?t=2619 should the solutions contain only two vectors rather than a plane or line in 3 dimension?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 13287.0 0.0 1.0 0.0
"I watched  the open course to renew my knowledge on linear algebra and I have to say Gil strange had helped me understand linear algebra much more than I was able to ." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6181.0 0.0 0.0 0.0
"This man is a beast!!! I love when he says, OK 👌 He’s extremely clear and detailed!  I wish I had professors like him🙏" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10855.0 0.0 0.0 0.0
"Are all things defined?  " sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2521.0 0.0 0.0 0.0
"Eh bien. Si j'avait vu cela avant le 1er semestre... j'aurais eu mon semestre ! Il explique très bien, merci MIT." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3552.0 0.0 0.0 0.0
"Going through the 18.06 course, it shocked me to see him in Full HD like this. I thought he only exist in 480p. :)) Wish you all the best of health Prof. Strang, I hope to be able to see you in 8K 240fps in the future." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4102.0 0.0 0.0 0.0
"I finished it too. Thanks a lot to MIT and to the professors for all the great work. See you in 18.02. Greece, 2020" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5420.0 0.0 0.0 0.0
"So happy!
" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 8766.0 0.0 0.0 0.0
28:30 UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 838.0 0.0 0.0 0.0
"This sub is much less comprehensive than the normal one. ):" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10931.0 0.0 0.0 0.0
"He is french, btw" tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4514.0 0.0 0.0 0.0
"完结撒花🎉 Thank you professor Strang!!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 15624.0 0.0 0.0 0.0
"Bookmarks.

10:46. What the Procrustes problem is." 0Qws8BuK3RQ "34. Distance Matrices, Procrustes Problem" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2908.0 0.0 0.0 0.0
"@Shazaaming  i seriously heard 'an orgy of problems' at around 15:40" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1725.0 0.0 0.0 0.0
"Thanks to Prof.Auroux from Korea !  전기공학을 배우는 분들 중 대학교 1학년 과정에 벡터미적분학을 배우지 않은 분들께 꼭 필요한 수업입니다. 전자기학 수강에 큰 도움이 됩니다. (다른 분야는 잘 모르겠음)" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9806.0 0.0 0.0 1.0
"Can we get the slides that sir is using for teaching" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 3113.0 0.0 0.0 0.0
"The classes you are talking about are introductory classes. They are for those who never had these subjects in high school before and thus have to take it in their first year of college. Many students at MIT place out of these classes. The difficult courses come later." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10047.0 0.0 0.0 0.0
https://youtu.be/NynHmcuc8Yw EBdgFFf54U0 "Lecture 14: Basic Hilbert Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 13296.0 0.0 0.0 0.0
"Hes the goat" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 4685.0 0.0 0.0 0.0
"I do believe a more efficient block stacking strategy was found that I saw on mathologer but I can't remember" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5286.0 0.0 0.0 0.0
"These lectures are really beneficial... Very lucid explanation... Thanks professor" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10408.0 0.0 0.0 0.0
"31:20 How does he know that the columns are headed off in different directions?" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 909.0 0.0 1.0 0.0
"5:56
Most glorious bracket ever" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1368.0 0.0 0.0 0.0
"@ 32:10 X subscript ""pivot"" and X subscript ""free"" are being treated as submatrices to enable block multiplication. Hope I'm right" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 1475.0 0.0 0.0 0.0
"THAT was the great insight? b must be in the column space of A to solve it? Well DUH, that's practically the definition of the column space. Major anticlimax." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 8991.0 0.0 0.0 0.0
"5:55 The imperial system showed its retardedness clearly. 1 inch = 2.5 cm is (nearly) right. But 6'0 isn't equal 150 cm. Because 6 feet isn't equal 60 inches !!! It's 72 inches, which means it's 180cm (more exactly, it's near 183 cm).
Shaq is 7'1, and according to above argument, his height is just 177 cm, seems like a normal person. In reality, his height is 216 cm, which is very huge.

Do i blame the professor? No. He gave a great lecture. I think it's just a slip of his mind. As a professor, i suppose he does work with meter system, which caused him to think 6 feet = 60 inches, which is very natural for those who don't use the retarded system (like the rest of the world). 

Can any American answer the following question in 1 second?
""131.4 feet = how many inches?""

Well i don't know how long it takes for them, but for us non-retarded system user, 131.4m = 13140 cm, take us less than 1 second." 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 1367.0 0.0 1.0 0.0
"Thanks MIT" phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9599.0 0.0 0.0 0.0
"ขอบคุณคับ เข้าใจง่ายมาก
" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15582.0 0.0 0.0 0.0
Brilliant!!! nrDkb2MAwSA "20. Definitions and Inequalities" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2941.0 0.0 0.0 0.0
"This guy is truly amazing , what an outstanding quality of teaching!" mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 10548.0 0.0 0.0 0.0
"Genius Professor and simple explanation" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 3994.0 0.0 0.0 0.0
"25:04 that some damn combination ruin the whole lecture Lol" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 762.0 0.0 0.0 0.0
"The camera work on these lectures is great." tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10035.0 1.0 0.0 0.0
"it started to getting harder." z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13682.0 0.0 0.0 0.0
"The mathematics of Quantum Mechanics!" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 10183.0 0.0 0.0 0.0
"The proof of A^tA being invertible around 39:00 was great!" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 10259.0 0.0 0.0 1.0
"LIKE for gilbert strang
i love this guy" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7227.0 0.0 0.0 0.0
"why did he ride a scooter during lecture?" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 15300.0 1.0 0.0 0.0
"This lecture was so smooth and clear! Thank you!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10836.0 0.0 0.0 0.0
"very useful but boring" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 15041.0 0.0 0.0 0.0
"thank you for the lectures." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14496.0 0.0 0.0 0.0
"32:50... 7 is a lucky number ...only muslims will understand ..." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 942.0 0.0 0.0 0.0
"We now have lecture 13 of 18.100A Real Analysis!
View the complete course: https://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/
YouTube playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw" cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 11331.0 0.0 0.0 0.0
"Does this guy realize how bad a teacher he is? KOIK abounds." or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3463.0 0.0 0.0 0.0
"He is awesome!" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4509.0 0.0 0.0 0.0
"Professor Strang, simply : Thank you again !!!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8383.0 0.0 0.0 0.0
"This was great. I only need some Harvard friends I can impress." P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 10970.0 0.0 0.0 0.0
"Thank you sir :)" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9331.0 0.0 0.0 0.0
"24:40 hahahaha" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 748.0 0.0 0.0 0.0
"Very nice snowing in the background." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11212.0 1.0 0.0 0.0
"We're thrilled that you geniuses are now doing or have done this stuff in high school, but have you considered that this was the first day of an entry level calculus class?  Perhaps this guy is a good enough teacher to, you know, start at the beginning and describe basic ideas that build the course.  But by all means, continue feeling like geniuses even though you couldn't figure that out." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11340.0 0.0 0.0 1.0
"I dont understant why choose 7 on that question.?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 5371.0 0.0 1.0 0.0
"@SHEMANROBOCOP no shit!! lol... im an engineering student and i have to youtube all of my electrical engineering classes because my professor literally cant teach shit!! great guy, but a horrible teacher... " 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 1712.0 0.0 0.0 0.0
"finished!!! But I probably need to watch them all over again" rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12867.0 0.0 0.0 0.0
"Thank you Prof. Strang" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9192.0 0.0 0.0 0.0
"I think this could act as a proof of min 18:15 claims: 
* for the degenerate case, we have a line ( x + b / (2a) * y ) = 0 for wich z is allways 0 . It acts like the case of z = x^2 but rotated ( because the term affecting  y^2 is zero in the deg. case ).
* for the opposite signs (saddle): if we fix y=0 and let x increase we get possitive values but if we move for the line ( x + b / (2a) * y ) =  0  (the same as for the deg case) we get a decrease in the z values. (because y^2 is positive and the term affecting it is negative for saddle point case).
For the conditions of the exercise we start moving from (0,0) and the signs from above are in the case ( 1 / 4a ) is possitive (so change if negative). You can plot some functions on Google: e.g copy paste 6*x**2+5*x*y+y**2 and x**2+4*x*y+4*y**2" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6073.0 0.0 0.0 0.0
"khan academy or this video" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13752.0 0.0 0.0 0.0
"Thank you MIT, for these incredible lectures! #Grateful" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9157.0 0.0 0.0 0.0
"I am truly impressed his lecture.... I have learned about derivatives so many times but I didn't really realize why formular be made like that way.. or act like that way. AMAZING" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5149.0 0.0 0.0 0.0
"Was it like Halloween or something? In spring? :p" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 11274.0 0.0 0.0 0.0
"Grazie per il contributo educativo." RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 4190.0 0.0 0.0 0.0
"He catches and corrects it in the next lecture." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 4464.0 0.0 0.0 0.0
"Where can I obtain professor sra's slide ?" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11662.0 0.0 0.0 0.0
"thank u MIC OCW." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14458.0 0.0 0.0 0.0
"Is this course for English majors?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6861.0 0.0 0.0 0.0
"Hats off sir" AdTvkFsqcDc "16. Derivatives of Inverse and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4440.0 0.0 0.0 0.0
"In times of Covid, I hope this makes young people realize why older people are so important. Long live Prof Strang." NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6691.0 0.0 0.0 0.0
"first thought:  that is some good ass chalk." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12871.0 1.0 0.0 0.0
"Linear Algebra runs in his blood (Prof. Gilbert Strang). I now understand Linea Algebra thanks to his amazing lectures and his  too much insight into this subject!!! He opens mind and unlocks concepts which are not naturally easy to grasp." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7373.0 0.0 0.0 0.0
"@Arbaces420 lol" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 1591.0 0.0 0.0 0.0
"1:40 That's what I used to think..." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 597.0 0.0 0.0 0.0
thanks 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 14540.0 0.0 0.0 0.0
"I think for the basis of row space, it should be all non zero rows instead of first r rows." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6010.0 0.0 1.0 0.0
"How can any mXn matrix A be factorized into SQ, where both are square matrices (symmetric and orthogonal)? The dimensions are not matching. Or, is this only for a square matrix A?" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4810.0 0.0 1.0 0.0
"After 25 minute  lecture I not understand  what you have done,please sir explain it" WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2243.0 0.0 1.0 0.0
"Very good, clear and concise lecture from Prof. Tsitsiklis. The teachers at my university may be extremely skilled in their field of study, but unfortunately many of them do not have the ability to pass on the knowledge to us students in an eloquent manner... These MIT-lectures are very much appreciated and I have used, and will continue to use them when needed during my undergraduate as well as graduate years!" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 11190.0 0.0 0.0 0.0
"18:42 Why did they start clapping? Lol" tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 546.0 0.0 0.0 0.0
"Man the first time I watched all this stuff I couldn't sit more than 5 minutes without saying What the F*S(FUA*FUAUF What are you saying what is i and j why don't u just say x and y lmao Now I watch it and I'm like well duh.. yeah obviously oh wow that makes sense yeah cool... I think I cursed these teachers like 100 times and I now take it all back and am very grateful for them lol It's amazing seeing how far you grow. For anyone watching stuff like this and scratching your head, stick with it. It gets easier with time." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7576.0 0.0 0.0 0.0
"Went to the later MIT lectures for this course about 900,000 people have watched this vid only about 50,000 people actually got all the way to the end. There's a huge drop right after he finishes what most colleges consider calc 1." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11379.0 0.0 0.0 0.0
"I would like if the subtitles also put in Spanish, please" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 6259.0 0.0 0.0 0.0
"The corn and vector analogy just killed it. I am not forgetting it till the end of my life. Kudos to Prof. Denis, simply amazing." xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10059.0 0.0 0.0 1.0
"you make me more confident about machine learning，thanks" l4NoMKEHQwM "11. Derived Distributions (ctd.); Covariance" "6.041 Probabilistic Systems Analysis and Applied Probability" 15509.0 0.0 0.0 0.0
"fancy tie!!!!" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 12841.0 0.0 0.0 0.0
"I love your way of teaching since I started studying engineering 9 years ago.
Thanks so much for your love of mathematics and causing us to love it too ☺️" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5854.0 0.0 0.0 0.0
"Math ❤️" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7611.0 0.0 0.0 0.0
"I don't buy the last proof.  If one never actually uses x = xzero, a zero never exists.  In the limit we don't know if f prime tends to zero, infinity, finite, or undefined.  Therefore, we don't know if the final product ever approaches zero." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5296.0 0.0 1.0 0.0
"Lecturer :""i am actually tend to speak faster , so I hope y'all understand""
Me           : play in 2x speed" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7303.0 0.0 0.0 0.0
"Hi how many total lectures are their in 18.01 and how many are skipped over because of exams mitocw?" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4713.0 0.0 0.0 0.0
"Wow that was a great example of convergence/divergence" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12035.0 0.0 0.0 0.0
"God bless you, Dr Strang! I've struggled with matrices and matrices operation since more than a year, and thanks to you I've finally had the 'Aha!' moment." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4087.0 0.0 0.0 0.0
"7:04
Gravity's value is 9,8m/s^2, not 10m/s^2. Hence, the equation is h = 80 - 4,9 t^2 (4,9 is half the acceleration - gravity in this case), and not h = 80 - 5 t^2 as shown. How can a MIT teacher say it's 10m/s^2?
The formula the student asked for is: y = y(initial) + v(initial)t + 1/2 at^2. 
y= position (y at ground level, y(initial) at the top)
v= velocity (zero at the top)
a= acceleration (gravity in this case)
t= time
Acceleration assumes a negative value because you're heading down in the y axis.
I just took my physics final exam and I feel quite picky about this. 9,8, not 10! I expect 10m/s^2 from bloggers, not from MIT teachers." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1393.0 0.0 1.0 0.0
"and he's much much younger on ocw" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 12368.0 0.0 0.0 0.0
"And the audience was speechless." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 2448.0 0.0 0.0 0.0
"Ahah! You exactly got it! I was very confused when he used the first time a limit without defining it! But I guess this is acceptable given that this course supposes a good high school education." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2284.0 0.0 1.0 0.0
"I miss Strang, but this is one hell of a lecture!" 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5872.0 0.0 0.0 0.0
"how can the dim of symmetric matrix be 6 ?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 13201.0 0.0 1.0 0.0
"I love MIT opencourseware." 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5717.0 0.0 0.0 0.0
"This is just a perfect lecture, pure perfection! 
Can't thank you enough for explaining these concepts so clearly Professor Strang!
I can listen to Prof Strang's lecture all day everyday!" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 10679.0 0.0 0.0 0.0
"terminal 2 iron profezor" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 14443.0 0.0 0.0 0.0
"on 31:09, the dimension of that subspace is 3, because there are 3 independent vectors: [-1 -1 1 1]', [-1 1 -1 1]', [-1 1 1 -1]'" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 14147.0 0.0 1.0 0.0
"Just Finished 18.02.
Thank you Prof. Denis Auroux and MIT OCW!" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7150.0 0.0 0.0 0.0
"Starts at 13:20" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8887.0 0.0 0.0 0.0
"@kotofu is there a sort of proof?" jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1925.0 0.0 1.0 0.0
"Did you guys notice the student have an Apple Pencil at 23:13" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3393.0 0.0 0.0 0.0
"how is the fisher information used in modern machine learning - especially in practice?" JTbZP0yt9qc "6. Maximum Likelihood Estimation (cont.) and the Method of Moments" "MIT 18.650 Statistics for Applications, Fall 2016" 13239.0 0.0 0.0 0.0
"Multiplication rule/ divide and conquer/ Bayes' Rule" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 7724.0 0.0 0.0 0.0
"Haven't watched it yet (perhaps in 6 month) but thanks Proff for putting such valuable content here , thanks again." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4449.0 0.0 0.0 0.0
"I don't understand" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 5336.0 0.0 0.0 0.0
"@jillybooty  no, i am with you" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1901.0 0.0 0.0 0.0
"Thank you MIT" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 9123.0 0.0 0.0 0.0
"This is THE Michael Sipser of Sipser's Introduction to the Theory of Computation." 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 10584.0 0.0 0.0 0.0
"https://youtu.be/srxexLishgY?list=PLE7DDD91010BC51F8&t=858
Oh, ohh, ohhh. There was a party before and now all the bottles are empty." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 13306.0 0.0 0.0 0.0
"quad et demonstratum - it's latin for 'which had to be demonstrated..it's commonly used at the end of a mathematical proof." Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14235.0 0.0 0.0 0.0
"늙지 마세요!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 15673.0 0.0 0.0 0.0
"这老师真好， 看了这个课之前，我以为我遇见的是好老师。
 我遇见的数学老师，从来没解释过，坐标系里，其实是很多个变量，而且重复使用了x 和 y 来表示不同的东西。 而这一点是非常重要的，也是复杂的根源。" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15665.0 0.0 0.0 0.0
"i need that applet to get a better understanding of tangent planes and gradients, where can i find it?
" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 13443.0 0.0 1.0 1.0
"Tee hee -__-" ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9025.0 0.0 0.0 0.0
"I WISH we had more such professor at my University when I was studing. Prof. Auroux, you are a rare ""bird""." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5005.0 0.0 0.0 0.0
"Can't help but notice that someone in that lecture hall has a bad cough." Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3123.0 0.0 0.0 0.0
"[Problem Set 1 (PDF)](https://ocw.mit.edu/courses/mathematics/18-650-statistics-for-applications-fall-2016/assignments/MIT18_650F16_PSet1.pdf )" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 12274.0 0.0 0.0 0.0
"Thanks for sharing that with us. It helps a lot! " FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9699.0 0.0 0.0 0.0
"""23:37 Wow... Respect to MIT. In my school everyone would have burst out in laughter and it would have taken like 15 minutes to shut everyone up again."" - $180k education comes to about $1.72 per minute to sit in, and let's be honest, joking around for 15 minutes isn't worth $26." wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 22.0 0.0 0.0 0.0
"The vector space part sounded like intro to abstract algebra. Nice!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 10310.0 0.0 0.0 0.0
"18:26 Different respect of theorem 6 on Lecture notes" os_XGBNPllM "Lecture 8: The Squeeze Theorem and Operations Involving Convergent Sequences" "MIT 18.100A Real Analysis, Fall 2020" 537.0 0.0 1.0 0.0
"After 15 year 
In 2020
You are amazing boos......" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 2242.0 0.0 0.0 0.0
"There's the great tie again" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 10390.0 0.0 0.0 0.0
"Thank you Dr.Jerison!!! and MIT for providing the videos! I start loving math just because of these lectures :D" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9107.0 0.0 0.0 0.0
"This is at least my third time to watch this video, barely I feel I learned clearly. Thanks Lord!" bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 10641.0 0.0 0.0 0.0
"@Evan2718281828 lol yeah i see it" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1620.0 0.0 0.0 0.0
"I have a question: is exact differential the same as total differential?" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5511.0 0.0 1.0 0.0
"23:54 ok bye" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 718.0 0.0 0.0 0.0
good H_k1w3cfny8 "10. Continuous Bayes' Rule; Derived Distributions" "6.041 Probabilistic Systems Analysis and Applied Probability" 12937.0 0.0 0.0 0.0
"Thank you so much for such helpful content! I really appreciate being able to self-learn through these videos." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 9369.0 0.0 0.0 1.0
"Amazing content" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2357.0 0.0 0.0 0.0
"About 6 years ago I tried teaching myself category theory. So much of it seemed arbitrary and ungrounded - though there were parts that made a lot of sense. Now I'm beginning to understand the ""general abstract nonsense."" I hope I can shake Prof. Strang's hand or give him a high five one day 🤓" 2K7CvGnebO0 "19. Saddle Points Continued, Maxmin Principle" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2194.0 0.0 0.0 0.0
"Surprised that Prof. Gilbert could finish this lecture without any mindblowing which shows how professional he is" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 8974.0 0.0 0.0 0.0
"My tears up" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7792.0 0.0 0.0 0.0
"What did the student say in the beginning? lol" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11481.0 0.0 0.0 0.0
"Anyone jee aspirant here?" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2501.0 0.0 0.0 0.0
"I really appreciate your work. You are such a kind and clever teacher. Greetings from Chile." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5907.0 0.0 0.0 0.0
"guys, what does it mean ""to take one credit""? does it mean ""to take one course""? (I'm not from U.S. or any english speaking country, btw)" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13029.0 0.0 0.0 0.0
"Es una universidad carísima y con un nivel de investigación formidable y enseñan cálculo de varias variables de la forma más pendeja y menos formal 
Creo que nivel licenciatura es una caca." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3577.0 0.0 0.0 0.0
"In which text book can I find these pieces of information about the GLMs?" mc1y8m9-hOM "22. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 6696.0 0.0 1.0 0.0
"I love this teacher" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5838.0 0.0 0.0 0.0
"If you have Mathematica it saves you the trouble from computing the nasty trigs. Yes it is pi/8" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6547.0 0.0 0.0 1.0
"I can't find a good Optimization course(with video lectures) on the MIT website, any suggestion?" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5215.0 0.0 0.0 0.0
"Thank you MIT and to a very excellent professor." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9141.0 0.0 0.0 0.0
"Seeing the concepts of linear algebra intertwined like this is quite amazing!  I have tremendous respect for this prof for taking the time to not only prepare these lectures but to put them together into a brilliantly clear and intuitively appealing mathematical tour-de-force." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8615.0 0.0 0.0 0.0
"If you aren't convinced that the derivative sinx = cosx only works if the angle is in radians, you may want to google ""derivative of sin measured in degrees"".  You will see that they are not the same.

As for the 0/0, the proofs are done geometrically here, so you must look at the side lengths and the ratios between them rather than from an algebraic perspective.  There are also algebraic proofs that can give the same answer, but these are intuitive and easy to visualize." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6538.0 0.0 1.0 1.0
"Thank you very much!" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9448.0 0.0 0.0 0.0
"@kc8omg IMO the black board is much better.. whiteboards shine too much and the lines are too thin" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1918.0 1.0 0.0 0.0
"best conept
may all the goods and/or Governments bless u" gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 12536.0 0.0 0.0 0.0
"In short, the constant zooming in and out distracted greatly from the lesson!" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6653.0 0.0 0.0 0.0
"Is it maths for biologists or smth?
P.S. There is not unrespect for biologists. I mean that they don't need to know maths very deeply" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6787.0 0.0 0.0 0.0
"The professor is wearing a green shirt and not a red one as in the previous video. *stares into space blankly*" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10249.0 0.0 0.0 0.0
"@KaLNFoRc3R why? I think you fail how to do and read proofs in the right way. That makes you hate them." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 1648.0 0.0 0.0 0.0
"agreed! Definitely going to help for college =)" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12314.0 0.0 0.0 0.0
"Row operations multiply on the left, Column operations multiply on the right. 41:00 - perfect clarification" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8576.0 0.0 0.0 0.0
"Oh, my dear professor Strang. How I'm glad to see You. Thank You, very, very much  on unselfish and true knowledge which you give us." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8030.0 0.0 0.0 0.0
"I can smell his IQ from here" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 5201.0 0.0 0.0 0.0
"NO account of twins in Birth-Death" ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 7803.0 0.0 1.0 0.0
"the great strang! tremendous lecturer as always!!" z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14696.0 0.0 0.0 0.0
"42:50 Look he's smiling...!!! LOL" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 1190.0 0.0 0.0 0.0
"Lagrange was bi national (born italian , dead french) and is descendant of Descartes" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7247.0 0.0 0.0 0.0
"the only part of single var calculus i don't like...mostly because i always run out of paper working these problems out! " HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14723.0 0.0 0.0 0.0
"Can someone explain colors to me in this context i don't follow. Are they discrete or continuous ? (As like integer or any number on number line)Followup: does it matter?" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 3069.0 0.0 1.0 0.0
"If you are confused why lim[f(x)-f(x0)] = lim f(x) - f(x0) like me:

lim[f(x) - f(x0)] = lim f(x) - lim f(x0) = lim f(x) - f(x0)

lim f(x0) = f(x0) because x0 is some known value and f(x0) is a constant." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6535.0 0.0 1.0 1.0
"But at sin(x)^10 couldn't we use the product rule? Like take the derivative of (sinx*sinx*sinx*sinx*sinx*sinx*sinx*sinx*sinx*sinx) and use it as d/dx(abcdefghij)=a'bcdefghij+ab'cdefghij+etc etc where a, b, c, d, e, f, g, h and i are all equal to sinx?" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2958.0 0.0 1.0 0.0
"I think the practical example with the blocks is wrong, if you draw them and track the centre of mass it will be 1/2 + 1/4 +1/8 and will form a geometric series. This will have a sum to infinity of 2 and therefore it can never cantilever more than double it's initial length. This makes perfect sense if you logically think about the centre of mass and considering the block sitting on the bottom. 
The power series stuff is good starting 22:47 but the practical example at the beginning is totally wrong (I think). Which is frustrating as it's good to actually see some application." wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6060.0 0.0 1.0 1.0
"Thank you, MIT!!!" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9502.0 0.0 0.0 0.0
"finished didn't knew linear algebra is this much simple on to 18.065 from tomorrow" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 12865.0 0.0 0.0 0.0
"Thank you Mr. Strang. You are an excellent prof. Thanks MIT too" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 9175.0 0.0 0.0 0.0
"This is not a lecture. It's a projection matrix that projects everything in the chapter onto the viewer's brain." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10697.0 0.0 0.0 0.0
"That moment when I realized teacher is giving so much energy and teaching with so much passion under a 3 by 3 space known as ""Empty Room Space"". 😢" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9907.0 1.0 0.0 0.0
"lol maybe thats the reason MIT is so prestigious, they have awsome teachers!" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 13829.0 0.0 0.0 0.0
"love itt!" 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 13869.0 0.0 0.0 0.0
"This man is genius..." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 10867.0 0.0 0.0 0.0
"GREAT! I was a bit confused at first but in the end, he rocked my world as always! Thaaaank you!" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 3976.0 0.0 0.0 0.0
"In one word, he cares about his students!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6647.0 0.0 0.0 0.0
"how did he calculate E[X] in Birth-Death Process? , E[X]=rho/(1-rho) ?" ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 13212.0 0.0 1.0 0.0
"At 11:00, he is doing the univariate case, so the det part can be omitted. For the multivariate case, you need the additional fact that det(AB) = det(A)*det(B), and the result follows similarly." k2inA31Gups "18. Bayesian Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 2585.0 0.0 1.0 0.0
"at 39:45 
can anyone please explain how we got that matrix?" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12449.0 0.0 1.0 1.0
"So this is from like 15 years ago yet it's exactly what I need now." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8795.0 0.0 0.0 0.0
"also if someone has the course material please tell me where to get them , the link shared below has a broken zip file" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 12332.0 0.0 0.0 0.0
"I've been in love with Math my whole life. This course is so satisfying to me." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 6404.0 0.0 0.0 0.0
"If in calc 1 they introduced the term argmin for the place where the minimum occurred there would be less confusion as students often mistake argmin for the actual min." AeRwohPuUHQ "22. Gradient Descent: Downhill to a Minimum" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6506.0 0.0 0.0 0.0
"I like it fine :)" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5675.0 0.0 0.0 0.0
"How much time did the exam take, I want to take it" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4890.0 0.0 0.0 0.0
"i'm done with linear algebra... but it fun to relearn stuff in a more natural way... :)" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13514.0 0.0 0.0 0.0
"Explaining the 3 planes converge on a point doesn't require a visual aid: two intersecting planes meet in a line such that they are perpendicular to each other along the z axis, the line on that z axis intersecting a third plane on that z axis is perceived as a dot in that z plane. The dot is the product derived by the 3 intersecting planes." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3707.0 0.0 0.0 0.0
"why such weird camera angle T T" yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 15362.0 1.0 0.0 0.0
"the yoda of linear algebra" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 14754.0 0.0 0.0 0.0
"@55:13 You can feel Professor's heartache at this point. We all do. 😥" TTArY7ojshU "6. TM Variants, Church-Turing Thesis" "MIT 18.404J Theory of Computation, Fall 2020" 1568.0 0.0 0.0 0.0
"I spend 5 years sitting through all this shit, i get bored easily especially with engineeering now i much rather go plant a tree or have fun than do crap like this." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5967.0 0.0 0.0 0.0
Thankyou z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9864.0 0.0 0.0 0.0
"About 48:48 exactly. Bloody MIT students don't appreciate Mathematics!" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2193.0 0.0 0.0 0.0
"Rich people chulk board." BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 8570.0 1.0 0.0 0.0
"This teacher is not vesy good even for secondarry school!  His demonstration is very poor, I couldndt  understand how it is possible, that hy is MIT teacher ???!!! His geometric demonstration and explanation is really bad !!!!" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10937.0 0.0 0.0 0.0
"I thank Grant Sanderson (3blue1brown) for kindling in me the love for calculus" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5990.0 0.0 0.0 0.0
"El profesor de universidad del que más he aprendido :')" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 3560.0 0.0 0.0 0.0
"Just want to thank him and say that I love the sparkle in his eyes when he teach" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7201.0 0.0 0.0 0.0
"49:15 - how can this curve ""blow up"" as you get close to zero? It's a probability density function so surely it has to integrate to 1?" CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 1306.0 0.0 1.0 0.0
"45:57 we assume equally likely, bu prof. wrote 1/3 and 2/3 ? why" XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 1263.0 0.0 1.0 0.0
"Taylor approximation gets almost as much hate as Steve Bartman" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9016.0 0.0 0.0 0.0
"@agapitoflores001 poor? you should see the doctors" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 1770.0 0.0 0.0 0.0
"Huge respect from india" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 4914.0 0.0 0.0 0.0
"Finished (30/11/22). To the exam! Thank you, Dr Strang and the MIT OCW team!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 3804.0 0.0 0.0 0.0
"I Really Like The Video From Your Max-min problems" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4963.0 0.0 0.0 0.0
"Wow! That was one great talk. Prof. Suvrit Sra's done a great job in giving examples just light enough to drive the key ideas of SGD." k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12053.0 0.0 0.0 1.0
"I love this professor..." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5835.0 0.0 0.0 0.0
"Anyone know where homework solutions are found?" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2507.0 0.0 0.0 0.0
"i hate vectors ^^" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 13390.0 0.0 0.0 0.0
"@sanjaigupta Here there is an elegant demonstration:

It's not the only one: you can infer that x>sin(x) banally if you consider that an arc of circle is always longer than the associated chord (arc=2x and chord=2sin(x))" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1999.0 0.0 0.0 0.0
"in greece the name of integral is ""ολοκλήρωμα""=""olokliroma which means ending total of a mathematic function." 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13587.0 0.0 0.0 0.0
"Next job application.
College attended: MIT's Free YouTube channel." k2inA31Gups "18. Bayesian Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 7829.0 0.0 0.0 0.0
"Thanks for the lectures! Just a comment there's posibility of putting subs for the students questions? Some times de the camera man dosen't have the time to change the audio setup. Thanks! " 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 9720.0 1.0 0.0 0.0
"@simkintube  How many Nobel Laureates did your school in Spain produce?  Careful dissing MIT.  This is a required INTRODUCTORY course for all students.  Of course it's easy." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2016.0 0.0 0.0 0.0
"my only beef with people here saying things like

""oh these must be kids who didn't have calculus or these classes are introductory classes for kids who never had them in high school""

is that it CLEARLY says on the MIT admissions website that a student MUST have 4 years of math education in high school INCLUDING calculus. And I don't expect MIT recruiting students who SUCK in math either.

Maybe these kids just want an easy A. I don't know." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13994.0 0.0 0.0 0.0
"How is e = I-P ?  I didn't get this part. is there some intuition behind this?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 4866.0 0.0 1.0 0.0
"He never covered board ." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4588.0 1.0 0.0 0.0
"what is the requirements or knowledge that any of the learners are supposed to have?? 
.
I wish to learn these but........ hope my age wont stopping me now.. LOL
.
thanks for helping" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15171.0 0.0 0.0 0.0
"Isn't that the first and the second degree terms of Taylor expansion. " BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6894.0 0.0 1.0 0.0
"@39:22 I was like watttt..?? how the heck did he do that?" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 1548.0 0.0 0.0 0.0
"Basic high school math" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2809.0 0.0 0.0 0.0
"Why do we have to use statistics in genetics" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 11831.0 0.0 0.0 0.0
"15:46 or you could do: (1)(5/6)(4/6)(3/6)(2/6)(1/6)
the total number of choices/the total number of possibilities

The latter implies no order" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 458.0 0.0 0.0 0.0
"These lectures > TV series/movie . Be proud of yourself for watching these" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 10403.0 0.0 0.0 0.0
"Camera man should zoom out and hold it steady on what the prof is writing on the blackboard." phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2998.0 1.0 0.0 0.0
"If I heard that voice I’m dropping that class haha" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 6469.0 0.0 0.0 0.0
"I think the grad(f) at 16:00 should be 0.5(S+S tranpose)x-a , right? anyway, thank you for the amazing lecture!" AeRwohPuUHQ "22. Gradient Descent: Downhill to a Minimum" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6055.0 0.0 1.0 0.0
"mark zuckelburg on front seat!" CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 13911.0 0.0 0.0 0.0
"@5ofa completely agree. I love math and physics. Somehow i was always good at them." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1571.0 0.0 0.0 0.0
200:10 FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 619.0 0.0 0.0 0.0
"Mic ❤️" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7662.0 0.0 0.0 0.0
"MIT is the best " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7533.0 0.0 0.0 0.0
"No not much alright iknij ,jin I  I hmm noko'l" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7878.0 0.0 0.0 0.0
"38:30 -Mr. Strang gives a hint about the Maximum Likelihood Estimate (MLE)." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1079.0 0.0 0.0 0.0
"Professor Strang should have a weekly podcast about math, calculus, or analysis in life." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8363.0 0.0 0.0 0.0
"i'm confused, he says at 12min that the ""we know.. the function stays constant, but we can also know how function changes using the chain rule"" didn't he just say it was constant? so confused.... T.T" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 13512.0 0.0 1.0 0.0
"That's why MIT is MIT." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9948.0 0.0 0.0 0.0
"I wish he was doing my math review in Physics, my prof is terrible and I have to pass" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6219.0 0.0 0.0 0.0
"lol never seen some1 put a period at the end of their equation (around 7:10)" XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13830.0 0.0 0.0 0.0
"I Really Like The Video Square systems; equations of planes From Your" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4996.0 0.0 0.0 0.0
"justice for schmidt" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 13747.0 0.0 0.0 0.0
"Great lecture! Thank you MIT!" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4268.0 0.0 0.0 0.0
"why Q IS SAME? WHEN IT DEPEND ON X OR Y ? OR HOW CAN YOU WRITE Q^2?" zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15276.0 0.0 1.0 0.0
"Lecture timeline Links
Lecture 0:00
Permutations 1:17
Possibilities of permutations 7:23
Transposes 10:15
General formula for transpose 11:38
Symmetric matrices 12:43
RᵀR is always symmetric 15:06
Chapter 3: Vector spaces 20:12
What ""space"" means 22:03
Why is Origin necessary in Vector spaces 25:33
Most important thing about Vector space 28:29
A case that's not a Vector space 29:41
All possible subspaces in R² 35:54
All possible subspaces in R³ 39:04
Subspaces come out from Matrices: Column Space 39:45" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 7298.0 0.0 0.0 0.0
"Much clearer than my prof." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7719.0 0.0 0.0 0.0
"Thanks for making these videos available for free MIT. They're simply awesome." xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9688.0 0.0 0.0 0.0
"Thank you, Prof Strang. 2019-05-17 12:32:56" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9506.0 0.0 0.0 0.0
"Thank you Prof. Gilbert Strang... You always give me confidence and trigger to re-learn math!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9191.0 0.0 0.0 0.0
"@ 30:01, in the loose graph, should the height of the rectangle based on [0,1] be 1/2 which is as tall as the arrowed upright line in the middle?" mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 1474.0 0.0 1.0 0.0
"I don't undertand why MIT publish such a good material with so terrible the audio" TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 5360.0 1.0 0.0 0.0
"11:20..   precisely (S n T) does not lead to a null .. ??" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 372.0 0.0 1.0 0.0
"It is just aumsum" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6952.0 0.0 0.0 0.0
"great that we can E=AR this lecture." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 13010.0 0.0 0.0 0.0
"No one teaches this better than him" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 7885.0 0.0 0.0 0.0
"Intuitive Ideas are actually helpful to understand the concept. How simply he has explained it." ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 6737.0 0.0 0.0 1.0
"Who is watching........." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11746.0 0.0 0.0 0.0
"this guy is grandios." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14827.0 0.0 0.0 0.0
Awesome.... j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 2788.0 0.0 0.0 0.0
"Amazing sir well explained." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2392.0 0.0 0.0 0.0
"how to proof that  eigenvectors are coulums of projection matrix" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 13251.0 0.0 1.0 0.0
"Everyone's listening to this because they understand, but I play this as background noise while I study high school math. People talking about incomprehensible topics help me focus lol" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3612.0 0.0 0.0 0.0
"@27:46 anyone would be kind to explain or direct me to some source that explains how is the matrix a 2-dimensional subspace in R4? [there is some explanation below but I could not really understand it]" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 1524.0 0.0 1.0 1.0
"A   =       S     0     0     0     0
               0     U     0     0     0
               0     0     P     0     0
               0     0     0     E     0
               0     0     0     0     R

Me - trace(A)" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 2090.0 0.0 1.0 0.0
"greaaaaaaaaaaaaaaaaaat professor.I watch his every video.He is a god." MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12963.0 0.0 0.0 0.0
"You are GREAT!" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12161.0 0.0 0.0 0.0
"That's the first time, i can't grasp the content delievered  by prof. strang till this lecture of series. Gonna dive into his book to understand." d32WV1rKoVk "12. Computing Eigenvalues and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9943.0 0.0 0.0 0.0
"the guys that have the money to attend such univerisities are really lucky.. we study in shitholes with professors that in 40mins cover 3 chapters o linear algebra and you leave without having a clue about what going on" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 14698.0 0.0 0.0 0.0
"Maldita sea, porque no hay maestros que intenten explicar las matematicas de manera simple... Porque creen que hay tantos reprobados en México? La verdad este  Dr.Strang sabe mucho! Gracias por hacer estos videos!! Saludos desde México!" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7568.0 0.0 0.0 0.0
😁👍 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 15732.0 0.0 0.0 0.0
"he is actually good." YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13093.0 0.0 0.0 0.0
"50:49 ""If the earth collapsed to a
 black hole at the center of the earth with the same mass, you wouldn't notice the difference immediately"" LMAO" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1341.0 0.0 0.0 0.0
"sure big professor" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14427.0 0.0 0.0 0.0
"How many Indians?
Raise your ✋" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 4879.0 0.0 0.0 0.0
"No words can describe how good Mr. Strang is." TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 7896.0 0.0 0.0 0.0
"Om shanti k good day" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8058.0 0.0 0.0 0.0
"Me: maybe they'll teach it differently in the US 
MIT: Oh by the way, there's our Frenchiest teacher" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7649.0 0.0 0.0 0.0
"I feel so fucking lost during my calculus class, and enlightened right away after watching this video. THANKS SO MUCH!" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 5399.0 0.0 0.0 0.0
"If im not mistaken the correct Latin expression is ""quod erat demonstrandum""" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6505.0 0.0 0.0 0.0
"What a legend, always oozing with enthusiasm. LOVE his classes! He is just so precious for this world." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11422.0 0.0 0.0 0.0
"Why prodcut rule works for cross procduct?" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11907.0 0.0 1.0 0.0
"Wonderful teacher here is the secret of math as I came to know..." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11992.0 0.0 0.0 0.0
"nice prof!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 14049.0 0.0 0.0 0.0
"This course is legend." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 10493.0 0.0 0.0 0.0
"He made a pretty good circle with one quick move xD" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 4576.0 0.0 0.0 0.0
https://youtu.be/23LLB9mNJvc?t=24m38s 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 13285.0 0.0 0.0 0.0
"The same subject in khan academy is way more easier . I don't know why he is making it too complicated." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10273.0 0.0 0.0 0.0
"Dr Strang is a Legend, Thank u Sir and MIT for this awesome 
course" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3494.0 0.0 0.0 0.0
"The easy way to solve problem 3 is to use [A] [A-1] =[ 1]" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10081.0 0.0 1.0 0.0
"Chalk moment" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3136.0 1.0 0.0 0.0
"Prezado nobre amigo do canal Mit OpenCourseWare professor Gilbert Strang interessante!!!! sua explanação e demonstração,  pois padronizei o ""Teorema de Sidney Silva"", esse ""Teorema"" diz A Hipotenusa ao quadrado é igual a Divisão dos quadrados dos Catetos(a^2=b^2:c^2) que tal um prova, vejamos como segue: (01) Em um determinado Triângulo Retângulo um dos seus Catetos mede 63 cm, o outro mede 45 cm, Qual é a medida da Hipotenusa?; (02) Em um determinado Triângulo Retângulo um dos seus Catetos mede 7 cm, o outro mede 5 cm, Qual é a medida da Hipotenusa?;onde o ""Teorema de Sidney , tem um fator muito importante a ser respeitado, não pode ser aproximado, não pode ser simplificado e principalmente não pode ser arredondado, segue mais  dois exemplos, um envolvendo PI, para Pi Radiano e o outro em Graus.onde também padronizei este enigmático número de Pi(3,15) para ser Racional, com Três inteiros e quinze centésimos  finito depois da vírgula, sendo um Algoritmo Irreversível, segue o mesmo enunciado para esse ""Teorema de Sidney Silva"", o Autor.

11*Pi/6 um dos catetos,5*Pi/3 outro cateto; 1408*Pi/768 um dos catetos, 640*Pi/384 outro cateto.Qual o valor da Hipotenusa? Agora em Graus 704*Pi/6,72 um dos catetos; 320*Pi/3,36 o outro cateto.Qual é o valor da Hipotenusa?; segue mais oito fórmulas padronizadas para o ""Teorema de Sidney Silva"".

(b^2:c^2=a^2); ( c^2*a^2=b^2) ; (a^2*c^2=b^2); (a^2=x^2:c^2); (a^2=b^2:c^2) ; (b^2:c^2=a^2) ; (a^2=b^2:x^2) ; (b^2=a^2*c^2).

Meu cordial abraço, Sr Sidney Silva." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8252.0 0.0 0.0 0.0
"25:13 toin coss. well i guess his brain needs a playback speed of 0.75. love these lectures" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 772.0 0.0 0.0 0.0
"👌 Forget the name of the law, but don't forget the law." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15699.0 0.0 0.0 0.0
"Why in the world does this video have so many dislikes. Absolutely amazing lecture." 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11862.0 0.0 0.0 0.0
"Do these courses pretty much teach you the same thing that a high school AP Calculus AB class would?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3413.0 0.0 0.0 0.0
"thanks a lot, this is very useful." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14575.0 0.0 0.0 0.0
"Kpdo cerdos" 0Va2dOLqUfM "5. Maximum Likelihood Estimation (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 7224.0 0.0 0.0 0.0
"1 (0)/0-1=g
H=pπ2
G=h" TSI3LR5WZmo "25. Interactive Proof Systems, IP" "MIT 18.404J Theory of Computation, Fall 2020" 312.0 0.0 0.0 0.0
"윈도우키 + I (설정) → 접근성 → 오디오 → 모노 오디오 켜기 켬
영상 다 보면 다시 끄기" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 15685.0 0.0 0.0 0.0
"Very nice explanation.Lot of thanks to you." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11207.0 0.0 0.0 0.0
"@youtubalisation Many american students also learn this in high school. It is the most introductory calc course offered at MIT. " HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2077.0 0.0 0.0 0.0
"Why can't professor answer by using ""Rolle Theorem"" prove LHopital at 18:42 ? That student asked a very GOOD question!!! It's not pleasent to see Professor getting struggled at 19:20 Down Voting this episode :(   Same thing at 38:00, if having LHopital proved, this question should be easy" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11798.0 0.0 1.0 0.0
"Wow, although he's all right but this is the problem when the bar is already set too high :)" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12066.0 0.0 0.0 0.0
"Thanks, alot sir. You are the greatest. A lot of students in Nigerian universities watch your courses" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9845.0 0.0 0.0 0.0
"Note that the slides in ocw website are missing the absolute values in the second TV formular" rLlZpnT02ZU "4. Parametric Inference (cont.) and Maximum Likelihood Estimation" "MIT 18.650 Statistics for Applications, Fall 2016" 7935.0 0.0 1.0 0.0
"cuteness level off the charts @49:35
" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12700.0 0.0 0.0 0.0
"Testing of Goodness of Fit: 22:19" a66tfLdr6oY "11. Parametric Hypothesis Testing (cont.) and Testing Goodness of Fit" "MIT 18.650 Statistics for Applications, Fall 2016" 9034.0 0.0 0.0 0.0
"Yes, he is correct. Since the multiplier for row 2 is 2, you need to multiply what's in the (2,3) position by 2 and subtract it from what's in the (3,3) position.1 - 2(-2) = 1 + 4 = 5. Hope this helps!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12149.0 0.0 0.0 0.0
"25:00 nice notes.

https://martin-thoma.com/solving-linear-equations-with-gaussian-elimination/" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 759.0 0.0 0.0 0.0
Z PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12270.0 0.0 0.0 0.0
"he just keeps pushing the boundaries!!
it's not that i don't understand but i never thought that u can use such tools this way!" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 13105.0 0.0 0.0 0.0
"I've always heard ""Jordan"" as kind of shoes but after this Wonderful Lecture I can see sth !! THANKS PROF. STRANG" TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 6402.0 0.0 0.0 0.0
"Can I tell people I went to MIT now?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 3006.0 0.0 0.0 0.0
"Thank you. Please we need Organometallic Chemistry .tq" V3Wg_jrMSQY "Lecture 19: Differentiation Rules, Rolle's Theorem, and the Mean Value Theorem" "MIT 18.100A Real Analysis, Fall 2020" 9560.0 0.0 0.0 0.0
21:10 vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 671.0 0.0 0.0 0.0
"MIT is MIT for a reason. Thank you for open sourcing such wonderful videos." k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7523.0 0.0 0.0 0.0
"Thank you MIT and Professor Strang!" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9138.0 0.0 0.0 0.0
"I think there's some confusing notations at 27:10, which should be :
The response variable is binary so there is no choic: Y|X is Bernoullli with expected value μ(Y|X) ∈(0,1)
We can't write μ(Y|X) = X^T * β." X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 6072.0 0.0 1.0 0.0
"this man deserves the money he get" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 14900.0 0.0 0.0 0.0
"I like how there's like 14 students in the class, and . you know... a few million watching at home..  Hard to imagine what a class of 2 million students would look like." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5670.0 1.0 0.0 0.0
"take my lifetime gilbert sir" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 14433.0 0.0 0.0 0.0
"Symmetry is dual to anti-symmetry.
Bosons (symmetric wave functions) are dual to Fermions (anti-symmetric wave functions) -- atomic duality, the spin statistics theorem.
Bosons (waves) are dual to Fermions (particles) -- quantum duality.
""Always two there are"" -- Yoda." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 8976.0 0.0 0.0 0.0
"A glitch in the matrix @ 31:27" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 2113.0 0.0 0.0 0.0
"I watched his 18.06 lectures online in the mid 2000's and it left a deep impression on me. I am so happy to see he's still teaching and share his excitement about him teaching this course. <3" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6184.0 0.0 0.0 0.0
"am I the only one that thinks his ""cos x"" looks like ""ws x"" ?!" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12335.0 0.0 0.0 0.0
"thanks for giving these video series online and free
financially week students can also study by these lectures.thanks a lot" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14579.0 0.0 0.0 0.0
WOW srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 11244.0 0.0 0.0 0.0
"@tangman093090 you would've gone if you could have." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2034.0 0.0 0.0 0.0
"Thank you." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9550.0 0.0 0.0 0.0
"lol calculus was not created with students in mind xD" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13823.0 0.0 0.0 0.0
"Amateur question: At the end of the lecture, on the use of limits for proving continuity of differentiable functions, is lim { [f(x) - f(x0)]/[x-x0] } = 1/[x-x0] lim [f(x) - f(x0)] if we see lim as an operator?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2346.0 0.0 1.0 0.0
"fielsjd is right.  Your comment is ridiculous b/c (a) this is the an introductory lecture, (b) you do not know the difficulty of the problem sets or exams, which are often much more difficult than the class material, and (c) you don't know the competitveness of the grading, i.e., the ""curve.""  As someone who took Multivariable Calculus at a school up the street from MIT, these are all VERY IMPORTANT considerations." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12855.0 0.0 0.0 0.0
"want to understand why A_s has two identical rows-.-" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 15054.0 0.0 1.0 0.0
"this is great, I found this video on YouTube and it explains the concept very well with an example 
https://www.youtube.com/watch?v=J41Ypt6Mftc" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 14861.0 0.0 0.0 1.0
"Sometimes I do prefer the more imaginative, romantic approach to the first several lectures in linear algebra, beginning with defining vector spaces and how operations are made, how these spaces are defined.  I do however really enjoy this approach as well, it's actually a bit more applicable." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8845.0 0.0 0.0 1.0
"i cant thank enough. this really help us a lot where we dont get proper teaching. Thank you so much for sharing the videos for free. I wish every famous university were doing that." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13349.0 0.0 0.0 0.0
"I don't understand, why so many dislike?" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5357.0 0.0 0.0 0.0
"But how do you find c1?" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 2959.0 0.0 1.0 0.0
"At 27:27 why he devided a*bt by s*pj? What for this pj?" z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2629.0 0.0 1.0 0.0
"Why is the dashed line not a subspace? Is it because when you multiply it by the zero vector, you aren't on the dashed line? Can someone please explain that some more?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11885.0 0.0 1.0 1.0
"This guy is a legend. I love him. The neatness of his lectures is just like the beauty of mathematics, and 18.02 is definitely my favorite MIT open course." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10518.0 0.0 0.0 0.0
"You can see how passionate he is to the idea of making everyone see linear algebra as intuitive as he sees it. This is what being a professor should  be all about. Absolutely fantastic." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 12193.0 0.0 0.0 0.0
"Your lectures are a pleasure to watch (and learn from)!" AeRwohPuUHQ "22. Gradient Descent: Downhill to a Minimum" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12261.0 0.0 0.0 0.0
"Simple Differentiation
y = x^n 
dy/dx = nx^(n-1)
Differentiation of a function
y = u^n
dy/dx = nu^(n-1)dy/dx(u)
Product rule
y = u*v
dy/dx = (u'*v) + (v'*u)
Quotient Rule
y = u/v
dy/dx = ((u'*v) - (v'*u))/v^2" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8659.0 0.0 0.0 0.0
"I never thought about the fact that Gauss' theorem could be expressed in the plane, although it is pretty obvious.

Same like Green's is just a form of Stokes' in the plane." _CdoRiNSrqI "Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5886.0 0.0 0.0 0.0
"Give Laplace his due." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 4046.0 0.0 0.0 0.0
"I can see why American people are by far well educated .
HAT OFF TO YOU" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 5198.0 0.0 0.0 0.0
"Good lecture; all familiar territory, but I guess it's better to start too basic than too advanced..." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4139.0 0.0 0.0 0.0
"findings
at every entry it seems that a ratio of energy of any element and hydrogen renders half its mass 
I think that the kinetic energy of any element is the total mass of hydrogen 
what does this mean 
I think that all the elements are moving at the same kinetic energy and their distiction is a result of something else 
more research I require 
tell me if you find the answer 
please come and get me anyone I am growing tired of a peasant's life" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12862.0 0.0 0.0 0.0
"Man I wish my college had those blackboards. Nah, I kid - MIT rocks! I wish I had this professor!" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7571.0 1.0 0.0 0.0
"You can hear the students chuckling as they recognized the Golden Ratio. Didn't quite recognize it as (1 + root 5)/2." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 12191.0 0.0 0.0 0.0
"ok... so mcdonalds it is" aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14130.0 0.0 0.0 0.0
"What about the gamma canonical link (-1/Mu)? it does not maps Mu = (alpha * beta), where alpha and beta strictly greater than zero, into the entire real line." mc1y8m9-hOM "22. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 11445.0 0.0 1.0 0.0
Interesting t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6725.0 0.0 0.0 0.0
"11:33 lol
I have a dirty mind" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 375.0 0.0 0.0 0.0
"good bless you, dear Professor" hwDRfkPSXng "Lecture 32: ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12941.0 0.0 0.0 0.0
"Thanks for making ideas come naturally professor ❤️" nvXRJIBOREc "Lecture 21: Minimizing a Function Step by Step" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9686.0 0.0 0.0 0.0
"Thanks sir" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9775.0 0.0 0.0 0.0
"At 47:43 how is the integral of 2pi * ex * dx equal to the area of a triangle?" aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2684.0 0.0 1.0 0.0
"Thanks for the course!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9708.0 0.0 0.0 0.0
"37:13 Can anybody tell me why that is that way? (-1/slope of tangent)" 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1057.0 0.0 1.0 0.0
"(When estimating theta1) Could someone please explain me why the reasonable estimate of variance is the one divided by n, not (n-1) which we learned in the previous lecture?" tBUHRpFZy0s "24. Classical Inference II" "6.041 Probabilistic Systems Analysis and Applied Probability" 224.0 0.0 1.0 0.0
"whoever's working the camera is a fucking idiot" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 15272.0 1.0 0.0 0.0
"im 16 and i learnt this i one 50 minute lesson at school" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13560.0 0.0 0.0 0.0
"Its very very useful. Thanks a lot." xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7095.0 0.0 0.0 0.0
"The last thing he wrote at the end of the lecture was ""FIN""... like the end of an old-fashioned French film.

I thought it was funny." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 10157.0 0.0 0.0 0.0
"If Jeremy Clarkson was to give us an insight into matrices like this....." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 6479.0 0.0 0.0 0.0
"https://www.youtube.com/watch?v=PFDu9oVAE-g&vl=en    exact video with beautiful graphics from 3b1b.  Prof Gilbert Strang has done a phenomenal job on blackboard." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 13275.0 1.0 0.0 0.0
"At 26:00 how did he find the inverses of E21 & E32 so easily? is he using some formula? I'm watching the videos in the MITs required order, but looks like I missed somewhere something" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 2625.0 0.0 1.0 0.0
"Well done Mr Gilbert, congratulations" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 11350.0 0.0 0.0 0.0
"Pure beauty. I just finished this course just for the joy of very nicely explained mathematics. Thank you very much prof. Auroux and MIT. God bless you." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8460.0 0.0 0.0 0.0
"Wow!!
It's indeed a Tremendous class!!❤❤❤Actually, this whole series is tremendous! 🇧🇩
Can't believe that 12 years have passed of this!!!!
If I could be there!!!😥" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12055.0 0.0 0.0 0.0
"if only we have such a professor in italy too..." 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13537.0 0.0 0.0 0.0
"Well,without any ambiguity, i claim that the A and B expression could have been proved somewhat easily and more plausible beyond the ground of probabilities by simply using L'HOSPITAL'S RULE!" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11374.0 0.0 0.0 1.0
"Simply excellent!! The Internet can save the world" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8666.0 0.0 0.0 0.0
"Professor Strang ,thank  you for an old fashion lecture on  Accelerating Gradient Descent.
These topics are very theoretical for the average student." wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8335.0 0.0 0.0 0.0
"Excellent how the instructor uses proofs to demonstrate examples.  Many instructors just say, ""this is the rule"" ...." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3645.0 0.0 0.0 1.0
"o.O i am doing this in high school..." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14098.0 0.0 0.0 0.0
"an “introduction” ..." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 12363.0 0.0 0.0 0.0
"The video on my recommendation .And I cant stop watching . One of my dream university when I was in secondary school." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10313.0 0.0 0.0 0.0
"Great man. Great teacher. He really gets teaching. He almost becomes the student while he's teaching. I love his humour. ""Feign confusion?"" I love how down to earth and unfussy he is. God why are my lecturers nothing like him" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4316.0 0.0 0.0 0.0
"1.25 speed seen to be normal." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 325.0 0.0 0.0 0.0
"man this guy is awesome." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13901.0 0.0 0.0 0.0
"Great cource!Thank you a lot!" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 4217.0 0.0 0.0 0.0
"Great lecture. Does anyone have good book tips about bayesian data analysis on longitudinal and time series data structures with R/Jags? 

More specifically, I have a case with several subjects and several observations within the subjects. In another case I only have one subject. In both cases, the consecutive observations are supposedly time-related." bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 4289.0 0.0 0.0 0.0
"EXCELENTE LA CLASE, ME GUSTA MUCHO LA FORMA COMO ABARCA Y EXPLICA TODOS LOS TEMAS, SEGUIRÉ VIENDO ESTOS VIDEOS. M.I.T. LO MEJOR.
 " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3541.0 0.0 0.0 0.0
"Has any body else spotted the error @25:21 

A^T A = sigma_2 ^2 /( sigma_1 * sigma_2 ) is that an error there?
sigma_2 ^2  relates to the vector v_2
while A^T A relates sigma^2 , a diagonal matrix 
i.e. A^T A = V sigma^2 V^T

or am I wrong, if so would appreciate an explanation

:)" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4431.0 0.0 1.0 0.0
"This teacher is great. He provides clear and concise explanations to what are potentially unfamiliar issues (to those that aren't well versed in maths such as myself.) Everybody has an accent depending on which part of the world they're from - even you. What's important is that his grammar is perfect and he knows the subject matter which makes him very easy to understand." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10935.0 0.0 0.0 1.0
"liked this first." CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 13795.0 0.0 0.0 0.0
"Thank you McLovin" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 9172.0 0.0 0.0 0.0
"What??? I never use math anymore. Labor is great" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11593.0 0.0 0.0 0.0
"For current p-sets, I doubt OCW would have them...otherwise ppl would be using them all the time" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3861.0 0.0 0.0 0.0
"44:42 ""Applied math is just physics with different notation"" LMAO" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 1242.0 0.0 0.0 0.0
"self-learning algebra here... thanks Prof Strang and MIT." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14287.0 0.0 0.0 0.0
"Gr8 Teaching !!" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4176.0 0.0 0.0 0.0
"The second time to see nobody in the classroom. The camera man is really happy to be a VIP student I believe." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10276.0 0.0 0.0 0.0
"Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 11836.0 0.0 1.0 0.0
"At 32:04 there was actually a question, someone actually raised a hand up." RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2645.0 0.0 0.0 0.0
"start 1:00" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 14392.0 0.0 0.0 0.0
"I love math" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5763.0 0.0 0.0 0.0
"What a life ,,," J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11423.0 0.0 0.0 0.0
"24:00 The combination of rows is 16*row1-9*row2-row3=0" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 724.0 0.0 0.0 0.0
"I love the ""Gauss given order"" part" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5772.0 0.0 0.0 0.0
"Damn! I hope I saw this last year" rLlZpnT02ZU "4. Parametric Inference (cont.) and Maximum Likelihood Estimation" "MIT 18.650 Statistics for Applications, Fall 2016" 3301.0 0.0 0.0 0.0
"omg.. this is just amazing, thank you MIT thank you professor Strang " Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14143.0 0.0 0.0 0.0
"29:40 why do we use p=2 norm rather than any other p?" ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 857.0 0.0 1.0 0.0
"I love this mathematician's logical way of thinking." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 5829.0 0.0 0.0 0.0
"There's a lot of magic going on here that Dr. Strang doesn't state explicitly. It makes this lecture worth a couple listen throughs." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 10385.0 0.0 0.0 0.0
"Now i remembered i studied in my 12th grade From INDIA" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7959.0 0.0 0.0 0.0
"Bạn viết chữ lớn." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2979.0 0.0 0.0 0.0
想知道他是什么口音，我怎么听着这么累。。5555.。。 PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15630.0 0.0 0.0 0.0
"I am amazed how few viewers here are. Professor, your first lecture alone is played at least 24 861 000 times on a single open course website (open.163.com) in the main land China, and your great lectures inspire and encourage great manly Chinese learners ." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5062.0 0.0 0.0 0.0
"Thanks MIT" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9598.0 0.0 0.0 0.0
"Uh, isn't every MIT frosh required to have Calc 1+2+3 under their belt before they even set foot on campus?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11117.0 0.0 0.0 0.0
"Just wondering...what keeps us from calling the eigenvector matrix E instead of S ?  Is E already used for something else ?" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 7206.0 0.0 1.0 0.0
"Wheres the applause?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 11702.0 0.0 0.0 0.0
"The views dropped from 3m  to 200k .
Quite impressive" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 10316.0 0.0 0.0 0.0
"These lectures are so clear" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10410.0 0.0 0.0 0.0
"Waiting to be informed why dim C(A) =dimC(A^T)=r but didn’t get it till the end :( Sad.
Were expecting a Prof.Strang–type of explanation." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 11267.0 0.0 1.0 0.0
"at 19:45 , when he says that that number of basis is 2, for the second order diff. equation. Can anyone point to a reference? I am somehow not so sure about it?
The basis could be three too, as x=sin(x) +cos(x) + e^(-ix) also satisfies?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 12421.0 0.0 1.0 0.0
"i thought calculus starts with sets and functions first" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13483.0 0.0 1.0 0.0
"saya tidak tau kenapa sy d sini" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 14282.0 0.0 0.0 0.0
"please share slides of this lecture." k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14190.0 0.0 0.0 0.0
"Phenomenal video. Thanks Prof Auroux (o est-ce que je dois dire merci?) and MIT for putting this together." YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8191.0 0.0 0.0 0.0
"This Lection was in 2007! here in 2022 i read in the back o tshirt of school boy ""CORONA"" (24:31)  hahah What a prophet he is.... ahead of his time!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10456.0 0.0 0.0 0.0
👍👍👍👍👍 J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 15706.0 0.0 0.0 0.0
"the interation is wrong cuz the answer is 3pi/16" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14702.0 0.0 1.0 0.0
"Minute 46: There might be a more simple solution. Instead of the Binomial formula I would suggest using Number of Edges + Number of Nodes + 1 = number of folds (spaces). N+E+1=S" sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7672.0 0.0 0.0 0.0
"Outstanding explanation. Thank you so much." gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 8141.0 0.0 0.0 0.0
"A mere thanks wouldn't be sufficient!! but still, Thanks a lot MIT !! and Prof. Strang, it clearly shows how beautifully explains the concepts, he really wants students to understand. I respect that ! Thanks alot once again :)" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 2141.0 0.0 0.0 0.0
Respect YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8554.0 0.0 0.0 0.0
"THANK YOU Prof Auroux. I adore the way you teach. You make the distinction between what is self-evident and what requires further explanation (i.e., through proof) so plain to see. It saves me so much headache and for that I thank you." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8982.0 0.0 0.0 1.0
"Is there any pre requisties for this course??" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6837.0 0.0 0.0 0.0
"Great lecture. Thank so much Professor." WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 4292.0 0.0 0.0 0.0
"I never thought I would understand spherical coordinates! This guy makes it easssyyyy" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5885.0 0.0 0.0 0.0
"I haven't reached college and I know all the stuff and more right now. Guess, Indian curriculum is ahead in this aspect." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5571.0 0.0 0.0 0.0
"So much comprehensive lecture I've ever seen!!!" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 8777.0 0.0 0.0 0.0
"June 15/2019-Very good lecture!" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 7146.0 0.0 0.0 0.0
"Yes, I know this is the most basic math, but seriously do you imagine yourself going to your day of work expecting to solve integrals and equations? 

They should prepare us how to solve problems, because all the calculus in a project is often done with it by other people. 

I don't know, what's your idea of being an ""engineer"" then? What do you imagine doing?" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12145.0 0.0 0.0 1.0
"he has blessed berkeley last semester *_*" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13082.0 0.0 0.0 0.0
"cook up numbers till they burn" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12671.0 0.0 0.0 0.0
"Darn GPS! It directed my car off a cliff because it was a whole nanometer off and thought I was farther over than I was!" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3315.0 0.0 0.0 0.0
"ın 25 :05 he says transpose of row1 tımes x is zero but transpose of a row is column so how is it even possible to multiply them. Shouldn’t it be just row tımes x ? thx" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 15541.0 0.0 1.0 0.0
"Wow Mr Strang! He looks so old now.. Why does a gem of a person like that have to age? 😕" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 12028.0 0.0 0.0 0.0
"I am very much thankful to the MIT educational society for such awesome lectures.................................... 🙂🙃🙂" MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5153.0 0.0 0.0 0.0
"""The one thing about Math is you're supposed to follow the rules.""" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 122.0 0.0 0.0 0.0
"could any tell me which book has similar explanations as his?" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12685.0 0.0 0.0 0.0
"Linear Algebra was never as intuitive as Prof. Strang made it seem! Brilliant!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 7375.0 0.0 0.0 0.0
"Waaay too much theory. It's much easier to watch Khan Academy and do the MIT exams than watch these lectures and do the exams. " Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11255.0 0.0 0.0 0.0
"Awesome lecture! Thank you  MIT!" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2760.0 0.0 0.0 0.0
"10:58 this is great motivative introduction to Courant & Fischer's characterization results." 2K7CvGnebO0 "19. Saddle Points Continued, Maxmin Principle" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 356.0 0.0 0.0 0.0
"Does he know how to proof anything? because it does not seem so. He says things and doesn't justify them, I don't like him." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3451.0 0.0 0.0 0.0
"because he hasn't given out the proof for L'Hopital's rule." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12525.0 0.0 1.0 0.0
"Wouldn't the simulation of multi-tape Turing machine on the single-tape Turing machine be a lot simpler if the virtual tapes were just interleaved. Like [a][1][c][a][0][c][b][1][c]... Then you don't have to move anything around and it would be much simpler." TTArY7ojshU "6. TM Variants, Church-Turing Thesis" "MIT 18.404J Theory of Computation, Fall 2020" 12015.0 0.0 1.0 0.0
"Such a pity this quality of education including all the course notes, textbook content, and sample problems are not available to everyone. I give the entire world's education system a big fat Fail for their incompetence." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8939.0 0.0 0.0 0.0
"I feel my prof is so fking stupid after I watched this video. So clear..." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5396.0 0.0 0.0 0.0
"16:45 why the second figure (square) 's rank is bounded by 1? I think that should be bounded by 2." 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 489.0 0.0 1.0 0.0
"Cofactors are at 28:30" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 3161.0 0.0 0.0 0.0
"@drunkdonutboy Exactly, it's all about getting that foundation in place, which is why, even at University level (usually in the first year), it's necessary to ensure that everyone has the 'basics' down. 

It's funny that all those 'this is easy' and 'I can't believe this is MIT' comments tend to peter out towards the latter stages of the modules..." twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1827.0 0.0 0.0 0.0
"I have watched lectures 14, 15, 16 over and over again, and gain new insights each time. Professors, including mine at the university, tend to drop the arrow sign above vectors while writing on the board. This causes great confusion for the uninitiated. For example, in this lecture there is an expression ""p=ax"" whether the writing ""ax"" means a (a scalar) times x (a vector) or a (a vector) times x (a scalar) is not that obvious. Admittedly, the confusion stems from my ignorance of the commutative property of scalar multiplication of vectors, which is, in fact, not mentioned explicitly in most textbooks (e.g., Lay et al, ; Larson & Hostetler). In retrospect, this ""p=ax"" notation is a prelude to the ingenious way of introducing projection matrix, which again, requires pre-knowledge of associative laws. Overall, these are great lectures that stimulate thinking. Thanks a lot." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5569.0 0.0 0.0 1.0
"why the column of b is chosen as [1;5;6] but it is not in the column space of A?" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 15367.0 0.0 1.0 0.0
"Now I get to know that why the children's of MIT are genious. This is just because of such a brilliant professors knowledge delivery. Best lecture ever had in maths." 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 7951.0 0.0 0.0 0.0
"Whenever i am going through his lecture I respond to the question asked as if he is taking note of that...
That much I get involved in the lecture
Thank u so much Sir Gilbert Strang ❤️" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11653.0 0.0 0.0 0.0
"I just want to say thank you to Sir Strang for making such an amazing series.I am really helped a lot by his series." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 5625.0 0.0 0.0 0.0
"The one guy who disliked....who r u??" aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10209.0 0.0 0.0 0.0
"To all you saying you did this in high school, well, I learnt this in the first week of kindergarten. Bozos." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11023.0 0.0 0.0 0.0
"Thank you so much. This is the proper education people should receive." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 9415.0 0.0 0.0 0.0
"At 48:10. the 1/x factor in the denominator should disappear to zero aswell when the limit goes to infinity? How can he keep that term? Please somebody explain?" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2685.0 0.0 1.0 0.0
"Thanks for this lesson, e-learning will be the future, we have all theory, advice books in the intro, we have all to study, this e-learning will be helpfull also because many people will be at home and this => minus traffic , so minus caos in the city." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 9733.0 0.0 0.0 0.0
"I'm self learner! Anyone else self learning mathematics?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6369.0 0.0 0.0 0.0
"To solve the problem with the sound just download chrome extension ""Ultimate Volume booster"" and increase the volume" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11043.0 0.0 0.0 0.0
" check how great this scientist by clicking mit.edu/~jnt/home.html
I am from yemen. I never heard someone like this miracle. I starting loving probability" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 9.0 0.0 0.0 0.0
"shoot!!Spent last 30minute trying to figure out where that -1 came from..." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14292.0 0.0 1.0 0.0
"Finished 6.041 on 14-07-2021. Thank you MIT OCW and Prof. Tsitsiklis! The series was well made and inspirational!   
Love from India <3 
Anmol, India" rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 3808.0 0.0 0.0 0.0
"ill be in this in my junior year of high school 
.-," PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13558.0 0.0 0.0 0.0
"Damn this is awesome" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3299.0 0.0 0.0 0.0
"The GOAT" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 9965.0 0.0 0.0 0.0
"From watching this lecture, DR. Strang continues to strength my knowledge of linear algebra. He makes the subject look so simple." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 3939.0 0.0 0.0 0.0
"How can it be called as discontinuity past and future when both are connected through present?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4814.0 0.0 1.0 0.0
"this is really not the quality i expected from MIT, pretty sloppy instructor" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 14874.0 0.0 0.0 0.0
"The way he explained (ridiculed) different notations for higher order derivatives is priceless.
Please, can someone reach out to this professor and ask him to say something about different forms of partial derivatives." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10325.0 0.0 0.0 1.0
excellent k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12813.0 0.0 0.0 0.0
"Lecturing to 20 students at slightly different skill levels is difficult. Lecturing to 150.000 spanning a huge range in existing knowledge, age and time(!) in a way that works for every one of them is impossible.

Personally, I like to do number crunching on my own. Once someone tells you an algorithm you can learn it on your own. Even if they don't explain it in detail there are ways to look it up. But knowing which piece of intuition he finds important is extremely valuable." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7310.0 0.0 0.0 0.0
"What is the form of the  line element on the surface of the sphere? Can we transform it to Cartesian coordinates?" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11526.0 0.0 1.0 0.0
"Thanks, got the hang of limits with log now!" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9848.0 0.0 0.0 0.0
"How these eigenvectors and eignvalues are Helpful In Industrial engineering field.....????" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4898.0 0.0 1.0 0.0
"I like Miller so much more than Jerison. He's much more coherent and methodical." Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5658.0 0.0 0.0 0.0
"A*I is A ... correction at 3.04" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 2171.0 0.0 1.0 0.0
"are the online assignments available for this course?" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12399.0 0.0 0.0 0.0
"Benedict Cumberbatch will like Gilbert Strang when he gets old." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 2846.0 0.0 0.0 0.0
"So dear learners, how many of you are doing homework exercises? 😊" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8749.0 0.0 0.0 0.0
"Hats off!
The best teacher I would want to be." TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 4442.0 0.0 0.0 0.0
"At 8:39 How the Projection matrix P is derived.?
I see that in the numerator it is dot product of a^T and b, which is a Real Number
How could the associative law of matrices is applied here is applied here?
Am I missing something here? Can someone enlighten me?
If You have, Give me link of any supporting lectures on this so as to clarify this particular point.!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2700.0 0.0 1.0 1.0
"The pedagogy is so good that I feel like I come up with the ideas myself." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 10222.0 0.0 0.0 0.0
"Watching this in 2021 and gasping when Prof Strang coughs ""oh no, he better not have Covid""" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 11302.0 0.0 0.0 0.0
"I’m An Engineering students and my school is doing basically the same thing and these videos are helping a lot" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7109.0 0.0 0.0 0.0
"how he know pivot columns before doing elimination?don't we need elimination to find pivot variables 42:20" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 13230.0 0.0 1.0 0.0
"Thank you very much Prof. Gilbert Strang, you're awesome as always :))" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9434.0 0.0 0.0 0.0
"greece says that this is an amazing lecture" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13022.0 0.0 0.0 0.0
"6:00 couldnt get what he means by det(a) is product of n and cofactor is product of n-1 entry; can anybody explain?" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 1373.0 0.0 1.0 0.0
"26:45 example of non-invertible matrix" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 808.0 0.0 1.0 0.0
"This professor is so fabulous! One of the best professors ever!" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 10906.0 0.0 0.0 0.0
"For everyone asking about the bowl and eigenvalues analogy:
 Let X= (x,y) be the input vector (so that I can write X as a vector) and consider the energy functional f(X)=X^t S X. What would happen if we evaluate on the eigenvalues?
First, why would I think to do this? The eigenvectors of the matrix give the ""natural coordinates"" to express the action of the matrix as a linear transformation, which then gives rise to all the ""completing the square"" type problems with quadratic forms in usual LA classes. The natural coordinates rotate the quadratic so it doesn't have off-diagonal terms. This means the function changes from something like f(x,y)=3x^2+6y^2+4xy to something like f(x,y)=(x^2+y^2)=(||X||^2), where ||X||^2 denotes the squared norm. So the functional looks like a very nice quadratic in this case, like the ones you may learn how to draw in a multivariate calc course. 
Going back to the current calculation which f(X)=X^tSX: if we evaluate in the eigen-directions, then our function becomes f(X_1)=X_1^t S X_1=X_1 lambda_1 X_1= lambda_1 ||X_1||^2 (a nice quadratic) and 
f(X_2)=X_2^t S X_2=X_2 lambda_2 X_2= lambda_2 ||X_2||^2 (another nice quadratic). The eigenvalues lambda_1, lambda_2 become scaling coefficients in the eigen-directions. A large scaling coefficient means we have a steep quadratic and a small coefficient means we have a quadratic that is stretched out horizontally.
 If the eigenvalue is close to zero, the quadratic functional will almost look like a horizontal plane (really, the tangent plane will be horizontal) and hence not be invertible, so any solver will have difficulty finding a solution due to infinitely many approximate solutions. Since the solver will see a bunch of feasible directions, it will bounce around the argmin vector without being able to confidently declare success. Poor solver. Of course, these are purely mathematical problems; rounding error will probably mitigate the search even further.

Edit: changed ""engenvalue"" to ""eigenvector"" in 2nd paragraph." xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3862.0 0.0 0.0 1.0
"Dear Prof. Strang, it is actually very easy to visualize a saddle point. x/|x| is an ort that is fully defined on a 3D spherical surface that can be projected on any 2D plane without loosing any info. Choose (u,0,w). Any point within the unity circle represents the 2D ort. Zero radius (0,0) -> (0,0,1) . Then you plot R(u,w) = R(u,v,w) provided u^2+v^2+w^2=1; i.e. v=sqrt(1-u^2-w^2); You will see max =5 at (1,0), min=1 at (0,1) and 3 at (0,0)." 2K7CvGnebO0 "19. Saddle Points Continued, Maxmin Principle" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3328.0 0.0 0.0 0.0
"1st Example:

U = [[0, 1], [1, 0]]
Sigma = [[sqrt(18), 0], [0, sqrt(32)]]
V = V^T = [[-sqrt(2)/2, sqrt(2)/2], [sqrt(2)/2, sqrt(2)/2]]

where [a, b] is interpreted as a row vector. A = [[4, 4], [-3, 3]] = U * Sigma * V^T .... try it.

We know what we're doing, but we're not computers...we make little errors once in a while that we can't track successfully. The core concept was brilliantly delivered, and Professor Strang did an exceptional job making us understand SVD. I didn't bother to find his computational error ☺️" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 606.0 0.0 0.0 0.0
"in 41:27 2,2 2,3 2,4 3,2 3,3 3,4 4,2 4,3 4,4 ? I did not understand" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 13579.0 0.0 1.0 0.0
"Jeez, slackers... Had I been lucky and/or wealthy enough to attend MIT, I would not have shown up late to my classes! " IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 7132.0 0.0 0.0 0.0
"thats it? I knew all of that and im only 13..." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14652.0 0.0 0.0 0.0
Legendary!! Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7325.0 0.0 0.0 0.0
"@reik2006 what????" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1989.0 0.0 0.0 0.0
"Projecting while doing projections." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 8415.0 0.0 0.0 0.0
"Great video thanks!" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4351.0 0.0 0.0 0.0
"I have forgotten SO MUCH algebra since I last took it eons ago..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5526.0 0.0 0.0 0.0
"That’s a really great course review! There are something new to learn at the same time" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 9951.0 0.0 0.0 0.0
"MIT is King. Period." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7522.0 0.0 0.0 0.0
"If i meet him, maybe tears will roll down in admiration and inspiration. Such a great guy and excellent teacher. Thank you professor!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 6504.0 0.0 0.0 0.0
"In bayes theorm if I know the value of p(symptoms/disease) let's 0.3 so,can I take  p(~ymtm/dise)= p(ymtm/~dise) = (1-p(symtm/dis))?" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 6625.0 0.0 1.0 0.0
"Very nice video. Good introduction to vectors." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11214.0 0.0 0.0 0.0
"Nice class from Matrix Inverse Transpose university." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7840.0 0.0 0.0 0.0
"This guy is the Mr. Rogers of linear algebra." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 10546.0 0.0 0.0 0.0
"where are the ppts?" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 15220.0 0.0 0.0 0.0
"Thank you Prof. Strang & thank you MIT.
Brilliant lectures, much appreciated." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 9195.0 0.0 0.0 0.0
"He is great guy, very polite even being a prof. in MIT." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 4516.0 0.0 0.0 0.0
"Thank you." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 9540.0 0.0 0.0 0.0
"have this guy at berkeley :)
" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13064.0 0.0 0.0 0.0
"why is the professor on a scooter?" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 15341.0 1.0 0.0 0.0
"OCW really helps me with my studies. I will donate once I have money again :,D" -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 7971.0 0.0 0.0 0.0
"If I were a cameraman at MIT, I would carry a notebook all the time." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 6476.0 1.0 0.0 0.0
"Gill uses his 'god' voice at ~8:00" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4045.0 0.0 0.0 0.0
"I have an A in my linear algebra course and it sure isn't because of the Textbook, thank you MIT and Gilbert Strang for making these videos free" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 5517.0 0.0 0.0 0.0
"On the contrary. People with insecurities are easy to manipulate. A superiority complex is a deeply rooted insecurity. Good luck surviving the world with that heavy baggage (your big ego)." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8070.0 0.0 0.0 0.0
wtf 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15441.0 0.0 0.0 0.0
"remember on looney toons when they would run in place before taking off?  thats how this guy is.  he just seems so excited his mouth wants to blurt it out but his mind is a fraction behind.... whose idea was it to include stutters in the subtitiles?" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14261.0 0.0 0.0 0.0
"OMG, this is magic." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7991.0 0.0 0.0 0.0
"why not use a bigger black board?
" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15355.0 1.0 0.0 0.0
"At 36:40 every right hand side 'b' corresponds to the ones within A's column space, right?" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 2654.0 0.0 1.0 0.0
"Special is good. Useful is even better..." k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8864.0 0.0 0.0 0.0
"am I the only one who used to pronounce it El - Hospitals's rule xD" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12336.0 0.0 0.0 0.0
"Young God" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12260.0 0.0 0.0 0.0
"What do I do if I want to allow also some dependent column vectors in A so that AtA is not invertible? The projection onto the column space of A surely must still be unique. How do I find the projection matrix using my A in this case?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 11482.0 0.0 1.0 0.0
"Thank you!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9470.0 0.0 0.0 0.0
"Any links that address 5:25 about whether deep learning and the iteration from stochastic gradient descent go to the minimum l1 norm?" Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2470.0 0.0 1.0 0.0
"Brilliant. This lectures connects the complex puzzle" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2946.0 0.0 0.0 0.0
"@matanorland1 lol exactly" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1940.0 0.0 0.0 0.0
"This is super intuitive. Much better than my lecturer who just writes down rigorous definitions and expect us to understand the concepts." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 10728.0 0.0 0.0 0.0
"Final problem seems wrong to me...   should it not be -e - 2 ?

Let me know people!" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3757.0 0.0 1.0 0.0
"Very clear I understood everything Thsnks." 7J1HD9rqEB4 "24. Probabilistic Computation (cont.)" "MIT 18.404J Theory of Computation, Fall 2020" 11160.0 0.0 0.0 0.0
"Too funny, people need to see this.

acesofclubs
1 year ago
 
Mafia Mob moment at 11:36" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11063.0 0.0 0.0 0.0
"Einstein tells me keeping information handy such as the speed of sound or light is not necessary but i like to anyway and the process to calculate it methods of  madness to quantum consciousness to many variables in chaos itself" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3558.0 0.0 0.0 0.0
"50:00 Well, who would thought that 3 Seasons of ""Dark"" could prepared me really well to understand Markov Chains" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 1335.0 0.0 0.0 0.0
"Time for a break. I'm starting to hallucinate that I smell chalk dust in the air!" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11013.0 1.0 0.0 0.0
"i never know that youtube have video like this.
good." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13445.0 0.0 0.0 0.0
"no because x is defined by the limit signifier.  it cannot be divorced from it" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14063.0 0.0 1.0 0.0
"Very nice and concise explanation. Thanks." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 11204.0 0.0 0.0 0.0
"I love this guy. He's so funny and good at explaining stuff." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5814.0 0.0 0.0 0.0
"5:27 He draws a very nice drawing of clouds. Nice artist." a1ZCeFpeW0o "20. Principal Component Analysis (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 1363.0 0.0 0.0 0.0
"thank you g. strang." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14497.0 0.0 0.0 0.0
"Self teaching linear algebra is 100x easier with these lectures!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 8624.0 0.0 0.0 0.0
"You don't need high-tech touch screens or ipads to learn anything.All a teacher needs is a chalk and a blackboard and all a student needs is a paper and a pen.Moreover It's very bold and legible to write on a blackboard and the visiblity is great." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12204.0 1.0 0.0 0.0
"the best course to learn linear algebra" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 14664.0 0.0 0.0 0.0
"I studied this in my school while preparing for IITs entrance exams , Even more tougher it's easy." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5978.0 0.0 0.0 0.0
"attend to the strang paradox; a vector field of unfinished sentences that form the basis vectors for a stunning range of interesting algebraic problems" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12481.0 0.0 0.0 0.0
"Thank you a lot." UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9244.0 0.0 0.0 0.0
"my distance to my crush is 100k GGs bois" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 13975.0 0.0 0.0 0.0
"I enjoy watching these videos.  Makes me wish I had paid attention to my studies and teachers when I was in school." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5381.0 0.0 0.0 0.0
"if differentiation is to find the rate of change. then why are we doing it to find the area?" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13531.0 0.0 0.0 0.0
"Great teacher. Thank you very much" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 4343.0 0.0 0.0 0.0
"so cul.
" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14327.0 0.0 0.0 0.0
"Thank you so much! This was so useful and easy to understand!" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 9388.0 0.0 0.0 0.0
"Oh wow 🤩 , almost get there oonly stroke’s thm left  over hahahah  finish all of 18.01 and 18.02 , learn more than I expected" wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 8026.0 0.0 0.0 0.0
"Yes in fact, the shoes-socks rule stands well in this science" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 12140.0 0.0 0.0 0.0
"Just once to see one of his lectures and not be amazed. He is simply awesome!" L3-WFKCW-tY "33. Neural Nets and the Learning Function" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7190.0 0.0 0.0 0.0
"is chalk bad for the lungs?" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13628.0 0.0 0.0 0.0
"what a don! i wish my lecturer was this guy, he makes it so simple" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 15105.0 0.0 0.0 0.0
"I love Linear Algebra!" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5716.0 0.0 0.0 0.0
"@pelemanov from what I understand we are projecting b in to the column space so that we can actually solve the system with a best estimate.  The closest (least squares) projection of b is p which will only be orthogonal if b happens to be in the null space of A transpose, but there is no requirement that this is the case.  In fact if b happens to be in the column space, then the projection doesn't change b at all (i.e. P = I.)" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 1969.0 0.0 0.0 0.0
"watching this in 2016. What's hillary's distance to Monica. LOL" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 15069.0 0.0 0.0 0.0
"which lecture did he speak about full column rank?" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 15253.0 0.0 1.0 0.0
"I can see and prove a covariance matrix with x and y independent is a positive definite matrix.  But when x and y are dependent, I don't think the covariance matrix V is positive semidefinite.  In the 2x2 case uT*V*u could be less than zero for the case when u = [1; -1] for instance." nrDkb2MAwSA "20. Definitions and Inequalities" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5196.0 0.0 1.0 1.0
"can anyone provide me notes" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 12613.0 0.0 0.0 0.0
"I Really Like The Video From Your Derivatives of products, quotients, sine, cosine" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4951.0 0.0 0.0 0.0
"Neat trick. Can we use this to find the circumference of an ellipse?" zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7810.0 0.0 1.0 0.0
"Nice video
#learnanytime" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7864.0 0.0 0.0 0.0
"I love the teacher's handwriting!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5786.0 0.0 0.0 0.0
"Cross product is easy." tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3262.0 0.0 0.0 0.0
"Isn't this theorem called after Ostrogradsky, since he is the first one to prove it?" WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6900.0 0.0 1.0 0.0
"28:14 I promise not to write another thing on this board xD :) Thank you so much Prof. your lectures are way more intuitive than my college Prof." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 833.0 0.0 0.0 0.0
"At around 32:45, Prof. Strang writes Lambda^100*S*c. Notation wise, shouldn't this be S*Lambda^100*c? " 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 2706.0 0.0 1.0 0.0
"At 8:11 shouldn't S be (1/n)*Σ(X*X^T) ? Why he omitted 1/n?
Edit: ok, he fixed it at 9:29 :)" a1ZCeFpeW0o "20. Principal Component Analysis (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 2699.0 0.0 1.0 0.0
"why the blackboard seems a little dirty?" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 15365.0 1.0 0.0 0.0
"Thank you!!! I’m excited" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9486.0 0.0 0.0 0.0
"some of the in class questions belong at Dartmouth not MIT" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14358.0 0.0 0.0 0.0
"I.got really confused when he said the elimination does change the column space. Why? Is that right?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 6442.0 0.0 1.0 0.0
"My distance to clinton updated to 3 from infinity after this lecture" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 7743.0 0.0 0.0 0.0
"A couple of questions:
1) if a single element has 0 probability, why a singleton has a probability greater than 0?
2) the first additivity axiom and the countable additivity axiom both say that the probability of the union of disjoint events is equal to the probability of the sum of each individual probability. In what they actually differ?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 2107.0 0.0 1.0 0.0
"Thank you!" -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 9464.0 0.0 0.0 0.0
"O, to have had a professor like this who wanted you to learn math, unlike my classes which were meant to eliminate as many students going forward as possible." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7968.0 0.0 0.0 0.0
"@MrDevin666  UCLA" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1682.0 0.0 0.0 0.0
"This is an ingenious way of determining number combinations" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 10628.0 0.0 0.0 0.0
"i have to say greatest lecture of any lecture out of all the MIT opencourseware ive watched, thanks a bunch" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 13399.0 0.0 0.0 0.0
"how is standard deviation is f(1-f)..at 19:40 ???" Tx7zzD4aeiA "20. Central Limit Theorem" "6.041 Probabilistic Systems Analysis and Applied Probability" 13238.0 0.0 1.0 0.0
"Don't give up. ( 加油！)" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3474.0 0.0 0.0 0.0
"The professor is looking rather green. He must sick. " YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10248.0 0.0 0.0 0.0
"@phtotti  So what, who cares?" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1970.0 0.0 0.0 0.0
"Hard to get the last idea he mentioned" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4428.0 0.0 0.0 0.0
"prof. says A, writes B, means C - while correct answer is D." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14214.0 0.0 1.0 0.0
"Well i can proudly say that in India a normal YouTube channel can explain this much much better than this one" V3Wg_jrMSQY "Lecture 19: Differentiation Rules, Rolle's Theorem, and the Mean Value Theorem" "MIT 18.100A Real Analysis, Fall 2020" 11352.0 0.0 0.0 0.0
"A good professor gets down to the level of a student and stops assuming things. A great professor gets down to the level of the weakest (new to the field) student in the class and makes them feel that they are not alone. And he is an excellent professor. Thank you MIT." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 2117.0 0.0 0.0 0.0
"45:10 I assume h(x) should be 1/sqrt(2pi)" X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 1248.0 0.0 1.0 0.0
"How is it 2 40:50?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4869.0 0.0 1.0 0.0
"Great lecture! But aren't we supposed to make an orthogonal projection? Instead he did a projection parallel to the Y-axis because he calculates p1, p2 and p3 by taking t-values 1, 2 and 3. You can also see it on his drawing. Why does he take this projection instead of the orthogonal one? And how can e turn out to be orthogonal to p anyway?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 4263.0 0.0 1.0 0.0
"did this in grade 9
" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12741.0 0.0 0.0 0.0
"I like how people in the comments section are mulling over the Professor's treatment of the material in this course, completely forgetting the fact that courses like these will usually have textbooks associated with them to augment learning and the professor's job is NOT to regurgitate things that can be found in a textbook but to focus on the key concepts required in problem solving. 

It amazes me that some people feel that there's a need to do 10 whiteboards worth of derivations in a 50 minute course when the focus should ALWAYS be on the concepts, with the professor encouraging students to look up the derivation or the individual proofs. It's good that the professor managed to do the derivation at the end, cos it just reinforces the concepts and also provides a general methodological framework which students can then use to solve general problems." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5668.0 0.0 0.0 1.0
"Let's keep it to oursselves/myself...






So y=1/x -> dy/dx * -1/x is also accurate by nx^(n-1)." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7337.0 0.0 1.0 0.0
"@Vegasred125 Seems like its not just young people who have it made.....old snobs who cant remember what they were taught are getting alot out of it too " 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1749.0 0.0 0.0 0.0
"He's the bob Ross of calculus" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4647.0 0.0 0.0 0.0
"Sseredmnnnbvcmnnm v  zzz CV c.   C Av. Toyoyoppyrweqlkbjjggfgfffssaàz





Aalvs 🥴😷🤒🤕🤢🤮😵🥱🤑 🤕🤠🤧😵‍💫😴😦😨33" Tx7zzD4aeiA "20. Central Limit Theorem" "6.041 Probabilistic Systems Analysis and Applied Probability" 8875.0 0.0 0.0 0.0
"He cited  images as an example for large feature set : nobody use standard ML for images, we use Convolution." k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4466.0 0.0 0.0 1.0
"Professor Gil Strang has spoilt our learning process, so much intuition is mesmerizing.  I started LA for the first time to learn on my own, and if I know this subject then all credits to him and MIT. ❤️" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 8324.0 0.0 0.0 0.0
"I just skipped my calculus class today to watch this video instead. I must say it was worth it." hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5617.0 0.0 0.0 0.0
"Anyone can explain how the did he get the term in the parenthesis at 39:07? Why does Transpose(v)[1] = Transpose([1])v?" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 2482.0 0.0 1.0 0.0
"Thank you MIT🙏" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9170.0 0.0 0.0 0.0
"I never Get bored watching these lectures.Prof.Gilbert Strang is awesome!!
Thank you Sir :))" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5878.0 0.0 0.0 0.0
"At 22:00 M = B only applies if B is invertible right? What about other cases when B isnt?" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2611.0 0.0 1.0 0.0
"funnily enough I was at secondary school in UK in 1968
and I completely agree with free-from-influence

well done Gabriella for badgering her husband to make this available" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12911.0 0.0 0.0 0.0
"why at 44:50 do all the linear combinations of col 1 and col 2 create a plane rather than all of R^3?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 15289.0 0.0 1.0 0.0
"Orthogonality is just a complicated word from Greek to say things are perpendicular! 😜😜" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8136.0 0.0 0.0 0.0
"Thanks for uploading.!" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 9740.0 0.0 0.0 0.0
"Prof. Tsitsiklis can not be thanked enough for his outstanding capability to bring immediate clearness into these topics. These videos truely are an invaluable contribution to education." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 8316.0 0.0 0.0 0.0
"There is a mistake the <-3,3,-6> from before is the vector of the line not a point on the line (even though that point does exist on the line, it is only because the line passes through zero),  so he shouldn't have written (-3,3,-6)" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10366.0 0.0 1.0 0.0
"This is the best explanation of matrix multiplication and inverse matrix ever." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10734.0 0.0 0.0 0.0
0:21 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 303.0 0.0 0.0 0.0
"1:12 good thing this lecture happened in 2007 or the whole class would be snickering from here on out" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 584.0 0.0 0.0 0.0
"Thanks a lot Gilbert Strang" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9654.0 0.0 0.0 0.0
"Thank you Professor Strang." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 9225.0 0.0 0.0 0.0
"4:20 Minha terra tem palmeiras onde canta o sabiá.
sen(a)cos(b)+sen(b)cos(a)

My land has palmtrees, where sings the thrush bird
sin(a)cos(b)+sin(b)cos(a)

(it doesn't rhime in English...)" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1318.0 0.0 0.0 0.0
"Amazing approach to teaching matrix algebra. Thanks a lot to professor Strang and MIT for bringing this lecture for free." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2354.0 0.0 0.0 0.0
"Seriously, it just doesn't get much better than this. What a well-delivered series of lectures from a clearly gifted teacher and mathematician. " 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 8630.0 0.0 0.0 0.0
"Would have been nice to put in the description or title or somewhere that this lecture focus on Fisher Information (Matrix) - to make it easier to search...I honestly don't know how or why I found this...especially since it was at the bottom of my search results. MIT videos that are relevant should be at the top..." JTbZP0yt9qc "6. Maximum Likelihood Estimation (cont.) and the Method of Moments" "MIT 18.650 Statistics for Applications, Fall 2016" 12008.0 0.0 0.0 0.0
"got everything down, except when he drew the plane of the column vector... I can't really visualize it.  " JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 12958.0 0.0 0.0 1.0
"This is such a nice lecture, learnt a lot. Great." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10726.0 0.0 0.0 0.0
"What a lame presentation. A completely ill prepared professor..." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 11418.0 0.0 0.0 0.0
"at 25:31, why did he exponentiate W ? can some one explain it to me please? thank you ! " 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12428.0 0.0 1.0 0.0
"Respect from Bangladesh <3" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8557.0 0.0 0.0 0.0
"Thank you very much, Professor" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9451.0 0.0 0.0 0.0
"Anyone else recognise the guy with the Corona beer t-shirt at 24:30" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2489.0 0.0 0.0 0.0
"i think i just figured it out actually. half makes sense to me" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13472.0 0.0 0.0 0.0
"the audio is so low even when i turn up all volume. prof needs to put his mike anywhere but his chest plz. specifically talking about parts around 33:18. mans whispering. and you can't even hear what the students are asking. but i guess since this is opencourseware, i can't complain much about free college lectures." rLlZpnT02ZU "4. Parametric Inference (cont.) and Maximum Likelihood Estimation" "MIT 18.650 Statistics for Applications, Fall 2016" 14661.0 1.0 0.0 0.0
"@g1code 
this dude explains sooo slowly..so its kinda not ur fault..." 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1845.0 0.0 0.0 0.0
"Another useful resource: https://metacademy.org/graphs/concepts/chernoff_bounds#focus=chernoff_bounds&mode=learn" nrDkb2MAwSA "20. Definitions and Inequalities" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2461.0 0.0 0.0 0.0
"God has written all these rules for human to discover them." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4093.0 0.0 0.0 0.0
"if we had youtube  or computors  could had two fulltime jobsan school  ttally differnt  miss a class  relyon book examples   ok butnotfull proof" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13545.0 0.0 0.0 0.0
"oh god, prof. strang is so funny. he is acting natural. like him so much." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 14105.0 0.0 0.0 0.0
"What an amazing lecture by Prof. Jerison" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11450.0 0.0 0.0 0.0
"Ty sensei" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11108.0 0.0 0.0 0.0
"You also have to realize people come from different backgrounds and won't know the same information. " ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12160.0 0.0 0.0 0.0
"camera guy needs to zoom out a bit in some parts." 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12590.0 1.0 0.0 0.0
"Wonderful teacher" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11991.0 0.0 0.0 0.0
"symbology after symbology after symbology....its like learning japanese or icelandic but less intuitive .... i think anybody can learn higher mathematics....but why would you want to?  what is the motivation for piling symbologies on top of definitions on top of rules ad infinitum?  it can be done with enough discipline and repetition, but why would anybody want to?  to make bigger better hydrogen bombs?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14430.0 0.0 0.0 0.0
"It will get even better - think I have seen all videos 3 times now - but a do not think my techer have." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7004.0 0.0 0.0 0.0
"Wow...52:33...what kind of students do they admit into MIT...
Nevertheless, great lecturer." sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12091.0 0.0 0.0 0.0
"I must say that I have been very disappointed by this lecture series so far. I am already familiar with single variable calculus. However, I am watching this series to review for some future classes (things like multivariable calculus and real analysis). 

However, here are some things I have noticed. Would that this instructor had spent some more time on the more rigorous concepts of limits and squeeze theorem, he would not have had to spend so much time trying to justify the proofs of the main two limits of this lecture. In addition to this, his students would be better prepared for future mathematics. As it stands, these students are really at a loss when it comes to their future.

I would really hope that instructors learn from this. Spend more time on the things you need to rigorously justify your claim: the foundations. If the ideas are glossed over, then everyone loses. Students don't understand why something is true, and so they become convinced that what the professor is doing is some kind of witchcraft that makes no sense. Please, if you are an instructor and you are reading this, work on the fundamentals!" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5876.0 0.0 0.0 0.0
"26:20 Can anyone explain for me why we can have the same column space when we throw column 1 of Matrix A.? I still don't get it." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 798.0 0.0 1.0 0.0
Lv QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7491.0 0.0 0.0 0.0
"What a doozy. Great lecture." JTbZP0yt9qc "6. Maximum Likelihood Estimation (cont.) and the Method of Moments" "MIT 18.650 Statistics for Applications, Fall 2016" 11404.0 0.0 0.0 0.0
"Around 18:02 when prof strang shows when we would get a symmteric matrix, he mutiplies R^t with R .  Didn't he wrote the order in reverse? wouldnt it be R into R^t??" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 2548.0 0.0 1.0 0.0
"YOU ARE A STAR, PROF. STRANG!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12111.0 0.0 0.0 0.0
"For those confused about Auroux's loose definition of ""potential,"" especially with regard to electrical potential, it comes down to an extra charge in the numerator that he somehow neglects.

The integral of (gradient of f dot dr) where f is the electric force (denoted by F) is equal to the Work, and also equal to the change in U, the potential energy. 

The integral of (gradient of f dot dr) where f is the electric field (denoted by E) is equal to the change in V, the electrical potential, which varies from U in that it has one charge in the numerator, rather than two. 

In other words: F --> U  by line integral ; E --> V by line integral. F does not --> V by line integral." z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3899.0 0.0 1.0 0.0
"Tip - Turn mono audio On in the windows 10 audio settings for better audio" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11018.0 0.0 0.0 0.0
"31:34 ... ""trouble with this visualization""? ... of course he is trying to visualize continuity ... hmmm ... that is gonna take more than a lecture ..." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 913.0 0.0 0.0 1.0
Done+++ ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3484.0 0.0 0.0 0.0
"I recommend watching the final video in the 3B1B “essence of linear algebra” series before you watch this one" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 5940.0 0.0 0.0 0.0
"cry about it. When you do something that stupid in MIT while tons of capable white and asian students get closed out due to ""fairness"" and ""equality"" I won't shut my mouth. Fuck you.
""...Thus, the libertarian opposes compulsory segregation and police brutality, but also opposes compulsory integration and such absurdities as ethnic quota systems in jobs.""" TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12696.0 0.0 0.0 0.0
"Hopefully I can still love science at this age" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4790.0 0.0 0.0 0.0
"God bless the internet. " YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4081.0 0.0 0.0 0.0
"14:11 - he just launched into this.  No theory, no description of the ""plan"" behind what we were doing.  Can we get some THEORY of this instead of taking up time working out algebra?  What we actually DO with these ideas?" z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 426.0 0.0 0.0 0.0
"Great lecture, Thanks prof. Strang." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4276.0 0.0 0.0 0.0
"I had the same problem as in 20:15 and the lecture notes had not pointed out the answer. I wish they had." hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5469.0 0.0 1.0 0.0
"matrix*vector is linear combination of the columns of the matrix, and vector*matrix is linear combination of the row of the matrix." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13921.0 0.0 0.0 0.0
"I finally get things better after this lecture.  All the examples really helped." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 5406.0 0.0 0.0 1.0
"An excellent step by step proof that the calculus I've been learning is garbage all these years" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2440.0 0.0 0.0 1.0
"Judging by his name and his accent I`m pretty sure that he is French " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7143.0 0.0 0.0 0.0
"save the chalkleader. save the world. (heroes reference)" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14281.0 0.0 0.0 0.0
"I am kind of confused about the definition of orthogonal vectors. Why do we need to make the product of the transpose A and another vector? I assume the product of A and B is zero as well. Can anybody answer my questions?" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5111.0 0.0 1.0 0.0
"Finally went to all the videos to upvote. The videos  were so absorbing that I couldn't upvote during the lectures.
Thanks Professor Gilbert. You're awesome. May God bless you." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 3787.0 0.0 0.0 0.0
"great lecture as always, I got lost when it comes Euler Equation. don't quite understand how column, rows become nodes, edges, and why do we need #node -1 in the equation. The answer is probably in the matrices representation of the graph.  248k views for this lecture, last one was close to 300k. lets see how many views is next lecture." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12981.0 0.0 1.0 0.0
"But what is the application of clarifying the partial notation in the presence of constraint, apart from a better understanding of what are the independent variables? Isn’t optimization with a constraint the job of Lagrange Multiplier?" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2967.0 0.0 1.0 0.0
"i appreciate how leaders in their field can     teach         the simple parts       with enthusiasm" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13340.0 0.0 0.0 0.0
"at 46:18 the equation written on the board A(T)CAx = f is missing the minus sign. When we calculate the potential drop e, AX is negative because potential is dropping, and if there is a Voltage Source b connected then e = b - AX. Now Balance equation becomes A(T)CAX = -f." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12457.0 0.0 1.0 0.0
"@charcoalfilter1101 His name is Denis Auroux. " 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1811.0 0.0 0.0 0.0
"now i can understand everything in terms of linear combination of column vectors" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 14091.0 0.0 0.0 0.0
"This was probably the most beautiful lecture I have ever watched. The way the knowledge is passed, step after is step is pure poetry. Thank you Prof. Strang." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 10972.0 0.0 0.0 0.0
"quem entender ingles me explique a finalidade do video!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14236.0 0.0 0.0 0.0
21:00 JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 665.0 0.0 0.0 0.0
"Can someone explain why exactly is it (P)(A)=(L)(U)?
I mean if I follow the steps one by one, its   
(P1)(E1)(A) = (U1),   (where E1 is the first row operation elementary matrix, P1 is the permutation matrix if any row exchange follows E1 and U1 is the resulting matrix)
then, (P2)(E2)(P1)(E1)(A) = (U2)
then, (P3)(E3)(P2)(E2)(P1)(E1)(A) = (U3)
... so on ....
finally, (Pn)(En)...(P3)(E3)(P2)(E2)(P1)(E1)(A) = (Un) = (U)
Now this means 
A = ((Pn)(En)...(P3)(E3)(P2)(E2)(P1)(E1))' (U), 
(' denotes inverse here)
How does this convert to PA=LU ???????" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 3076.0 0.0 1.0 0.0
"Does this course need a prerequisite course - 18.01 Single variable Calculus?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3462.0 0.0 1.0 0.0
"At 46:00 professor says SVD in this case is neither side inverse but Right side is one side inverse, then he says at end under independent columns SVD gives same result as Guass, but sigma matrix in pseudo inverse should still have missing values how will they give same result?" ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2681.0 0.0 1.0 0.0
"Prof. Gilbert Strang inspires everyone. I respect him a lot." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8296.0 0.0 0.0 0.0
"the professor is really into the subject and is really explaining   good. i guess he is a pupil of albert einstien.wallah professor" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14729.0 0.0 0.0 0.0
❤ TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 15605.0 0.0 0.0 0.0
"F. how can every single lec can be quality guaranteed?" aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3719.0 0.0 0.0 0.0
"You are amazing sir.... None can copy you" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12167.0 0.0 0.0 0.0
"very true!
" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 15036.0 0.0 0.0 0.0
"these are wonderful lectures, please upload the lectures on Probabilistic Method from Prof. Yufei Zhao. THANK YOU!" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 14771.0 0.0 0.0 0.0
"I thank MIT for uploading these videos, and thanks to them I can learn physics and math better than my high school, where unfortunately education is terrible, now enters University, and and I can solve all the guides for the exam too fast thank all videos of MIT I saw, my warmest thanks from Mexico" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5991.0 0.0 0.0 0.0
"Reminds me of the role of Alan Turing in The imitation game." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8551.0 0.0 0.0 0.0
"it was explained in the previous lecture" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13685.0 0.0 0.0 0.0
"Second derivative test starts at about 30:00
:)" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8609.0 0.0 0.0 0.0
"I think that for to figure out how a space looks like, you must ask yourself how a space looks like... because a subspace is in fact a space inside another space, so just imagine that instead of being in a three dimensional space we are in a 3 dimensional subspace inside another bigger-dimensional space and a null-space turns to be the space of all vectors in that bigger-dimensional space that when multiplies any array of 3 basis vector of our ""subspace R^3"" that nullifies our space (makes it 0)" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6042.0 0.0 0.0 0.0
"listening to Strang is like getting a brain massage" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13808.0 0.0 0.0 0.0
"Lets use distributive law without proving it. We only live so long :D :D" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 7341.0 0.0 0.0 0.0
"57:30 Log space" 4dFPVJrNLDs "19. Games, Generalized Geography" "MIT 18.404J Theory of Computation, Fall 2020" 1353.0 0.0 0.0 0.0
interesting VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 13616.0 0.0 0.0 0.0
"so..did you fail?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14356.0 0.0 0.0 0.0
"@riyadhelalami  What is this stuff about ""right and normal""?  Why do you associate here with right or wrong?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1991.0 0.0 0.0 0.0
"Did you all the the final ultimate formula of life here?" XhSk_Lw2X_U "14. Low Rank Changes in A and Its Inverse" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3391.0 0.0 0.0 0.0
"this is entertaining" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14859.0 0.0 0.0 0.0
25:32 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 781.0 0.0 0.0 0.0
"The lecture was great up until Keppler's second law, then they lost me :(" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10166.0 0.0 0.0 0.0
"I've been able to do two years' worth of my university math over a single summer thanks to MIT OCW." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6403.0 0.0 0.0 0.0
"And my teacher just said ""this is the formula""(explained a sum) and that's it for the topic" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 2446.0 0.0 0.0 0.0
"Mit cant afford dry erase...." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7675.0 1.0 0.0 0.0
"At sme 30 min he completely forgets ot 18.01 he is addressing." HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2720.0 0.0 0.0 0.0
"Closing comment was confusing. What did he mean by permutations can either be odd or even?" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 3160.0 0.0 1.0 0.0
"This is taught at what level?" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10729.0 0.0 0.0 0.0
"Isn't it great that the sum total of all human knowledge is in this age at our fingertips? The idea that I could learn absolutely anything to any depth I please with effort and time has never been truer, and I find it inspiring :)" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6893.0 0.0 0.0 0.0
"16:20 small signal analysis? hahaha" l4NoMKEHQwM "11. Derived Distributions (ctd.); Covariance" "6.041 Probabilistic Systems Analysis and Applied Probability" 474.0 0.0 0.0 0.0
"I think that was a kids stuff" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6044.0 0.0 0.0 0.0
"Lecture 1: Dot Product
Lecture 2: Determinants
Lecture 3: Matrices
Lecture 4: Square Systems
Lecture 5: Parametric Equations
Lecture 6: Kepler's Second Law
Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds)
Lecture 8: Partial Derivatives
Lecture 9: Max-Min and Least Squares
Lecture 10: Second Derivative Test
Lecture 11: Chain Rule
Lecture 12: Gradient
Lecture 13: Lagrange Multipliers
Lecture 14: Non-Independent Variables
Lecture 15: Partial Differential Equations
Lecture 16: Double Integrals
Lecture 17: Polar Coordinates
Lecture 18: Change of Variables
Lecture 19: Vector Fields
Lecture 20: Path Independence
Lecture 21: Gradient Fields
Lecture 22: Green's Theorem
Lecture 23: Flux
Lecture 24: Simply Connected Regions
Lecture 25: Triple Integrals
Lecture 26: Spherical Coordinates
Lecture 27: Vector Fields in 3D
Lecture 28: Divergence Theorem
Lecture 29: Divergence Theorem (cont.)
Lecture 30: Line Integrals
Lecture 31: Stokes' Theorem
Lecture 32: Stokes' Theorem (cont.)
Lecture 33: Maxwell's Equations
Lecture 34: Final Review
Lecture 35: Final Review (cont.)" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7276.0 0.0 0.0 0.0
"Dear Prof Strang, You are my hero in mind. I want to be grow old like you." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3327.0 0.0 0.0 0.0
"39 people have MBA's.
" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1089.0 0.0 0.0 0.0
"Just started my probability journey at MIT OCW" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 7193.0 0.0 0.0 0.0
"Thank you Professor Gilbert Strang. FROM ALGERIA" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9210.0 0.0 0.0 0.0
"Thank you Sir." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 9238.0 0.0 0.0 0.0
"11:00 brave man, dozing off on the front row (or he might've just been taking notes, idk)" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 361.0 1.0 0.0 0.0
"Thanks a lot" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 9649.0 0.0 0.0 0.0
"39:30 LOL : ""We only live so long, we just skip that proof.""" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 1098.0 0.0 0.0 0.0
"Statistics is replacing expectations with average. Thank you" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8895.0 0.0 0.0 0.0
"freaking perfect. amazing proff
" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12896.0 0.0 0.0 0.0
"28:47 ""PHYSICISTS BE OVERJOYED RN!!""" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 844.0 0.0 0.0 0.0
"Does anybody know which textbook is being used for this course?" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 3431.0 0.0 0.0 0.0
"i think the s should be squared in the variance 1/s^2(c^2 - ||AB||^2) ?" z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13477.0 0.0 1.0 0.0
superelipses NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14423.0 0.0 0.0 0.0
"I know this doesn't have anything to do with the video, but I would like to share these questions and this message with as many people as possible.
 
1. What do you think happens to someone after they die?
2. Do you think there is an afterlife? 
3. If heaven exists, how do you get there? 
4. Do you think you are good enough to get into heaven?
 
No one is good enough to get into heaven. Here are a few questions to test your goodness: 
 
1. How many lies have you told in your whole life? 
2. Have you ever stolen? 
3. Have you ever used God's name in vain?
4. Jesus said that ""whoever looks at a woman to lust for her has already committed adultery with her in his heart"" (Matthew 5:28). Have you ever looked with lust? 
5. If you have broken any of these commandments, would you be innocent or guilty on Judgment Day? 
6. Would you go to Heaven or Hell?
 
The Bible says that ""all liars shall have their part in the lake which burns with fire and brimstone"" (Revelation 21:8) and ""Those who indulge in sexual sin, or who worship idols, or commit adultery, or are male prostitutes, or practice homosexuality, or are thieves, or greedy people, or drunkards, or are abusive, or cheat people — none of these will inherit the Kingdom of God"" (1 Corinthians 6:9-10). So, if you are guilty of any of the ten commandments, then you are in trouble when Judgment Day comes! Do you know what God did for guilty sinners so that we wouldn't have to go to Hell? 
 
2,000 years ago, God became a human being, Jesus of Nazareth, who suffered and died on the cross for our sins and rose from the dead on the third day, defeating death. The punishment that we deserve for breaking God's law, Jesus took in our place. He paid the fine that we could never pay so that God can legally set us free by forgiving our sins. He is just, by punishing evil through Jesus’ death on the cross, while being rich in mercy towards us. 
 
What you have to do is repent, or turn toward God, and believe in Jesus Christ. Don't trust your own goodness, because, as Jesus said, “No one is good — except God alone” (Mark 10:18). Trust alone in the savior. The moment you do that, God will forgive every sin you have ever committed and grant you eternal life, and He will give you a new heart with new desires, so that you will love to do what is right. You will be born again. But you must repent and trust in Jesus. 
 
When are you going to do that?
 
Here is a short Christian movie on this subject and depression: https://www.youtube.com/watch?v=fcqxzXMRGoc" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5641.0 0.0 0.0 0.0
"Great explanation Kudos professor
I initially had doubt at why E(x-1/x-1>0)=E(x)+1 but i did not understand there.But then u explained that he wasted one toss + he started again that make sense to me.
Really i'm loving probability because of u 
Last but not least Thanks for mit for providing such excellent videos" -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 4225.0 0.0 1.0 1.0
"selam beyler " QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 14286.0 0.0 0.0 0.0
"my shoe your face...discuss 
" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14003.0 0.0 0.0 0.0
"You'd think MIT would figure out the equation for chalkboard erasers. I guess that's more of a Harvard specialization." C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 12244.0 1.0 0.0 0.0
"I just remembered 18650 is a battery model 😂" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 5615.0 0.0 0.0 0.0
"cant believe i watched it fully" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12644.0 0.0 0.0 0.0
Respect! RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 8562.0 0.0 0.0 0.0
"Amazing lecture! disrespectful and quite dumb students tho." 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2369.0 0.0 0.0 0.0
"Những ví dụ hay đó. 🦌🦓🐺" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7831.0 0.0 0.0 0.0
"The camera guy is pretty bad. I'm getting a headache" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10029.0 1.0 0.0 0.0
"more and more and more and more please" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13960.0 0.0 0.0 0.0
41:13 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 1150.0 0.0 0.0 0.0
"At around 18:00, why did he take p1, p2 and p3 on the same vertical line as b1, b2 and b3 respectively? Why not take them on the line perpendicular to the line we drew (I mean why not project them properly??) Bcos the line we drew is not perpendicular to the vertical. Help pls. Thanks :)" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 2704.0 0.0 1.0 0.0
"What does Professor Strang mean with “you cannot overflow…”?" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11485.0 0.0 0.0 0.0
"I want to know more about sample sets with no probability." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 6138.0 0.0 1.0 0.0
"It amazes me how much a good teacher helps in grasping the subject. Thank you professor Strang" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 6906.0 0.0 0.0 0.0
"I think he made the mistake on propose to show the column space and row space have the same dimension lol" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6018.0 0.0 1.0 0.0
"For a moment I thought my left ear had given up." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 3843.0 0.0 0.0 0.0
"very cute old man" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15001.0 0.0 0.0 0.0
"Is it a bird? Is it a plane? No, its a vector space!" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 6777.0 0.0 0.0 0.0
"""It could be positive SEMI-definite - you know, consolation prize"" :D hahaha" HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 74.0 0.0 0.0 0.0
"professor john tsitsiklis is a G.O.A.T" gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 14220.0 0.0 0.0 0.0
"Con someone help me understand what happens in 12:30? cant understand what he did there." z0ykhV15wLw "Lecture 13: Randomized Matrix Multiplication" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3190.0 0.0 1.0 0.0
"How can we find his 5 lines proof of why SGD works? It is fascinating." k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4815.0 0.0 1.0 1.0
"wtf MIT students can't do taylor series? what a fucking joke" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15443.0 0.0 0.0 0.0
"Is this course enough to satisfy the prerequisites for machine learning and deep learning? (I am referring to the probability and statistics part)" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 6860.0 0.0 1.0 0.0
"Board ❤️" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2904.0 0.0 0.0 0.0
"I have the property 'memorylessness of math concepts'

Whatever happened in the lecture has no bearing on my exam." -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 5561.0 0.0 0.0 0.0
"Completed till:: 20:00" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3185.0 0.0 0.0 0.0
Here. LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 4681.0 0.0 0.0 0.0
"For those too lazy to read the comments or the notes to this course, THERE IS NO LECTURE 8 because there was an exam administered on that day. The same holds for the OTHER MISSING LECTURES." BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3910.0 0.0 0.0 0.0
"""we only live so long, we can skip that proof"" 
wow maybe if my LA prof had the same outlook i would actually remember something from the classes" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 189.0 0.0 0.0 1.0
"what am I saying... XD" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 15119.0 0.0 0.0 0.0
"do people still use blackboards.?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12756.0 1.0 0.0 0.0
"9:09 start of the lecture" IycOPFmEQk8 "5. CF Pumping Lemma, Turing Machines" "MIT 18.404J Theory of Computation, Fall 2020" 1435.0 0.0 0.0 0.0
"Came for the Bayesian statistics lecture, stayed for the whole class. Great lectures! thank you" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 2990.0 0.0 0.0 0.0
"They flirting at 19:29 :,))))" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10438.0 0.0 0.0 0.0
祝老爷子健康，非常感谢您！ wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15645.0 0.0 0.0 0.0
"Absolute legend !" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 2197.0 0.0 0.0 0.0
"Jajajajajaa estoy a cuatro grados de conocer a Mónica" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 7125.0 0.0 0.0 0.0
13:22 VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 412.0 0.0 0.0 0.0
"Wtf, i learnt this when I was 15. How is MIT one of the best uni in the world??" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12098.0 0.0 0.0 0.0
"Thank you MIT OCW, and thank you Prof Tsitsiklis. Your ability to explain so clearly is truly oustanding." gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 9131.0 0.0 0.0 0.0
"I find it funny how towards the very end of the lecture, most students hurrying up to get away 😂😂" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5412.0 0.0 0.0 0.0
"@1:08:20 Here a student states that NFA and DFA are equivalent. Prof Siper states that this is not true. In the last lecture ( https://youtu.be/KAySmSEGc9U?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWY&t=56 ) he states this IS true. And in fact we showed that we can model a NFA by using the powerset on the states of a DFA. Even empty strings can be substituted. I was wondering if I got this wrong or whether he just wanted to state that the ""general"" functionality of a DFA and NFA are different in principal." m9eHViDPAJQ "4. Pushdown Automata, Conversion of CFG to PDA and Reverse Conversion" "MIT 18.404J Theory of Computation, Fall 2020" 1505.0 0.0 1.0 0.0
"Anyone else thinks he talks with the same passion for math, as Walter White does for Chemistry? Love this guy." Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2491.0 0.0 0.0 0.0
"It surprised me that there were only 200k views for this amazing lecture over 10 years." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 6988.0 0.0 0.0 0.0
"I can imagine that the algorithm where you subtract a1 from all subsequent a would also be much easier to parallelize." MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5191.0 0.0 0.0 0.0
"Erf 😂" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3574.0 0.0 0.0 0.0
"this video is enormous.45 min?" 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14921.0 0.0 0.0 0.0
"Brilliant lectures!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 2931.0 0.0 0.0 0.0
"Audio starts at 1:15" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 2743.0 0.0 0.0 0.0
"Why are you trolling the introductory lectures of elementary classes then? You're the one choosing the lectures you hear, dumbass." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11789.0 0.0 0.0 0.0
"many black kids are in MIT. What followed proved my assertion. You could have been more subtle in your argument by veiling your comments discretely. Then you distance the premise by talking about poor whites, meritocracy, etc. Your argument about poor whites is also irrelevant. For centuries, it was gov't policy to exclude blacks from society, not so for poor whites. Now gov't has the MORAL OBLIGATION to assist and include them into society via all the programs available. But, it doesn't matter" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13907.0 0.0 0.0 0.0
"I'm really happy that great lectures are available for free. Young people should appreciate it that they have internet and they can learn from materials from other universities especially from other countries from another part of the globe." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6365.0 0.0 0.0 0.0
"Professor Strang ,thank you for a beautiful lecture on minimizing x subject to Ax equal b and the application of the Gram-Schmidt method." MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8336.0 0.0 0.0 1.0
"Dr. Strang  is a national treasure." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3503.0 0.0 0.0 0.0
"Why did he use the '¿' character?" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11811.0 0.0 0.0 0.0
"saludos gran maestro de parte del académico yiyo gigo free arequipa lima peru" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14275.0 0.0 0.0 0.0
"if that many people can do it, so can i " ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13540.0 0.0 0.0 0.0
"p16:34 not so convincing" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 14164.0 0.0 0.0 0.0
"What happens when in the region R, for a same value of x there are 3 or more values of y? How does the integral change?" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11499.0 0.0 1.0 0.0
"No one: Dr. Strang kept the same attire except on 2-3 lectures where he donned the sweater over the shirt." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 7886.0 0.0 0.0 0.0
"Superb lecturer! No wonder MIT charges so much lol ;)" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8962.0 0.0 0.0 0.0
"Lots of info loaded" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 7428.0 0.0 0.0 0.0
"You're the best teacher in the world." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12253.0 0.0 0.0 0.0
"Gilbert Strang + these videos = the beast in Calculus" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4011.0 0.0 0.0 0.0
"Hello ,Area=1/2 Base x Height = 1/2(2x0) x (2Y0)=2xy0,Derivative i.e. 6x^8=48x. Go Fly  a Kite ""Sir. My Chemical Engineering Logarthrymic Algebriac-Calculus up here in CANADA, will blow your ""mind-away""!!Derivatie ie. 8xy^9=72xy!!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4652.0 0.0 0.0 0.0
"Probably, this has been said before, so forgive me if I repeat someone else's words. 

I acknowledge here, that professor Strang is a good pedagogue. I learnt some math over the years. I completely support the use of the geometrical visualization of some properties, as it is a learning need. I can say that for me it is easy to see how to derive properties like the one he gave for the assignment on the Frobenius norm. I say this, because I may not be the only one thinking it and I wanted to tell those people that there is more to math here. 

Only recently, I understood the huge degree of humility and teaching wit that it takes one to pass one's knowledge along. It requires to pretend or to honestly feel you are no better than any of your students. For instance, as I could witness here, Pr Strang shared with his students the latest cool research topics as if they were his colleagues, he thanked them for contributing to the course by giving out some answers. That's what allows him to successfully challenge them in solving some assignments, like the Frobenius norm - SVD problem. All of it is summarized by Gilbert himself at the very end in 48:12, when he explains his view of his relationship with the students (such as ""We have worked to do!"", an honest use of the pronoun ""we"" by the lecturer). 

This 48 min long lecture, honestly impressed me in this regard. Today, I had the privilege of a double lecture: one in math (that could have been compressed to 15 min, since most proofs were skipped) and one in being a better passer of knowledge (that could be extended to 10+ years). Hat off!" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8260.0 0.0 0.0 1.0
"french  is so hhhhh" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12898.0 0.0 0.0 0.0
"multi-variable was easy. I am a bussiness major but decided to take the class cuz i was bored. Didn't even go to lecture one time still managed an A+" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13966.0 0.0 0.0 0.0
"Wow, yea this guy is a great teacher!" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12081.0 0.0 0.0 0.0
"All together * Whoa! :)" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2314.0 0.0 0.0 0.0
"Excellent, very didactic and clear, thanks, prof!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3691.0 0.0 0.0 0.0
"Lets says  I have  two vectors (1,2,4) and (3,y,z) how to get the cartesian equation like ax + by + cz + d = 0 ?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 7340.0 0.0 1.0 0.0
"I love Math!" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 5720.0 0.0 0.0 0.0
"1:10:29
X_i follows gaussian(or normal) distribution" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 583.0 0.0 1.0 0.0
"Amazing lecture learned a lot!!" cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 2364.0 0.0 0.0 0.0
"and the most boring teacher award of the day goes to....." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12371.0 0.0 0.0 0.0
"This is a great series as so much of understanding math comes from the instructor's ability to convey the material in an understandable way.  I have a very intelligent instructor at my university, but he does not take an intuitive, step by step approach.  Many students are therefore left scratching their heads and trying to make sense of the text, which is bad enough.  These videos have been invaluable to me.  Thanks for posting them!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10595.0 0.0 0.0 1.0
"this lecture is so helpful" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14893.0 0.0 0.0 0.0
"why is everyone laughing?  is it at his accent?" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15331.0 0.0 0.0 0.0
"Gil has been my math professor for the last 12 years. These online courses are so amazing." Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4008.0 0.0 0.0 0.0
"36:20  ""I quit without trying, I shouldn't have done that."" So true" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 1035.0 0.0 0.0 0.0
"are proofs taught in some other class, or are they not relevant for the course at MIT?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12397.0 0.0 0.0 0.0
"those first words ""the final class in linear algebra at MIT this fall"" makes you feel nostalgic already :'(" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 14932.0 0.0 0.0 0.0
"Цікавий ""парадокс"". Слухав із задоволенням. Дякую!" XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 15558.0 0.0 0.0 0.0
"This is the best lecture I have ever listed to. Thank you Professor." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 10738.0 0.0 0.0 0.0
"Audio channels, resolution, and aspect ratio fixed!" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 2741.0 0.0 0.0 0.0
"I like the LaTeX slides" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 5680.0 0.0 0.0 0.0
"how many  chalkboards are in that classroom? lol" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13243.0 1.0 0.0 0.0
"excellent lecture.thanks a lot" bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 12823.0 0.0 0.0 0.0
":DDD ahora si, a aprender!" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1454.0 0.0 0.0 0.0
"prof gilbert strang : teaching the beauty of linear algebra 

me : wondering how we are going to get those erasers stuck behind the backboard ........" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14210.0 1.0 0.0 0.0
"I wish I had profs like him. I love this series. I am reviewing multivariant calculus to apply it to Mathematica coding. This is great. Thanks." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6200.0 0.0 0.0 1.0
12:25 ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 395.0 0.0 0.0 0.0
"@fateplus1 Recitation is when students meet up with an instructor outside of the lectures and watch the instructor work through problems in greater detail than is done in the lectures, in order to reinforce the concepts that are taught in the lectures." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1835.0 0.0 0.0 1.0
"I've taken an associates degree worth of MIT opencourseware classes.  Incredible" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6432.0 0.0 0.0 0.0
"@eligray . YEAH U ARE RIGHT." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1829.0 0.0 0.0 0.0
"yes it is xD" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15483.0 0.0 0.0 0.0
"I know that feel. :P 

Good luck!" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5639.0 0.0 0.0 0.0
"this is awesome. thank you. 😀" 9_xG0AGRa-w "Lecture 2: Cantor's Theory of Cardinality (Size)" "MIT 18.100A Real Analysis, Fall 2020" 14857.0 0.0 0.0 0.0
"can someone please tell me why they are laughing at 19:55" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12629.0 0.0 0.0 0.0
"I got an an A on my undergrad Linear Algebra class but I am still learning a great deal by watching these lectures and reading Mr. Strang's book. A great big thank you to Professor Strang and MIT." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5443.0 0.0 0.0 0.0
"Thanks @MIT opencourseware!
It would be great if you can put the lecture title for ease of student. 
thanks!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9584.0   
"Is this enough for jee advanced??" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 6865.0 0.0 0.0 0.0
"Marvellous lecture. Thank you MIT." 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7598.0 0.0 0.0 0.0
"Jee was way tougher lol" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7130.0 0.0 0.0 0.0
"This blew my mind. It was Awesome!" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10469.0 0.0 0.0 0.0
"Liking all the Jupyter SymPy MIT 18.06 notebooks on GitHub ..." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7366.0 0.0 0.0 0.0
"After watching this course I ask myself why does MiT reject 1200 sat scores when they can make a 980 sat person understand things  flawlessly" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 2264.0 0.0 0.0 0.0
"Making H_0=gaussian is cheating, isn't it?" a66tfLdr6oY "11. Parametric Hypothesis Testing (cont.) and Testing Goodness of Fit" "MIT 18.650 Statistics for Applications, Fall 2016" 7566.0 0.0 1.0 0.0
"Thanks this is very helpful,  my fav teacher :D" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 9797.0 0.0 0.0 0.0
"I actually walked by his current office. He's on the top floor of the math department of UC Berkeley if you're interested." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5021.0 0.0 0.0 0.0
"@BYMYSYD so he plugged in the WHOLE term, which was multiplied with X - Xo, to the derivative formula?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1598.0 0.0 1.0 0.0
"i am only a high school student studying pure maths, but idk why the students in MIT ask stupid questions that even i can answer... and yet, many smarter people out there can't get in:(" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13336.0 0.0 0.0 0.0
"I followed to about 7 minutes lol" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5426.0 0.0 0.0 0.0
"Professor Strang is the BEST! Makes me motivated to enter MIT" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 8354.0 0.0 0.0 0.0
"Nice explain well done" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7842.0 0.0 0.0 0.0
"Great Work .. Really appreciate you making the knowledge available to the world." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 4211.0 0.0 0.0 0.0
"1/16
" -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 329.0 0.0 0.0 0.0
"this should be called mr. rogers teaches mathematics" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14916.0 0.0 0.0 0.0
"Wow all the concepts make so much more sense now. Dr. Strang really is a great teacher!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12030.0 0.0 0.0 0.0
"would just love to make a small addition to the theorem, just an intuative way to look at it is, there is no tangent to a point but there is a definite tangent to a point on a curve, hence the theorem must be correct, hope i make sense :)" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15405.0 0.0 0.0 0.0
"@KatherineRogers First: When he says that y=x^2, he's talking about the Magnitude of x squared, not the unit squared. Here is an example: Imagine I have a sheet of paper whose width is 10 cm and its length is the width squared. The length will then be 100 cm, NOT 100 cm^2 right? This is because only the magnitude (the number itself) was squared, not the unit. The same thing happens with the problem he's solving. " ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1651.0 0.0 1.0 0.0
"Thank you! This is an amazing lecture" P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 9482.0 0.0 0.0 0.0
"love this course" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 13877.0 0.0 0.0 0.0
"The teacher has mistake in the result" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10296.0 0.0 1.0 0.0
"Thank you so much for refreshing my brain. I found you when I'm retired. Do we know-how this knowledge came from? I just start my channel not long ago, please check it out, I'll appreciate it, thanks." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 9365.0 0.0 0.0 0.0
"Wow this is the end" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 12042.0 0.0 0.0 0.0
"So far exactly what I need. A note: This is a hybrid of algebra and statistics so you may rewrite  A as X, b as y, and x as b. This has helped me relate the presented material to associated material in the statistical literature." Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8754.0 0.0 0.0 1.0
"147K views with 700 likes, human beings are not very generous about their likes" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 423.0 0.0 0.0 0.0
"bruv, clean up your blackboard. Your blackboard is whiter than my whiteboard tho" X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 12562.0 1.0 0.0 0.0
"I Really Like The Video Solving Ax = b: Row Reduced Form R. From Your" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 4995.0 0.0 0.0 0.0
"Watching this as someone without a clue as to what any of this means, and I'm still fascinated. No wonder MIT is so sought after." RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 11298.0 0.0 0.0 0.0
"Dr. Strange." k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3515.0 0.0 0.0 0.0
24:46 TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 756.0 0.0 0.0 0.0
"It feels that the right side is louder than the left. Anyone feels the same?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 6916.0 0.0 0.0 0.0
"For BPP, deep learning and for the general structure of neural networks the following comments may be useful. 

To begin with, note that instead of partial derivatives one can work with derivatives as the linear transformations they really are. 

It is also possible to look at the networks in a more structured manner. The basic ideas of BPP can then be applied in much more general cases. Several steps are involved. 

1.- More general processing units. 
Any continuously differentiable function of inputs and weights will do; these inputs and weights can belong, beyond Euclidean spaces, to any Hilbert space. Derivatives are linear transformations and the derivative of a neural processing unit is the direct sum of its partial derivatives with respect to the inputs and with respect to the weights; this is a linear transformation expressed as the sum of its restrictions to a pair of complementary subspaces. 

2.- More general layers (any number of units). 
Single unit layers can create a bottleneck that renders the whole network useless. Putting together several units in a unique layer is equivalent to taking their product (as functions, in the sense of set theory). The layers are functions of the of inputs and of the weights of the totality of the units. The derivative of a layer is then the product of the derivatives of the units; this is a product of linear transformations. 

3.- Networks with any number of layers. 
A network is the composition (as functions, and in the set theoretical sense) of its layers. By the chain rule the derivative of the network is the composition of the derivatives of the layers; this is a composition of linear transformations. 

4.- Quadratic error of a function. 
...
——-
Since this comment is becoming too long I will stop here. The point is that a very general viewpoint clarifies many aspects of BPP. 

If you are interested in the full story and have some familiarity with Hilbert spaces please google for papers dealing with backpropagation in Hilbert spaces. A related article with matrix formulas for backpropagation on semilinear networks is also available. 

For a glimpse into a completely new deep learning algorithm which is orders of magnitude more efficient, controllable and faster than BPP search in this platform for a video about deep learning without backpropagation; in its description there are links to a demo software. 

The new algorithm is based on the following very general and powerful result (google it): Polyhedrons and perceptrons are functionally equivalent. 

For the elementary conceptual basis of NNs see the article Neural Network Formalism. 

Daniel Crespin" sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3838.0 0.0 0.0 0.0
"1:06:49 when he wrote ""b is an upper bound for -A"", I'm pretty sure he meant ""-b is an upper bound for -A"", since b is actually the lower bound for A." mlPLLXHZ8_U "Lecture 4: The Characterization of the Real Numbers" "MIT 18.100A Real Analysis, Fall 2020" 580.0 0.0 1.0 0.0
"Great courses! Thanks from France!
" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 4221.0 0.0 0.0 0.0
"at @29:31 he says the rate of change is supposed to determine a function upto this ""starting value"". I didn't the meaning and significance of starting value , and he is referring to." -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12468.0 0.0 1.0 0.0
"The guy is fast :D 28:21" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 10131.0 0.0 0.0 0.0
"Thank you!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 9471.0 0.0 0.0 0.0
"Why this got only 300k views = 30k views per year from all over the world. There are millions of engineering, math and science students that need linear algebra each year." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 11928.0 0.0 0.0 0.0
"I am definitely impressed!" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5084.0 0.0 0.0 0.0
"@13:10 WHY IN THE WIDE WIDE WORLD OF SPORTS WOULD THAT WORK?!?!?!? Mind. Blown." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 1496.0 0.0 0.0 0.0
https://youtu.be/DDUC23useww osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 13293.0 0.0 0.0 0.0
"Amazing lectures in this course are so underrated and it was the best course I attended this year." rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 2378.0 0.0 0.0 0.0
"I cant understand why avg (divf) in D= avg(-u sub t) in D ,then Divf= -u sub t? Because if we actually plug a coordintate in the equation, it is no guaranteed the equation will be true." wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 5234.0 0.0 1.0 0.0
"1:14:30
Omg I must say this class is a delight specially the sigma part. I was so surprised. Maybe it is something simple but it wasnt for me because I always Just use the equation." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 589.0 0.0 0.0 0.0
"Great teacher." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 4340.0 0.0 0.0 0.0
"At 31:44 
in order to find the dimension of subspace S, Prof Strang takes A as [1 1 1 1] of which S is null space.

My question is, we could have taken A as 4 * 4 identity matrix for which S  would have acted as null space.
In that case rank(A) is 4 and hence no free variable thus its null space which is S has (4-4) 0 dimension
So why are we restricted to take A as [1 1 1 1] in which case the dimension of S comes out to be 3 as rank(A) = 1 ?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 2642.0 0.0 1.0 0.0
"Gilbert Strang greatest  mathematics professor in 21st century.... Thank you a lot." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 4016.0 0.0 0.0 0.0
"im confused with top z and bottom z can someone help me with it/" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13566.0 0.0 1.0 0.0
"At 41:54, Strang gets the eigenvalues correct from memory.  I'm impressed!" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 2664.0 0.0 0.0 0.0
"@meetmeon31 you realize less than 10% of freshman are in this course. This is the lowest level math offered at MIT. " eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1942.0 0.0 0.0 0.0
"At 45:20, if we are talking about null space then indeed there would be an infinite number of solutions, but if we are talking about Ax=b then there needs to be a particular solution in the first place for the infinite solutions to be existing. 
Am I right?" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 2679.0 0.0 1.0 0.0
"what seems to be the problem with lady at 43:39? She apparently has slipped half off her seat.. Respect to teacher please !!" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15182.0 1.0 0.0 0.0
"If only I had seen this video before my third uni maths assignment T_T" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6510.0 0.0 0.0 0.0
"20220525 簽" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 635.0 0.0 0.0 0.0
"11:10 WTF! is she eating on lecture?
" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 366.0 1.0 0.0 0.0
"Another mistake at 44.20. it only makes sense talking about the continuity of a function in a value that belongs to the domain of that function. f(x)= Sin(x)/x is continuos in all the domain R-{0}.
" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2459.0 0.0 1.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8434.0 0.0 0.0 0.0
"thanks prof. for this lecture ..." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14598.0 0.0 0.0 0.0
"00:00 Course overview
01:00 Lecture overview
04:25 Row picture 2D
08:35 Column picture 2D
15:38 Row Picture 3D
22:00 Column Picture 3D
27:55 Can I solve Ax=b for all b?
32:25 ""Visualise"" 9-dimension
35:33 How to multiply a matrix and a vector?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 278.0 0.0 1.0 0.0
"This is like a trip down memory lane for anyone that studied Electrical Engineering. Freshman year, when things were simple 😂" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10685.0 0.0 0.0 0.0
"Thank you very much! Amazing lectures!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9449.0 0.0 0.0 0.0
"Mit's beauty" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7682.0 0.0 0.0 0.0
excellent J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12812.0 0.0 0.0 0.0
"VERY crappy,  A WASTE OF TIME, and i spent too much hours in this lecture but still cannot get in." Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11147.0 0.0 0.0 0.0
"Prof Strang is mathematical elegant in delivering linear algebra in an understandable way" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8273.0 0.0 0.0 0.0
"The meat begins at 12:00.
05:30 Errr, no, the square is not ""made of"" points. It *contains* those points. A point just marks a certain location inside that (pre-existing) square. One _cannot_ build the area of the square from points, because POINTS DON'T HAVE ANY AREA BY THEMSELVES!!! Areas could be made only from smaller (e.g. unit) areas. Otherwise there would be no difference between a scalar, a vector, a pseudovector, and a pseudoscalar in Clifford Algebras etc. There's a reason we distinguish those dimensions, right? :P
The ridiculousness of that statement comes out nicely at 06:10 where he writes the sum of the probabilities for these points. He said in the previous lecture that the probability of a point is 0 (because it has no area, and we assumed that area = probability in this model), and he restated this assumption again in this lecture here. So we're actually *adding up 0s here*! And we _cannot_ get a positive result (in this case: 1) from summing up zeros, no matter how much of them we add up (be it 10, 100 or infinitely many). So the right side of this equation cannot be equal to the left side, and the entire equation is false.
06:40 No, the mistake is not in this point. The union is fine, as long as we're adding up actual areas. The mistake is in assuming that a point can have an area :P
07:20 Of course I can! Cantor's diagonalization argument is one example. Another one is Hilbert's space-filling curve. Long story short: yes, there are ways of ordering points on a surface, as well as in space, by threading them on a line. In other words, there exist functions which map points on a surface (or in space) onto a line. And this is another proof that this is not what is wrong with this argument. The ""points have area"" assumption is.
17:20 If the probability of B is 0, then we're contradicting ourselves, because the ""|B"" in ""P(A|B)"" was supposed to mean that B occurred *for sure*. So it _cannot_ be 0! The very statement that ""B occurred"" means that this probability is _not_ 0, and we are OK to put it in the denominator. Logic, Mr. Titskills :P" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 10186.0 0.0 1.0 0.0
"39:05 This is it. Weighting definitions are where the magic lies." bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 1093.0 0.0 0.0 0.0
"This course really rocks in the math series," J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10495.0 0.0 0.0 0.0
"two dee dee dee dee tee." sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14963.0 0.0 0.0 0.0
"lol at the clinton joke" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 13822.0 0.0 0.0 0.0
"The cycloid curve is used for the tooth profile on the gear.." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10068.0 0.0 0.0 0.0
"Good lecture again; he explains things well. Takes me up to about the limit of my previous knowledge on vectors, but I hadn't fully appreciated the link between the cross product/triple scalar product and areas/volumes. Hopefully onto new stuff soon..." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4132.0 0.0 0.0 1.0
"Who here still a teenager 😅" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11736.0 0.0 0.0 0.0
"Just Finished this course! Huge thanks to MIT OCW <3 
Anmol, India, 09-06-2021" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7151.0 0.0 0.0 0.0
Excellent! IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 3684.0   
"How to prove the dimension of A and A transpose are the same?or Why they are the same value?can any one explan to me ?thanks" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4900.0 0.0 1.0 1.0
"He is French I think" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4494.0 0.0 0.0 0.0
"In a traditional multivariable calculus class, the concept of Hessian matrix will be introduced at this point.  I wonder why he doesn't.

Anyway, a Hessian matrix of 2 variables is just a matrix of [ fxx fxy; fxy fyy ].  Let D = det(H), then:
1) If D < 0, saddle point
2) If D > 0, either relative min or max.  Furthermore, if fxx  > 0, then it's relative min.  If fxx < 0, it's a relative max." 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6622.0 0.0 1.0 1.0
"thank you sir..." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14510.0 0.0 0.0 0.0
"Excellent explanation !" jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 3642.0 0.0 0.0 0.0
"Honestly I think there should be people moderating the comments section that delete those judgmental comments. The students have rights to learn in a safe environment. Asking “stupid” questions is an integral part of learning as much as making mistakes. It’s just sad to see students swallow their doubts bcs they worry about how they look in front of others.
So if you know the answers to the questions, shut up and watch the video without being a judgmental jerk." TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4782.0 0.0 0.0 0.0
"EPIC AUTO-BLACKBOARD @ 2:35
And that chalk sounds really soft, the stuff my teacher uses is all hard and you can hear the scratching ;_;
Oh and thanks, this is really helpful for my final next week :P" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3539.0 1.0 0.0 0.0
"Sir, I wanted to thank you for your commitment to teaching. It's a great opportunity for me to watch those courses. I'm considering myself as one of your students and wishing you health and all the luck in the world." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8710.0 0.0 0.0 0.0
"The VIBE, energy, enthusiasm!, God he is such a legend yet so decent and humble!." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9976.0 0.0 0.0 0.0
"Hello ,Area=1/2 Base x Height = 1/2(2x0) x (2Y0)=2xy0,Derivative i.e. 6x^8=48x. Go Fly  a Kite ""Sir. My Chemical Engineering Logarythmic Algebriac-Calculus up here in CANADA, will blow your ""mind-away""!!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4653.0 0.0 1.0 0.0
"I used to think calculus was more fun than linear algebra, I was wrong." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 6130.0 0.0 0.0 0.0
"15:06 lovebirds" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 448.0 0.0 0.0 0.0
"3:45 TURING MACHINE - REVIEW
7:05 Multi Tape TM
20:10 NON DETERMINISTIC TM
29:55 TURING ENUMERATORS

48:20 Church Turing THESIS
56:00 HILBERT'S 10th PROBLEM
1:00:45 Notation for Encodings and TMs" TTArY7ojshU "6. TM Variants, Church-Turing Thesis" "MIT 18.404J Theory of Computation, Fall 2020" 1116.0 0.0 0.0 0.0
"It appears that from engineering math  view that there’s the problem." k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6909.0 0.0 0.0 0.0
"why won't the rest be uploaded?" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15379.0 0.0 0.0 0.0
"thanks for sharing the lectures !!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14580.0 0.0 0.0 0.0
"Teaching just like IIT Professors" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9021.0 0.0 0.0 0.0
"for a square matrix with orthogonal columns will ||Qx||^2 = || x ||^2 hold or the columns have to be orthonormal for this equality to hold ??? a bit confused please help" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12879.0 0.0 1.0 0.0
"I used this to self-learn Vector calculus in my summer finishing year-1 of basic Multi-Calc in college starting from Lesson-15 to Lesson-29. I also made use of Schaum's Vector Analysis for problems and SJ Colley's Vector Calc as an additional reference. I watched all vids in at min 1.25x finishing it up in 2 weeks time.
 
Dennis Auroux is an absolutely delight and his board-rubbing skills are sooo impressive! His explanations are spectacular & I really enjoyed his emphasis on applications (particularly from physics-inertia, maxwell's eqns etc).

One thing I missed was lack of info on the Frenet-Serret Equations which I found awesome in general & the lack of practicing more problems but hey, you could do both on your own like I did!

Anyways, 12 years after this vid has been released, I'd still recommend this course with all my heart. It is awesome! Thanks MIT for releasing this to the public & thanks Prof. Auroux for just being an amazing lecturer!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6127.0 0.0 0.0 1.0
"I think you meant ""hahaha""" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6082.0 0.0 0.0 0.0
Wow xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12022.0 0.0 0.0 0.0
"I watched this video in x1.5 speed aswell. Habits I guess." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6188.0 0.0 0.0 0.0
"If I had to follow a companion text book which one should I get to go with the course? @MIT" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6468.0 0.0 0.0 0.0
"Excellent quality of teaching.. really appreciate the initiative taken by MIT to make these lectures available to everyone across the world for free" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 3671.0 0.0 0.0 0.0
28:05 wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 831.0 0.0 0.0 0.0
"OXOME :)" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7992.0 0.0 0.0 0.0
"Very good presentation. Thanks for posting MIT ..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11182.0 0.0 0.0 0.0
"here i am, still seven videos so far," UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 13140.0 0.0 0.0 0.0
"NI SIQUIERA SIRVE PARA CALCULAR EL VOLUMEN DE LA ESFERA MENOS PARA PROBLEMAS MAS COMPLICADOS." RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7800.0 0.0 0.0 0.0
"I really encourage you to buy The Introduction of Linear Algebra which Pf Strang wrote. If I say these videos are rank r, then I can definitely say the book is the orthogonal complement of these videos that makes perfect dimension of Linear Algebra." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5911.0 0.0 0.0 0.0
"Jerison is only comparing the highest degree terms in both the numerator (1) and the denominator (1/x), because that's all that matters when the limit approaches infinity. And yes, the factor does disappear to zero, after that comparison is made. He's just eliminated the rest of the terms in advance because they're irrelevant when x approaches infinity." PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7133.0 0.0 0.0 0.0
"Some people don't understand the importance of fundamental understanding." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8825.0 0.0 0.0 0.0
"Gilbert Strang, the name that all college students around the world know. He's a genius and a great teacher" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4035.0 0.0 0.0 0.0
"This is the best introduction to determinants, that I have seen so far." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 10736.0 0.0 0.0 0.0
"He simplifies everything while other mathematicians try to complicate things" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4608.0 0.0 0.0 0.0
"@tj1990 INDEED" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2046.0 0.0 0.0 0.0
"Brilliant stuff." dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 2934.0 0.0 0.0 0.0
"We got this result without proving it. But then, we only live so long. (laughter). [We're not laughing because we only live so long, even though that's funny, too.]" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 11321.0 0.0 0.0 0.0
"Thanks to Almighty God and thanks to you MIT and teacher in this quarantine time my teacher couldn’t help me to study because we cannot go to classes so i have studied this course and i have finished all the lectures thank you my teacher" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9798.0 0.0 0.0 0.0
"What a cute professor!" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 11402.0 0.0 0.0 0.0
":0

Why is it not a crime yet to not teach like this in high school?" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1451.0 0.0 0.0 0.0
"Damn easy." twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3293.0 0.0 0.0 0.0
"I think just plotting a vector on new axes with reference to a given axes.
New axes not necessarily orthogonal to each other." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6032.0 0.0 0.0 0.0
"46:08 It should be F_100 is similar to c_1 * lambda1 * x_1. The professor missed x_1 here. But if you assume x_1 is 1 (which is the case here), then this is correct." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 1266.0 0.0 1.0 0.0
"at 21:04 , the min(X,Y)=2, does the red shaded area cover the whole area of event B? can someone explain, I'm confused" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 12424.0 0.0 1.0 1.0
"i love this professor!! he's awesome!!" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13434.0 0.0 0.0 0.0
"This series is a LIFE SAVER for review before exams." Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10922.0 0.0 0.0 0.0
"I think it's because that is usually covered with Power Series, not Taylor/McLaurren Series." wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6029.0 0.0 1.0 0.0
"The lecturer is awesome." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 10167.0 0.0 0.0 0.0
"The lectures of Prof. Gilbert Strang are the best and right to the point most of the times, but i don't know why his book; Fourth Edition Of Linear Algebra and Its Application, is such a boring and complicated book." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 10172.0 0.0 0.0 0.0
"This board is awesome, and so is the teacher." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 10470.0 1.0 0.0 0.0
"Doesn't a random vector in the plane P added up to a line L form a new line that goes trough the origin and forms a new subspace?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 3467.0 0.0 1.0 0.0
"I Really Like The Video Topological considerations; Maxwell's equations.From Your" BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 4998.0 0.0 0.0 0.0
"I am student from RIT and this is excellent supplementary material for CSCI 262: intro to cs theory" KAySmSEGc9U "3. Regular Pumping Lemma, Conversion of FA to Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 5144.0 0.0 0.0 0.0
"I Really Like The Video Dot product From Your" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4943.0 0.0 0.0 0.0
"If I replace u => Sc, I get d/dt Sc = A Sc. But, at 30:20, he gets S d/dt c = A Sc. Did he say anywhere that d/dx and S commute?" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 6472.0 0.0 1.0 0.0
"What happens if you had: only 10 people in this particular class, would everybody eventually be happy?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 11498.0 0.0 1.0 0.0
"Thank You Professor!!! 
" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9053.0 0.0 0.0 0.0
"Why they hate Taylor's approx tho? I think that's so cool" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11926.0 0.0 0.0 0.0
" 
Thanks Prof. Strang and IMT for sharing these lectures." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 15535.0 0.0 0.0 0.0
"his english is absolutely flawless. just has a thick accent which makes him seem even more intelligent, almost as if he mastered english overnight" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13163.0 0.0 0.0 0.0
"So many questions answered in 40 minutes. Thank you so much, Professor Strang." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8773.0 0.0 0.0 0.0
"Very astute remark.
If you are going to eat  a lot of cream cheese you will say it the same way." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 11157.0 0.0 0.0 0.0
"thanks a lot. great job!" mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 14576.0 0.0 0.0 0.0
"Yes, please upload the rest of this. Seen the first 12 lectures and they are really great. Want to see the rest since I missed most of my own single variable calculus lectures, and I want to really master the basics.

And how great it feels to learn college level stuff from another side of earth. Really love this. This is the future. Education for anyone who wants it.

Go MIT! from Sweden." YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12151.0 0.0 0.0 0.0
"A good class! Thanks for all your effect(Thank teacher extra)!" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 2114.0 0.0 0.0 0.0
"Haar wavelet
https://en.m.wikipedia.org/wiki/Haar_wavelet" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4411.0 0.0 0.0 0.0
"""the vast majority"" someone came into MIT with out having to us vectors, damn you universe, with out it Physics is just a 10th grade math lesson. " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 180.0 0.0 0.0 0.0
"@28:35, the set of vectors given are not a basis. They don't span R^3 since the nullspace corresponding to those vectors have a common form: [c,-2c,c] which is not only the zero vector. But however, the intended idea is clear from whatever he has explained :)" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 1526.0 0.0 1.0 0.0
"Excellent lecture. Professor Strang is a legend." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 3659.0 0.0 0.0 0.0
"At 41min, Why is the number of nonzero eigenvalues the same as rank(A)?" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2665.0 0.0 1.0 0.0
"His lecture make me cry." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4757.0 0.0 0.0 0.0
"Hi, at 39:00 how did he so quickly find the roots of the equation?" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 4724.0 0.0 1.0 0.0
"Great! Thanks." IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 4369.0 0.0 0.0 0.0
"This lecture was pretty confusing" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 10834.0 0.0 0.0 0.0
"He just simplified the algebra of it a little. He could have wrote u(X + deltaX)/v(X + deltaX) instead, more like the previous deduction of the product rule. However recall that u(X + deltaX) - u(X) = deltaU, and since we are missing the -u(X) term, u(X + deltaX) = deltaU(X) PLUS u(x). Hence as written, u + deltaU. " 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4560.0 0.0 1.0 0.0
"I am not so familiar with the US education system, but isn't this 9th grade level calculus?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5127.0 0.0 0.0 0.0
"Not impressed so far. Prof. Auroux does not do a good job on explaining the details, e.g.: he explains that the dot product for 2 vectors <x,y,z>*<a,b,c> = a*x + b*y + c*z, but does not explain that the orthogonal components that are multiplied in this dot product result in zero. The dot product <x,y,z>*<a,b,c>  is actually

a*x*cos(0) + b*x*cos(90) + z*x*cos(90) + a*y*cos(90) + b*y*cos(0) + c*y*cos(90) + a*z*cos(90) + b*z*cos(90) + c*z*cos(0) = a*x + b*y + c*z

All too often math teachers jump over steps that they consider trivial, but these jumps can be rather confusing for the student! Combine this with students' lack of (ability for) disciplined thinking and/or having gotten lost at an early stage, and you have the reasons why so many people fail at math." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7925.0 0.0 1.0 0.0
"16:20:""where did he put his good god white foot on lol🤣""" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 475.0 1.0 0.0 0.0
"game over ! (Pi / 8)*4 =Pi /2 so our teacher says that a cercle'area of 1 for radius, is Pi/2, game over, the answer it's PI" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12914.0 0.0 0.0 0.0
"Thank you MIT
Also, the accent his so cool" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 9124.0 0.0 0.0 0.0
"Great videos. Explains much better than my prof. " xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4364.0 0.0 0.0 0.0
"how do we know that E-1 will be a lower triangular matrix?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 13224.0 0.0 1.0 0.0
"Thank u sir" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9074.0 0.0 0.0 0.0
"These people are a stand-up comedian's wet dream." 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10424.0 0.0 0.0 0.0
"@raffk I don't want to come off as an ultimate smarthead, but I have been asking myself the very same question for quite some time now..." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1983.0 0.0 0.0 0.0
"The plural of Formula is Formulae
Aiio.
" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10228.0 0.0 0.0 0.0
"I found another solution : y=-ln(abs(x))/2a+c, where the parabolas are y=ax^2" 60VGKnYBpbg "Lec 16 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5429.0 0.0 0.0 0.0
"""I think of these matrices as people"". thank you so much professor to making me feel the same." TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 63.0 0.0 0.0 1.0
"thank u prof Auroux and MIT" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14459.0 0.0 0.0 0.0
"Great instructor. The materials are well organized, and the lectures are really helpful and enlightening. Thanks a lot!" ZwpwmGP5ITM "Lec 34: Final review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4234.0 0.0 0.0 0.0
"Time 39.20, vector v and r are always changing as planet rotate around the Sun.  How does he know abs (r cross v) = constant?  He is using the law to justify it's a constant.   It should be the other way around,  we need to understand why it's a constant in order to justify the law.  So why is it a constant?" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11012.0 0.0 1.0 0.0
"@PhilOrzechowski , he says that he just adds it to create a system of equations. " 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 1699.0 0.0 0.0 0.0
"Give this man a medal" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4048.0 0.0 0.0 0.0
"Listening to cinematic musics while watching the lecture makes me feel like I'm in a top secret project and I'm the most important agent" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7386.0 0.0 0.0 0.0
"47:25 bottom left: How is Var(u^TX)defined? What does the ""variance"" of a random vector mean? Thank you so much" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 1281.0 0.0 1.0 0.0
"A thanks from me as well. I've really enjoyed this series, and have thoroughly learned linear algebra, which is now my favorite branch of math." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 2159.0 0.0 0.0 0.0
"sir is lec 8 not there?" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14310.0 0.0 0.0 0.0
"100× 100 matrix will take max  49950 steps of ellimination to form an Identity , if and only if -> all the elements are not equal 0 ;  explanation -formula as per me 😁 i.e  100 × 100  matrix = 10000 elements  , so 100 num of pivots , which are no to be changed  and so remaining  elements ;10000-100 = 99900  ; we are supposed to make either upper or a lower Tri. , So now we  have to change 1/2 of the  elements skipping the pivots i.e = 1/2 × 99900 = 49950 elements  so 49950 steps 😎" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 337.0 0.0 0.0 0.0
"Is it necessary through all Lectures for Machine learning preparation?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 6793.0 0.0 0.0 0.0
"Dr prof yes yes yes MIT the best because they make difficult things easy hehehehe" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 3495.0 0.0 0.0 0.0
"great vid sweet on my ears." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 13011.0 0.0 0.0 0.0
"IN the last proof how did f(X0) get included into the limit in the next line ? can anyone explain please?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6448.0 0.0 1.0 0.0
"dont assume that his life is consumed by this... he has math skills with exceptional social skills which is extremely rare in scientists... which simply put just means that he is a genius..." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12773.0 0.0 0.0 0.0
"Great lecture, really concise. " 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 4281.0 0.0 0.0 0.0
"I love this guy. He would deserve a 'Gilbert Strang fan club'." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5813.0 0.0 0.0 0.0
"Yufei Zhang is a legend" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 12268.0 0.0 0.0 0.0
"Note: Videos of Lectures 28 and 29 are not available because those were in-class lab sessions that were not recorded." p-bXJIa7QVI "Lecture 30: Completing a Rank-One Matrix, Circulants!" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7938.0 0.0 0.0 0.0
"Greatest of teachers inspire the students to fall in love with learning" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4378.0 0.0 0.0 0.0
"While I have little clue as to what he is talking about, I have to say that this lecturer speaks well." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11719.0 0.0 0.0 0.0
"Gotta love when the golden ratio shows up out of nowhere" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 4171.0 0.0 0.0 0.0
"24:40 a Physicist walks into a math lecture" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 747.0 0.0 0.0 0.0
"Respect for 9th graders watching this" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8556.0 0.0 0.0 0.0
"The introduced concepts are much simpler than the way they are presented in this lecture." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10144.0 0.0 0.0 0.0
"Mit, I request in comment to mit every time and thanks they provide it. Please complete the algorithm trioglogy 6.854 please 🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻" 3PzuSPQPEU4 "8. Undecidability" "MIT 18.404J Theory of Computation, Fall 2020" 7683.0 0.0 0.0 0.0
"Intuitively, a positive definite matrix is one that has more stretching weight than a rotation weight. If it operates on a vector in the first quadrant, it guarantees that the output vector is also in the first quadrant. This is almost like a closure property under the transformation of a matrix. I need to examine the case when the x vector in Ax is not in the first quadrant. The entire underlying theme is creating something that is very close to an Eigen matrix with more weight around the diagonal. The important of Eigen matrices is well known in applications where the power matrix has the same effect of a power scalar function. With big matrices, there is nothing more valuable than decomposing a matrix in terms of simpler matrices among which the Eigen matrix is one of those decompositions. Diagonalizing a matrix and SVD is very related to this theme. Any analysis that attempts to transform the effect of a matrix to one that resembles a scalar transformation is the goal." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 6738.0 0.0 0.0 0.0
"Thank you very much for this interesting presentation." hwDRfkPSXng "Lecture 32: ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9444.0 0.0 0.0 0.0
"the whole lecture was incredible.
godlike.
gausslike.
stranglike..!!!!!!!!!!!!
" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 14752.0 0.0 0.0 0.0
"A_s = A screwed up." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 2188.0 0.0 1.0 0.0
"Use beta function to solve at 38:45" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11133.0 0.0 1.0 0.0
"Professor Strang can almost always explain a concept from an angle other professors rarely touch upon. Excitingly, that angle seems always to be the right angle most appropriate to understand that concept." lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 8346.0 0.0 0.0 0.0
"studying for calc 3 before i even take it..." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14407.0 0.0 0.0 0.0
"i love how at the end he keeps nodding his head for the video to end xD" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 13426.0 0.0 0.0 0.0
"I find this lecture little chaotic." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5419.0 0.0 0.0 0.0
"For those of you who don't understand this lecture, read this notes https://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/2.-partial-derivatives/part-b-chain-rule-gradient-and-directional-derivatives/session-38-directional-derivatives/MIT18_02SC_notes_20.pdf" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 3909.0 0.0 0.0 0.0
"@cb2198 why wouldn't you cheer? (o.O) 
it's just a thing their students have been doing since 18.01, they get bored i guess..." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1809.0 0.0 0.0 0.0
"It is better not to rotate when getting ellipse. Ellipse has to be done without rotating, because multipling by lambda makes stretching along axes. Then of course should be rotating by matrix U. I.e. when ellipse first appeared on the board it should be vertically placed, not inclined.
It is possible to draw - you should placed vectors 1 and 2 inclined initially on the first step. Then after multipling by V they will be along axes. Then stretching, then once again rotating. Still, it is a good lecture! :)" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6939.0 0.0 1.0 0.0
"At 15:34.  Did he make a mistake here?  The two normalized vectors 1/3(1, 2, 2) and 1/3(-2, -1, 2) aren't orthonormal because their inner product is not zero.  It is 1/3(1*-2 + 2*-1 + 2*2) = 4/3." 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 2594.0 0.0 1.0 0.0
"Thanks so much..it has been too many times I followed the lectures...still not bored." l4NoMKEHQwM "11. Derived Distributions (ctd.); Covariance" "6.041 Probabilistic Systems Analysis and Applied Probability" 9793.0 0.0 0.0 0.0
"The best lecture Ive ever seen, Thank you very much!!!" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 9999.0 0.0 0.0 0.0
"An Indian edition of this book is available only in India
http://www.wellesleypublishers.com/buy.html" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 2418.0 0.0 0.0 0.0
"i really don't get the rotation bit at around 45:00. ive been staring at it for like 5m at this point." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13451.0 0.0 1.0 0.0
"After all that and he did not explicitly state that e^ix = cos(x) + i*sin(x) what a shame." wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2246.0 0.0 1.0 0.0
"That seems to be the Google's video about T-SNE that prof. Rigollet mentions in 3:16 https://www.youtube.com/watch?v=wvsE8jm1GzE" a1ZCeFpeW0o "20. Principal Component Analysis (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 9911.0 0.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8438.0 0.0 0.0 0.0
"fuck,.i just love this prof so much!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12906.0 0.0 0.0 0.0
"he was probably pirate in his past life. " JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 13118.0 0.0 0.0 0.0
"@katee808 Starting next month, I'll be paying the price for you =)" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 1916.0 0.0 0.0 0.0
"@42:59 There is no power of 2 on the l1 norm for the lasso problem." Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1556.0 0.0 1.0 0.0
"that e^y stuff blew my mind O_o" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14628.0 0.0 0.0 0.0
"Not so illustrated. A lot of notions are not clearly defined" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7930.0 0.0 0.0 1.0
"""oh, did I just invent a negative one?"" - made me laugh =)

Love these lectures, very well explained and at a comfortable pace. Thank you for this." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 167.0 0.0 0.0 0.0
"Great lecture Professor Tsitsiklis,  very clear, pretty neat as well as the ones from your TA´s.  I am following MIT OpenCourseWare." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 4248.0 0.0 0.0 0.0
"im really glad MIT put up these series. im about to go into college and the summer breka and all gave me a chance to learn more classes, like single variable calculus which was fairly easy. but now that im learning this, I found that I had to really change my perspectve on certain fields of mathematics, particularily linear algebra. the whole beginning of the series with vectors took me a while to understand because id never thought of systems of equations in that way. " 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 13570.0 0.0 0.0 1.0
"Very nice." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11219.0 0.0 0.0 0.0
"guys i have a question 
if we have something like this one -->
f(x)>x^2 +e and this is true for every real x
Can i differentate this and say
First derivative of f (x)   >=   2*x  ?
Please i need help on this one" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13025.0 0.0 1.0 0.0
"Damn!!!was eagerly waiting for these lectures!!!!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3302.0 0.0 0.0 0.0
"Thank u for the awesome lectures" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9071.0 0.0 0.0 0.0
"e^x and ln x are inverse functions. Their approximations are also inverse functions. Is this true for all invertible functions?" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12785.0 0.0 1.0 0.0
"Oh, they make things so much simpler at good schools where people are smarter and have an easier time making connections that are actually not that obvious.

Like I didn't get any explanation about the intuitive aspect of dot product in my classes...

-.-" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8032.0 0.0 0.0 0.0
"is there one who know this guy's accent" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 13654.0 0.0 0.0 0.0
"Derivative 10-11th form in Russia . Easy-peasy piece of cake  " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3356.0 0.0 0.0 0.0
"guys if you are here because of machine learning then trust me this course is the most most useful one to do before even starting machine learning i can ensue you it worth it 100% i myself have completed this series and it just gave me leg up in ML trust me after this course you will be able to understand ml concept that some of highly paid ML people can't! it will be such a leg up in you ml career i swear i wish i can erase it from my memory and do all it all over again 
p.s please do it right tho understand every concept go through book and do exercise if needed give it good 3 months atleast" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13026.0 0.0 0.0 1.0
"Of course I know how to use it, but I once didn't. Same goes for you. Which is why you shouldn't think people who don't know how to use this method are stupid." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7995.0 0.0 0.0 0.0
1:02:26 N28g_YBXY8Y "9. Reducibility" "MIT 18.404J Theory of Computation, Fall 2020" 576.0 0.0 0.0 0.0
"Mit please provide a series on propositional logic and predicate calculus." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7679.0 0.0 0.0 0.0
"1:02:16 It should be |x-y| < ɛ?" PnDtMfyZSIE "Lecture 6: The Uncountability of the Real Numbers" "MIT 18.100A Real Analysis, Fall 2020" 574.0 0.0 1.0 0.0
"Jee aspirants liko thoko" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7129.0 0.0 0.0 0.0
"35:53 ""this is terrible"" lmao" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 1021.0 0.0 0.0 0.0
"Student: Is this stuff you are supposed to understand?


Prof: laughs slightly


Me: NO NO NO, please say no" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8916.0 0.0 0.0 0.0
"Fantastic! But it's better to relate math to physics." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 3741.0 0.0 0.0 0.0
"screw the chalk, i have money! (ygotas reference)" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14283.0 1.0 0.0 0.0
"From about 20:00 onward the professor didn't explain clearly how he switched dx.dy to r.dr.d(theta).
Could anybody help me? I mean, show me step by step.
I'd get so thankful.[iminent=aqC6F9gUWfOB] 
Noble atitudes deserve recognising." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3929.0 0.0 1.0 1.0
"Imagine being late for a lecture and becoming famous in the web because of it after thousands watch that lecture on YouTube. I think this is what accidentally happens here." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6581.0 0.0 0.0 0.0
"Very comprehensive. Thanks" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11166.0 0.0 0.0 0.0
"Put on socks > put on shoes, thus to inverse the process take of shoes > take of socks 😂 Great analogy!" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 8464.0 0.0 0.0 1.0
YESSSSSSSSSSSSSSSSSSSSSSSS LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 12110.0 0.0 0.0 0.0
"@MIT OpenCourseWare  will the 13 lecture be uploaded soon ?" bBESL68iX6s "Lecture 14: Limits of Functions in Terms of Sequences and Continuity" "MIT 18.100A Real Analysis, Fall 2020" 1667.0 0.0 0.0 0.0
"In the KL divergence near the end, there's a step that was mentioned quite quickly which went from the expectation of the logs to the average of the logs by the law of large numbers, and n seems to have been introduced. Am I right in saying that the average is after taking n samples, sampled according to the theta star distribution?" rLlZpnT02ZU "4. Parametric Inference (cont.) and Maximum Likelihood Estimation" "MIT 18.650 Statistics for Applications, Fall 2016" 6658.0 0.0 1.0 1.0
"integration of 1/x^2+2x+3 is =1/2^1/2 tan inverse of x+1/2^1/2" aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13614.0 0.0 0.0 0.0
"thank you MIT, all these linear algebra lectures are very helpful, and Prof. Gilbert Strang teach very well

thank you very much!!:))
" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 14485.0 0.0 0.0 0.0
"This lecture taught the algorithm but did not explain or prove why it will work... Anybody know where I can find the proof?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 10827.0 0.0 1.0 1.0
"O cancer está na alma não no corpo. Cure a alam que ele desaparecerá. O Alien" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7966.0 0.0 0.0 0.0
"Like if you come here for the Lockdown. Thanks Gilbert." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7354.0 0.0 0.0 0.0
"wow it actually makes sense now :D" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 15418.0 0.0 0.0 0.0
"you write much slower than single variable calculus teachers, gggreat!" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15518.0 0.0 0.0 0.0
"why x-free is identity?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 15380.0 0.0 1.0 0.0
"He’s still alive?" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4705.0 0.0 0.0 0.0
"What's the second way to prove the AtA is invertiable" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 11585.0 0.0 1.0 0.0
"a beautiful person." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 12278.0 0.0 0.0 0.0
"Quality matters!! ❤️
Awesome professor. Thanks MIT for this..." 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8470.0 0.0 0.0 0.0
"Good observation." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4148.0 0.0 0.0 0.0
"27:13 I understand you can throw away column 3 because it's the addition of other two columns, but how can you throw away column 1??" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 816.0 0.0 1.0 0.0
"There are very few instances in which I did have difficulty in understanding
what Prof. Tsitsiklis is saying ...

one of them is -- 

21:48: There is going to be a fair amount of probability that Y takes the value close to 0.
Why ? Can someone please explain to me ...

Anyways, these are some of the best (and rigorous) lectures on Probability on youtube. I just love them.
Prof. Tsitsiklis and his team of TA's show their complete dedication to deliver this outstanding content, which is commendable.
Their commitment and dedication made contribute small funds to MIT OCW for furthering the cause of MIT to spread
education to masses." l4NoMKEHQwM "11. Derived Distributions (ctd.); Covariance" "6.041 Probabilistic Systems Analysis and Applied Probability" 10359.0 0.0 1.0 0.0
"There must be a really attractive girl in the front row because he keeps winking even in this video." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10381.0 1.0 0.0 0.0
"The professor did a good job of explaining these concepts so that they seem intuitive :) Thanks!" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 10247.0 0.0 0.0 0.0
"is it 14:40 there is a mistake? should it be perpendicular to the line not vertical distance to the line?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 13634.0 0.0 1.0 0.0
"Anyone else likes to watch those in speed x1.5 ?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 2487.0 0.0 0.0 0.0
"I really wish there was a higher resolution or a new version. I have to concentrate hard to see some of the stuff." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5939.0 0.0 0.0 0.0
"What if Mr Strang has to take square root of r" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11501.0 0.0 1.0 0.0
"Was launching matlab to play fifteen, prof immediately speaks of matlab. How did you know 11 years prior!?" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11275.0 0.0 0.0 0.0
"Thank you Prof. Strang.
It was wonderful learning from you!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9201.0 0.0 0.0 0.0
"Well...im a greek student and I study economics in University of Patra... The lesson could be way more easy,if we had this equipment and not based only on what the teacher wrote on the board" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11376.0 1.0 0.0 0.0
"Curve sketching is at 30:35" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3268.0 0.0 0.0 0.0
"“Just a sec”😂" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15594.0 0.0 0.0 0.0
"Thanks, dear Sir" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9847.0 0.0 0.0 0.0
"How the fuck did these students get into mit, the educational system is so fucked up!" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4895.0 0.0 0.0 0.0
Awesome! Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 2778.0 0.0 0.0 0.0
"At 5:45 finding derivative of inverse matrix A looks too complicated. It should be much simpler by starting from inv(A)*A=I and then simply applying chain rule. This leads to d(inv(A))/dt * A+inv(A) * dA/dt = 0. From this, the solution is obvious." z3SmljnD_nQ "15. Matrices A(t) Depending on t, Derivative = dA/dt" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2693.0 0.0 1.0 1.0
"These lectures are amazing. For people like me working in related industry, I also recommend the book of ""trustworthy online controlled experiments"" as a companion book to these lectures (lectures 7-12) to gain a deeper understanding how these concepts are applied to real world product and business problems." phbw9r1iUDI "7. Parametric Hypothesis Testing" "MIT 18.650 Statistics for Applications, Fall 2016" 10405.0 0.0 0.0 1.0
💖💖💖🙏 NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15723.0 0.0 0.0 0.0
"What kind of chalk does MIT use? It looks like they write and erase so easily!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11547.0 1.0 0.0 0.0
"sure it's rudimentary, but it's certainly not taught the same everywhere. Teachers are different. I remember my teacher and he couldnt even compare to this guy. It's the matter of preparation and speaking skill." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14428.0 0.0 0.0 0.0
"Prof Leonard is way better" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8268.0 0.0 0.0 0.0
"well, think of it this way: The control of mathematics is allowing you to view this youtube video right now. All technology is based on math. If you control mathematics, you in a sense control the future, and yes that's pretty fucking cool." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15094.0 0.0 0.0 0.0
"53:33 is a little confusing to me." os_XGBNPllM "Lecture 8: The Squeeze Theorem and Operations Involving Convergent Sequences" "MIT 18.100A Real Analysis, Fall 2020" 1348.0 0.0 0.0 0.0
"At 23:05 kid in red shirt isn't sure of answer...." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2615.0 0.0 0.0 0.0
"in hong kong or china.. we learn it in 10th grade(sec. 4)= =
do they learn it in university?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13589.0 0.0 0.0 0.0
"well duh, someone spelled out how build a triangle out of paper like they do in your classes i'd know how to do it too." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15086.0 0.0 0.0 0.0
"Fast fourier transform part was too tough for me" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 3747.0 0.0 0.0 0.0
"17:27 he said if you find a limit along a subsequence. This subsequence is not defined and is very miss-leading for me." 0_w-R_g5lRA "Lecture 10: The Completeness of the Real Numbers and Basic Properties of Infinite Series" "MIT 18.100A Real Analysis, Fall 2020" 506.0 0.0 1.0 0.0
"Which book edition was sir using cz Vector spaces  starts as 2.1(chap 2) in  4edition?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11710.0 0.0 1.0 0.0
"How did they engineer the chalk outline?  That has to be some effect." tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4842.0 1.0 0.0 0.0
"I was so lucky to have a really great linear algebra teacher" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6164.0 0.0 0.0 0.0
"""Is f ' (x) squared the same as f ""(x)?"" asks an MIT student." TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 73.0 0.0 1.0 0.0
"no doubt that he is a great professor, but this example for Backpropagation was so dissapointing!" lZrIPRnoGQQ "27. Backpropagation: Find Partial Derivatives" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14065.0 0.0 0.0 0.0
"I rewatch this at least once a year and it never fails to amaze me, beautiful work professor" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5954.0 0.0 0.0 0.0
"thank you!
wish i have money to donate ;)" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14529.0 0.0 0.0 0.0
"Is this from a maths course or somthing like physics or engineering" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6871.0 0.0 0.0 0.0
"Hocam sıhatler olsun." 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 4776.0 0.0 0.0 0.0
"Finished 8/1/2021. Thank you MIT for the wonderful lectures." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3809.0 0.0 0.0 0.0
"Gilbert strang a great math teacher............" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 4040.0 0.0 0.0 0.0
"Yes, he does." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12148.0 0.0 0.0 0.0
"This lecture of sprang has inspired me to initiate a collision point of two planes that moves at the same speed same altitude that point that was forbidden by the two pilots perhaps an outside topological information whether the gradient points that is moved by the landing plane is within the perfect landing boundary for a safe landing with the locking gear opened for timely landing and the angle of gracing may be evaluated by Prof.Sprang's plane of analysis.The plane may be auto stimulated by the laser gracing angle fitted in front of Goose Neck emitter.
Sankaravelayudhan Nandakumar ,Hubble Telescope Reseaech committee." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10822.0 0.0 0.0 0.0
"watched for 1hr and learned nothing. Nice job, MIT, I'm out" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 15067.0 0.0 0.0 0.0
"I didn’t really got this now but I will review previous material to finally understand this lecture!!" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 5284.0 0.0 0.0 1.0
"People are probably going to hate this comment but I thought his lecture was a little bit disorganized. It's clear that he knows his subject but I think he needs to develop everything one step at a time and not be in such a rush." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8164.0 0.0 0.0 1.0
"This Prof's handwriting is unbelievable. It's SO neat!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10460.0 0.0 0.0 0.0
"Student in a blue shirt at front is sleeping 😴 what a waste of an opportunity." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 8915.0 1.0 0.0 0.0
"It is better than Chinese mathematic class!" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6940.0 0.0 0.0 0.0
"To be honest though, i learnt calculus in france through highschool and university and i've never heard them call an integral : ""somme"", they call a sum ""somme"" and an integral is intégrale and antiderivative: primitive..
Weird because he does know what he's talking about. Maybe they used to call it that way a long time ago, but not anymore." 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11027.0 0.0 0.0 0.0
"So Smiley You Make Available This Video Arc Length Surface Area and My Favourite the Parametric Equation" TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8737.0 0.0 0.0 0.0
"Brilliant!  Great presentation." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2939.0 0.0 0.0 0.0
"Regarding the problem at 26:28
It would be solved if the matrix U was [1 0; 0 -1]. (Replace the 1 at the bottom right of the 2x2 identity with -1).
This can be found by following the argument that Prof Strang makes in this video: https://youtu.be/rYz83XPxiZo?t=1177 (Skip to 19:37).  
The problem is that here the eigenvectors of U that we found are [1, 0]' and [0, 1]', but they should be [1, 0]' and [0, -1]'.
The negative in the 2nd eigenvector allows the scaling term (sigma) to be strictly positive.  

Let S = Sigma (for ease of typing).
I think the main problem is that the general form A = U*S*V' does not mathematically enforce that S should be a strictly positive matrix.
So even though A'A and AA' will output the squares of the eigenvalues, simply choosing the positive roots is not enough.
We would need to choose the right sign for the eigenvector that corresponds to the positive root. E.g. [1,0] and [-1,0] can both have the same eigenvalue, so we have to decide which to use.
Hence, we need to check the cases and manually negate the vectors in U or V so that S can be positive.
However, if we follow what Prof Strang does in the video whose URL ive included in the earlier part of this comment, then this is accounted for by the computation." TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 8543.0 0.0 1.0 0.0
"Wolfgang J. Paul, if you are here: make homework and exams easier!" asjAc90L8rE "12. Time Complexity" "MIT 18.404J Theory of Computation, Fall 2020" 11978.0 0.0 0.0 0.0
"Don't worry if you have a good teacher, only worry if you have a teacher who has never heard of calculus before lol.  That might be a slight problem.  
Will you be taking the AP exam?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3479.0 0.0 0.0 0.0
"I'm too dumb for this. I'm sure if I learned it, I would understand it, but math isn't my thing. I try and try and even that isn't enough. It is enough to get me a C every year I had in high school math. I'm a Senior now, taking pre-calc and it's easier than my other maths, but I think it's only because we've been working on the same things for almost a whole semester!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6393.0 0.0 0.0 0.0
"24:51 seriously? Basic LCM is a doubt in an MIT class?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 757.0 0.0 1.0 0.0
"This class is essentially week one of a Machine Learning class XD" tBUHRpFZy0s "24. Classical Inference II" "6.041 Probabilistic Systems Analysis and Applied Probability" 10475.0 0.0 0.0 0.0
"I was literally shocked when students asked que for 1 q" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6158.0 0.0 0.0 0.0
"Wait, this was published 4 days before I decided I needed this? Thank you!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11264.0 0.0 0.0 0.0
"i think there is a very small mistake in the graph of (a_i*x-b)^2. The confusion area is bound is not a_i/b_i but b_i/a_i" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13480.0 0.0 1.0 0.0
"what on earth are they talking about? This makes no sense." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15177.0 0.0 0.0 0.0
46:55 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1277.0 0.0 0.0 0.0
"33:51 True hero." d32WV1rKoVk "12. Computing Eigenvalues and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 970.0 0.0 0.0 0.0
"Perfect! this is what i was looking for...detailed, step by step lecture." BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8181.0 0.0 0.0 1.0
"you'd figure mit would use markerboards and not chalkboards" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15519.0 1.0 0.0 0.0
"If Plato was right about theory of forms I'm pretty sure that this is the IDEAL lecture." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6483.0 0.0 0.0 0.0
"I like it!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5677.0 0.0 0.0 0.0
"Max ||Ax||/||x||=Max ||Akx||/||kx||=Max ||Ax||/||x||, ||x||=1.
So you can think of a unit circle ||x||=1 with ||Ax|| plotted on the radius which might look like a circle and ellipse with a point on the Ellipse being at Max ||Ax||/||x||." NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7625.0 0.0 1.0 0.0
"Thx i am from India and really i am enjoying it" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11008.0 0.0 0.0 0.0
"Awesome, i´m glad I found this videos =D" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 2784.0 0.0 0.0 0.0
"Explanations r clear as mud😅😅" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3709.0 0.0 0.0 0.0
"What about decomposition into hermitian and skew-hermitian, how could we visualize that?" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 11441.0 0.0 1.0 0.0
"MIT cheap blackboard !! lol ..." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 7513.0 1.0 0.0 0.0
"You are great sir" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 12171.0 0.0 0.0 0.0
"Glad to have finished this topic. Can someone provide me the link of next topic which I should cover." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4056.0 0.0 0.0 0.0
"Amazing lecture, i am delighted by the smooth explanation of this complex topic! Thanks" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2372.0 0.0 0.0 1.0
"ALLAH razı olsun hocam :)" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2179.0 0.0 0.0 0.0
"Why the camera is wobbling? Why not focusing on the board? more distractions" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 11917.0 1.0 0.0 0.0
"13:22 , lucky to sleep in mit lecture hall" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 414.0 1.0 0.0 0.0
"Just a clarification.  Dr. Strang got a bit confused while testing the convergence rate to solution 3 (in his example) and was wondering about -3 solution, blowing up etc...  He should have remembered that he was testing CR for solution 3 by subtracting 3 from both sides of Xk+1 equation.  To test the other solution (-3), he would have subtracted -3 from both sides or adding 3 to both sides and that would have yielded (1/2Xk)(Xk+3)^2." nvXRJIBOREc "Lecture 21: Minimizing a Function Step by Step" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7153.0 0.0 1.0 0.0
"To do the negation he used a direct proof with contradiction" dcUKdwHRSD8 "Lecture 16: The Min/Max Theorem and Bolzano's Intermediate Value Theorem" "MIT 18.100A Real Analysis, Fall 2020" 11033.0 0.0 0.0 1.0
"it'd be interesting to see how topology is used to convert a general domain to simply connected regions.  Amazing how youtube/Mooc has totally changed education. no need to pay 50K a year  to acquire the same knowledge." PnPIqh7Frlw "Lec 24: Simply connected regions; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13691.0 0.0 1.0 0.0
"This guy is really good. If he is 20 years younger, I might send him love letters. ha" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10540.0 0.0 0.0 0.0
"8:09 when someone forces you to look at their memes" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1415.0 0.0 0.0 0.0
"nonsense,,not worth learning...the end of the road is no WHERE! " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14078.0 0.0 0.0 0.0
"Man, what an awesome teacher. Dr. Strang is definitely somebody to emulate if you're considering teaching." t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7590.0 0.0 0.0 0.0
"God bless MIT!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4075.0 0.0 0.0 0.0
"we made it boys!" sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15076.0 0.0 0.0 0.0
"with covid making it hard to go to my schools math clinic, I'm using these videos to help me in my Cal 3 class. Thank you for making this available!" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15387.0 0.0 0.0 0.0
"He is actually providing the algorithm behind the matrix operation used in coding. Amazing and extraordinary skills. now I'll be able to understand how to play with Maths.Thanks a lot Sir." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4506.0 0.0 0.0 1.0
"Nodes - Edges + Loops = 1 must be assuming a connected graph since you can just have 3 unconnected Nodes and its obviously not true ;)" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7910.0 0.0 1.0 0.0
"Man, I want those donuts" mc1y8m9-hOM "22. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 7584.0 0.0 0.0 0.0
"love u professor" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 13885.0 0.0 0.0 0.0
"it took a lot of time but i finally finished this series. Thank you, Professor Strang!  You are a wonderful teacher and an inspiration." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 13684.0 0.0 0.0 0.0
"Conclusion: A set of orthonormal vectors combine into a matrix called Q. Q'Q always get an identity matrix. If Q is square, it's an orthogonal matrix, and Q'=Q^(-1). If we use Qx=b instead of Ax=b to solve the projection problem, it will be much easier. Because the projection matrix P=Q(Q'Q)^(-1)Q'=QQ'.
For the A'Ax=A'b problem, if we use Q instead of 'A' we can simplify it as x hat equal to Q'b. 
Gram-Schmidt method: A way to transform independent column vectors into orthonormal basis.
A=QR => Q^(-1)A=Q(-1)QR => Q'A=R" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 3195.0 0.0 0.0 0.0
"oh yeah, this stuff on the board is as hard as british A level calculas. but, it's at the lower end" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14116.0 1.0 0.0 0.0
"graphs! yeyy! lol" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 12961.0 0.0 0.0 0.0
"Is the derivative of kx equal to k because we are treating k as a constant?" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6810.0 0.0 1.0 0.0
"How comes no one asks questions? The dude was flying through this jawn, I'm pretty sure someone HAS to have a question..." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4827.0 0.0 0.0 0.0
"36:59 he changed the way whe wrote x" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1050.0 0.0 1.0 0.0
"Going through a tough time, I hope things get better" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 4101.0 0.0 0.0 0.0
"I Really Like The Video Lecture 14 Non-independent variables From Your" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4982.0 0.0 0.0 0.0
"@DGMedonja it's only for up 21 yo" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1607.0 0.0 0.0 0.0
"Good job! Such a refreshing lecture and easy to follow if you have background in Statistics." TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 4131.0 0.0 0.0 0.0
fantastic!!! 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12850.0 0.0 0.0 0.0
"29:14 “You have to admire the beauty of this answer”. 😂😂" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 853.0 0.0 0.0 0.0
"The only bothersome thing in this video is the dirty is the blackboard." WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 10211.0 1.0 0.0 0.0
"Nano printing" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7806.0 0.0 0.0 0.0
"vai br" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14991.0 0.0 0.0 0.0
"I just want to know who gets into MIT without having already taken Calculus I." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5623.0 0.0 0.0 0.0
👏👏 J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 15718.0 0.0 0.0 0.0
"I was very surprised to see you here, really, i wan not lloking for you but i remembered your profile picture" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 6173.0 0.0 0.0 0.0
"I have no doubt about his knowledge but he looks less interested in teaching." uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 5543.0 0.0 0.0 0.0
"This is awesome. We use the fourth edition of Dr. Strang's Intro to Linear Algebra in class and I am so glad these videos are available online. I found vector spaces to be a tricky topic in class, via my notes, even in the book. This lecture was executed beautifully. Makes so much more sense now. I am definitely the type of learner who really needs to have a deep understanding for the concepts to stick. Thanks so much!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 10646.0 0.0 0.0 0.0
"What is a difference equation in 11:00?" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11514.0 0.0 1.0 0.0
"Is a hyperbola in high dimensional spaces called a hyperhyperbola?" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 6756.0 0.0 0.0 0.0
"At 30:00 - It doesn't matter wether you go with with Alice or Bob. They should be getting the same amount of money, as the number of dots greater than or equal to 3 has  4/6 sides of the dice covered (3, 4, 5 and 6 -> 4/6 -> 2/3). Am I mistaken?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 2636.0 0.0 1.0 0.0
"Do all matrix have eigenvalue and eigenvector? (including complex eigenvalue )" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 3407.0 0.0 1.0 0.0
"what does the matrix space actually means? and how to understand the all R^{3 by 3) matrix?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 15137.0 0.0 1.0 0.0
"Thanks MIT :P " kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9605.0 0.0 0.0 0.0
"he ask ques to audience and answer himself  before they gave that and it is interesting point in his lecture . it seem like he teaches himself not  the audience ." 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 13068.0 0.0 0.0 0.0
"Thank you for being the best teacher on the planet." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9247.0 0.0 0.0 0.0
"I have a question. Why does he let the limit be delta x to zero? Can it be done with the limit being delta y to zero?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5509.0 0.0 1.0 0.0
"just goes to show how important these basic concepts are i guess." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13734.0 0.0 0.0 0.0
"The legend himself." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 10174.0 0.0 0.0 0.0
"@MIT OpenCourseWare , at 18:20 when we take Det(A) out from every row shouldn't it result into Det(A)^n like it happened in last chapter for 2^n volume increase case?" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 1668.0 0.0 1.0 0.0
"I wish he was my teacher, what a nice class. excelent" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6221.0 0.0 0.0 0.0
"He's a smart guy, but I'm glad I went to school where I did. MIT is vastly overrated." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 4628.0 0.0 0.0 0.0
"Ahh! Suddenly everything is easy to understand, there is great enlightenment. In the previous lessons I sometimes had difficulties and now the dark forest is thinning out." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2287.0 0.0 0.0 0.0
"Ey insanlar!
Sizleri, nefsinize KUL OLMAKTAN ;
ALLAH'A KUL OLMAYA DAVET EDİYORUM.
UNUTMAYALIM Kİ;
""'LA İLAHE İLLALLAH MUHAMMEDURRASULULLAH"" DEYİP KALBİMİZLE İMAN ETMEDİKÇE DÜNYADA DA AHİRETTEDE kurtuluş yoktur." V3Wg_jrMSQY "Lecture 19: Differentiation Rules, Rolle's Theorem, and the Mean Value Theorem" "MIT 18.100A Real Analysis, Fall 2020" 3712.0 0.0 0.0 0.0
"at 40:00, is the block elimination right? I guess [ I 0 : -A*inv(S) I]" xaSL8yFgqig "Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12451.0 0.0 1.0 0.0
💝 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15725.0 0.0 0.0 0.0
"At 36:10 how did he deduce that alpha=beta?" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2650.0 0.0 1.0 0.0
"The Largest Singular Value is the same as largest Eigen Value for a fully connected layer which is also called as spectral Normalization." NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9968.0 0.0 0.0 0.0
"Professor: What is the variance of *this thing* ? It's the expected value of *the thing* minus the square of the expected value of *the thing* ....
John Carpenter: Since when is my movie a random variable???!!!" P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 8409.0 0.0 0.0 0.0
"My native language isn't English, but this prof explains things so well that I feel like he's from my country." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7776.0 0.0 0.0 0.0
"I wish I knew about this professor before. 
The best explanation. I remember I did gauss jordan elimination back in university but never understood why even are we doing it.. thank you mit for posting it." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6206.0 0.0 0.0 0.0
"DEATH ... LOL" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3271.0 0.0 0.0 0.0
"Why the hell does my video freezes when it reaches 00:27 secods it feels like my ethernet service provider is preventing me from lisnening to a great lec! anyways need some coffee..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11918.0 0.0 0.0 0.0
"Lecture 1: Dot Product
Lecture 2: Determinants
Lecture 3: Matrices
Lecture 4: Square Systems
Lecture 5: Parametric Equations
Lecture 6: Kepler's Second Law
Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds)
Lecture 8: Partial Derivatives
Lecture 9: Max-Min and Least Squares
Lecture 10: Second Derivative Test
Lecture 11: Chain Rule
Lecture 12: Gradient
Lecture 13: Lagrange Multipliers
Lecture 14: Non-Independent Variables
Lecture 15: Partial Differential Equations
Lecture 16: Double Integrals
Lecture 17: Polar Coordinates
Lecture 18: Change of Variables
Lecture 19: Vector Fields
Lecture 20: Path Independence
Lecture 21: Gradient Fields
Lecture 22: Green's Theorem
Lecture 23: Flux
Lecture 24: Simply Connected Regions
Lecture 25: Triple Integrals
Lecture 26: Spherical Coordinates
Lecture 27: Vector Fields in 3D
Lecture 28: Divergence Theorem
Lecture 29: Divergence Theorem (cont.)
Lecture 30: Line Integrals
Lecture 31: Stokes' Theorem
Lecture 32: Stokes' Theorem (cont.)
Lecture 33: Maxwell's Equations
Lecture 34: Final Review
Lecture 35: Final Review (cont.)" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7267.0 0.0 0.0 0.0
"I want to really thank MIT OpenCourseware. This has helped me very much along with the other material you have released. I will make a donation as soon as I can. Great help since I am now prepared for my upcoming classes. Thank you very much" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6141.0 0.0 0.0 0.0
"Can someone please explain why the condition for pivot test is (ac-b^2)/a > 0? If I just do the elimination to figure out the pivot, shouldn't the second pivot just be （c-b^2)/a?" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 3092.0 0.0 1.0 0.0
"4:02, you would think that people at MIT would have this down by now 
still a good lecture though" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1311.0 0.0 0.0 0.0
"Here's a paper by prof. Strang related to this lecture. 
http://web.mit.edu/18.06/www/Essays/newpaper_ver3.pdf" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4677.0 0.0 0.0 0.0
Good J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 4108.0 0.0 0.0 0.0
"The eraser's accident 😂" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10091.0 1.0 0.0 0.0
"Loved the bit at the end where he showed that upper triangular or symmetric or diagonal matrices form a subspace." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7478.0 0.0 0.0 0.0
"Is anybody solving the assignment sets? I need help with Assignment 2> Problem 2...." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6759.0 0.0 1.0 0.0
"This is probably one of the best courses I have ever taken, Prof Gilbert Strang really rocks! Never though linear algebra can be this beautiful" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 10706.0 0.0 0.0 0.0
"My math teacher need that fucking chalk" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7772.0 1.0 0.0 0.0
"Great lecture but unfortunately it got ruined by the stupid robot filming it" -sfaHVFWBU8 "Lecture 22: The Spectral Theorem for a Compact Self-Adjoint Operator" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 4251.0 1.0 0.0 0.0
"Difficult class. Reasonable questions but feels like ""Bueller? Bueller?""" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 3400.0 0.0 0.0 0.0
"The eigenvectors of A should have been [1/(lambda - 1), 1], not [lambda, 1] as the professor wrote. He of course had the right idea but computationally, the result is simply wrong. Happens, still a great lecture! I know how to solve difference equations using multidimensional finite element method, but this approach by generating a matrix system and solving via eigenstuffs is new to me. Thank you for opening my mind! ☺️ This channel is making me a better dropout day by day lol" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 10086.0 0.0 1.0 1.0
"Thank you ... Linear Algebra Magician Dr Strang !!!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9095.0 0.0 0.0 0.0
"The continuation of rhe single variable calculus..........I´m so happy  :D :D !!!!!" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10058.0 0.0 0.0 0.0
"Brings back some great memories" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2949.0 0.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8420.0 0.0 0.0 0.0
"Is there any lecture notes that I can refer to?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 6833.0 0.0 0.0 0.0
"dddd  :D  here i am" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 12728.0 0.0 0.0 0.0
"What my lecturer took 2 hours,you sir took 50 mins." 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 11551.0 0.0 0.0 0.0
"12:12 
prof: it's just exploded in importance.
me: I just burst in laugh :)" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 391.0 0.0 0.0 0.0
"One of the crown jewel lectures of MIT OCW." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 8097.0 0.0 0.0 0.0
"I have a query guys at 36:00  professor speaks about the no. of components in U, Sigma, V just looking at A for 2x2, 3x3 and 4x4, how do we look at rectangular matrices for such cases? Any help would be appreciated." rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5495.0 0.0 1.0 0.0
"can someone pls explain how n,n^2 , n^3....n! come ? ??  at 29:46 ." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 12630.0 0.0 1.0 0.0
"Around 21:20 isnt he doing the multiplication wrong? 3.line 1, 4.line2, 5.line3?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2552.0 0.0 1.0 0.0
"11 years now, he is very old but the effect that he made is still young and going." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 358.0 0.0 0.0 0.0
"Are there any pre-requisites for taking this course?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2532.0 0.0 1.0 0.0
"""Gauss-given order"" made me chuckle" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 50.0 0.0 0.0 0.0
"@ 7:40 - ""Let me take an example where I have a vector and twice that vector...If the word dependent means anything, these should be dependent""" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 1482.0 0.0 1.0 0.0
"subtitles are not timed " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14408.0 0.0 0.0 0.0
10:08 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 342.0 0.0 0.0 0.0
estiMAYter TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 12800.0 0.0 0.0 0.0
"High and low are relative terms. If you *want* to hit your little brother with a dart, then yeah, 1% is subjectively low, but in probability questions that deal with risk of bodily harm like this, 1%  is unacceptably high.

Similar if trying to find probability that a new medicine will have a fatal side-effect. Even if the chance of death is .001% - that still means that if one million people take the drug, you'd expect ten people to die from it. Are ten people dying too high or too low to you?" jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4735.0 0.0 0.0 0.0
"This lecture was real GENIUS, even a non technical stream student like me knows the pixels compression now." 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 10835.0 0.0 0.0 0.0
"7:00 WHy you want that computers should do what a human brain can do. WHY WHY WHY? ? humans are aready very huge in no. 
there is no shortage of them." 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 1392.0 0.0 0.0 0.0
"7:20 ASSA SASA heh" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 1398.0 0.0 0.0 0.0
"Excellent lecture" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3649.0 0.0 0.0 0.0
"43:00 For interpretation of QQ plots" vMaKx9fmJHE "12. Testing Goodness of Fit (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 1195.0 0.0 1.0 0.0
"an essential theorem like this its proof is not explained in the so-called great university .
and a stupid algebric operation in an integral is proved .
such a shame" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12362.0 0.0 0.0 0.0
"ALL I KNOW NOW IS  circle with line is theta and sin and 2 thats pretty much bout it in trig" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2177.0 0.0 0.0 0.0
"You mean that he puts periods at the end of his sentences?
" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12225.0 0.0 0.0 0.0
"lol this prof is french? what does that have to do with anything. u r funny." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13834.0 0.0 0.0 0.0
"I'm in love" X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 6332.0 0.0 0.0 0.0
"Very good instruction.  He goes at a perfect speed: good review pace, but if you don’t know about vectors that well, you can learn it very quickly with this speed. Très bon" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11177.0 0.0 0.0 0.0
"35:52 that student was using phone in the class :)" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 1020.0 0.0 0.0 0.0
"For the first time in my life that understand what the heck is Gauss-Jordan idea!  Thanks Mr. Strang" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3889.0 0.0 0.0 0.0
"may ALLAH bless you people with the best of this world... THANK U!" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13922.0 0.0 0.0 0.0
"I thought in Lecture 20, Prof Denis said that all closed loop integral of F.ds = 0? Then where does Green's theorem comes from?" tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6090.0 0.0 1.0 0.0
"I aspire to be like Dr. Strang when I grow up :)" nvXRJIBOREc "Lecture 21: Minimizing a Function Step by Step" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5161.0 0.0 0.0 0.0
"this guy is amazing" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 14816.0 0.0 0.0 0.0
"a  positive or negative circumferential concavity in the plan" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12276.0 0.0 0.0 0.0
excellent sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12814.0 0.0 0.0 0.0
"He is soo good! I finally have a better intuitive undertanding of determinant" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4541.0 0.0 0.0 0.0
"Andrew NG didn't explain it in this detail
That is why MIT is MIT,
Thanks professor." k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2456.0 0.0 0.0 0.0
"The fact that he is talking about spaces and somehow he is unable to manage tha space of the board is so very funny! I love this guy; the way he chooses his words is so proper, everything gets clear...Regards and respect from Greece mr Strang." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 10100.0 1.0 0.0 0.0
"where can i find the answer of problem sets？" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15228.0 0.0 0.0 0.0
"Usually, they are quite difficult.  They are somewhat designed, really, to be solved by a study group.  " 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11142.0 0.0 0.0 1.0
"Truebit Protocol." TSI3LR5WZmo "25. Interactive Proof Systems, IP" "MIT 18.404J Theory of Computation, Fall 2020" 11088.0 0.0 0.0 0.0
"@LittleMeSmiley Lol yeah. I know its sad. I go to college in America and its really hard to take it seriously when everyone else in the East learns Calc 3 by the time they are 12, and we have to wait until we are 18. " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1660.0 0.0 0.0 0.0
"The cameraman got a lot better for this video." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10036.0 1.0 0.0 0.0
"I have never thought about this series in terms of building up a pyramid. Such geometric explanation is so straightforward and I fking love it. Thanks, prof." hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5542.0 0.0 0.0 0.0
"It's amazing how many succinct and elegant proofs use associativity. 👽🤔🤓🧐" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7027.0 0.0 0.0 0.0
"WTH!? " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11252.0 0.0 0.0 0.0
"Thanks, this helped a lot!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 9852.0 0.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8421.0 0.0 0.0 0.0
"was not expecting that scooter after watching part 1" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 15056.0 0.0 0.0 0.0
fantastic k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12844.0 0.0 0.0 0.0
"wait how did they know that the area of e^(-x^2) from 0 to infinity is sqrt(pi)/2?" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15050.0 0.0 1.0 0.0
"Here I was, thinking I was gonna breeze through this lecture when BAM! I got hit with subtle logic 👨🏽‍🏫" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4674.0 0.0 0.0 0.0
"It is for students in university right?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6944.0 0.0 0.0 0.0
"why a chalk board..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15277.0 1.0 0.0 0.0
"best applied prob course out there for free" rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 12535.0 0.0 0.0 0.0
"How can you use right pseudo-inverse to solve Ax = b?" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 4818.0 0.0 1.0 0.0
"These recitations are actually very good. It is helpful to quickly revise the concepts." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10425.0 0.0 0.0 0.0
"I think that in 21:40 it should say ""For all e > e' > 0"" Or something of that nature. Otherwise there is not connection between e and e'." 3eiio3Tw7UQ "19. Weak Law of Large Numbers" "6.041 Probabilistic Systems Analysis and Applied Probability" 6043.0 0.0 1.0 0.0
"About 19:55 minutes in to subject." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 2191.0 0.0 0.0 0.0
"google OCW MIT and name of course
" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12955.0 0.0 0.0 0.0
"39:07 - man I was shitting myself up until this moment" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1094.0 0.0 0.0 0.0
"the part of n choose k  is  a brilliant explaination." 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 14724.0 0.0 0.0 1.0
"haha, déjà vu. He's at UCB now teaching Math 53 (multivariable calculus) and his lectures are pretty much the same as this =D" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13046.0 0.0 0.0 0.0
"And hot do I use this in real life?" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 2443.0 0.0 0.0 0.0
"I think the best title for this video is Understanding Null Space. " VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 6049.0 0.0 0.0 0.0
"https://j.gifs.com/0VrmQ7.gif 

Dahh.. He is still there" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13261.0 0.0 0.0 0.0
"Great analogy of infinite basis for functions" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 4213.0 0.0 0.0 1.0
"unit1 : What is love ? (baby don't hurt me, don't hurt me no more...)" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14979.0 0.0 0.0 0.0
"40:39 ... where are all the students?" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1132.0 0.0 0.0 0.0
"Thanks to Prof Strang and MIT, for putting so much work into this, for the benefit of the entire world, while asking nothing in return. Thanks from mankind." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9805.0 0.0 0.0 0.0
"12:18 Conditional Probability" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 394.0 0.0 1.0 0.0
35:15 vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 1002.0 0.0 0.0 0.0
"He has excellent blackboard penmanship." 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4490.0 1.0 0.0 0.0
0:28 JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 305.0 0.0 0.0 0.0
"Super video lecture" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8959.0 0.0 0.0 0.0
"u are worldclass...u are better than any german docent.." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 14970.0 0.0 0.0 0.0
"THANK YOU SO MUCH MIT, I REALLY APPRECIATE THIS..." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8985.0 0.0 0.0 0.0
"My god this is so beautiful. So much insight making things fall into place. ""Finding coefficienes in a Fourrier series is exactly like an expansion in an orthonormal basis"". Now I get it!" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 7755.0 0.0 0.0 1.0
"Anyone have a favorite Calculus textbook? (Or several?)" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2495.0 0.0 0.0 0.0
"You guys should really really give the time for when the actual lecture starts past the administrative stuff" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 12209.0 0.0 0.0 0.0
"Definitely it was a great decision to close the lecture with Kepler's law example. IMHO, it is always good (when possible) to exercise a physics example along with the math topic in question." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3340.0 0.0 0.0 1.0
"The taste is different with MIT people! You ""feel"" the science with them! I envy the ones who had the opportunity to sit in these class rooms!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 10295.0 0.0 0.0 0.0
"The only way to explain that is by using Euclid's elements ... otherwise you get stuck in the arguments ... observe that he is trying to explain the Euclid's element without actually mention it ... I do not know why ..." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10215.0 0.0 0.0 1.0
"If only probability questions had half the clarity in their information as the way Professor talks..!

As he mentioned at the end, it is very easy to get confused while solving the probability questions based on real situations because the information provided can easily have multiple interpretations if utmost clarity is not maintained." 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 6513.0 0.0 0.0 0.0
"Jai subbu" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7124.0 0.0 0.0 0.0
"Being quite about matrix multiplication about rest of the day is what i need at min 20. This guy know how to make a good joke and being helpful with it. Thanks Strang!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2842.0 0.0 0.0 0.0
"Prof Gilbert String moves me from ""need to"" to ""want to"" learn Math. Thank you so much!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8266.0 0.0 0.0 0.0
"@mphmm that sucks...how are we supposed to get those..by guessing?" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 1952.0 0.0 0.0 0.0
"This  is the first that I heard  the terms Wavelets and Image Compression in the same lecture when it comes to linear algebra. Wavelets  and Image Technology have been changing things that we  used in this world over the past few years. From fingerprints to camera technology, this is how linear  algebra impacts real life." 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 10453.0 0.0 0.0 1.0
"he's gonna kill all of them, what an assassin:D" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 13123.0 0.0 0.0 0.0
"thank you MIT OCW for sharing such wonderful knowledge with detail explanation, for those who are not able to get source to learn things, it is really very great and awesome platform. thank you!" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 14480.0 0.0 0.0 0.0
"mn . np = mp" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13958.0 0.0 0.0 0.0
"respect sir !" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 14265.0 0.0 0.0 0.0
"Two people go to Harvard..." UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11105.0 0.0 0.0 0.0
"Comment on the liar analogy:  liars do not feel bound by logic always to make false statements.  Liars lie when it suits them.  Case in point:  Trump." nbENJ-Ce7Nc "Lecture 3: Cantor's Remarkable Theorem and the Rationals' Lack of the Least Upper Bound Property" "MIT 18.100A Real Analysis, Fall 2020" 3174.0 0.0 0.0 0.0
"To those confused with why y's units need not be consistent with x's units:

say, the population of rabbits grows exponentially with time that:
where A is the initial number of rabbits,
Y is the final number of rabbits,
Y= A^t.

So are we saying we should say the number of rabbits at time t should have units rabbits^time? No, rabbits are still counted in rabbits." ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11047.0 0.0 1.0 0.0
"What a teacher." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11433.0 0.0 0.0 0.0
"2019-09-17 02:27:12

Thank you Prof. Strang, I wish you all the best" rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 622.0 0.0 0.0 0.0
20:23 lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 649.0 0.0 0.0 0.0
"My right ear learned a lot from this lecture." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 7787.0 0.0 0.0 0.0
"Really useful, thanks:)" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8535.0 0.0 0.0 0.0
"Which book the professor is talking about? 12:19" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11713.0 0.0 0.0 0.0
"@stevewalker12321 what about it? I don't see anything bad in that. It doesn't effect the teaching so what's the harm?" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2027.0 0.0 0.0 0.0
"20:14 What's example that elements of basis are not orthogonal?" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 647.0 0.0 1.0 0.0
"This video is gold, not everyone gets the fact." RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 10954.0 0.0 0.0 0.0
"oh God the distractions." k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14100.0 0.0 0.0 0.0
"Y=x^2  NO!. Meters does not equal meters squared.  Try Y=kx^2  where k is a unit conversion factor ie 1/(1meter).In cm,  the k would be 1/(100cm)  Make SURE your equation is dimensionally correct BEFORE you work with it.  The constant k also appears in the answer making volume be in meters cubed (or cm cubed) as volume should be.  This lecture was a mess and should be redone!" ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12104.0 0.0 1.0 0.0
excellent! IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 12828.0 0.0 0.0 0.0
"How are their so many empty chairs? I would die for an opportunity to listen his video live" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4803.0 1.0 0.0 0.0
"He's a little boy genius (accademically speaking) , he had 2 BSc in maths and physics (1st class)  by the age of 17!" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4627.0 0.0 0.0 0.0
"for det( A + B ) = ? there is no formula...." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 12883.0 0.0 1.0 0.0
"I was using the first edition of his book in 1982/83." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6172.0 0.0 0.0 0.0
"And the title of one of the book of MIT was surprising for me, it made me unhappy, now I have to pretend (like some antik philosopher) that nothing existed before me, but that will make them unhappy too. (I met even someone that said because I learned english, everything and anything that I say is hot from me!!!!)" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 2450.0 0.0 0.0 0.0
"My heartfelt thanks to Prof. Strang. You have been forever immortalized in the minds of students by your stupendous teaching!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 7761.0 0.0 0.0 0.0
"You know a man's the GOAT if lectures from almost 2 decades ago with chalk and a blackboard are better than 90% of the content online. Thank You, Professor Strang and MIT for bringing such amazing content to the world..." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12219.0 1.0 0.0 0.0
"If only my textbook had been like this" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6512.0 0.0 0.0 0.0
"what is the best book or resource to learn the whole mathematics behind stochastic gradient descent?" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15163.0 0.0 1.0 0.0
"thanks ..." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 14550.0 0.0 0.0 0.0
"Thank you." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9547.0 0.0 0.0 0.0
"Gauss be with you Gilbert" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3980.0 0.0 0.0 0.0
"Thanks for the lecture! I've tried to learn these things before and gotten out more confused than I was when I came in, but Dr. Strang's approach makes it all seem so simple!" ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9716.0 0.0 0.0 0.0
"This problem has been over-flogged by the learned Prof. The simple answer (from linear algebra standpoint) is the projection of the origin onto the multilinear SET:  { Ax = b }.  This would almost always yield  the invertible matrix  A*At, such that the solution of: (A*At)y = b. Which you then plug into the given constraint to get:
x = At.y  which is the solution to the problem. A need not be a square matrix for all the respective dimensions to match. This particular form of the solution coincides with the projection of the point [ x = 0] onto the linear subspace: { x | Ax = b }. This is infact a trivial problem since we can project any other points e.g. x = (1, 2, 3,...., n ), onto { Ax = b } to arrive at yet another point on this subspace. This problem can also be viewed from linear analysis standpoint where the vector function: f(x,t) = ||x||^2 - t(Ax - b) is being minimized, wrt the vector x. And the same result is found. Cheers." MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10887.0 0.0 0.0 0.0
"He teach too fast.. I guess im so stupid i can't follow him LOL! " xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4612.0 0.0 0.0 0.0
"do you even lift" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12758.0 0.0 0.0 0.0
"His explanations have always been impeccable. What a legend." rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4749.0 0.0 0.0 0.0
"@OriakoPhi 
I agree, it's really just an issue of ego, which everyone seems to gain too much of when going to college. 

Once they lose their ego, they might actually learn something. " 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1696.0 0.0 0.0 0.0
Amazing!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2401.0 0.0 0.0 0.0
"I Really Like The Video From Your Limits, continuity" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4960.0 0.0 0.0 0.0
"Man this video is such a torture! :D" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 7578.0 0.0 0.0 0.0
"Really appreciate MIT for such great material and lecture." u4qQ1oIQcW8 "Lecture 25: Power Series and the Weierstrass Approximation Theorem" "MIT 18.100A Real Analysis, Fall 2020" 8504.0 0.0 0.0 0.0
"something understand.........." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14364.0 0.0 0.0 0.0
"جدو جلبرت ❤️" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 15570.0 0.0 0.0 0.0
"Excellent courses from the comfort of your home.." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3639.0 0.0 0.0 0.0
"@chenhsi4 Meh perhaps most of them are first years, and this class lasts only one semester anyway, there to make sure everyone has the basics down.

Eitherway, why the hell do you care, and if this stuff is below you, why are you watching it?" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1814.0 0.0 0.0 0.0
"2:43 Why disturb Siri after midnight?" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 868.0 0.0 0.0 0.0
"Thank you soooooooo much, prof Auroux and MIT for making this course available to everyone." 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9421.0 0.0 0.0 0.0
"MIT is a Scam" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7524.0 0.0 0.0 0.0
"Great explanation" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 4224.0 0.0 0.0 0.0
"Why does he do 1/root2 at 11:00?" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 11839.0 0.0 1.0 0.0
"This professor is so wordy" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 10909.0 0.0 0.0 0.0
"HAHA.... everyone chose 1 for the 1st question. LOL!!!!!!!" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4395.0 0.0 0.0 0.0
"one question:
why the nullspace 

    | 1 |
c  | 1 |
    | -1|

passing through the origin is a line and not a plane?
Can anyone help me with this." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 14151.0 0.0 1.0 0.0
"That is one of my most elegant proof of the fundamental theorem of line integrals I've ever seen. " z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9899.0 0.0 0.0 0.0
"21:49 wrong conclusion. What you have is a subsequence of <Au_n,u_n> that converges to either ||A|| or -||A||. The sequence <Au_n,u_n> itself may not converge." O0Tw47okZJM "Lecture 21: The Spectrum of Self-Adjoint Operators and the Eigenspaces of Compact Self-Adjoint..." "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 686.0 0.0 1.0 0.0
"@2:48 Why'd he have the chalk in his pocket?" Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1532.0 1.0 0.0 0.0
"I love you so much MIT!!!" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5849.0 0.0 0.0 0.0
"Love this" f_sNWn7zujU "Lecture 17: Uniform Continuity and the Definition of the Derivative" "MIT 18.100A Real Analysis, Fall 2020" 7456.0 0.0 0.0 0.0
"is this course enough to get started with ml ?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 13660.0 0.0 0.0 0.0
"what a beautiful functions. that's why i love linear algebra." AeRwohPuUHQ "22. Gradient Descent: Downhill to a Minimum" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15102.0 0.0 0.0 0.0
"This kind of lecture is only possible when your deep passion for your work! Huge Thanks, Sir Strang!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10781.0 0.0 0.0 0.0
"expectation mean and var are the most difficult to be understood." P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 12832.0 0.0 0.0 0.0
"Thank you MIT professors. Thank you MIT so much. I really appreciate it." sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9150.0 0.0 0.0 0.0
"Spammers. I think they are trying to fool youtube's subscription/advertisement system." 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8862.0 0.0 0.0 0.0
"I am amazed at the number of people that freaked out at the Taylor expansion and seemed to hate them. I thought they were one of the most elegant and powerful things I has seen in mathematics and they answered so many questions.

Now trig substitutions, those are ugly." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5061.0 0.0 0.0 0.0
"I love this lecture so much. I turned from hating math to see a useful part of its application. Thank you OCW" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5815.0 0.0 0.0 0.0
"amazing lecturer.
" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 12350.0 0.0 0.0 0.0
"Most of our memory is used up in notaion only,chopping is required." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7701.0 0.0 0.0 0.0
"thank you! MIT" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14530.0 0.0 0.0 0.0
"Thank you for the lecture, extremely useful!" 3eiio3Tw7UQ "19. Weak Law of Large Numbers" "6.041 Probabilistic Systems Analysis and Applied Probability" 9266.0 0.0 0.0 0.0
"PFD is probably my favorite method of integration, it's a pretty satisfying process and you end up with a very nice and simple answer." HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8150.0 0.0 0.0 0.0
"He just gives you much more than he has to. I understand people who comment that it is hard to follow him sometimes, but come on, you can watch the video as many times as you need and you can use some books also (not to mention that we should use more those old fashioned friends). For me, the best statistician available in youtube giving a high level lecture which combines a practical but theoretical approach." yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 4557.0 0.0 0.0 0.0
"This is a seriously gifted teacher" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10602.0 0.0 0.0 0.0
"How did you do on the test mate?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4846.0 0.0 0.0 0.0
"Thanks dear Sir,  love you. You are like God for us" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 9677.0 0.0 0.0 0.0
"That's the most complicated way of finding cofactors I have ever seen.... Use the simple formula.....A(ij) = (-1)^i+j M(ij)" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9944.0 0.0 1.0 1.0
"so if my probability of a event B ocurs doesn't change if A ocurrs, A and B are independent?" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 14334.0 0.0 1.0 0.0
"I love the way this instructor presents this subject!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5794.0 0.0 0.0 0.0
"@60000133 The point is, they doesn't have the greatests! All american intellectual grandiosity is feeded by foreigns!. Aside from a very limited proportion of notable american scientists, almost all contributions of americans to science, has been made by foreings residing in USA, mainly europeans. Today's american science survives thanks to the influx of scientists from the former USSR, China and India. They are just clever employers to chose who, and good salesmans of their universities." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1572.0 0.0 0.0 0.0
"If this is what classes were back at the 2000's, I wonder how good they have become as of now 2010" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 6529.0 0.0 0.0 0.0
"My brain. I can feel it." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7738.0 0.0 0.0 0.0
"Thank you Mr Strang." rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9174.0 0.0 0.0 0.0
"I like the column perspective." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5681.0 0.0 0.0 0.0
"Thanks MIT.  Views of (video 7.)/ Views of (video 1.) is about 10%." EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 9621.0 0.0 0.0 0.0
"This is an excellent, step-by-step proof that I will never be a mathematician." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10627.0 0.0 0.0 1.0
"how is the line intergral limit of example 1: c3 curve from 0 to 1/root2 ??? why is that point (1/root2,1/root2)" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13240.0 0.0 1.0 0.0
"What is good homework to test if we clearly understand this lecture? Is there such corresponding homework?" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 11518.0 0.0 1.0 0.0
"Ah, the functional analysis. Together with topology, my favorite subjects in uni." uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 2280.0 0.0 0.0 0.0
"7:31 

I once read a comment on some OCW video in which a guy said that it was his dream to go to one of these classes, raise his hand and ask the professor if he should draw 4 with the top two line segments joined or not. The student @7:31 almost realized that dream.

😂" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1399.0 0.0 0.0 0.0
6 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 1369.0 0.0 0.0 0.0
"Probably I am missing something. Keeping in mind the graph of the area going to infinity, If the limit approaches a finite positive number, let's say 3, wouldn't the area under the curve still be infinite?" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8255.0 0.0 1.0 0.0
"Sir is exceptional . I have never ever seen a mathematician and a teacher with such impeccable command over his knowledge and his art of teaching. It seems he know how to present a hypothesis, how to negate it and eventually explain the validity of that hypothesis. He’s the best in the business" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8696.0 0.0 0.0 1.0
2:50 oNsscmUwjMU "2. Nondeterminism, Closure Properties, Conversion of Regular Expressions to FA" "MIT 18.404J Theory of Computation, Fall 2020" 874.0 0.0 0.0 0.0
9:35 dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 1441.0 0.0 0.0 0.0
"Awesome Teacher Gibert Strang" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2754.0 0.0 0.0 0.0
"i love this guy so much" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13432.0 0.0 0.0 0.0
"This guy wasted 44 minutes of an 80 minutes(?) lecture with bullshit and I gave up. I'll read a book instead." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 10564.0 0.0 0.0 0.0
"I had to check how old he is - 84 and still going strong. Hell I know an 83 year old who swims  4km a day in the surf.   His a superb mathematical communicator - up there with the late, great Eli Stein at Princeton who is sadly missed.  May Gil continue to do his thing for many years to come." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5471.0 0.0 0.0 0.0
"Best way to teach determinants. I used to worry about how this is the worst part of linear algebra since it involved a big formula that was thrown to me. I loved the intuition about the property 9 about volumes of n dimensional cubes. Never thought determinants would get me this excited.
Long Live Prof. Strang.
Thankyou MIT." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 2882.0 0.0 0.0 1.0
"Good 😘🇮🇳" PBMyBVPRtKA "Lecture 19: Compact Subsets of a Hilbert Space and Finite-Rank Operators" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 4161.0 0.0 0.0 0.0
"by far the best video of integrals I've ever seen. he made it so clear to me..thanks" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12581.0 0.0 0.0 0.0
"Lecture aside, I just wanna say that the course structure of 30% assignments, 2x 15% midterms and a 40% Final is very smart. 

Looks like grading is more focused on learning throughout the semester to engage the students. 

Courses with 50% Final and 2x 25% midterms or similar does not do anything to help students learn in the long term. Great class structure" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7291.0 0.0 0.0 0.0
"he is indeed very good but actually he is greek" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 13096.0 0.0 0.0 0.0
"44:16 When you see your ex again" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1231.0 0.0 0.0 0.0
"I remember falling asleep in all my linear algebra classes @ UWaterloo. Not until now that I'm starting to like linear algebra!" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5944.0 0.0 0.0 0.0
Brilliant hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2923.0   
"wish were admitee t o   mit   orelesi  significally   outcasted  by   harvared   yet  loe we  cambridgr   buut  remainerexit oxfordrr.." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 15385.0 0.0 0.0 0.0
"What if you have a function f(x,y) of which the partial derivatives f_x and f_y are known, but not the relation between x and y as if they were both functions of t? Is it possible to find the function definition of f somehow?" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11508.0 0.0 1.0 0.0
"le recomiendo usar geogebra teacher" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13763.0 0.0 0.0 0.0
"Does anyone know this professor's name?" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3442.0 0.0 0.0 0.0
"What Software does Prof. Rigollet use to make these slides?
I guess it's RMarkdown but can someone confirm?" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 11385.0 0.0 0.0 0.0
"Since the box is hollow, shouldn't the total surface area be 2 x (bottom) + 8(side) ? Since it will have inner and outer surfaces (the box being hollow)? So essentially 2 * x^2 + 8 * (V / x)" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8680.0 0.0 1.0 0.0
"@29:90
Hendersen-haselbach equation for pKa and pH is using this method least square method" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1531.0 0.0 1.0 0.0
"at 19:16 ""Well, don't speak all at once""......he is goddamm awesome guy." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 12420.0 0.0 0.0 0.0
"2:01 Don't run into either one!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 866.0 0.0 0.0 0.0
"26:06 What did the professor mean by-> orthogonal v's in the ""row space"" ?" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 795.0 0.0 1.0 0.0
"humans will start learning machine learning here." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13315.0 0.0 0.0 0.0
"Can anyone tell me which book should i prefer with these lectures.??" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3049.0 0.0 1.0 0.0
"We won't get a teacher like him possibly in our life time. 100 years fast forward people would be amazed to listen to his lectures and would marvel at the quality of education 100 years ago." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 11336.0 0.0 0.0 0.0
"Very good teacher." wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11185.0 0.0 0.0 0.0
"""You can't raise it from the dead""... How true, how true, prof. Strang :))) Even though there are some in this world that think it's actually possible to raise people from the dead, LoL :)))" ZUU57Q3CFOU "9. Four Ways to Solve Least Squares Problems" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 137.0 0.0 0.0 0.0
"THANK YOU MIT FOR THIS VALUABLE LECTURE !!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8981.0 0.0 0.0 0.0
"As x tends to 0,
 sinx/x tends to 1.
At x=0.1,
 Sinx/x = sin(0.1)/0.1 
= 0.99833416646....
At x = 0.01,
Sin(0.01)/0.01
= 0.99998333341....
At x = 0.0001
Sin(0.0001)/0.0001
= 0.99999999833....
At x = 0.00000001
sin(0.00000001)/0.00000001
= 0.99999999999...." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2576.0 0.0 0.0 1.0
"Best teacher for machine learning. God bless him." t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2878.0 0.0 0.0 0.0
"Professor Strang ,thank you so much for a straight forward lecture on computing eigenvalues and singular values in numerical linear algebra." d32WV1rKoVk "12. Computing Eigenvalues and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8338.0 0.0 0.0 0.0
"This was really helpful, thank you!" TSI3LR5WZmo "25. Interactive Proof Systems, IP" "MIT 18.404J Theory of Computation, Fall 2020" 10973.0 0.0 0.0 0.0
"When U and V transposed are the same, do these matrices represent a change of basis matrix? Because for this to happen, A has to be positive symmetric, so then the singular values of A would equal the eigenvalues of A right? So if A represents a transformation , then the diagonal matrix sigma could be understood as that same transformation matrix but in the basis of eigenvalues, so then U = V transposed,  should be change of basis matrices ????
But when are change of basis matrices equal to each other????
Thank you!!" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11610.0 0.0 1.0 0.0
"I use Newton's method a great dal in my numerical work. I am always shocked how fast it is to home in on the solution." 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6124.0 0.0 0.0 0.0
"not sure how he got 5 on the 3x3 matrix" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14082.0 0.0 1.0 0.0
"900,000 people did not like the change in sound quality." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1431.0 0.0 0.0 0.0
祝老先生身体健康 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 15644.0 0.0 0.0 0.0
"what an awesome professor" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 15122.0 0.0 0.0 0.0
"Hey, it’s my favorite guy again. 
Dr. StrangELOVE. 😂" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4699.0 0.0 0.0 0.0
Awesome! NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2779.0 0.0 0.0 0.0
"Thank you." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 9548.0 0.0 0.0 0.0
"What a wonderful lecture! I wish Prof. Gilbert a very long life." Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11436.0 0.0 0.0 0.0
"""As independent as siamese twins""-priceless" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 31.0 0.0 0.0 0.0
"he is a living legend" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 13091.0 0.0 0.0 0.0
"Really u an excellent and wonderful lecturer for me" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8532.0 0.0 0.0 0.0
"lol @ 32:20 and the class reaction..." WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13820.0 0.0 0.0 0.0
"GOD PLEASE HELP ME UNDERSTAND CALCULUS..." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3972.0 0.0 0.0 0.0
"im amazed that these top universities don't upgrade to whiteboards...or just go ask the tech department for a virtual reality board or something" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13565.0 1.0 0.0 0.0
"2 people didn't pass the course." xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 610.0 0.0 0.0 0.0
nice dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 14028.0 0.0 0.0 0.0
"I just finished watching 3Blue1Brown’s first video on matrix exponentials, it’s so well made.
Even though I feel like I haven’t fully understood  every aspect of this lecture, I do believe that with the help of 3Blue1Brown, this lecture might turn into intuition for me someday." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 5605.0 0.0 0.0 1.0
"maybe using p for both the matrix P and the projection p is a bit unfortunate" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 13932.0 0.0 0.0 0.0
"You are the god-gift in this world, thank you, Professor Strang" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12183.0 0.0 0.0 0.0
"How to solve 24.06 matrices by using last described column multiplication number" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4902.0 0.0 1.0 0.0
"Very natural way of teaching. Thank you sir" AeRwohPuUHQ "22. Gradient Descent: Downhill to a Minimum" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11202.0 0.0 0.0 0.0
"It's Christmas and I'm reviewing Linear Algebra." QuZL5IKpO_U "24b. Quiz 2 Review" "MIT 18.06 Linear Algebra, Spring 2005" 7012.0 0.0 0.0 0.0
"but will it be easy to find the C vector in c1x1+c2x2+...cnxn where xi are eigen vectors and n is very big." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 12578.0 0.0 1.0 0.0
"Thank you!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9468.0 0.0 0.0 0.0
"The real master." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 10268.0 0.0 0.0 0.0
"worth spending time to see this wonderful video" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 15403.0 0.0 0.0 0.0
"I can't find how to derive the Loss func. in respect to weight1 or 2,3etc, SO how the math is done behind the derivative part of the gradient descent formula. Everyone is showing the result or a smaller reshaped formula, but I would need the steps inbetween. An example where we backprop a single perceptron (with 1 or 2 weights, L2 function) would do it.  Pls someone give me a link or a hand. Thanks!
 I do understand the essence of chain rule, but I wanna know dL/dw = dL/dPred * dPred/dw    (dL/dw is the change in the weight1 respec to L2 Loss function, dPred is the derivative of the neuron's output (mx+b) )
I don't get  why the result is 2(target-pred) * input1.
Is that because L2 is a squarefunction and the derivative of x^2 or error^2 is 2X , so 2error --> 2(target-pred), but then why the other parts of the formula disappear." lZrIPRnoGQQ "27. Backpropagation: Find Partial Derivatives" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5216.0 0.0 1.0 1.0
"youtube link for lec 14 is actually lec 4" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15528.0 0.0 1.0 0.0
"14:48 EE -> TT -> FF -> aa. You could interpret a* as exponentiation but I think that in general this leads to ambiguity if you're interpreting the CFG as a model for arithmetic." m9eHViDPAJQ "4. Pushdown Automata, Conversion of CFG to PDA and Reverse Conversion" "MIT 18.404J Theory of Computation, Fall 2020" 439.0 0.0 1.0 0.0
"min 25:04 it would have been worth mentioning that the resulting integral is a mix of real + imaginary components" TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13943.0 0.0 1.0 0.0
"This is an amazing video! Here is my tutorial on Stochastic Gradient Descent with code explanation (in python). Hope it could be of help too. https://youtu.be/uXuBUkW_0tA" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10625.0 0.0 0.0 1.0
"Thanks don’t call me bro, bro bro. MIT APPROVED SPAM! Amazing thank God, all my winners" sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9678.0 0.0 0.0 0.0
"By increasing the row but decreasing the column my volume getting decreased the square becomes a rectangle parallellogram diagonalised volume decreased piezo electricity flows parallelgram getting squeezed for reduction in volume but critically screwed at one degree topological screwing to produce superconductivity in certain materials requiring some information from the Hon.Prof Strangler please.
Sankaravelayudhan Nandakumar on behalf of Hubble Telescope Research Committee." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 2975.0 0.0 0.0 0.0
"I've only just learnt about eigenvalues and eigenvectors from KhanAcademy and Strang's Lecture 21 so a lot of this went whoooosh over my head, but managed to find the first 20 minutes useful. Hope to come back to this when I've looked at differential equations (which AFAIK are very daunting), etc and understand more of it." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 6428.0 0.0 0.0 0.0
"he is patient ,and i am a little confuse of why he always put his hand in pocket?" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13098.0 0.0 0.0 0.0
"Jazz ❤️" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7127.0 0.0 0.0 0.0
"i feel lost here...." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 13377.0 0.0 0.0 0.0
https://youtu.be/DDUC23useww J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13292.0 0.0 0.0 0.0
"thanks slippy lol that works" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14606.0 0.0 0.0 0.0
"For anyone wondering about the last claim, how $1 + (m + 1)c$ could be the (n = m+1) case, plug (m+1) into the inductive assumption, which results in $(1+c)^(m+1) \ge 1 + (m + 1)c$" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 3858.0 0.0 1.0 0.0
0-+0 --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 274.0 0.0 0.0 0.0
"It's a best job .
Thank you!" t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7017.0 0.0 0.0 0.0
"The example for Markov inequality seems not proper. For sequence 1,2,3,4,5, the mean can be 1 only if P2, P3, P4, P5 are all 0" nrDkb2MAwSA "20. Definitions and Inequalities" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10094.0 0.0 1.0 0.0
"what a guy!" mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 15109.0 0.0 0.0 0.0
helP 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13129.0 0.0 0.0 0.0
"41:03 *The capital D done 3 times to u.*" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1146.0 0.0 1.0 0.0
"""nice""=measurable ;)" mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 166.0 0.0 0.0 0.0
"Thank You Frof. Strang..." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9047.0 0.0 0.0 0.0
"ha ha." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13030.0 0.0 0.0 0.0
"Are there any awards given out in America for best Prof of the year, he knows how to teach a subject I knew something about know alot more thank you prof Strang" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 2530.0 0.0 0.0 0.0
"I dub this lecture as ""Everything your parents didn't tell you about Linear Independence and you were afraid to ask"" 
Thanks Professor Strang, you are a wonderful human being" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 5379.0 0.0 0.0 0.0
"I'm a junior who is majoring in math and my calc professor in my university never taught me how he derived derivative of x^n. Imgaine the sheer difference of knowledge that students will aggregate when they graduate from MIT and other shit universities like mine :(. I envy students in MIT so much." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6297.0 0.0 0.0 0.0
"Thank you very much .You are great teachers" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 9429.0 0.0 0.0 0.0
https://www.youtube.com/watch?v=J5d1Ioen3fw&list=PLiGoMXc3nXBzRUlXQKAj9TnLhh3xo1Ucy 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 13273.0 0.0 0.0 0.0
"Where is lecture 17 ?" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11683.0 0.0 0.0 0.0
"Could anyone tell me why we usually take the doubly infinitesimal number to be 0 but here it is valid to write ds^2 =/= 0?" TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3228.0 0.0 1.0 0.0
"I have always heard that everything is big in America - I kind of understand what they mean every time I see that fantastic board eraser." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 5516.0 1.0 0.0 0.0
"strang gang!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 14401.0 0.0 0.0 0.0
"MISTAKE @29:30? The set of vectors S is NOT a subspace bc (1)*(1,0,-1,0) + (-1)*(-1,0,1,0) = (2,0,0,0) which is not in S!" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 7499.0 0.0 1.0 0.0
"Really appreciate for the courses, I studied math in college at 2005 in China and nearly forgot everything, maybe I never really understood them, but this course taught me so much, thanks for Dr Jerison and the substitution teacher, and each guy who contributed for these excellent work." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8505.0 0.0 0.0 0.0
"for fast learner, none at all i guess but for folks like me? several. as an example i have an odd habit of going ""huh?"" if something new is taught. i cant do that over the internet, but somehow the live answers ""sink in"" a bit better. i guess im just thick." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12884.0 0.0 0.0 0.0
"awful course!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 12499.0 0.0 0.0 0.0
"Im in 9th grade and am in Algebra 1 so i think this just melted my brain, lol" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 6571.0 0.0 0.0 0.0
"43:35 the professor will remember him at the end of the semester for phrasing his questions this way :D" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1213.0 0.0 0.0 0.0
"wats wrong with that teacher lol" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 15070.0 0.0 0.0 0.0
"this guy is so great.  My linear algebra teacher is horrible.. He makes it actually kind of interesting!" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14833.0 0.0 0.0 0.0
fascinating 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 12851.0 0.0 0.0 0.0
"Strang for president" nvXRJIBOREc "Lecture 21: Minimizing a Function Step by Step" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8901.0 0.0 0.0 0.0
"16:55 What about  transition q2->q1 after reading ab?" oNsscmUwjMU "2. Nondeterminism, Closure Properties, Conversion of Regular Expressions to FA" "MIT 18.404J Theory of Computation, Fall 2020" 493.0 0.0 1.0 0.0
"very impressive teacher - obvious expertise and love for his subject, lucid, unhurried, kind" jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15019.0 0.0 0.0 0.0
"I can see why Dr. Strang is a professor at MIT. The best of the best." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5199.0 0.0 0.0 0.0
"""I kind of pulled it out of my hat, I mean I don't have a hat"" bahaha" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 58.0 0.0 0.0 0.0
"I've watched several MIT lectures for supplementry and/or personal benefit and I am always amazed how good their professors are!" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6437.0 0.0 0.0 0.0
"I Freaking LOVE MATH! The feeling you get when solve a problem is just beautiful. It's my drug!" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4922.0 0.0 0.0 0.0
"Where is your camara man... what u r doing" yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 11695.0 1.0 0.0 0.0
"oh my gosh. I laughed out loud at that too. I bet you did this when you were 5 years old." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14108.0 0.0 0.0 0.0
"why did he put Quantum Electro-Dynamics (QED) after the end of FTC 2 proof?" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15299.0 0.0 1.0 0.0
"Brilliant man!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 2933.0 0.0 0.0 0.0
"A thousand years from now, people will still be learning matrix algebra from this guy." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 2160.0 0.0 0.0 0.0
"Dear MIT rejects of the past,

We know you are still embittered over not getting admitted to our prestigious institution. We promise - it was never about your lack of academic ability or your IQ. Or your second place medal at that math competition.

This, here - MIT Open CourseWare -  is our long overdue apology to you. Behold, the MIT world-class education (that you should have gotten) - all from the convenience of your computer screen as you sip iced tea while in your PJ’s.

You’re welcome. And no hard feelings, we hope.

Love,
MIT" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3324.0 0.0 0.0 0.0
"By convention sin⁻¹(x) means h/o whereas it really intends here is arcsin(x)? Has MIT adopted this confusing notation?" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2971.0 0.0 1.0 0.0
"The second part of the lecture going from Ux = 0 to Rx = 0 and further on to RN = 0, and proposing what is N, seemed to be full of leaps that I could not follow completely. I have done a ML course, and a Neural network course without a deeper knowledge of Linear Algebra. I thought of filling that gap. The rabbit hole seems to go deep, and again I seem to be taking a few magical things that happen to be as axiomatic. I will persist. If I can not get it from Prof Strang, I may not get it at all. Hope the pennies will drop as I move forward, and I will get rich!" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 10275.0 0.0 0.0 0.0
"fuck, did anybody else find the last proof ""sloppy""?? i'm guessing he made a mistake" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12905.0 0.0 1.0 0.0
"I have... is that right? sorry am I getting this correct. oh, I'm not. my God!!!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 5570.0 0.0 1.0 0.0
"i wish i had a math teacher like that in my college. i can't complain about other teachers but my math teacher is a nightmare." jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13497.0 0.0 0.0 0.0
"my ffff do butiful" seO7-TwXH_I "Lec 30: Line integrals in space, curl, exactness... | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13982.0 0.0 0.0 0.0
"enjoying these lectures tremendously - cant say I expected to find linear algebra that interesting" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 12796.0 0.0 0.0 0.0
"13:13
How is delta(u/v) =(u+deltau)/(v+deltav) - u/v at x+deltax?" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 407.0 0.0 1.0 0.0
"@thejugglenaut91 my teachers are excellent!!! and i guess its a preference? MTU has black boards in some classes but smart boards are mostly what they have. i love them, and i learn excellent from them." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2043.0 1.0 0.0 0.0
"I would lose some points because I would use the standard coordinate system (looking at the contour plot form above) :(" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6263.0 0.0 0.0 0.0
"Is this an undergraduate mathematics course? If so what year would students typically take this course?" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 6855.0 0.0 0.0 0.0
"Mitx Edx real analysis PLEASE………" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 7684.0 0.0 0.0 0.0
📚 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15727.0 0.0 0.0 0.0
🙏🙏🙏 3PzuSPQPEU4 "8. Undecidability" "MIT 18.404J Theory of Computation, Fall 2020" 15741.0 0.0 0.0 0.0
"can somebody provide lecture notes of this course?" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12618.0 0.0 0.0 0.0
"DR. Strang thank you for another great lecture on matrices and their inverses." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3282.0 0.0 0.0 0.0
"Lol. The 'R' in the ideal gas equation is not 'radius'." yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 7408.0 0.0 1.0 0.0
"9:41 Independence is dead lol" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 1443.0 0.0 0.0 0.0
"All right. Area in space is explained a few minutes later. " 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2307.0 0.0 0.0 0.0
"It's easier to understand than on my native language :)" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7036.0 0.0 0.0 0.0
"2:51 goals of the course" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 875.0 0.0 0.0 0.0
"what is recommended book to read in this course" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15160.0 0.0 0.0 0.0
"Amazing lecture!" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 2367.0 0.0 0.0 0.0
"this one video gave me  more knowledge than my college." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14909.0 0.0 0.0 0.0
"You heard wrong then : P" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12216.0 0.0 0.0 0.0
"who is so so so much foolish to dislike the video]" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15263.0 0.0 0.0 0.0
"I love this lesson and the sound of chalk against that board-this vectors lesson gave me goose pimples, merci beaucoup !" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5819.0 1.0 0.0 0.0
"Am I the only person who is watching this videos with 1.25x speed? :D" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 2341.0 0.0 0.0 0.0
"This guy's accent is seriously the best." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10565.0 0.0 0.0 0.0
"appear up here" CXKoCMVqM9s "Lec 28 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12394.0 0.0 0.0 0.0
"it's really weird he said ""you don't have"" a formula for solving a 3rd degree polynomial http://www.math.vanderbilt.edu/~schectex/courses/cubic/ he's a mathematician so clearly he knows that such a formula has existed for 500 years and good bet a fair number of his students knew that as well, but he said ""you don't even have such a formula"".  at 42:35" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13698.0 0.0 1.0 0.0
"1:28 LOL" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 594.0 0.0 0.0 0.0
"These are best lectures I have ever find in entire YouTube." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 10394.0 0.0 0.0 0.0
"Thank you, Dr. Strang!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9492.0 0.0 0.0 0.0
24:32 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 735.0 0.0 0.0 0.0
"How is this free? Thank you!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 4876.0 0.0 0.0 0.0
"Thanks a lot Dr. Strang, i'm really excited for the next lecture." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 9653.0 0.0 0.0 0.0
"Don't  act confused guy, i'm not saying anything about the teaching capabilities if the lecturers or the work they cover at MIT. All i'm saying is that the title of being one of the greatest engineering schools in the world is due to talented students every now and then and a wide range of resources available to them." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3470.0 0.0 0.0 0.0
"Its Heaven for Mathematics Lovers...." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7080.0 0.0 0.0 0.0
"ım just suprised how easy this is" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15540.0 0.0 0.0 0.0
"Well done .....MIT!" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 11349.0 0.0 0.0 0.0
"material bursar" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13914.0 0.0 0.0 0.0
"In Arabic language  "" albegra "" = البقرة  which means a cow" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6606.0 0.0 0.0 0.0
"That chalk ! :-D" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9879.0 1.0 0.0 0.0
"nice handwriting" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14036.0 0.0 0.0 0.0
"This is the very first lecture. Just sayin'" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10756.0 0.0 0.0 0.0
"""I see what you did there!"" STRANGthen!" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 61.0 0.0 0.0 0.0
"Thank you MIT. I scored 88% for both calculus and algebra in my August test" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9165.0 0.0 0.0 0.0
"This one was one of the hardest ones for me thus far" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10885.0 0.0 0.0 0.0
"The professor artfully covers the fundamental idea of probability with deceptive ease. Many teachers easily confuse the students by writing the total probability theorem and Bayes' Theorem formulas first and try to fit in an example into the formula to explain the topic. One would lose intuition as to what is happening underneath those equation quickly and simply churn out the results by putting in values into the equation. But, the professor here only at the end mentions the name of Bayes and hardly uses the word Total probability theorem. He arrives at those generalisations with pure logic by intuitively applying multiplication rule, total probability theorem and Bayes’ rule to solve a problem at hand." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 10245.0 0.0 0.0 1.0
"Cool absolutely loved it" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3207.0 0.0 0.0 0.0
"I`m learning English watching these incredible classes, thank you so much Teacher Strang and MIT" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 6453.0 0.0 0.0 0.0
"Very excited to learn one more Video course from Prof Gilbert Strang, One of the best teachers I have ever had!!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11170.0 0.0 0.0 0.0
"Thank you, professor Strang!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9524.0 0.0 0.0 0.0
"@tikilikiboomboom93 
I so badly want to write on that blackboard only to erase using that amazing ""eraser"" (am I correct calling that an ""eraser""? My english is prety poor).  I've never seen these things SO large. I'm going to get one of them for my own teaching." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2044.0 1.0 0.0 0.0
"oh my! Everything's just crystal clear! Thanks Professor!" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14109.0 0.0 0.0 0.0
"This is like pure intellectual chocolate. Gilbert Strang should've taken over Wonka's Chocolate Factory, not Charlie." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 10686.0 0.0 0.0 0.0
"I am midway in 18.06. It makes me so very happy and extremely saddens me at the same time. I am so happy that he's doing well and contributing so much, just shows how much he loves teaching and simplifying things. It saddens me to see the stark difference between him now and in 18.06. I wish he could just live forever." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5117.0 0.0 0.0 0.0
"Love the laugh & clap at 43:20 !" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7452.0 0.0 0.0 0.0
"what GUI software professor Suvrit is using to change the step size instantly?" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15100.0 0.0 0.0 0.0
"What interesting lecture is this. you showed how maths is a pillars of statistics. during the lecture I think of the assumptions of least square estimation. it comes from maths (like the independency assumption). great work.  God bless you prof." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 11510.0 0.0 0.0 0.0
"Please name this beautiful lecture “A tour of the zoo of dicontinuities.”" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8208.0 0.0 0.0 0.0
"I tried to Get MIT but i was failed 
still iam in IIT Bombay" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6113.0 0.0 0.0 0.0
"Flawless victory!" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3832.0 0.0 0.0 0.0
"19:54 ""Let me suppose I got as far as u"" lol" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 569.0 0.0 0.0 0.0
"i like it how he said zero was his favorite number. My calc teacher said zero is boring. They should get into a math teacher debate." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13418.0 0.0 0.0 0.0
"The way Mr Strang asks Why? Each Time a new case comes up just wins my heart with his innocence and curiosity ." TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 10320.0 0.0 0.0 0.0
"Thank you so much Professor Strang. Thank you MIT." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9360.0 0.0 0.0 0.0
"Stat is very hard sub.." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8889.0 0.0 0.0 0.0
Merci yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 7657.0 0.0 0.0 0.0
"This is an amazing job. Thank you David Jerison , and everyone else who contributed this." XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10623.0 0.0 0.0 0.0
"Thank you!" 0Qws8BuK3RQ "34. Distance Matrices, Procrustes Problem" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9465.0 0.0 0.0 0.0
"Thank you Prof Strang & MIT. Very clear lecturer" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9181.0 0.0 0.0 0.0
"Dedicated review lectures such as this one are so helpful. They are certainly useful for tying everything together and identifying remaining questions that students may have. However, at least in my experience this kind of lecture also has some psychological benefits, at least for some students, because they end up realizing they actually know most of the material. This is very important since what often holds students back is lack of confidence and overcomplicating things. And of course a review lecture by Prof. Strang himself is extra special!" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 3338.0 0.0 0.0 1.0
"next level stuff :) .... null space = c*[-Free; Identity ] thanks" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 14022.0 0.0 0.0 0.0
"It could be better if the camera was still" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6910.0 1.0 0.0 0.0
"chalk hurts my ears" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12648.0 1.0 0.0 0.0
"Loved your way of teaching sir. It's seems like everything for registered in my memory.😃" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7483.0 0.0 0.0 0.0
"basis is a bunch of vectors and not too many." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 12511.0 0.0 0.0 0.0
"I've  really felt terrible, when there's  no students  in there... But prof. Strang   done it in a   simple  way 🥰🥰🥰" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 6401.0 0.0 0.0 0.0
"thank you mit!!" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 14500.0 0.0 0.0 0.0
"Thank you #MitOpencrouseware. Live long professor strang. lots of love and respect from Pakistan." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9093.0 0.0 0.0 0.0
"How lucky we are to have another wonderful Strang lecture! His insightful presentations are always a treat, and it's great to see his take on deep learning applications. 
Minor chalk-o: he rotated Ax the wrong way at 27:22 (but the math is still right)" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4878.0 0.0 1.0 1.0
"I followed through the whole series, and this is the BEST Statistics course I have ever taken. Thank you Prof Tsitsiklis for being so clear and concise. I had never imagined a starting statistics course enhancing my understanding so much and giving me so much confidence. This is magic!" gMTiAeE0NCw "13. Bernoulli Process" "6.041 Probabilistic Systems Analysis and Applied Probability" 5425.0 0.0 0.0 0.0
"Is this a real MIT Calc class recording? or a modified version for the public with easier material? I looked at the exams in the link and I was in SHOCK!!
I go to McGill and this is way too easy compared to my uni.. NOT FAIR!!!!!!!" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6853.0 0.0 0.0 0.0
"Fantastic advice, he is our elder he is really smart at this task and all the while he is level in head to realize what he knows you are learning so patients.
I cannot do math, however he is really a pleasure to listen to and learn wisdom form regardless. I will still go watch his 18-06 course. humor is easy for all of us if we are the current one as the top in our skill set regardless the skill set we are sharing with others willing to learn that skill from each of us.
Lance & Patrick." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 3727.0 0.0 0.0 0.0
"Why does he call it a ""vector""  ??" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11838.0 0.0 1.0 0.0
"Can someone please help me with the drawing of the column space at the end of the video? Is he saying that if I summed up all the possible linear combinations of the two columns made from matrix A, I'd end up with a 2D plane in a 3D space?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 3094.0 0.0 1.0 0.0
"thank you MIT!" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14484.0 0.0 0.0 0.0
"Projectile motion equations https://www.youtube.com/watch?v=vEDjmZ_Gg84" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8414.0 0.0 0.0 0.0
"I love blackboards! I am glad they still use them." 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 5728.0 1.0 0.0 0.0
"at 38:00 , we take a non-linear transformation of Xn bar as the statistic. How can it still be Gaussian? He said in a previous lecture it is not Gaussian." 4HRhg4eUiMo "8. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 12447.0 0.0 1.0 0.0
"@kuronekocfu 
in my opinion it doesnt matter if you do that stuff in high school or not. if you like mathematics you find a good book and learn anything you like. i live in greece and when i finished high school i bought a book on calculus 2 and studied it alone. it was waaay better than school or uni.university is overpriced really" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1926.0 0.0 0.0 0.0
"This lecture made so much sense. My current professor doesn't do a good job in keeping it interesting. Great lecture!" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 10820.0 0.0 0.0 0.0
"this question is asked way too much, maybe it would be easier for mit to just relabel lectures (i mean an in class exam dosent really count as a lecture)" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14915.0 0.0 0.0 0.0
"What will be matrix A if I want to express y''+y=0 in the form Ay=0 ?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 11568.0 0.0 1.0 0.0
"""at least that was the artist's intent when he drew it"" lol love these lectures" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 145.0 0.0 0.0 0.0
"Is every DFA an NFA? My initial guess was yes but not every DFA accepts the empty string. NFA must accept the empty string. 
Thanks in advance." oNsscmUwjMU "2. Nondeterminism, Closure Properties, Conversion of Regular Expressions to FA" "MIT 18.404J Theory of Computation, Fall 2020" 6766.0 0.0 1.0 0.0
"I like how this free class even excludes the errors, making it ten times better than the paid for class above...those two mistakes with the x (should have been u) could greatly confuse one" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5671.0 0.0 1.0 0.0
"my mind is blown! not by linear algebra... but by Gilbert Strang's teaching <3" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 13991.0 0.0 0.0 0.0
"Could anyone please tell me: what does he mean by saying ""to first order it will not change (27'50'')""? Thank you so much." 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3227.0 0.0 1.0 0.0
"36:00 Someone wake up the damn camera guy." 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1026.0 1.0 0.0 0.0
"Can MIT OCW please make short video lecture series complemented with interesting problems, so that it is easier and more effective to learn?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3007.0 0.0 0.0 0.0
"Way ❤️" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11311.0 0.0 0.0 0.0
"27:45. Shouldn't it be just A? i mean A=[a1  a2]. but now we have a1(trans) and a2(trans) in its columns, not just a1, a2. How could that be A(trans.) ??" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 826.0 0.0 1.0 0.0
"Not even a chuckle at the ""B movie"" joke?" jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 7921.0 0.0 0.0 0.0
"I am confused about the second and third methods. How is c a linear combination of A's column. My first thought it is a linear combination of A's row.
I am talking about the second merhod." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5073.0 0.0 1.0 0.0
"He looks like Moriarity from the new ""Sherlock"".... and he is a real professor too!!!" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4568.0 0.0 0.0 0.0
"12:56 How did he get the formula for σk(x). Can anyone explains?" 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 399.0 0.0 1.0 0.0
"45:50 Wait, isn't that only true for orthoNORMAL matrices? If matrix is just orthogonal, there will be squares of it's vector's lengths on the diagonal." HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 1261.0 0.0 1.0 0.0
"@29:30, why does d/dx( L' (A x) )  become A' L? ( ' = transpose, L = lambda, d/dx = partial der.)" xaSL8yFgqig "Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1530.0 0.0 1.0 0.0
"Absolutely amazing lectures." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2199.0 0.0 0.0 0.0
"20 people picked #6" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 616.0 0.0 0.0 0.0
"@1:08:40 - ""it is weakly convergent if it converges in probability, and strongly convergent if it converges al naturel?""" TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 1506.0 0.0 1.0 0.0
"28:10 - I've done an interactive graph of this exercise at:  https://www.desmos.com/calculator/lfc29dwtt6" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 832.0 0.0 0.0 0.0
"Professor Strang be drawing lines straighter than my life" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8345.0 0.0 0.0 0.0
"Lecture is a replacement of your reading for obtaining information. Learning new information cannot be done by someone else regardless of your laziness. Lecture is actually to understand the thought process of the experts that is not obvious from words. Focus is NOT on the information itself, which should have been obtained through reading, but rather on his path of thought while exploring these concepts. Go to Khan if you're looking for someone to spoon you with new information." yP1S37BiEsQ "13. Regression" "MIT 18.650 Statistics for Applications, Fall 2016" 7292.0 0.0 0.0 0.0
conjugate M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 12670.0 0.0 0.0 0.0
"i wish i was a bird" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 13500.0 0.0 0.0 0.0
"17 lectures in one streak! hope i will finish tomorrow" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 497.0 0.0 0.0 0.0
"Thanks this is priceless.Great interview." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9796.0 0.0 0.0 0.0
"Lecture 1: Dot Product
Lecture 2: Determinants
Lecture 3: Matrices
Lecture 4: Square Systems
Lecture 5: Parametric Equations
Lecture 6: Kepler's Second Law
Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds)
Lecture 8: Partial Derivatives
Lecture 9: Max-Min and Least Squares
Lecture 10: Second Derivative Test
Lecture 11: Chain Rule
Lecture 12: Gradient
Lecture 13: Lagrange Multipliers
Lecture 14: Non-Independent Variables
Lecture 15: Partial Differential Equations
Lecture 16: Double Integrals
Lecture 17: Polar Coordinates
Lecture 18: Change of Variables
Lecture 19: Vector Fields
Lecture 20: Path Independence
Lecture 21: Gradient Fields
Lecture 22: Green's Theorem
Lecture 23: Flux
Lecture 24: Simply Connected Regions
Lecture 25: Triple Integrals
Lecture 26: Spherical Coordinates
Lecture 27: Vector Fields in 3D
Lecture 28: Divergence Theorem
Lecture 29: Divergence Theorem (cont.)
Lecture 30: Line Integrals
Lecture 31: Stokes' Theorem
Lecture 32: Stokes' Theorem (cont.)
Lecture 33: Maxwell's Equations
Lecture 34: Final Review
Lecture 35: Final Review (cont.)" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7265.0 0.0 0.0 0.0
"who dislikes a video with this man in it?" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 15259.0 0.0 0.0 0.0
"Today i completed this course, i'm not a science major I'm an Eco student and just started learning Maths so that i can pursue Masters later and this is the 1st course that i took and it truly inspired me to learn more maths and never leave Linear Algebra, This could not have been possible without  Prof. Stang and MIT OCW. Thank you so much words cannot express my gratitude." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 11054.0 0.0 0.0 0.0
"It's a bit sad to see such brilliant people age... Let's hope and work towards that someday they won't have to struggle with age constrictions anymore. Just imagine how much more humanity could have achieved?... On the other hand I'm trully happy to see dedicated people like him, still spreading knowledge and wisdom - no matter what!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7019.0 0.0 0.0 0.0
"what kind of book does the class use?" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15176.0 0.0 0.0 0.0
"if f=x+1, x>=0 and f=-x+1, x<0, is this function continuous? How will tangent to this function look at x=0?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13532.0 0.0 1.0 0.0
"about couples,  what if x is male and y is female. and male control the position. and x isnt changing and y is changing." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 12300.0 0.0 1.0 0.0
"40:38 Wait...where is everyone? How many are there?" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1131.0 0.0 0.0 0.0
"Yeah, it should have been s= velocity, and ds/dt=acceleration.  The derivative of velocity is acceleration." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12129.0 0.0 1.0 0.0
"Thank you." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9555.0 0.0 0.0 0.0
"Thank you Professor Strang for showing us the beauty of math!" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 9219.0 0.0 0.0 0.0
"When there is no derivative of a funtion?" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11637.0 0.0 1.0 0.0
"viva la france !!" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15047.0 0.0 0.0 0.0
"I highly recommend doing the Frobenius norm proof he mentions. It is elegant and uses some nice properties of linear algebra. If you took 18.06 (or watched the lectures) using the column & row picture of matrix multiplication really helps. I'll finalize my proof and post a link - hopefully I didn't make a mistake ;)" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5577.0 0.0 0.0 1.0
"I Really Like The Video Applications to logarithms and geometry From Your" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4936.0 0.0 0.0 0.0
"looks like it wasnt professor jerison's best day" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13854.0 0.0 0.0 0.0
"dat sin graph was hella sexy" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 12725.0 0.0 0.0 0.0
"why take a calculus course out of boredom? why not music or arts?" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15363.0 0.0 0.0 0.0
"I have never seen teacher like u.....ur way of teaching and clearing the concepts of students is amazing sir..
..." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 5541.0 0.0 0.0 0.0
"This lecture literally get me addicted 😁" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10817.0 0.0 0.0 0.0
"Camera man is crazy" 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 2996.0 1.0 0.0 0.0
Great 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4192.0 0.0 0.0 0.0
"Thanks for an amazing lecture. So matrixA and matrixB follow commutative property if and only if B is inverse of A, correct?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9682.0 0.0 1.0 0.0
"Positive Semi-Definite matricies: 38.01" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8231.0 0.0 1.0 0.0
"Thanks Professor Gilbert Strang" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9640.0 0.0 0.0 0.0
"I agree. The problem with folks back then is that something that was obviously simple was made difficult to justify their supposed intelligence. Calculus and basically nothing is hard if explained CORRECTLY. Descartes said this many centuries." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5031.0 0.0 0.0 1.0
"Amazing for MIT to make such high quality lectures available worldwide. Well worth time investment to go thru these lectures. Thanks Prof Strang & Prof Suvrit & MIT" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2361.0 0.0 0.0 0.0
"I love this man omg TT" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5823.0 0.0 0.0 0.0
godd PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12934.0 0.0 0.0 0.0
"I love that he uses transparencies." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 5770.0 1.0 0.0 0.0
"Great!!

😍" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 4371.0 0.0 0.0 0.0
"Lecture 1: Dot Product Lecture 2: Determinants Lecture 3: Matrices Lecture 4: Square Systems Lecture 5: Parametric Equations Lecture 6: Kepler's Second Law Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds) Lecture 8: Partial Derivatives Lecture 9: Max-Min and Least Squares Lecture 10: Second Derivative Test Lecture 11: Chain Rule Lecture 12: Gradient Lecture 13: Lagrange Multipliers Lecture 14: Non-Independent Variables Lecture 15: Partial Differential Equations Lecture 16: Double Integrals Lecture 17: Polar Coordinates Lecture 18: Change of Variables Lecture 19: Vector Fields Lecture 20: Path Independence Lecture 21: Gradient Fields Lecture 22: Green's Theorem Lecture 23: Flux Lecture 24: Simply Connected Regions Lecture 25: Triple Integrals Lecture 26: Spherical Coordinates Lecture 27: Vector Fields in 3D Lecture 28: Divergence Theorem Lecture 29: Divergence Theorem (cont.) Lecture 30: Line Integrals Lecture 31: Stokes' Theorem Lecture 32: Stokes' Theorem (cont.) Lecture 33: Maxwell's Equations Lecture 34: Final Review Lecture 35: Final Review (cont.)" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7285.0 0.0 0.0 0.0
"Prof. Strang is a Magician, he shows that  Matrix is synonymous to Magic." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 8302.0 0.0 0.0 0.0
"VIVA LA FRANCE! This man knows his stuff." 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11149.0 0.0 0.0 0.0
"So if anyone is interested for an explanation of 38:00-38:31 roughly. x takes on values which are all the Natural numbers 1,2,3,4.... etc. Now if we want to find the probability values after some number of trials we'd obviously have to start after some variable, lets say 'n' amount of numbers. Expressing where we start by x, given the values that x takes would mean we'd have to write x+n whatever n is. In the video it is 1.

This implies that the expectation value given that x is all values greater than some n:
E[x|x>n]
notice how the specification of 'greater than n' is only nontrivial insofar as x takes on values from all the natural numbers. We specify this since we dont change the domain of values that x itself takes. Our problem would be solved if we just suggested that x take on values greater than n in itself, however we do not.

Now given this, we basically have to restrict the expectation values to when x>n, we'd have to start calculating expectation values at x+n. So suppose we start at the point n=5, ie. x is always greater than 5 (again, in the video it starts at n=1), then we'd do add 5 to natural number in x and thus we could attain the distribution we we're trying to attain by adjusting the random variables this way from the initial distribution.

In other words for any E[x+n] (note it is implicit here however this means E[x+n|initial sample space]).
This is a calculation of the expectation values of x greater than n.

We can express it in terms of the actual formula to make it more evident.
(x+n)p_X(x+n)=E[x+n] again, where x takes on the value of the natural numbers. Meaning that thus for every natural number from 1, we are adding n, making the formula apply on the values that are n greater than what would otherwise be in just E[x].

So as a consequence then E[x|x>n]=E[x+n|initial sample space]=E[x+n]." -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 8770.0 0.0 1.0 0.0
"How a perfect thing that being able to be a great mathematician and a great teacher at the same time! Especially, being a great teacher is priceless!" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4797.0 0.0 0.0 0.0
"Because they can get an orgasm out of linear algebra as if polynomials weren't enough." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 2834.0 0.0 0.0 0.0
"One Month And Am done..... Ten days of serious revision and problem set rehandling... thanks mit and iit (India)" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8072.0 0.0 0.0 0.0
"The level of the calculus might be low, but he is explaining the proof and intuition in very clear, insightful ways that you don't normally get from a high school teacher. Well worth watching. Thank you MIT!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10177.0 0.0 0.0 1.0
"When you think there is no more sliding boards 33:16" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 11647.0 0.0 0.0 0.0
"I had a much better teacher at Leningrad State University." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5461.0 0.0 0.0 0.0
"Are there also row-subspaces?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 2529.0 0.0 1.0 0.0
"Because of you I love math ❤️" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 2833.0 0.0 0.0 0.0
"I wish I was in MIT. I hate being poor." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6210.0 0.0 0.0 0.0
"I wasn't just talking about this lecture....I was talking about their practice exams involving the gradients and tangent line equations you build about   1/2 way thru multvariable calculus. MIT is a great school, that teaches you what you need to know for your future. However, I think it is not where you go to college but rather what you do at the college you go to." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6178.0 0.0 0.0 1.0
"I thought that i'm not smart to understand probability, but turned out that it depends on who is teaching it. this prof. is great." 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 6094.0 0.0 0.0 0.0
"leucter study gudie
canvas ascuess" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 13785.0 0.0 0.0 0.0
"That was a harry potter on broom entry!" JTbZP0yt9qc "6. Maximum Likelihood Estimation (cont.) and the Method of Moments" "MIT 18.650 Statistics for Applications, Fall 2016" 9916.0 0.0 0.0 0.0
"Superb explanation sir 🙌🙌🙌" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8961.0 0.0 0.0 0.0
"6:45 he does reply as far as he can! I sent him am email thanking him for the lectures before watching this interview, and I actually did not expect a reply. But he did sent an appreciation reply to my email and he was so nice as well!

What a wonderful professor!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 1385.0 0.0 0.0 0.0
"@47:05 was THE best question raised by that girl, which was missed by professor badly in his entire explanation." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1564.0 0.0 1.0 0.0
"Such a great professor" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8931.0 0.0 0.0 0.0
"He certainly shows there is a big difference between knowing a subject and knowing how to teach it to others." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4465.0 0.0 0.0 0.0
"if you are given the components of two vectors (e.g. u=(2,3,6) and v=(2,3,-6)) how do you use this to find the angle between them?" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13549.0 0.0 1.0 0.0
"did he say ""an orgy of problems"" at 15:30?" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12739.0 0.0 0.0 0.0
"i like this teacher but he has explained very badly the related rates problems. Is very difficoult to see the beuty of maths with this man but is ok for practical instances.
Thanks MIT" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13421.0 0.0 0.0 0.0
"@26:00 shouldn't it be det >=0 to account for the solutions with steady state? And I suppose yes, this lecture is clear if you have been previously exposed to at least basic differential equations. But hey! OCW offers that course for free too! ;)" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 1519.0 0.0 1.0 1.0
"From 21:24, he starts covering Inverse, the section before covers 5 ways of matrix multiplication" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3925.0 0.0 0.0 0.0
"If theres four variable then how to draw a 4d pic like that of row and column...." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6527.0 0.0 1.0 0.0
"This is a VERY well done lecture.  At around 25:46 when the camera pans away, I can see all the material that was covered, and not only do I remember all of it clearly, I'm surprised we've covered so much, because I don't feel overwhelmed." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10586.0 1.0 0.0 0.0
"@gerax89gunner1 don't blame the professor." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1851.0 0.0 0.0 0.0
"19:40 if you turn the volume down everything he says changes its meaning" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 566.0 0.0 0.0 0.0
"The maths Professor I've been wanting my whole life, finaaaallly I understand these things. Thank you! =)" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10184.0 0.0 0.0 0.0
"Excellent courses by professor Tsitsiklis .Ευχαριστώ πολύ κύριεΤσιτσικλή" ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 3638.0 0.0 0.0 0.0
"Well, this is a lecture to people who have no idea what a vector, Matrix or Eigenvalue is!
They have to learn first before using the PC to solve problems.
If not,  it is GIGO!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 11371.0 0.0 0.0 0.0
"I've never understood null space, rref, and how null basis is immediate from rref better.
I'd recommend Dr. Strang to anyone that tries to learn linear algebra." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 6426.0 0.0 0.0 1.0
"Such a wonderful instructor. I learnt Linear Algebra from his great video lectures." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8941.0 0.0 0.0 1.0
"you are hero" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 15493.0 0.0 0.0 0.0
"How I-P gives projection matrix. Can anyone describe that?" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 4796.0 0.0 1.0 0.0
"Thank you for this wonderful lecture :)" H_k1w3cfny8 "10. Continuous Bayes' Rule; Derived Distributions" "6.041 Probabilistic Systems Analysis and Applied Probability" 9288.0 0.0 0.0 0.0
定理が発表されずに4月に入ったら、溝口に私は定理の発見者じゃありませんって言います。 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 15625.0 0.0 0.0 0.0
"One third into the lecture, I'm lost." bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8114.0 0.0 0.0 0.0
"idiotyczny wykład!!!  gościu, który przez całe dorosłe życie zajmuje się macierzami - zamiast podawać teorię z dowodami ciekawych faktów - oczekuje od studentów laików - wywarzania otwartych drzwi! sposób wykładania jak w szkole podstawowej w moim kraju!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13525.0 0.0 0.0 0.0
https://youtube.com/playlist?list=PLgS_IeGjATOftefL9ZRBt79sTrbwgjS1k XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13312.0 0.0 0.0 0.0
"watch these videos and pickup openstax calculus 1 book,you have a solid combination to understand calculus." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15063.0 0.0 0.0 0.0
"5:20 These are MIT kids?" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1361.0 0.0 0.0 0.0
"really ironic that the first question asked was about the algebra involved....arent these people supposed to be super duper smart?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14253.0 0.0 0.0 0.0
"I love this series. Thank you professor. Thank you MIT. " YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5836.0 0.0 0.0 0.0
"For those like me, who did not get about the free columns and pivot columns fiasco at first.
Firstly, note that the free columns are linear combinations of the pivot columns (you can do some scribbling to confirm this).
This gives some intuition as to why we can allow the free columns to be scaled freely by    any number, then solving for the scalars of the pivot columns, such that you get zero column/vector if you add all these scaled columns. 
Pivot variables and free variables are the names for those respected scalars.
I hope this cleared some doubts...wish you the best of luck." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 3905.0 0.0 0.0 1.0
"I miss the days when professors / instructors took pride in their appearance.  Not expecting someone to wear a suit (though it's professional-looking), but a wrinkled up shirt?" SFDMFbzCsH0 "Lecture 20: Compact Operators and the Spectrum of a Bounded Linear Operator on a Hilbert Space" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 5873.0 0.0 0.0 0.0
"At 20:41, we can write {2-2cost}^1/2=|2sin(t/2)| ,the integral thus equals 8." 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2607.0 0.0 0.0 0.0
"There is a reason that the ground goes down.  If anyone else saw the electric outlets on the wall, the thumb doesn't contact any of the bare connectors but the finger below the thumb does and many people get electrocuted unless the ground is down." uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 10368.0 1.0 0.0 0.0
"he is using the term log as natural log and i am writing the wrong things down." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13103.0 0.0 1.0 0.0
https://youtu.be/e3ZdAJTSIas J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 13301.0 0.0 0.0 0.0
"Most of us trying to learn math are often not made aware of the fact that Math is a tool for understanding how the world works and it's not just the computations that make up the god damn thing. I am amazed by this way of teaching, in which the professor asks the question why and gives it much more importance than all the nitty gritties of how. At 33:44, the professor even points it out. I don't know why all the professors can't seem to see the learning process in the same way. Hats off to this amazing teacher!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7705.0 0.0 0.0 1.0
"Strang has reinvented himself and his knowledge and teaching style of Linear Algebra with the advent of Deep Learning projects and applications." t36jZG07MYc "An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,..." "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8903.0 0.0 0.0 1.0
"@qwqerty12345 
I meant (>)
This was just an example.I wanted to ask if it was possible to differentiate
things like f(x)>g(x) and have still the  >
But after some thinking i understanded that this canNOT happen no way because the fact that f(x) > g(x) for every real x means that the graph of f(x) is higher from g(x) for every real x.But f derivative represents the slope of the tangent of f at x, giving us the monotony of f.Hope you understanded what i mean.Also thanks for the reply" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1982.0 0.0 1.0 0.0
"Thank you very much. I have a hard time with this course. This video helps me a lot." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9458.0 0.0 0.0 0.0
"42 i think so..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1167.0 0.0 0.0 0.0
"Why is sound volume so low?" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 11883.0 0.0 0.0 0.0
"40:03 why the fixed count part is 32? I thought 64 since we have 2 D in the left matrix." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 1124.0 0.0 1.0 0.0
"This man is brilliant!" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10863.0 0.0 0.0 0.0
"He is a damn good teacher" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4497.0 0.0 0.0 0.0
"9:00 cough....Distance Formula.....Cough " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1432.0 0.0 1.0 0.0
"Thanks a lot, Prof. Strang." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9668.0 0.0 0.0 0.0
"Copy the URL and play it in VLC with volume 200%" X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 3217.0 0.0 0.0 0.0
"Professore: ""How many of you actually knew about vectors before that?""
Class: -______________- ... seriously?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8410.0 0.0 0.0 0.0
"This is my MATLAB code for his example at 23:35 min, 
----------------------------------------------------------------------------
clear all
clc
outcome = 2; % outcome # of a coin (Head & Tail)
n = 4; % tossing #
k = 0:n; % # of getting Head or Tail ( zero means no Head or no Tail)
p = 1/outcome; % the probability of a single outcome

Px = zeros(1, size(k,2)); % store the results in a vector

for i = 1:size(k,2)
        Px(i) = nchoosek(n,k(i))* p^k(i) * (1-p)^(n-k(i));
end

plot(k, Px)
xlim([  min(k),    max(k)])
ylim([min(Px), max(Px)])
-----------------------------------------------------------------------------------
The only thing you need to change is n. Play around with it." 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 10692.0 0.0 0.0 0.0
"Somehow, I managed to forget all that. Now, I have watched this lecture 3 times with an interval of one week. After that I should never forget how to find inverse :)" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8833.0 0.0 0.0 1.0
"Having a great teacher is so important! I have known all these operations for over 20 years, but really until now I know what it truly means by matrix multiplication! All my previous teacher just shown me the operations but never explained what it is trying to do." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4451.0 0.0 0.0 1.0
"18:38 I thought the derivative is not a number? *_* I'm confused" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 545.0 0.0 1.0 0.0
"@middleCmusic Maybe it's because i already understand lagrange multipliers, but they should not be that lost. this explanation is pretty decent, imho" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1951.0 0.0 0.0 0.0
"In Russia we learn this in 10th grade. In America they also learn this in 10/11 grade however this is just an review + some new stuff. This course lasts for only 1 semester. In school it takes you a year, while this is ONE SEMESTER. 

US still has and will have the best engineers in the world because they think creatively, and not just learn everything in the world. They apply their skills instead of inventing new. And no offense to anyone not in US, every country has amazing universities. " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6619.0 0.0 0.0 0.0
"Once we know one value of c from the mean value theorem, we can differentiate the function and let it be equal to (f(c))' that we found from the mean value theorem, and therefore we can find the other values of c where the slope of the tangent line to the function equals (f(c))'!" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8071.0 0.0 0.0 0.0
"Rotation vector Eigen 0,1  -1,0 as Q swing between cos theta and sin theta ." cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 8575.0 0.0 0.0 0.0
excellent! XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 12829.0 0.0 0.0 0.0
"@28:46 i never thought matrix multiplicatiom could work this way" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1527.0 0.0 0.0 0.0
"I think the secret to this is that we're finding parts of triangles." 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 6064.0 0.0 0.0 0.0
"couldn't be better." 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 12693.0 0.0 0.0 0.0
"36:20 the cameraman fell asleep or what?" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1036.0 1.0 0.0 0.0
"17:10 perfectly strait equals sign, mad props!" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 504.0 0.0 0.0 0.0
"ha that is not as bad as at my school when the grads are having their iron ring ceremony they all run through the 1st year classes hammered and spraying silly string and whatever else they find yelling and causing a general ruckus." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 13032.0 0.0 0.0 0.0
"Just the best.... MIT I lov it

" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7195.0 0.0 0.0 0.0
"I asked to my prof "" why do we minimize the square of the error in the LSM?""
He replied ""To reduce the distance""
today I understood what does he mean by that after 3 years" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5160.0 0.0 1.0 0.0
"Professor Gilbert Strang is a story teller !!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8327.0 0.0 0.0 0.0
"Aula trivial ." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2744.0 0.0 0.0 0.0
"Using the definition of matrix multiplication to come up with a matrix that performs the elimination process is indeed a fascinating idea." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11138.0 0.0 0.0 0.0
"yeah thats pretty awesome, help me understand like one equation" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15470.0 0.0 1.0 0.0
"Is there a way for senior citizens to audit these classes in person? This would be a dream retirement." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6827.0 0.0 0.0 0.0
"Thanks for the lecture...they are  quite intuitive 😊" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9719.0 0.0 0.0 0.0
"yea he almost looks like the number 1" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 15460.0 0.0 0.0 0.0
"الله يبارك في عمره ويعطيه الصحة والعافية. ما شاء الله عليه.  
Pure Pleasure ." sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15566.0 0.0 0.0 0.0
"Thank u very much Prof. Strang !" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9079.0 0.0 0.0 0.0
mu HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13961.0 0.0 0.0 0.0
"Excellent series, but why is the tenth lecture missing?" QXkOaifVfW4 "9. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 3673.0 0.0 0.0 0.0
"So this is my idea of a ""vector subspace"": It's an (N-1) dimensional slice of an N dimensional space, although it's only (N-1) dimensional in a certain sense of dimensionality size, because it has a sort of location information in N dimensions. So a vector space in R3 can be thought of a plane, a 2 dimensional object, relative to a 3 dimensional space. And the plane in this example must contain the origin of R3. 

It's hard to describe in terms of ""dimensionality"". Yay or nay" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 8797.0 0.0 0.0 0.0
"Starbuck's has poor internet
" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8878.0 0.0 0.0 0.0
"mmmmmmmmmmmmmmm i love this sooo much" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13957.0 0.0 0.0 0.0
"This teacher, oh boy I can`t remember his name... Well... I really appreciate how he uses intuition to teach Linear Algebra. I'd like to have had classes with him at the school. I would have saved many hours of my life studying for silly tests.

Sometimes I feel like studying Engineering made me less smart than I was as child. Sometimes I can really know that my teachers are trying to kill my creativity and coercing me to learn the hardway, nor the better way nor the easy way: just the way they had learned or the only way the can teach." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10942.0 0.0 0.0 1.0
"41:42 : ""it turns out to be 5/18, we won't do it""..... yeah I think they should have done it XD. I also think it's (5/24)/(4/3), which makes (5/32) as the final answer." R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1159.0 0.0 1.0 0.0
"At 41:40 it should be 5/32" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2663.0 0.0 1.0 0.0
"Thank you very very much!" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 9459.0 0.0 0.0 0.0
"The way he revealed the likelihood function in its usual form from that series of steps is super mindblowing. I wish my professor showed me how it comes from the TV to the KL then to that." 0Va2dOLqUfM "5. Maximum Likelihood Estimation (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 10329.0 0.0 0.0 0.0
"Happy Halloween! I see a student cosplayed as Grim Reaper." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 4420.0 0.0 0.0 0.0
"Last segment is interesting: |A_n| = |A_n-1| - |A_n-2| looked awfully fibonacci-like.  It turns out that the determinants of the symmetric tridiagonal matrices with i in the non-diagonal entries exactly follows the Fibonacci sequence.

Mind blown yet again." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 7250.0 0.0 0.0 0.0
"great professor.  that is why mit is mit. --comment from a freshman from cuhksz" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12999.0 0.0 0.0 0.0
"He is abolute legend !" cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4505.0 0.0 0.0 0.0
"It's pleasure to be a student at a time when great teachers like Gilbert Strang are there for you. 
Professor Strang is one of the teachers because of whom I decided to follow my career in mathematical research rather than going for engineering." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7064.0 0.0 0.0 0.0
"fun fact: number of ppl watching the next coming lectures are linearly decreasing oops." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 12908.0 0.0 0.0 0.0
"God, I love this man!" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4100.0 0.0 0.0 0.0
"I think he made a mistake when he said ""the other rows are a combination of the first two"" at 32:52..." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 6015.0 0.0 1.0 0.0
"Woot, Strang just dropped a hot track." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11997.0 0.0 0.0 0.0
"am surprised to see chalk being used in such a ""top-notch"" school. they don't even use chalk in our primary schools........lol........but good job anyway!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12341.0 1.0 0.0 0.0
"Trump 2024." QTg7040uSc0 "Lecture 23: The Dirichlet Problem on an Interval" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 11094.0 0.0 0.0 0.0
"wow these lectures are crystal clear how do others manage to blur it out so badly ;-;" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15419.0 0.0 0.0 0.0
"Who is watching from india" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11743.0 0.0 0.0 0.0
"I just want to get my hands on some of that chalk..." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5622.0 1.0 0.0 0.0
"These lectures are great" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 10407.0 0.0 0.0 0.0
"why is y^Tx equal to 1?" z3SmljnD_nQ "15. Matrices A(t) Depending on t, Derivative = dA/dt" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15350.0 0.0 1.0 0.0
"one way to prove property 4 is to use property 2: ( a b; c d) = ( tc td; c d) then the determinant is t* (cd-cd) which is 0. I love the way prof. Strang teaches it's inspiring" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 14154.0 0.0 0.0 1.0
"I did a maths degree, I've know about Kirchoff's Rule, and I studied linear algebra.  No one explained how it was all connected like this." 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5256.0 0.0 0.0 0.0
棒 ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15637.0 0.0 0.0 0.0
"at 51:00 did he mean e^(8*pi/3) which would be 1 instead of e^(6*pi/3)?" 1pFv7e9xtHo "31. Eigenvectors of Circulant Matrices: Fourier Matrix" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12463.0 0.0 1.0 0.0
"7:19 to 8:09 were the most hopeless and confusing seconds of my life." 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1397.0 0.0 0.0 0.0
"who needs proofs!?" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15266.0 0.0 0.0 0.0
"I thought that single variable calculus was a highschool subject i the US. Why are they giving that in MIT?" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6095.0 0.0 0.0 0.0
"Is is necessary to be fluent in matrix and determinants before taking this course ?
Note-I asked this because the prerequisites are not clear on MIT OCW web page." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6776.0 0.0 1.0 0.0
"Pretty awesome.. (y)" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8246.0 0.0 0.0 0.0
"Is the problem set somewhere accessible to general public members?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6814.0 0.0 0.0 0.0
"there is nothing wrong with him...he only has a french accent...but goes figures!!! MY mult calc prof sure has a heavy accent!!!" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14764.0 0.0 0.0 0.0
"Speed cannot be negative" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8867.0 0.0 1.0 0.0
"So the independent columns are associated with dependent variables whereas dependent columns give us free variables that can be  arbitrarily assigned in the equation." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 8791.0 0.0 0.0 0.0
"I am gonna watch the whole series. What a great teacher man! 👌 Keep it up." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5097.0 0.0 0.0 0.0
"the man's intelligence x his ability to teach is off the charts! it's sexy and, even better, it makes me want to learn more" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14716.0 0.0 0.0 0.0
"The one person that disliked this didn't get into MIT." UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10210.0 0.0 0.0 0.0
"I guess you simply don't understand it or you don't know/forgot that all of this matrix stuff is an abstraction (or not even that, just a different notation) of solving systems of linear equations. Oh besides, linear algebra is often used to simplify functions in calculus. " 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 5459.0 0.0 0.0 0.0
"lovely blackboard :)" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13888.0 1.0 0.0 0.0
"I wonder that half of students who are taking this class don't even know about Law Cosine." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6247.0 0.0 0.0 0.0
"Olm biliom la bunları ayt mat 40da 40 yapmıştım yani bunlar ezzzz mayonezzzz" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8057.0 0.0 0.0 0.0
"a toin coss" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 12293.0 0.0 0.0 0.0
"The first 34 minutes of this lecture are devoted to a probability problem from lecture 23 that he didn't have time to get to because he answered so many questions during that lecture.  There was NO accompanying reading so far as I know, so this is all there was on this topic.   Probability is supposed to be seen as another example of weighted averages, which WAS in the reading for lecture 23." jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10106.0 0.0 0.0 1.0
"1:04:25 we also cant store the t because t is both exponential and indirectly affected by length of n which means space becomes non-polinomial" cT_qwkTigv4 "17. Space Complexity, PSPACE, Savitch's Theorem" "MIT 18.404J Theory of Computation, Fall 2020" 578.0 0.0 1.0 0.0
"Love it." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 7447.0 0.0 0.0 0.0
"@afjkaf312 Ok, but mathematically, how can you define that? In Differential geometry, an expression like dx maybe means a 1-form. But the ""vector"" (dx,dy,dz) has no sense." seO7-TwXH_I "Lec 30: Line integrals in space, curl, exactness... | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1768.0 0.0 1.0 0.0
"The definition is just brilliant" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 10070.0 0.0 0.0 0.0
"Best video I have watched so far, I was with him all the way and my concentration never dipped." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 2880.0 0.0 0.0 0.0
"at 5:42, wasn't it supposed to be b*d*i rather than b*f*g?" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 12464.0 0.0 1.0 0.0
"Thank you MIT and professor Auroux !" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9139.0 0.0 0.0 0.0
"Thanks a lot sir :-)" mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 9663.0 0.0 0.0 0.0
"really humous,nice guy.wish i can watch this video earlier" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 14252.0 0.0 0.0 0.0
"This teacher sucks. How on earth did he get a job at MIT?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 10941.0 0.0 0.0 0.0
"I Really Like The Video From Your Stokes' theorem (cont.); review." sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4971.0 0.0 0.0 0.0
"A Beautiful Man" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 2092.0 0.0 0.0 0.0
"At 21:20, he says ""I set this delta x to zero."" So just like that? You can just set it to zero randomly? I'm so confused as to why/how it is zero, then magically disappears." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2609.0 0.0 1.0 0.0
"after you learn the math, learn how to teach it." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12311.0 0.0 0.0 0.0
"10:56 ""With new notations comes new responsibility."" ~Auroux" wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 354.0 0.0 0.0 0.0
"Best lecture from India" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2862.0 0.0 0.0 0.0
"Why didn’t he explain method of washers? They mention it in the recitation vid." ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11818.0 0.0 1.0 0.0
"perhaps he applied it to find a living. how about you where you think he put what he learned from MIT....want to say something again. how about you, where you at?" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14179.0 0.0 0.0 0.0
"haha 'If you are European and dont know what sec is...' that made me laugh" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13035.0 0.0 0.0 0.0
رائع UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 15572.0 0.0 0.0 0.0
"Deepest thanks Prof. Strang!!!!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3339.0 0.0 0.0 0.0
"From the thumbnail of this video, I almost thought it was Filthy Frank teaching this course lol. Anyways, awesome video, thanks for the lesson." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3934.0 0.0 0.0 0.0
"Because MIT is just that awesome. Too bad I never heard of the process for applying to US universities. Only 19 people made it to US universities from my country this year. That shows how our country lacks in terms of progress. " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2830.0 0.0 0.0 0.0
Cool QTg7040uSc0 "Lecture 23: The Dirichlet Problem on an Interval" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 3206.0 0.0 0.0 0.0
13:19 VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 409.0 0.0 0.0 0.0
"His classes get u hooked up like its some sitcom that u wanna binge watch." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 4744.0 0.0 0.0 0.0
"So cute mistakes. Love you sir from India 😊😊😊" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8748.0 0.0 0.0 0.0
"U0 == ""you know it""

First time I've heard his boston accent c:" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 11115.0 0.0 0.0 0.0
"@ahmad nadeem ur absolutely right. David jerison assumes many things to be understoos. And he completely is incapable of understanding his students and what should be hard and confusing at their level. For god'sake he couldn't even understand that a student who asked a question had the very basic problem of how negative number is larger or smaller than other negative numbers ie -3 is larger than -4. He is simply a incompetent teacher. I wish they let christine breiner lecture instead of him" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1771.0 0.0 0.0 0.0
"I am  stuck at this point where he finds out the minima and maxima of ax^2+bxy+cx^2 through sum of squares. As per my understanding, to find out the critical point, we need to find if the slope at that point is 0. But, through the quadratic equation, we did not actually find the slope. How was the the critical point determined in that case?" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5049.0 0.0 1.0 0.0
"Thank you MIT. It is helping me to understand the fundamentals of linear algebra." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 9167.0 0.0 0.0 0.0
"Ooooh, I'm excited! This is exactly the sort of course I've been looking for :D" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8127.0 0.0 0.0 0.0
"What happene'd at 18：00？" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11496.0 0.0 1.0 0.0
"Instruction begins at 13:22" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 6718.0 0.0 0.0 0.0
"I find the way he explains the material absolutely amazing!" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 5416.0 0.0 0.0 0.0
"""projectors are trying to be identity, but it's impossible.""" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 170.0 0.0 0.0 0.0
"Sir, Ty for your video.  Easy to understand your teaching, I don't need to go school anymore." IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 8711.0 0.0 0.0 0.0
"Does anyone know to which exact paper by Dr. Jon Kleinberg does Prof Strang  refer to towards the end?" sx00s7nYmRM "26. Structure of Neural Nets for Deep Learning" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3443.0 0.0 1.0 0.0
"He definitely says it backwards at 49:18. I love this guy though" mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 4471.0 0.0 1.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8439.0 0.0 0.0 0.0
"guy in white at 14:39 votes for the both possible answers. He is probably reasoning with quantum physics using the Schrodinger equation, where you can and cannot simultaneously extend a stack of blocks any arbitrary length." wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13023.0 0.0 0.0 0.0
"i literally search oof moment" JTbZP0yt9qc "6. Maximum Likelihood Estimation (cont.) and the Method of Moments" "MIT 18.650 Statistics for Applications, Fall 2016" 13422.0 0.0 0.0 0.0
"Thank you so much.  I now understand how to L'Hop around! " PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9417.0 0.0 0.0 0.0
"I won't pay attention in class, but I'll watch 3 of these in a row and actually make an effort to learn." RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6238.0 0.0 0.0 0.0
"I 8 it" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4919.0 0.0 0.0 0.0
"@planeshaperman Yeah MIT'S signature chalkboards..." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1975.0 1.0 0.0 0.0
"Thank you so much, what an amazing lecture! 23:50 - 24:12 is definitely going in my notes word by word!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 9405.0 0.0 0.0 0.0
"Education for all MIT thanks." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 3551.0 0.0 0.0 0.0
"I Really Like The Video Projections onto Subspaces From Your" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4994.0 0.0 0.0 0.0
"Fantastic lecture!" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 3731.0 0.0 0.0 0.0
"Thank you for this priceless journey to wonderlands of beautiful mathematical structures!" 0_w-R_g5lRA "Lecture 10: The Completeness of the Real Numbers and Basic Properties of Infinite Series" "MIT 18.100A Real Analysis, Fall 2020" 9284.0 0.0 0.0 0.0
"This is amazing. Why am I paying for my current education. I get so much more  from these vids." _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10619.0 0.0 0.0 0.0
"Around 1:02:00 , the instructor mentions that C is complete , meaning that for all x belongs to X,  u(x) = lim u_n(x). What i got confused is that he mentioned that it has a point wise limit(space of continuous bounded functions), however, this would mean given an x, and epsilon, we can find an N, such that u_n(x) converges to u(x). But by completeness of C, it says for every x , un(x) has a limit( isnt this uniform convergence in C)? and if so, doesnt that show uniform convergence in set of bounded continuous functions? Im confused" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 2549.0 0.0 1.0 0.0
"Protect him with all cost MIT" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8452.0 0.0 0.0 0.0
"This lecture is a true masterpiece. I was in awe with the similar feeling of watching suspense thrillers." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 10791.0 0.0 0.0 0.0
"Thank you, Prof. Strang. You made the world a better place" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9512.0 0.0 0.0 0.0
"One question I have here is with the rotation and stretching - if A is a rectangular matrix does it not project  x into a lower or higher dimensional space?" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8106.0 0.0 1.0 0.0
"Any faces with combination Eigenfaces!!!" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 2468.0 0.0 0.0 0.0
"Which book do they refer in MIT? Anyone please tell.(for linear algebra)" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 11706.0 0.0 1.0 0.0
"@ShaneHayes123 This will be a recap before the harder stuff is tackled." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1723.0 0.0 0.0 0.0
"thanks for these lectures" JBIz7UadY5M "14. Regression (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 14586.0 0.0 0.0 0.0
"thank you
was following till 40'57""
how does 2x0y0 = 2    ?

realise this lecture is 13 yo but anyone out there
appreciate any advice
mark" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14472.0 0.0 1.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8419.0 0.0 0.0 0.0
"Prof. David Jerison, i'm glad to have access to his class, thank you from Peru" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8291.0 0.0 0.0 0.0
"can anyone explain to me the sense of the points he makes at the end of every word he writes on the board?" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12602.0 1.0 0.0 0.0
"Double Toin Coss. 25:08" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3489.0 0.0 0.0 0.0
"It will be great if the answer to the psets can be posted same as exams as for studying the way to write proofs!" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 7002.0 0.0 0.0 1.0
好正！！！ 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15622.0 0.0 0.0 0.0
"At 45:30 he describes the ""L"" matrix as ""Lower triangular matrix with 1s on the diagonal"". In this case ""L"" is not exactly lower triangular but a special form of lower triangular matrix. Isn't it? Because I think the diagonal of lower triangular matrix doesn't have to consist of 1s ..." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 2680.0 0.0 1.0 0.0
LOL srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 7229.0 0.0 0.0 0.0
"How many black boards does this guy have?!" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 4882.0 1.0 0.0 0.0
"can someone explain to me, why we cant think of two coin flips as two connected experiments instead of just one ?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 12624.0 0.0 1.0 0.0
thanks! srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 14610.0 0.0 0.0 0.0
"What sort of camera do they use........YOu get sucha gud picture when zoomed in" wu8kXZSAp20 "Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 11552.0 1.0 0.0 0.0
"46:00 about the Taylor expansion. Why is it always that students think that you don't need previous course information to go through the next course? I remember in highschool on physics when we've had the mechanics and started thermodynamics. Then on the mid term there was a question that how high a sentimeter cube of ice at temperature -1 degree of celsius should be dropped so that it would melt on impact. Of course all was taken in vacuum. More than half failed that question and complained that why is the motion formulas needed in calculating thermodynamics. What morons." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1265.0 0.0 0.0 0.0
"I wish he had covered hypothesis testing of parameter estimates !" lWW54ts9Ubo "24. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 6218.0 0.0 1.0 0.0
"Who else watches these at 2x??" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11734.0 0.0 0.0 0.0
"love the accent, great video
" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13872.0 0.0 0.0 0.0
"Awesome quality" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2766.0 0.0 0.0 0.0
"We used m,n, and p." tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11335.0 0.0 0.0 0.0
"Lectures with my prof feel like fistfighting a grizzly bear, lessons with gilbert feel like being sung a lullaby by celine dion" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 7308.0 0.0 0.0 0.0
"@ashishkrrai further, don't  give such nonsense reply  to such interesting video." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1786.0 0.0 0.0 0.0
"@NothingPersonalTA no it cant be as the pivots are the elements in the diagonal of the matrix." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 1693.0 0.0 1.0 0.0
"Why, because they'are not finished with writiing it down on their papers ..." _CdoRiNSrqI "Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11941.0 0.0 0.0 0.0
"I'm smart." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6370.0 0.0 0.0 0.0
"@mdgreg , Looked At What I Said, Pretty Stupid." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1941.0 0.0 0.0 0.0
"An awesome professor💗" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2437.0 0.0 0.0 0.0
"This course is awesome!" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10491.0 0.0 0.0 0.0
"Very nicely acting as if students are watching." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11223.0 0.0 0.0 0.0
"damn, I thought the first draft was an Italian bread, lol... Honestly I have to go over this stuff in maybe two years from now and I was trying to get ""in-touch"" whit this stuff....REALLY CRAZY" sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12714.0 0.0 0.0 0.0
"at 33:00, in Y=1 universe, f(x)dx=P(x) where dx=1, P(x)=1, therefore f(x)=1, now var(X|Y=1)=integral of ((x-E[X|Y=1])^2*f(x)) from 0 to 1. . that's how he got 1/12. and similarly for Y=2 universe..Is this correct?" P7a4bjE6Crk "12. Iterated Expectations" "6.041 Probabilistic Systems Analysis and Applied Probability" 12441.0 0.0 1.0 0.0
"أول عربية استاد رائع و بناء جميل لدرس" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15564.0 0.0 0.0 0.0
"I am intoxated by just the name of MIT! I am intensely in love with MIT! I am not just rich enough to be known as part of MIT! And also smartness..wel..I just dont work as hard...." MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5110.0 0.0 0.0 0.0
"I am wondering why Strangs vectors 1 2 3 4 and 1 1 1 1 and 2 3 4 5 are a good example because the 3rd vector 2 3 4 5 is the sum of 1 2 3 4 and 1 1 1 1. I think this is a shit example. and nobody pointed this out in class. which is no surprise. Everybody in class is in a coma already." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 5157.0 0.0 1.0 0.0
"34:00 ,I just wanted to mark this point for future reference" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 974.0 0.0 0.0 0.0
"MIT is going for 1000 contributors (any amount) until June 28th.
If anyone reading this has not donated, then pls care do so at below URL. 
Participation Drive 721 Donors 72% Towards goal of 1,000 Donors  $39,710.00 Raised 4 DAYS LEFT.
FYI: I am NOT affiliated in any way. I actually graduated from a competing institution on the West Coast. Just showing appreciation by posting this.
https://crowdfund.mit.edu/project/15796?utm_source=ocw&utm_medium=overlay&utm_campaign=2018ocw500&utm_content=hex" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 7528.0 0.0 0.0 0.0
"I cannot thank you enough for this clear, insightful lecture. It is very inspiring that you are calling the matrices ""beautiful"", and I can feel your love for them :) For me your lectures are beautiful." rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5231.0 0.0 0.0 0.0
"This is what I was looking for. Mamy thanks MIT." k2inA31Gups "18. Bayesian Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 10770.0 0.0 0.0 0.0
"those MIT blackboards are like Hogwarts...secret boards out of nowhere" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 14931.0 1.0 0.0 0.0
"Mind is now blown" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7668.0 0.0 0.0 0.0
"why is E[X^2] equal to the sum of all the X^2 plus the sum of all X_i and X_j (at minute 45)" EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 15324.0 0.0 1.0 0.0
"very articulate :)" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14996.0 0.0 0.0 0.0
"What's the connection between differentials/total differentiation and the implicit function theorem or implicit differentiation?" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11577.0 0.0 1.0 0.0
"This is incredible. First time seeing Markov Chains, and I can't believe I never took the time to check it out. Plugging in the Poisson blew my mind." HIMxdWDLEK8 "18. Markov Chains III" "6.041 Probabilistic Systems Analysis and Applied Probability" 10678.0 0.0 0.0 0.0
"each side has a different audio, one from microfone and another from the hall(something like that).
BAD idea" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12786.0 1.0 0.0 0.0
"This video is a masterpiece!!!" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 10951.0 0.0 0.0 0.0
"Love this guy! Thank you so much!
" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 7457.0 0.0 0.0 0.0
"Monkeyrunky, you're misunderstanding the point of MIT.

Some of the material taught in MIT is really the same as in other universities. In fact, vectors are taught in many high schools already. 

MIT definitely exceptional. I haven't been there myself, but you can see for yourself if you do ever attend it." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7691.0 0.0 0.0 0.0
"One person disliked this video because he realized once 3d flux was explained excellently he still didn't understand it" WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8103.0 0.0 0.0 0.0
"I am grateful for utilizing your gift masterfully ^ beautifully. Thank you Mr. Gilbert Strang!!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5100.0 0.0 0.0 0.0
"4:10 Can G₁ be simplified to S → 0S1 | ε?" m9eHViDPAJQ "4. Pushdown Automata, Conversion of CFG to PDA and Reverse Conversion" "MIT 18.404J Theory of Computation, Fall 2020" 1313.0 0.0 1.0 0.0
"Why does it seem like sometimes the square of a matrix is seen as AA and other times it's seen as A^TA?" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 11841.0 0.0 1.0 0.0
"I really don't know what to say..... Satisfying? Grateful? OMG I just love it!!!!" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 5908.0 0.0 0.0 0.0
"i am like schmdit in my group projects." 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 13335.0 0.0 0.0 0.0
"Prof Strang...my respects sir..." NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8277.0 0.0 0.0 0.0
"isnt this like constructing an iteritve formula for approximating the root?" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13669.0 0.0 1.0 0.0
"Thank you, Professor! Elimination matrix inverses are one thing that I admire about this video. They are so intuitive to construct now." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 9516.0 0.0 0.0 0.0
"Increasing the speed to 1.5 to 2x makes this really interesting :)" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6701.0 0.0 0.0 0.0
"Using the radar example instead of talking in ""math speak"" helps so much!!" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 11139.0 0.0 0.0 1.0
"I see that this professor does not take question in class. .  Maybe if you email him." xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5960.0 0.0 0.0 0.0
"immortal in 2020!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 13573.0 0.0 0.0 0.0
"Interesting that nobody on the first row of seats looked like taking notes." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 6731.0 1.0 0.0 0.0
"The graphic quality is really sucks but the lecture is good" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10126.0 0.0 0.0 0.0
"it took 5 months to my teacher to explain this 30 minutes video" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13683.0 0.0 0.0 0.0
"Just finished. Absolutely loved the series. Is there any series for Abstract Algebra too?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7181.0 0.0 1.0 0.0
"This is like a post-apocalyptic scene, where all other humans are gone and Gilbert is the only person left alive. He still does his lectures for an empty class because he has gone insane X)

I just want to be clear: I love Strang and this video series. It helped me pass a course on visalization <3" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 10684.0 0.0 0.0 0.0
"Ok two things. First - That is one giant piece of chalk. Second - To be able to lecture this well with nobody sitting in front speaks volumes about the qualities of this great teacher." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 8048.0 1.0 0.0 0.0
"patrick JmT teaches better than this dr." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14169.0 0.0 0.0 0.0
"@yyttr4 , well I have a different theory about it, I don't think everybody have the same knowledge or intelligence, I am all for happiness, it will make me happy to have a big farm and all kind of animals with me roaming free in the plains, also to have  beautiful women with my babies, but none of these is true, instead I study math and buid from nothing an abstract theory which sometimes is false, then computers come along with electronics, which is the only rational true machine we have." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2078.0 0.0 0.0 0.0
"This lecture is gonna be a little ambiguous at first BUT once you have a firm grip on the previous lectures from 18.06, you’ll surprisingly realise it is the most beautiful lecture on SVD available in all of YouTube." TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 10802.0 0.0 0.0 0.0
"haha, some magic happens" YAo1sd4kuOQ "2. Forbidding a subgraph I: Mantel's theorem and Turán's theorem" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 13048.0 0.0 0.0 0.0
"Wonderful course" u4qQ1oIQcW8 "Lecture 25: Power Series and the Weierstrass Approximation Theorem" "MIT 18.100A Real Analysis, Fall 2020" 11984.0 0.0 0.0 0.0
"I am completely lost in the last two lectures" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 5070.0 0.0 0.0 0.0
"Oh, so you kids find calculus to be too easy ?  

Should any of you be able to find the general theorem for integrating a system of n variables/n dimensions by yourselves then yes, MIT is too easy for your level." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8031.0 0.0 0.0 0.0
"Ok. You can touch the tangient point you find the fourt dimension.....:)
It`s a short way to the another galaxy.:)


" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8051.0 0.0 0.0 0.0
"Was the sentence at 9:21 supposed to be “Columns of C are combinations of columns of B”  instead of “Columns of C are combinations of columns of A” since he said that First column of C is equal to A*(B col1). And was the sentence at 11:12 supposed to be “Rows of C are combinations of rows of A” instead of “Rows of C are combinations of rows of B” ???" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11278.0 0.0 1.0 0.0
"Nice .....

Very nice explaination sir....
Brilliant" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7837.0 0.0 0.0 0.0
"At first this guy's style seems awkward and clumsy but then 30 minutes later you realise he's sucked you in completely and totally mesmerised you. Amazing teaching." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2712.0 0.0 0.0 0.0
"Whew! Just finished the whole single variable Calculus course (Calculus I/II)!  That is time to take Calculus III (multi-variable Calculus)....." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11703.0 0.0 0.0 0.0
"I didn't really understand what he said around 37:42. Can someone please clarify a little bit? Thank you!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5277.0 0.0 1.0 0.0
"I really miss the 18.01 lecturer David Jerison. I don't think this guy explains concepts very well." 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5931.0 0.0 0.0 0.0
"I like this passion by teaching math 😍
Thank you for this nice example of teaching math in the best way 🤓" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5690.0 0.0 0.0 0.0
"38:10
Go Sex" aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1076.0 0.0 0.0 0.0
"If anyone is interested in a better lecturer than david. Then check out herbert gross lectures. He is a truly genious educator of math. His videos are the black and white ones but do not be discouraged by the age of the videos. The quality is superb,the cameraman focuses on the board and mr gross will make you fall in love with calculus" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6495.0 1.0 0.0 0.0
"i think i've fallen in love" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13473.0 0.0 0.0 0.0
"The problem u not agreeing with the equation is that, after sigma and V have been determined, we no longer have freedom in constructing u. The u obtained with AA^T is still valid, but require different arrangement of sigma and V to accommodate. u has to equal [1 0; 0 -1] to agree with the sigma and V pair." TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 10239.0 0.0 1.0 0.0
"love this course" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 13878.0 0.0 0.0 0.0
"the 7 dislikes are wierd.. cus if you like math i dont understand why you wouldnt like the video... and if you dont like math... why the hell would you view it?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14657.0 0.0 0.0 0.0
"Linear approximation is the first order fit - i.e. tangent plane approximation. See previous lecture.
Let z ~ z0 + fsubxat(x0) *(x-x0) + fsubyat(y0) * (y-y0). Pardon terrible notation." 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7382.0 0.0 0.0 0.0
"He's wearing the same shirt and pants as in Lecture 1" BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4649.0 0.0 0.0 0.0
"I think professor Strang made a slight mistake @ 23:23 , it should be check q_1^T A_2 = 0 not q_1^T a_2 = 0" MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6038.0 0.0 1.0 0.0
"Genius 👏👏👏" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3998.0 0.0 0.0 0.0
"really like this class" QXkOaifVfW4 "9. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 14255.0 0.0 0.0 0.0
"I can never draw a 4-dimensional space on a 2-dimensional blackboard. It would look wrong no matter how I do it. (There is a vector perpendicular to an entire 3-D universe?)" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 5192.0 0.0 0.0 0.0
"Than you Professor Strang for your compromise with education !!!!!!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9039.0 0.0 0.0 0.0
"Thank you!" a1ZCeFpeW0o "20. Principal Component Analysis (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 9475.0 0.0 0.0 0.0
"God bless this teacher and MIT...I'm gonna be King -- I'm learning this....hehehe...I'm gonna rule the universe...and go to Mars...hehehe" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4082.0 0.0 0.0 0.0
"go professor strang!!!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12925.0 0.0 0.0 0.0
"do me a favor...evaluate:
double integral of e^(y^2)dydx with the limits on the inner integral being: lower =
3x, upper = 3; limits on the outer integral being: lower = 0, upper =1." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12752.0 0.0 1.0 0.0
"Yeah theres an equivalent notation in the function notation two but it contains parentheses f^(2) (x)  (the 2's little), yeah nothing much, just thought it was funny, but it does happen- smart people can derp moment sometimes XD. " TpWQlKHPyJ4 "Lec 31 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12121.0 0.0 0.0 0.0
"What's this guy's name? 
" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11588.0 0.0 0.0 0.0
"Completely lost with this lecture.   " BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 3188.0 0.0 0.0 0.0
"@DNYAP Exactly, thats the geometric way of seeing it.
In fact for very small numbers you can aproximate with low error sin(x)=x
Thats part of the Taylor Polinom" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1610.0 0.0 0.0 0.0
"Saddle Points in 4D example at 6:30 and 16:30😃. This reminds me of the cover of the book ""Linear Algebra and Learning from Data"", the man with hat actually steps on the saddle ""ring"" of the net cage, which is also the most ""comfortable"" point to step on. Thanks a lot, Professor Strang!!" 2K7CvGnebO0 "19. Saddle Points Continued, Maxmin Principle" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8588.0 0.0 0.0 0.0
"Excellent. It is so to the point and brilliant. It is like a diamond!" 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 3693.0 0.0 0.0 0.0
"33:50 for Numerical integration" jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 969.0 0.0 0.0 0.0
"Best explanation of the subject I have seen. The camera man is really good too and the chalk and the boards are easy to read.." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2859.0 1.0 0.0 0.0
"Wow, this professor gave a full review!" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12077.0 0.0 0.0 0.0
"My lecturer in Linear Algebra was pretty good at doing mathematics but he was not so good at explaining it. I have really enjoyed these lectures and came back to the start just to encourage others to watch and enjoy." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7764.0 0.0 0.0 0.0
"what's the sample space, experiments of Markov Chains? 
If Markov Chains has two steps, is the experiment of the first step the same as the experiment of the second step?" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 15197.0 0.0 1.0 0.0
"1:00:00 shouldn't it be 1-P(Z<(-mean/sigma))" TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 570.0 0.0 1.0 0.0
"that is just bullshit  this lecture suck eventhough its mit lecture cuz u can simply feel   We see vectors but  why did old people that lived in past feel vector necessary to find  the thing they called as vector subject  what does applications exist to use vector for real life  ur specifying a thing equals  to onether thing but ur not saying Why it is like that or  proof of that so  i didnt like" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14634.0 0.0 0.0 0.0
"the professor is not only brilliant but humorous!" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 14728.0 0.0 0.0 0.0
"Why do they teach derivatives before limits in MIT? Aren't limits the basis for both differential and integral calculus?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11827.0 0.0 1.0 0.0
"15:36 where does he pull these numbers out from ?" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 455.0 0.0 0.0 0.0
"Completed the course just now , it was amazing 
Orz to the prof" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3182.0 0.0 0.0 0.0
"A lot equivalent propositions here, prof strang beautifully demonstrated that they are all connected with the basic eliminations process, it helps a lot." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 2135.0 0.0 0.0 0.0
"""The thing is I like students, I like math, and putting them together is just the best job in the world."" (G.Strang)" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 125.0 0.0 0.0 0.0
"type ""html5"" after youtube in the address bard and then click the button next to the html5 trial (it'll be by the bottom of the screen). It makes most of the videos have the option of playing at 1.5 or 2 times the speed. :D 
" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14968.0 0.0 0.0 0.0
"The prerequisite for this course is 18.06 Linear Algebra. For more information and course materials, see MIT OpenCourseWare at: https://ocw.mit.edu/18-065S18." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10232.0 0.0 0.0 0.0
"He made dA/dx = 0 because that´s the way to find the critical points." YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4577.0 0.0 0.0 0.0
"Thank you Dr Strang for the amazing videos. I love the way you explain things so simply. Most of my teachers at University fail to explain simply things. They go into big terms while the basics is tough. With your videos I barely attend my classes but I am able to nail my exams. Thank you again!!" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 9098.0 0.0 0.0 0.0
"Thank you very much, from the bottom of my heart, Professor Strang! It took me around 40 days to finish this course. I learned an incredible amount, and I feel just as happy to have finished it as I am sad that it's over. It feels like finishing a very good, long and satisfying book. I'm studying meteorology, so I don't need the follow up courses for engineers, but you inspired me so much that I will watch them in my free time to solidify my understanding of linear algebra." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9454.0 0.0 0.0 0.0
"at 27:40 , how we got -3 1 0 in second column?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12432.0 0.0 1.0 0.0
"these operations it's like wizardry" or6C4yBk_SY "Lecture 2: Multiplying and Factoring Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14781.0 0.0 0.0 0.0
"Nu/Mu +-1" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7963.0 0.0 0.0 0.0
"@Djole0  ""It is the second semester in the freshman calculus sequence"" " UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1616.0 0.0 0.0 0.0
"How many are watching just for fun here? 🙋‍♂️" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4881.0 0.0 0.0 0.0
"Funny how the writer of the book I have on my left is also giving me a lecture at the same time." m9eHViDPAJQ "4. Pushdown Automata, Conversion of CFG to PDA and Reverse Conversion" "MIT 18.404J Theory of Computation, Fall 2020" 3961.0 0.0 0.0 0.0
"Thank you so much for putting analysis online!" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 9364.0 0.0 0.0 0.0
"@DaisyLouLaCaz Yea it was a lame joke. As a part-time teacher I can tell you these jokes never work least of all in the beginning of class. But A for effort lol" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1611.0 0.0 0.0 0.0
"Professor Strang - thank you for the amazing lectures and all the insights that you share with us!" p-bXJIa7QVI "Lecture 30: Completing a Rank-One Matrix, Circulants!" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8341.0 0.0 0.0 0.0
"What the hell kind of multivariable calculus course is this? thats 3 full lectures on vectors and 1 so far on matrices..." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11560.0 0.0 0.0 0.0
"I actually passed my 3 Applied Linear Algebra courses with flying colors by just remembering all these results because the lecturer never tried to explaine what's happening behind the scene. So after almost 20 years I'm still here trying to figure out what's what. I shoulda gone to MIT." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 5019.0 0.0 0.0 1.0
"Words can't describe how important it is for a mathematics lecturer to have passion in providing clarity with his explanations." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11998.0 0.0 0.0 0.0
"when r< m, n, i.e. the last case in the summary board, can it have exactly one solution?" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 15210.0 0.0 1.0 0.0
"Unwatchable due to random unnecessary camera changes, such a shame. Seemed like it was gonna be an awesome lecture" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11128.0 1.0 0.0 0.0
"https://www.youtube.com/channel/UCd9MR3W9EGwicP6fTJQN5Gw/videos     Here is a helpful playlist for you to revise linear algebra quickly. Do like, share and subscribe for more such content!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13266.0 0.0 0.0 0.0
"Thanks for this great video Prof Jerison/MIT." BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9731.0 0.0 0.0 0.0
"@1:16:00 what is convergence in l2, why does it imply convergence in probability" TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 1507.0 0.0 1.0 0.0
"Theorem: The world is smooth
Proof: it is QED
Now, an example...
😜" 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10343.0 0.0 0.0 0.0
"for some reason he reminds me of Jude Law" 9BYsNpTCZGg "Lecture 17: Rapidly Decreasing Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12886.0 0.0 0.0 0.0
"8:45 that girl eating" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1424.0 0.0 0.0 0.0
"33:39 Maximum Likelihood Estimation" rLlZpnT02ZU "4. Parametric Inference (cont.) and Maximum Likelihood Estimation" "MIT 18.650 Statistics for Applications, Fall 2016" 965.0 0.0 0.0 0.0
"48:04...""Thank you, God"".  I love this man." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 1289.0 0.0 0.0 0.0
"How is that 2dimenisonal  subspace of R4?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 4872.0 0.0 1.0 0.0
"دكتور من اروع ما يكون" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 15571.0 0.0 0.0 0.0
"By column picture, professor plot each of 3 columns and also b for 1st example case, but did not tell about solution point (x,y,z)=(0,0,1). But he pointed out in row picture that all three planes intersect a point and it is (0,0,1) but difficult to locate by this row picture way! That’s why reverend professor present it in column picture way. Did I missed something? Please anyone help me out. Thanks" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 2970.0 0.0 1.0 1.0
"""three person game"" !" feb9j65Iz4w "24. Linear Programming and Two-Person Games" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 183.0 0.0 0.0 0.0
"The courses I took in my local university were just theorem then proof proof proof. Zero explanation of why we even wanted to do this, nor ANY attempt to associate linear algebra to anything in the real world.  All students sat quietly and I wondered anyone would be able to point out anything wrong on the whiteboard.

One reason an university becoming world class is because of their enthusiastic and motivated teachers and students!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 10064.0 0.0 0.0 1.0
"hello Sir please guide me 
First of all
Which book I read during taking this course???
Assignment reference provide me" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13134.0 0.0 0.0 0.0
"i certainly like the humor this professor incorporates. makes me giggle lol." ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13351.0 0.0 0.0 0.0
"I accidentally clicked into this, and watched it. I was supposed to watch Yoona's Big Mouth on Disney+. Thanks Prof Strang for the knowledge." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5010.0 0.0 0.0 0.0
"Math has consumed this man, and whats left of him is pure logic and extraordinary teaching skills." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7605.0 0.0 0.0 0.0
"I am quite enjoying his accent." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5133.0 0.0 0.0 0.0
"God bless you profesor!" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4083.0 0.0 0.0 0.0
"I am controlled by the combination of FFT and linear algebra...." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 5078.0 0.0 0.0 0.0
"nice one" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14046.0 0.0 0.0 0.0
"My exam is the day after tomorrow. Thanks MIT" ZulMqrvP-Pk "17. Markov Chains II" "6.041 Probabilistic Systems Analysis and Applied Probability" 7747.0 0.0 0.0 0.0
"@phtotti It is quite possible you learned it in highschool... but more than likely a simplified version. Calculus theories like limits, derivatives, integrals...etc can be taught at a lower level math if you skip the details of the how and why. In college you need to learn those things that they left out so that you can move on in math. Try taking a college level math class in differential equations with only a base level understanding of calculus." 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1971.0 0.0 0.0 1.0
"11:10 That person if munching a sandwich" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 365.0 0.0 0.0 0.0
"You have to admit that this course makes you realise youtube comment sections can be good too!" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12211.0 0.0 0.0 0.0
"arctanx graph is wrong, it never intersects tanx" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12396.0 0.0 1.0 0.0
"Is Prof Strang saying here at:  https://www.youtube.com/watch?v=NcPUI7aPFhA&list=PLUl4u3cNGP63oMNUHXqIUcrkS2PivhN3k&index=10&t=47m36s that this big idea is that  all of the matrix norms are really norms of the matrix Sigma, for Sigma in SVD (A) = U (Sigma) V^t ???" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6753.0 0.0 1.0 0.0
"@Echtellou It's the FIRST lesson...How long did you study in school until this? DO YOU GET IT?! :O" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1617.0 0.0 0.0 0.0
"Why probability of arrival  for k>1 in time delta is zero.?" jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 11906.0 0.0 1.0 0.0
"then having such superior intellect go do something useful in society and stop wasting your time watching a youtube video about something you learned in the 8th grade." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14755.0 0.0 0.0 0.0
yes 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15480.0 0.0 0.0 0.0
"I've my linear algebra class early in the morning, and I never make it to the class
was frustrated to catch up all this stuff but watching these videos are helping me so much
Sincerely thank professor Strang and this channel!" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 6423.0 0.0 0.0 1.0
"multivariable? more like two-or-three-variable" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13967.0 0.0 0.0 0.0
"This guy was a Rhodes scholar." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10563.0 0.0 0.0 0.0
"What a beautiful, humble human being!. He is such an amazing professor" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11391.0 0.0 0.0 0.0
"Calculus is around from times  of Newton.  However, I see tempo  alive today. Amazing to see how language has evolved. New terms and reasoning  is more enjoyable. We missed exam review in sixties. Let new generation enjoy cumulative knowledge Over years. Sir, decide everything. So old and young both enjoy and make it user friendly.
DECODE INSTEAD OF  DECiDe" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2986.0 0.0 0.0 0.0
"I like this professor" _CdoRiNSrqI "Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5691.0 0.0 0.0 0.0
"At 0:22; you need a better duster" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 2580.0 1.0 0.0 0.0
"43:46 To prove intersection of 2 convex sets is still convex, I think x1, x2 are both in K1, then since K1 convex, any line from x1 to x2 are also convex. We don't need to consider whether K2 is convex or not. Am I correct?" nvXRJIBOREc "Lecture 21: Minimizing a Function Step by Step" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1219.0 0.0 1.0 0.0
"The instructor’s name on the beginning screen is not “substituted.” lol" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10142.0 0.0 0.0 0.0
"dinh sang tieng viet di
" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12747.0 0.0 0.0 0.0
"Solid material, but what is happening with the camera pans?" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 8818.0 1.0 0.0 0.0
"To make it a bit less confusing when subtracting rows, I like to just say R2-3R1 (row 2 vs 3* row 1). Easier to imagine for me and this was the way it was taught to me." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11040.0 0.0 0.0 1.0
"Great Lecture, boiled down to simplicity :) Thank you prof." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 4204.0 0.0 0.0 0.0
"sound quality can be improved." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 14384.0 0.0 0.0 0.0
"From pre-algebra in Junior HIgh

x=.99999999999999999
10x = 9.999999999999999
10x - 1 = 9
9x=9
x=1
QED" zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3931.0 0.0 0.0 0.0
"instead of using a Taylor approximation to determine the behavior of the cycloid at theta=0, couldn't you just use L'Hospitals rule to determine the limit at that point. Using L'Hospitals rule once, I got 1/0 which is infinite. Is this a coincidence or no?" 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13612.0 0.0 1.0 0.0
"Pure math is boring af" 9_xG0AGRa-w "Lecture 2: Cantor's Theory of Cardinality (Size)" "MIT 18.100A Real Analysis, Fall 2020" 8462.0 0.0 0.0 0.0
"superb lectures and glad these are posted in youtube for free. great job mit." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14422.0 0.0 0.0 0.0
"25:17 Is it necessary for those vectors to be orthogonal to satisfy the projection?
Let's say c is 0. That means that vectors x1 and x2 are in the nullspace of P because they both have eigenvalue 0. Within this subspace, I can pick any two vectors as my eigenvectors, even if they're not orthogonal, can't I?" HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 775.0 0.0 1.0 0.0
"This guy is a fantastic teacher." QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 10514.0 0.0 0.0 0.0
"1~2:38. Important: the self-driving vehicle must know, hit pedestrians, don't hit telephone poles." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 607.0 0.0 0.0 0.0
"45:12  Paraphrasing (and trying to cast it in the best light), here's what I heard:

Given a function whose derivative f'(x) exists at x0, prove that the function is continuous at x0.

1. By definition,  a function f(x) is continuous at the point x0 iff the lim as x->x0 of f(x) is equal to f(x0).
2. Stated equivalently, a function f(x) is continuous at the point x0 iff the [lim as x->xo of f(x)] -  f(x0)  is equal to zero.
3. So Let Z = [the lim as x->x0 of f(x)] - f(x0)  (and we'll see if we can get it to come out zero somehow).
4. Z = [the lim as x->x0 of f(x)]  -  [the lim as x->x0 of f(x0)].
5. Z = the lim as x->x0 of [f(x) - f(x0)].
6. Z = the lim as x->x0 of [f(x) - f(x0)] *  { [lim x->x0 of (x-x0)] / [lim x->x0 of (x-x0)] }.
7. Z = the lim as x->x0 of { [f(x) - f(x0)] / [lim x->x0 of (x-x0)] } *  [lim x->x0 of (x-x0)].
8. Z = the lim as x->x0 of { [f(x) - f(x0)] / (x-x0) } * [lim x->x0 of (x-x0)].
9. Z = f'(x0) * [lim x->x0 of (x-x0)].  (a critical step.  it removes the divide-by-zero conundrum.)
10. Z = f'(x0) * 0.
11. Z = 0.

Therefore, Given the existence of f'(x0),  which makes step 9 possible, the [lim as x->xo of f(x)] -  f(x0)  is equal to zero, and consequently the given function is continuous.

This is proof by demonstrating that the hypothesis plays an indispensable role in the conclusion.  Not my favorite method (by far!), but in the absence of a review of the algebra of absolute values and in the absence of an introduction of the epsilon-delta definition of a limit, I can't see how else the professor could have done it.

This course will be challenging to me in ways the authors never intended.  :)" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1250.0 0.0 0.0 0.0
"Sir I would like you check my video  in math... about ""Bernoulli numbers, Solution to solve areas under any polynomial step function..

" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8693.0 0.0 0.0 0.0
"thanks a lot for the series of videos. i hope MIT  will continue to help people understand the mathematical knowledge." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14570.0 0.0 0.0 0.0
"That's what I call a good teacher!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9946.0 0.0 0.0 0.0
33:00 VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 948.0 0.0 0.0 0.0
"The ""c1+c2+c3"" method is def better!" seO7-TwXH_I "Lec 30: Line integrals in space, curl, exactness... | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9953.0 0.0 0.0 0.0
"This man is a literal God at teaching linear can he please teach my lecturer how to teach." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 10858.0 0.0 0.0 0.0
"I wish he could have explained better how it is that the angle QPR is theta. He was just like ""you flip it over 90 degrees and there you go."" There was barely any explanation of how it is that those triangles are similar! I had to pause the video, draw my own picture, and stare at it for half an hour to figure it out." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6217.0 0.0 1.0 0.0
"What a brilliant man.. I wish I had a teacher like that in all my courses!" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 11398.0 0.0 0.0 0.0
"i just got a rather low grade in my class, wish i spent more time watching his videos..." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 13405.0 0.0 0.0 0.0
"Well, you've convinced me of the autism at least." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11373.0 0.0 0.0 0.0
"@Merky2k you can use gradients and stuff in economics to work out when you 'break even' if you are selling something " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1674.0 0.0 0.0 0.0
"lecture 15 and up is on integration" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13770.0 0.0 0.0 0.0
"In the last example, aren't GB and BG are same? Does order matter?" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 6672.0 0.0 1.0 0.0
"Joe Pesci.." 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 7137.0 0.0 0.0 0.0
"I love Gilbert <3" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 5715.0 0.0 0.0 0.0
"John Tsitsiklis is a God. He exemplifies what amazing teachers are. Grateful beyond words." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 7138.0 0.0 0.0 0.0
"from 44:51 LOL" QuZL5IKpO_U "24b. Quiz 2 Review" "MIT 18.06 Linear Algebra, Spring 2005" 12900.0 0.0 0.0 0.0
"Imagine giving this video a thumbs down. Who does that" osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 6583.0 0.0 0.0 0.0
"My dream is MIT
I am from Bangladesh" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 7745.0 0.0 0.0 0.0
"""Euler again ! that guy never stopped""" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 45.0 0.0 0.0 0.0
"Thank you so much. I study at HKU, and our lectures are not 1/2 as good as these ones. Honestly, without YouTube videos, I think, we would have been in big trouble." H_k1w3cfny8 "10. Continuous Bayes' Rule; Derived Distributions" "6.041 Probabilistic Systems Analysis and Applied Probability" 9410.0 0.0 0.0 0.0
"32:36 anyone notice that he did not say that ? :D" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 932.0 0.0 1.0 0.0
"is there any way to change the bounds of integrations without drawing? because most of the times it wont be so easy to draw. (or i wont have the time to do it)

cant i just plug in the bound values into the change of variable's equations or do some other calculus?" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13653.0 0.0 1.0 0.0
"Does anyone else really like the yellow chalk at 13:37 ?" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3436.0 1.0 0.0 0.0
"at 12:08 in transcript it says ""OK. A word of warming,"" It should be ""warning."" haha" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12412.0 0.0 0.0 0.0
"Waiting eagerly for 18.100B !!" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 11266.0 0.0 0.0 0.0
"1:42 ""The idea of elimination ... I mean you would have thought of it .. Gauss thought of it before we did only because he was born earlier which is natural idea .. ahh .. died earlier too"" ... ROFL! This prof has a geeky sense of humor ..." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 598.0 0.0 0.0 0.0
"Dayum, stuff makes sense" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 3320.0 0.0 0.0 0.0
"Someone know why the x1 in he nullspace is (1 0) and not (0 1) as he said 26:36." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 8837.0 0.0 1.0 0.0
"they learn the general derivate formula at the mit, whats next :(" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14784.0 0.0 0.0 0.0
"is there a book we are supposed to refer to?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 13649.0 0.0 0.0 0.0
"For the curious:

F_100 = (a^99 - b^99) * b/sqrt(5) + a^99 , where a = (1 + sqrt(5))/2 and b = (1 - sqrt(5))/2 are the two eigenvalues of our system of difference equations.

Numerically, F_100 = ~3.542248482 * 10^20 ... it's a very large number that grows like ~1.618^k 😲

Overall, great lecture Professor Strang! Thank you for posting, MIT OCW ☺️" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 3885.0 0.0 0.0 0.0
"pueden poner por favor subtitulos en español" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 14229.0 0.0 0.0 0.0
"Professor Strang is absolutely amazing! The best math teacher I have ever seen!" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8348.0 0.0 0.0 0.0
"Big shaq" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 2893.0 0.0 0.0 0.0
"Unit circle, p=1." RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11125.0 0.0 0.0 0.0
"The choice you can make at a stage multiplied by each other." 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 10043.0 0.0 0.0 0.0
"Thank you professor! I am amazed by the fact that professors from top institutes like MIT explain the mere basics without any expectation that we are supposed to know those topics earlier. On the other side our university professors just avoid the whole thing by saying ""it isn't the part of syllabus, you are expected know this already"". A huge salut and thanks to professor Strang and MIT team for publishing these videos free of cost." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9326.0 0.0 0.0 1.0
"THIS IS A STUPID LINEAR ALGEBRA." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 8994.0 0.0 0.0 0.0
"This guy teaches as if he is having an argument with himself in his mind & finally 1 part of the mind speaks out .." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10562.0 0.0 0.0 0.0
"I don't understand where delta squared multiply norm x squared come from ? why it help us fix problem ?" Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 5349.0 0.0 1.0 0.0
"Thank you professor!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9325.0 0.0 0.0 0.0
"this is really amazing" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 14870.0 0.0 0.0 0.0
"Could somebody please explain to me what fast way they used to find the dimension of the subspace S (all v's in R^4 with v1+v2+v3+v4=0)? in 30:20" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 3231.0 0.0 1.0 1.0
"FaZe Strang" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3723.0 0.0 0.0 0.0
"Awesome, thanks!" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2786.0 0.0 0.0 0.0
"Nice licture #civilsquad" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7852.0 0.0 0.0 0.0
"great lecture..I really learned many things." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12990.0 0.0 0.0 0.0
0_0 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 311.0 0.0 0.0 0.0
"Xparticular is calculated by setting all the free variables to zero. But in case, when rank=n, there wont be any free variables. How to find the Xparticular in this case?" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 12101.0 0.0 1.0 0.0
"I’m really glad i didn’t give up and came this far, thank your Prof. Strang" nrDkb2MAwSA "20. Definitions and Inequalities" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7115.0 0.0 0.0 0.0
hi MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13154.0 0.0 0.0 0.0
"Lesson doesn't start until around 25:00" 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 7329.0 0.0 0.0 0.0
"Simpson came before Riemann , how come his method is more accurate ?" zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8673.0 0.0 1.0 0.0
"Ohh God! I am following his course now and how good is he. The best. Seeing him getting old is so sad. Love from India." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8036.0 0.0 0.0 0.0
"Exellent class" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3701.0 0.0 0.0 0.0
"My way to make myself feel good: 2X speed + occasionally press →" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7796.0 0.0 0.0 0.0
"An Indian edition of this book is available only in India
http://www.wellesleypublishers.com/buy.html" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 2419.0 0.0 0.0 0.0
"thank you very much. this is a very good source. we really appreciate your work." 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14527.0 0.0 0.0 0.0
"WOW this was intense. Really really high density of concepts, yet everything is presented so clearly. This is a beautiful lecture." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11246.0 0.0 0.0 0.0
"36:32 He says that the decomposition is incorrect since the numbers in the diagonal matrix should be positive. Why can't the eigenvalues of A^T*A be negative? Didn't he just say how to find the signs of the number in the diagonal matrix using the expression: Av=sigma*u. Am I missing something here?" HgC1l_6ySkc "32. Quiz 3 Review" "MIT 18.06 Linear Algebra, Spring 2005" 1041.0 0.0 1.0 0.0
"ok, it's starting to go over my head, guys...." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 14129.0 0.0 0.0 0.0
"In my highschool book, it proved the factoring of x to the n - y to then n with polynomials and horner. You devide that by x-y such that the remainder is 0 and if you do the horner, the factored identity comes out." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6646.0 0.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change
Lecture 2: Limits

Lecture 3: Derivatives

Lecture 4: Chain Rule

Lecture 5: Implicit Differentiation

Lecture 6: Exponential and Log

Lecture 7: Exam 1 Review

Lecture 9: Linear and Quadratic Approximations

Lecture 10: Curve Sketching

Lecture 11: Max-min

Lecture 12: Related Rates

Lecture 13: Newton's Method

Lecture 14: Mean Value Theorem

Lecture 15: Antiderivative

Lecture 16: Differential Equations

Lecture 18: Definite Integrals

Lecture 19: First Fundamental Theorem

Lecture 20: Second Fundamental Theorem

Lecture 21: Applications to Logarithms

Lecture 22: Volumes

Lecture 23: Work, Probability

Lecture 24: Numerical Integration

Lecture 25: Exam 3 Review

Lecture 27: Trig Integrals

Lecture 28: Inverse Substitution

Lecture 29: Partial Fractions

Lecture 30: Integration by Parts

Lecture 31: Parametric Equations

Lecture 32: Polar Coordinates

Lecture 33: Exam 4 Review

Lecture 35: Indeterminate Forms

Lecture 36: Improper Integrals

Lecture 37: Infinite Series

Lecture 38: Taylor's Series

Lecture 39: Final Review" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8427.0 0.0 0.0 0.0
"@32:47 it's not an accident, because R is specifically designed so that when multiplied with C, A is produced.

The fact that this proves that the dimension of the row rank and column rank are the same (because the dimensions of C and R must agree) is kind of messing with my brain right now..." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1540.0 0.0 0.0 0.0
"Easy stuff times horrible stuff" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 3548.0 0.0 0.0 0.0
"I hate constrained partial derivatives. I'd just got to grips with Lagrange multipliers, and then he goes and introduces this. Evil :(" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5479.0 0.0 0.0 0.0
"Skipped lectures, so watching these before test" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8719.0 0.0 0.0 0.0
"Does the last equation (At*y=f) add any new information? I suppose find y (currents) from C*e would be last step right?" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3460.0 0.0 1.0 0.0
"I love how smart and passionate yet chill the professor is. His personality perfectly fits that of a world-class serial killer." Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5752.0 0.0 0.0 0.0
"http://math.stackexchange.com/questions/714131/derivatives-of-sine-and-cosine-at-x-0-give-all-values-of-fracddx-sin-x so can somebody answer this question?" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13253.0 0.0 1.0 0.0
"Long live you, sir" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 7409.0 0.0 0.0 0.0
"Great picture quality; thanks for updating this lecture." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 4318.0 0.0 0.0 0.0
"This is exactly what I'm doing in class!" aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10660.0 0.0 0.0 0.0
"In the least-squares vs. PCA discussion that starts at 37:44, he's comparing minimizing sum of squares of vertical distances to minimizing sum of squares of squares of perpendicular distances.  However, each vertical error is related to each perpendicular error by the same multiplicative constant (cosine of the angle made by the estimated line), so in a way, minimizing one is tantamount to minimizing the other. Where the two methods do seem to differ is that least squares allows for an intercept term, while the PCA line goes through the origin.  However, when we look at the estimate of the intercept term (  b_0 = mean(y) - b_hat*mean(x)  ), least squares appears to be performing a de-meaning similar to the first step in PCA.  In summary, I think we would need a more thorough discussion than we see in the video in order to conclude that least squares and the first principal component of PCA are different." Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6675.0 0.0 1.0 0.0
"There's no one in the audience." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 10388.0 0.0 0.0 0.0
"53:33 
He speaks facts here" feb9j65Iz4w "24. Linear Programming and Two-Person Games" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 1347.0 0.0 0.0 0.0
"Thank you MIT" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9121.0 0.0 0.0 0.0
"1. What are eigenvectors and eigenvalues? @00:00
2. Example 1: Eigenvectors of Projection Matrices @5:24
3. Example 2: Eigenvectors of Permutation Matrices @10:42
4. How to find eigenvalues and eigenvectors @16:35
    a. Det(A - lambda * I) = 0 @16:45
    b. Finding eigenvalues @23:25
    c. Finding eigenvectors @26:20
5. A + 3*I has same eigenvectors as A while the eigenvalues added by 3 @29:37
6. Eigenvalues(A + B) != Eigenvalues(A) + Eigenvalues(B) @32:53
7. Eigenvalues of rotation matrices @37:00
    a. Complex eigenvalues @42:04
8. Eigenvectors of shear matrices @45:42" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 323.0 0.0 1.0 0.0
"I finally completed this amazing course today on 08/06/2022, it took 34 days to complete and it was totally worth it.
I watched all lectures, read all lecture summaries, recitation videos solved each problem set and exams.
Thanks to Professor Strang, the lectures were not difficult to understand, the hard part was doing them neatly and regularly.
Thank you Professor Strang for this amazing course !!!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 5405.0 0.0 0.0 0.0
"Wow♡♡
Thank you" phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12096.0 0.0 0.0 0.0
"Watching this to review calculus and my only issue with this instructor so far is this lecture. I love probability. it is usually fun and relatively straight forward... his approach to this problem was precisely the opposite of fun and straight forward." jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11307.0 0.0 0.0 0.0
"Nice to see his speech." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7861.0 0.0 0.0 0.0
"can anyone explain why A*C^t=det A*I
i though it equals to (det A )^n * I
because we will factor det A from each row by property 3a" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 12605.0 0.0 1.0 0.0
"I hope I don't get ridiculed for this because I'm just trying to learn. Ok so can someone please explain how:

0-1/Xo = -X/Xo^2 + 1/Xo

 becomes:

x/Xo^2c = 2/Xo

I've done a fair bit of algebra but just don't get it. Any help greatly appreciated!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5581.0 0.0 1.0 0.0
"Is this the next course after single variable calculus 18.01. I ask because they did some other topics b4 vector calculus in my school, Stuff like Taylor expansions and advanced integration techniques using trig identities." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6883.0 0.0 1.0 1.0
"Thank you Prof. Strang. Nice and clear lectures." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9202.0 0.0 0.0 0.0
"34:36 gradient descent" AeRwohPuUHQ "22. Gradient Descent: Downhill to a Minimum" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 984.0 0.0 0.0 0.0
"James Harden walking in at 9:07" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7126.0 0.0 0.0 0.0
没有学生在底下，但老师依然很投入地在讲，辛苦了！ JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 15638.0 0.0 0.0 0.0
"He's the Mr. Rogers of linear algebra." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 4646.0 0.0 0.0 0.0
"What's nice is YouTube allows you to change the speed...the lecture goes much faster and still very clear to understand this brilliant professor." l4NoMKEHQwM "11. Derived Distributions (ctd.); Covariance" "6.041 Probabilistic Systems Analysis and Applied Probability" 11574.0 0.0 0.0 0.0
"Wait, did he ever account for vector N not being a unit vector? He never required that the N vector represented the area of the delta slanted plane did he?" WfEQabCGAqI "Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11261.0 0.0 1.0 0.0
"If s/t is velocity what does ds/dt mean?" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6516.0 0.0 1.0 0.0
Great VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 4194.0 0.0 0.0 0.0
"The last example was really neat." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 10153.0 0.0 0.0 0.0
"Yes if I do it on a t" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12139.0 0.0 0.0 0.0
"what Went wrong with lec 4 ?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 15101.0 0.0 1.0 0.0
"That's too much !!" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9945.0 0.0 0.0 0.0
"Real great explanation" Xa2jPbURTjQ "3. Orthonormal Columns in Q Give Q'Q = I" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8497.0 0.0 0.0 0.0
"i got so invested in the lecture i was replying whenever he asked the class a question" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 13382.0 0.0 0.0 0.0
"thank you mit for this" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 14498.0 0.0 0.0 0.0
"It's interesting that he constantly regards on the fact that he exposes things without proving them, but in fact I think he explains the things so clearly an understandable that he does'nt need to prove them, because we can realize about them almost in an axiomatic way." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7050.0 0.0 0.0 0.0
"I am reading his book for several months now. Didn't know he also have videos. It feels like listening to a living legend. I am happy :)" 4MgN6uxd4i4 "7. Decision Problems for Automata and Grammars" "MIT 18.404J Theory of Computation, Fall 2020" 5134.0 0.0 0.0 0.0
"Good day. Is there a certain textbook recommending?" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 4126.0 0.0 0.0 0.0
"@bmcilhone It's easy : 5*45X^4+144+3000X^2-8X" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1798.0 0.0 0.0 0.0
"Was there an inconsistency in what he did at 34:33 and 34:37, he pointed to different lines? It seemed intentional, can anyone explain why he multiplied by a number on the ""y=g(X)-axis"" and then a number on the ""x-axis"" when everything maps to the same number on the y-axis?" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 11280.0 0.0 1.0 0.0
"Very nice" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11203.0 0.0 0.0 0.0
"Let's make Matrix Orthonormal Again!" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 7338.0 0.0 0.0 0.0
"Nikola Tesla could solve calculus equations in his head. Why don't we all just do it like Tesla?? " PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7870.0 0.0 0.0 0.0
"At t = 38:00, Strang shows a way that expedites finding L:  find E, then solve [E| I | to get E inverse which = L. Now we can quickly decompose A into LU if we do Gaussian elimination only--not Gauss-Jordan elimination--from the beginning. 
At t = 43:00, he defines a vector space out of 3x3 matrices, call it M_33.
At t = 47:00, he covers the dimensions of subspaces of M." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2723.0 0.0 0.0 1.0
"Really,  we should say thanks to you, from the bottom of the heart." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8539.0 0.0 0.0 0.0
"43:55 Who else calculated the area while the professor is erasing the board?" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1223.0 1.0 0.0 0.0
"Can’t I also choose other values for x2 and x4 to find other particular solutions? Would they not also shift the null space to another spot and cover regions which were not already defined? Or does the particular solution + null space contain the set of all possible solutions for Rx=b?" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 3133.0 0.0 1.0 0.0
"Dr. Strang: in the example where you draw that plane in 3space does that plane contain the origin?" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 3514.0 0.0 1.0 0.0
"I think another title for this course could be.

If we knew everything, we wouldn't need statisticians. But we don't know shit, so statisticians rule the world.

Haha 😂 (no offense to statisticians! It's interesting stuff!)" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 6007.0 0.0 0.0 0.0
"you don't see many youtube videos with 100k plus views in 7 years with 0 dislikes" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 15503.0 0.0 0.0 0.0
"Where are the next lectures for A^TA ???" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 11656.0 0.0 1.0 0.0
"This is SO helpful, more than thankful for this upload. I really like this professor too." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 10583.0 0.0 0.0 0.0
"God Bless professor Strang! :)" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 4066.0 0.0 0.0 0.0
" lol ! I am sorry but ""chalk board at MIT"" in this day and age of ""advanced computer screens and computer technologies??? lol ! Educational tools should all be digitized and less time spent ""writing aggressively on chalk board"" ! lol..Just a bad way to each lots of supposedly smart students ! :)))" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11.0 1.0 0.0 0.0
"The courses taught by professor Gilbert is just aaaawesome!!!" cxTmmasBiC8 "35. Finding Clusters in Graphs" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10066.0 0.0 0.0 0.0
"Ooooooooooooooooh my god this is soooooo beautiful. Thank you." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 8128.0 0.0 0.0 0.0
"Thank you very much, prof Strang." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9455.0 0.0 0.0 0.0
"@ShaneHayes123 First year calc is usually review of high school math. I wouldn't be surprised if you understand these concepts already." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1719.0 0.0 0.0 0.0
"Every student should have at least one professor like Prof Strang. Motivating, illuminating and such great energy. I truly appreciate these classes. Thank you!" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 3599.0 0.0 0.0 0.0
"I am lost with calculation for last question at 29:46 ... Probability of 11th toss being H, given that first 10 tosses are heads.. If I compute using conditional probability, it comes to be same as Probability of 11th toss being H (without any condition, previous question)

x1/y1 events when first coin is picked
x1 => 11th toss is H
y1 => first 10 tosses are heads
P(x1|y1) = P(x1 intersect y1)/P(y1)

Assuming first coin => P(x1 intersect y1) => probability that first 11 tosses are H => (0.9)^11
P(x1) = (0.9)^10 
Thus , P(x1|y1) = 0.9.. and multiple by 1/2 since we picked first coin.

on similar grounds P(x2|y2) = 0.1 * 1/2

final is 0.9*1/2 + 0.1*1/2 => 1/2   , which is same answer as previous question.. I might be missing something very basic.. please correct me if I am mistaken in my computation" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 5113.0 0.0 1.0 0.0
"excellent teaching" xrypSZU8cBE "Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12826.0 0.0 0.0 0.0
"Love the cool idea to light up the U and V!" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7451.0 0.0 0.0 0.0
"No other video about LA is better than this! respect and tks prof so much :)" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 7887.0 0.0 0.0 0.0
"I love what you doing" RDO6Py97IDg "1. A bridge between graph theory and additive combinatorics" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 5841.0 0.0 0.0 0.0
"Thanks for reviewing Matrix." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9697.0 0.0 0.0 0.0
"It hurts so indefinitely much that I see him getting old ,
He is the most beloved teacher that I ever had." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6920.0 0.0 0.0 0.0
"I love Prof. Gilbert's lecture videos on Linear Algebra. I read his books and watched his videos five years back, but I enjoy it watching him again." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5722.0 0.0 0.0 0.0
"@valtih1978 I'm not exactly sure what portion of the lecture you're referring to, but if you're talking about the later 3/4, I think he means that A imparts transforms upon the vectors that are expressed with the basis {v1, v2,...,vn} and transforms them into a new basis {w1, w2,..wn} where T(v1), T(v2), etc. are all functions used to express the original bases {v1, v2, etc.} ""in terms of"" {w1, w2, etc.}  So the system of equations is just a generalization of that concept." Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2059.0 0.0 0.0 0.0
"what would be a sub space if the two columns of the r3 are same." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 15189.0 0.0 1.0 0.0
"37:04 But what's going on !!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1054.0 0.0 1.0 0.0
"Thank you so much for this lecture series. This helps a lot! Great professor with great and easy to understand explanations." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9374.0 0.0 0.0 0.0
"need to rewatch" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 14015.0 0.0 0.0 0.0
🤔🤔🤔🤔🇺🇳🇺🇳🇺🇳🗣️🗣️🇺🇳🇺🇳🇺🇳🗣️🗣️🗣️🇺🇳🇺🇳🇺🇳🇺🇳🗣️🗣️🗣️🗣️🇺🇳🇺🇳🇺🇳🇺🇳🗣️🗣️🗣️🗣️🇺🇳🇺🇳🇺🇳🇺🇳🇺🇳🗣️👷💝💝💝💞💞💝💝💝💞💞💞💞💝💝💝💝💞💞💞💞💞💞💝💝💝💝💝💞💞💞💞💞💞💞💝💝💝💝💝💞💞💞💞💞💞💝💝💝💝💞💞💞💞💞💝💝💝💝💝💞💞...💞💞💞💞💝💝💝💝💞💞💞💝💝💝💞💞🤳💅🤳💅🤳💅🤳✍️✍️✍️✍️✍️✍️✍️🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄🏄 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15745.0 0.0 0.0 0.0
"@goryans123 This professor is teaching out of a textbook he wrote too." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 1858.0 0.0 0.0 0.0
"i am eternally greatful to MIT OPENCOURSEWARE!!! Thank you so much !! I will advocate for everyone to see these videos and will donate!" -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 13329.0 0.0 0.0 0.0
"In the proof of the theorem of the convergence monotone , there is the case where f(x)=0 , which is easy to discuss" ZWzCHjN3_3s "Lecture 11: The Lebesgue Integral of a Nonnegative Function and Convergence Theorems" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 6682.0 0.0 0.0 0.0
"Never seen it this way. He actually teaches the way things work, not just how to apply concepts. Wish I had seen it 10+ years ago. Thanks for sharing!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 7820.0 0.0 0.0 1.0
"This is amazing
Thank you MIT OCW team for all these incredible lectures being posted ... sending respects.. from Delhi, India" asjAc90L8rE "12. Time Complexity" "MIT 18.404J Theory of Computation, Fall 2020" 10612.0 0.0 0.0 0.0
"Oh my dear advisor, Gilbert Strang :)" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8016.0 0.0 0.0 0.0
"Watching 1.25x speed, feeling normal , LOL" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11290.0 0.0 0.0 0.0
"Thank you." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 9554.0 0.0 0.0 0.0
"At 10:00 why can't the 2nd pivot be at point (1,2). i.e. be the value 2 from row 1 column 2?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2582.0 0.0 1.0 0.0
"As viewed from above" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2575.0 0.0 0.0 0.0
"> Orgy of greek letters

😏" sr7kCpzAuYw "Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1459.0 0.0 0.0 0.0
"Amazing Lecture Professor, well done!" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2350.0 0.0 0.0 0.0
저자직강 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 15689.0 0.0 0.0 0.0
"Thank you so much Prof. John!" rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 9357.0 0.0 0.0 0.0
"what's the diference between the first speed (unit speed - condition for ""teta"" = t) and the next one |velocity vector| ???" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15192.0 0.0 1.0 0.0
"Thanks Professor Auroux , this video was great" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9638.0 0.0 0.0 0.0
"omg it's snowing outside and these kids are sitting in a nice cozy room listening to one of the greatest linear algebra teachers in the world...I think I could die happy after such an experience" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14138.0 1.0 0.0 0.0
"Goat !!! 👽👽‼‼🧛🧛🩸🩸🤑🤑" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 4064.0 0.0 0.0 0.0
"I love MIT so much for all of these free lectures. I have watched all of physics, this and electronics and circuits." dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 5718.0 0.0 0.0 0.0
"the method about which we cancel out higher order terms, does that only work in this arbitrary case which prof picked x at x=0?, what about other x's that are non zero?, then the value of the higher order terms would be significant." BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14717.0 0.0 1.0 0.0
"Thank you for existing" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 9249.0 0.0 0.0 0.0
"can anyone please recommend a book for what he is teaching." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12608.0 0.0 0.0 0.0
"Who knows this? The locus of a point that moves in  such a way that the difference of its distances from two fixed points is always constant. What type of curve(s) is it?" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11748.0 0.0 1.0 0.0
"@joeglimmix ...i think you need to calm down... and you dont know how smart i am or how smart they are. no one can say whos ""smarter"" and i honestly dont care. that comment was intended to be critical of the primary school teachers they have at what ever schools these students are coming from, or at least the curriculum of said schools. " YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1904.0 0.0 0.0 0.0
Wow! VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 12048.0 0.0 0.0 0.0
"48:58 why isn't that 1/2 * a1 * 2u1/sqrt(u1^2+h^2) ?" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1302.0 0.0 1.0 0.0
"Is Calc 2 included in this lecture series, or can I just move to multi variable calculus right away after this?" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6746.0 0.0 1.0 0.0
"Туда и там собираем" a66tfLdr6oY "11. Parametric Hypothesis Testing (cont.) and Testing Goodness of Fit" "MIT 18.650 Statistics for Applications, Fall 2016" 15557.0 0.0 0.0 0.0
"nine people accidentally missed the like button by a couple centimeters" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14060.0 0.0 0.0 0.0
"Ok can someone tell me what we will learn from this video" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8044.0 0.0 0.0 0.0
"It's all easy with this professor" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7025.0 0.0 0.0 0.0
"Not many viewers left at lecture 24 !" lWW54ts9Ubo "24. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 7926.0 0.0 0.0 0.0
"This is a pure enjoyment to take Prof. Auorox lectures" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10601.0 0.0 0.0 0.0
"The instructor’s name on the beginning screen is not “substituted.” lol" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10142.0 0.0 0.0 0.0
"That sine graph is amazing." dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 9912.0 0.0 0.0 0.0
"The clearest explanation with clearest English. That accent is very clear and manly." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 10048.0 0.0 0.0 0.0
"These videos have totally increased my understanding of vector calculus - I'm no longer just doing the trick but I'm actually manipulating the maths.

Thanks MIT." tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10434.0 0.0 0.0 0.0
"At 28:00, he did the thing that Walter Lewin does. Is it a prerequisite for all MIT professors to have the ability to do that ""dotted line""?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 2632.0 0.0 0.0 0.0
Amazing! srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 2395.0 0.0 0.0 0.0
"Good Job Professor" zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4118.0 0.0 0.0 0.0
"The god of matrices" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10122.0 0.0 0.0 0.0
"Professor Strang is an iconic figure in Linear Algebra, but in this video, he uses notation that violates one of my pet peaves:  R^3 for the space of (3x1) matrices with all real entries.  The trouble is that in essentially every linear algebra text at this level, the early introductory material includes very strong admonitions to students that they MUST NOT say that a matrix A is equal to a matrix B when B does not have exactly the same number of rows as A.  (To be continued...)" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 8350.0 0.0 1.0 0.0
"This lecture on factorization is very helpful ,however   I don't fully understand why this concept. is important." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 10823.0 0.0 0.0 0.0
"The guy one The first bench looks like kanye west from back" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10134.0 0.0 0.0 0.0
"@Boeing1991 oh, right, I used to do that. You tend to forget about these things quickly ;)" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1603.0 0.0 0.0 0.0
"Brilliant ! A masterpiece from a French man !" lWW54ts9Ubo "24. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 2924.0 0.0 0.0 0.0
"MIT professors teach like their students have no background knowledges, and my professors assume I have learnt all shit already in High school" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 7539.0 0.0 0.0 0.0
"its amazing that he can do the lesson in a fun and creative way with real problems and great humor..awesome lecture again" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13703.0 0.0 0.0 1.0
"You must be a star" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12228.0 0.0 0.0 0.0
"I love Prof. Jerison, but sometimes I feel he over-complicates stuff which ends up confusing me" Pd2xP5zDsRw "Lec 20 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5723.0 0.0 0.0 0.0
"The legend...." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 10176.0 0.0 0.0 0.0
"In short, A^T*A is invertible if and only if A is full column rank!" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6652.0 0.0 0.0 0.0
"This lecture is amazing! This is the deepest understanding of linear regression one could get.
Thanks MIT for sharing it with the world ❤️" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10793.0 0.0 0.0 0.0
"much better than my prof ! I like him" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 13962.0 0.0 0.0 0.0
"who was mean enough to click ""dislike""?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 15269.0 0.0 0.0 0.0
"We study this at just 12 years of age in India. This is very simple maths, why do you Americans need to attend MIT for such basic maths? Please look at India as it has a better education system than America." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 11334.0 0.0 0.0 0.0
"Remember I saw prof. Strangs other linear course many years ago. So unbelievable good lecturer he is!" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8547.0 0.0 0.0 0.0
"36:24   
...SPORTS. IT'S IN THE GAME!" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1040.0 0.0 0.0 0.0
"Very good video. Amazing what mathematics can do." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11187.0 0.0 0.0 0.0
"but what why doesn't matrix multiplication works as matrix. addtion. ?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12576.0 0.0 1.0 0.0
"I couldn't find assignment 1 in the website the 30 problem I founded assignment 4 in the place of 1 help please thanks in advance" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 5250.0 0.0 1.0 0.0
"Thank MIT and Professor for your course!" rYefUsYuEp0 "25. Classical Inference III" "6.041 Probabilistic Systems Analysis and Applied Probability" 9043.0 0.0 0.0 0.0
"guys at the end of the video, why isn't  b(transpose) * q1 = 0, like a(transpose)*q2 is 0  ?" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 13024.0 0.0 1.0 0.0
"24:00 what does the capital after the transition function stand for? new variable for states (Q)? And is it the same variable as 54:00?" oNsscmUwjMU "2. Nondeterminism, Closure Properties, Conversion of Regular Expressions to FA" "MIT 18.404J Theory of Computation, Fall 2020" 726.0 0.0 1.0 0.0
"X²+y²+z²1 is the equation of the unit sphere" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12102.0 0.0 0.0 0.0
"Satellite preferably above the earth." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8600.0 0.0 0.0 0.0
"MIT cheap board !!!!!   LOL" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 7515.0 0.0 0.0 0.0
"I don't understand why MIT can only afford a minimum waged camera man to shoot this video, pathetic !!!" 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5352.0 1.0 0.0 0.0
"This teacher is excellent because you are able to follow along with the gears that are turning in his head.  He actually reasons with you.  I remember that the linear algebra teacher I had was hopeless and would merely bark canned lectures at you without a thought.  Yeah, that guy wasn't a man of reason but a weight lifter, ex wood worker, simply there for a pay check." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 10934.0 0.0 0.0 0.0
"This dude sucks" EBdgFFf54U0 "Lecture 14: Basic Hilbert Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 10501.0 0.0 0.0 0.0
"very well explained!" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 15044.0 0.0 0.0 0.0
"Please record your introductry number theory lectures" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 8212.0 0.0 0.0 0.0
"At 21:30, when Strang is performing the linear transformation of the unit circle, shouldn't the image be rotated 90 degrees. 

It seems like the x stretching is by a factor of 2 and the y stretching by a factor of 3. But he did it the opposite way. 

I am but a humble pupil looking to understand and correct any bugs in my intuition." NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2610.0 0.0 1.0 0.0
40:00 VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 1120.0 0.0 0.0 0.0
👍👍👍👍👍👍👍👍👍👍👍👍👍👍 XhSk_Lw2X_U "14. Low Rank Changes in A and Its Inverse" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15715.0 0.0 0.0 0.0
"When you dont hear anything and then realise you have to put in the other earphone." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 11645.0 0.0 0.0 0.0
"thanks for this, 

please keep uploading" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14590.0 0.0 0.0 0.0
"I don't think I'd pass linear algebra without your lectures" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 5332.0 0.0 0.0 0.0
"A magician telling all his secret tricks..." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 2139.0 0.0 0.0 0.0
"Oh, how I wish my LA prof had been this good!  Prof Strang is indeed a highly skilled teacher." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 8029.0 0.0 0.0 0.0
"@Merky2k poor ignorant." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1673.0 0.0 0.0 0.0
"Thank You MIT OCW. Thank you Prof. Strang." RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9049.0 0.0 0.0 0.0
"I think the derivative of U(x)V(x) ,we should add and substract u(x+deltax).v(x) instead of u(x) ..... " 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6052.0 0.0 1.0 0.0
"I'll certainly come back to revisit, I wish I had seen the series during my undergrads. Anyway, great course, thanks to MIT!
Evelyn 2019" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6286.0 0.0 0.0 0.0
"In the theory of ordinary differential equations, spectral methods on a suitable Hilbert space are used to study the behavior of eigenvalues and eigenfunctions of differential equations." EBdgFFf54U0 "Lecture 14: Basic Hilbert Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 6686.0 0.0 0.0 0.0
"I wonder how they could understand all of that in 47 min !??" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6242.0 0.0 0.0 0.0
"Gauss given order :D" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 3981.0 0.0 0.0 0.0
"18:13 to review the meaning of span" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 531.0 0.0 0.0 0.0
"I lost at 31:53. Somebody help..." IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 5711.0 0.0 1.0 0.0
Thanku H_k1w3cfny8 "10. Continuous Bayes' Rule; Derived Distributions" "6.041 Probabilistic Systems Analysis and Applied Probability" 9861.0 0.0 0.0 0.0
"The complexity of matrix multiplication is of the order O(n^3), that's fine. But in every step in the we are changing just one row...therefore, shouldn't the cost be n+ (n-1)+ (n-2) + ........+1, ie O(n^2), if we have a suitable algorithm?" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 10055.0 0.0 1.0 0.0
"Thank you" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 9083.0 0.0 0.0 0.0
"lots of help!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 13857.0 0.0 0.0 0.0
"I'm just starting online with Prof Strang's class on youtube..  I love his style, his speed and his passion to inspire thought about the answers.  The man appears to be one of the truly gifted educators and thinkers.  Thanks to MIT for posting this and other knowledge online!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6341.0 0.0 0.0 0.0
"Excellent lecture  -- very difficult material --- expert presentation.  Suggestion: let the students work out the mathematical manipulations, and emphasize the concepts in the lecture:  Yes, state the theorems, but then present lots of real world examples, such as weather data,  demographic data, economic data, especially cases where the data might be modeled in a variety of ways etc .  The point:  mathematical manipulations are relatively easy once you know the rules, but the ideas are subtle and (probably) can only be grasped/conveyed via examples.  Yes, the lecture had lots of simple examples expertly woven into the theory, but the emphasis was on the mathematical manipulations and not enough on the concepts.  Bottom line: superior lecture in any case.  Two thumbs up!" rLlZpnT02ZU "4. Parametric Inference (cont.) and Maximum Likelihood Estimation" "MIT 18.650 Statistics for Applications, Fall 2016" 3651.0 0.0 0.0 1.0
"AT we reach 35 minutes of this lecture,
Why they have written -rsin∅? what is x sub theta?" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2184.0 0.0 1.0 0.0
"Thanks so much" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9782.0 0.0 0.0 0.0
"Linear algebra had been mystery for me until I saw these types of lecture online. Thanks" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7377.0 0.0 0.0 0.0
"linear transformation is defined before matrix" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13806.0 0.0 0.0 0.0
"in india we study all this in standard 10" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13590.0 0.0 0.0 0.0
"who is this magnificent instructor?! He puts all of my math professors to shame!" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 15264.0 0.0 0.0 0.0
"The derivative of cos(x) is -sin(x) and not sin(x)" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10072.0 0.0 1.0 0.0
"In the first lecture, from 14:10  to 15:26 the dude threw on the gem. If you notice this is the idea of vector spaces something which really you don't understand when you start linear algebra. Moreover, he pushed the argument at 22:00 with all the beauty to show that a column picture is a preferred way of looking when it goes into a higher dimension, the point on which he comes back in vector spaces. Finally, at 28:00 he concludes an important thesis for vector spaces." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6666.0 0.0 0.0 0.0
"I'm 15 and do this in school" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6291.0 0.0 0.0 0.0
"Proffesor g.strang is the best.most advanced .mit.he deserves the honors for his intellectual abilities. Thank y2k very much for all your online lectures.i enjoy learning from you very much.thank you.lLSHALM BETTY M." nvXRJIBOREc "Lecture 21: Minimizing a Function Step by Step" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8413.0 0.0 0.0 0.0
"If only we could actually see the jokes....." 57jzPlxf4fk "Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6515.0 0.0 0.0 0.0
"What a great professor!!!" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 11415.0 0.0 0.0 0.0
"Time well spent watching your video. Thanks.
" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11014.0 0.0 0.0 0.0
"hocam boş duvarlara konuşuyon" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 13180.0 0.0 0.0 0.0
"Thanks, any other 15 year olds watching these lectures, pretty useful for GR actually" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9846.0 0.0 0.0 0.0
"He is not only a master lecturer, he is a master of writing on a chalkboard. I swear, it looks like he is using a paint pen." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4528.0 1.0 0.0 0.0
"hmm - after first 2min profesor says: what you'r gonna learn here - is how to read/write a proof about (... - input here any field of interest)
if I would imagine worst introduction to the math course - that would be the one :(" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 13173.0 0.0 0.0 0.0
"24.41, this guy is a legend. I wonder where he is now." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 722.0 0.0 0.0 0.0
"why at the last example there is no second eigen vectors .. why it can't be equal {-1 , 0 } .. is that because it will be // to it in the other direction .. and there is no one perpendicular to it ??" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 15290.0 0.0 1.0 0.0
"No students...??" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 7893.0 0.0 0.0 0.0
"Can someone please explain why property 3b is also true for the volume?" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 3091.0 0.0 1.0 0.0
"""in that Gauss given order"" ... I'm taking this one to the bag" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 159.0 0.0 0.0 0.0
"Thank you professor Strang for your excellent work and your outstanding book. It Took me a little bit more than a semester to finish the book and the class and the book but I think it was well worth it. I only wish there was a lecture about Hermitian matrices and Fourier series! You will always be in my heart as the best teacher I ever had.  


Kind Regards,
Emiliano Isaza" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9318.0 0.0 0.0 0.0
"There is only one profession where handwriting improves with age" ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10377.0 0.0 0.0 0.0
"no quite understand why ""a"" which is the distance between the curve and the origin, is interpreted as the speed. Also, how to interpret ""a"" if the origin is not at the centre of the circle." XRkgBWbWvg4 "Lec 32 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14073.0 0.0 1.0 0.0
"God (although highly unlikely to exist), i hate this man's speech parameters and habits. So i think i beter go and read smth on statistics, rather than cripple my nervous sys." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 4065.0 0.0 0.0 0.0
"Find solution and let me be the head master" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 3797.0 0.0 0.0 0.0
"wtf is he writing in a messed up white board???" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 15445.0 1.0 0.0 0.0
"40:52 broke my heart to see all those empty chairs" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1140.0 1.0 0.0 0.0
"as a French, I really appreciate his English accent (too much ""you know"" tho)" bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 12405.0 0.0 0.0 0.0
"@pedroissler But what happens if the volume is defined by a bunch of intersecting planes?
Same method?" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1964.0 0.0 1.0 0.0
xgh srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 15457.0 0.0 0.0 0.0
"May Allah Almighty bless him with health and happiness. He's my spiritual father from my entire graduation level to my Master's. Thank you so much Sir for everything. Love you.😍🥰🥰 #Pakistan" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 7626.0 0.0 0.0 0.0
"Professor Strang's lectures taught me a lot. Thanks professor and MIT OCW." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 8378.0 0.0 0.0 0.0
"Don't understand why (a) is not a solution for check-in 14.1.

Consider the NTM which decides whether <G,s,t> \in HAMPATH or not.

NTM *decides* this in poly(m) time, where m = size of input (say, the number of vertices).

Thus, NTM is able to accept or reject input in poly (m). 

Since it is also able to reject in poly(m) time, why can't you invert the solution? 

Or am I wrong in believing that it can also reject in poly(m) time?" 1VhnDdQsELo "14. P and NP, SAT, Poly-Time Reducibility" "MIT 18.404J Theory of Computation, Fall 2020" 3478.0 0.0 1.0 0.0
"Why didn´t I see this videos in the university?" BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 11817.0 0.0 0.0 0.0
"Thank you! :)" -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 9477.0 0.0 0.0 0.0
"Watched 18.065 right after 18.060, finally finished both playlists now, thank you MIT and Prof. Strang for this two informative and engaging courses!" rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11284.0 0.0 0.0 0.0
"41:00 I was thinking this is like RegEx and then I was like hey this IS RegEx .. Fun to learn TOC at a random point in my education" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 1143.0 0.0 0.0 0.0
"0 probability can mean impossible because you will never be able to measure with infinite precision, so you never can tell for sure that you hit a certain point." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 273.0 0.0 0.0 0.0
"""I shouldn't do this, but I will""" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 62.0 0.0 0.0 0.0
"19:07 second piece of the lecture" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 554.0 0.0 0.0 0.0
"@zkhandwala only the one who can efford :)" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2084.0 0.0 0.0 0.0
"Well, it's a good thing I'm taking this in grade 11 (voice dripping with sarcasm). " jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11368.0 0.0 0.0 0.0
"At 44:31 why did sir say solving 3 equation by 2 variables is not possible. We have seen in our schools that the number of variable should be equal to number of equation in order to evaluate the variable. Plz explain." YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 2676.0 0.0 1.0 0.0
"MIT is doing affirmative action?" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7526.0 0.0 0.0 0.0
"So glad I never have to do this stuff again😵  Would have been great, though, having this available way back when.  Remember having a YA who spoke ZERO English.  You had to get up with your book and go to the front and point out the problem to him😬" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8760.0 0.0 0.0 0.0
"6:13 why aTxa equals to xaTa" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1378.0 0.0 1.0 0.0
"What's the sum of the two eigen values? Just tell me what I just said. :D" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 11586.0 0.0 1.0 0.0
"How much i have to pay for electrical engeneering on mit?" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4889.0 0.0 0.0 0.0
"@TheVAGES correction: YOU don't understand shit what he is teaching you. I guess you're one of the people who are doing very bad in school or you dropped out." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1744.0 0.0 0.0 0.0
"25:11 amazing" _CdoRiNSrqI "Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 769.0 0.0 0.0 0.0
"I go to texas tech university and amidst covid 19 I have been having a hard time with linear algebra help, this was a nice relief. My question is transforming the basis of numbers I completely get and I want to know if this applies to unit conversion with physical properties.  Like in doing stochiometry to convert between units (same plane). Or the relationships we get from integration and derivation like mass and force. Thank you for this resoucre incredibly helpful" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 5439.0 0.0 1.0 1.0
thanks RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 14543.0 0.0 0.0 0.0
"@SuperMafioBrother cool story brah" jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1731.0 0.0 0.0 0.0
"great video. A discussion woth my dad about him failing real analysis is what played the seed of being a math major. We had that conversation probably 6-7 years ago and now i’m a junior in college pursuing a math degree. So happy to have this information at my fingertips. I get to watch these lectures in my own time and learn a lot by myself" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 13017.0 0.0 0.0 0.0
"NO CHILL GIL" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 7802.0 0.0 0.0 0.0
"6:34, how is that z=z0 + dz/dx(x-x0) a equation of straight line. y=mx+c is a eqaution of straight line in 2D space. and x = x0 + st is vector form of equaiton in higher dimension. how is  the above euqation realted to this? Thanks in advance" UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1384.0 0.0 1.0 0.0
"May God bless this teacher.These are those kind of people that makes you to love learning anything even if that thing might be boring." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 7627.0 0.0 0.0 0.0
"GREAT PROFESSOR" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3975.0 0.0 0.0 0.0
"plug and substitute I finally recon that teacher like to talk and write a lot, you have already made the Pascal triangle in ! combinatory arithmetic, now after calling some algebraic Newton parabols and keep on playing with some curves aproximations like a baby nursing around sins and cos return to the exponential functions,differential, derivatives integrals exponents vectors determinants matrix, how about using some computers and projectors  for your classes This is worst than the stone age." eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14195.0 0.0 0.0 0.0
"Why does the method for Ex 3 have dtheta, it makes sense to me when you find the integral wrt dx you multiply the function by dx to form a series of rectangles, but why are we multiplying the height given by sintheta by the angle?" R9a_NHXrBcg "Lec 23 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11846.0 0.0 1.0 0.0
"Conclusion: 1. To calculate Ax=0 in other words calculate the null space of A, we can use 'reduce row echelon form'  (rref) method.
2. The rank of A equal to the number of pivots or rows after reducing row echelon, notation as r.
The column of A equal to the number of variables, notation as n.
So n-r is equal to the number of free variables.
3. Consider the solution of Ax=0, if we calculate the reduced row echelon form of A consisting of [T F], the solution matrix will be the transform of [-F T], where T stands for identity matrix and F stands for free matrix.
The solution matrix would be n*(n-r) shape." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 3194.0 0.0 0.0 1.0
14:15 ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 427.0 0.0 0.0 0.0
"Wonderfully explained - matrix, linear combination, vector, basis, etc.  Sc kani" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 11995.0 0.0 0.0 0.0
"Where the fuck is part two?!" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11697.0 0.0 0.0 0.0
"This is so beautiful!" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 10716.0 0.0 0.0 0.0
"This time he is wearing the same green shirt that he wore in the previous lesson as opposed to the red shirt he wore in the first lesson.
 
*stares blankly into space*" bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10945.0 0.0 0.0 0.0
"Every time I see one of Professor Strang’s lectures I run and get my old Finite Math with Calculus book just to see how much I’ve forgotten 😉 He’s awesome to listen too🙏" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 3603.0 0.0 0.0 0.0
"ln|x+1|+3ln|x+2|+C.    2:21" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13815.0 0.0 0.0 0.0
"I wonder why these kids are so unresponsive and dumb, I'd jump to answer such a brilliant teacher. This man made me fall in love with math!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 6253.0 0.0 0.0 0.0
"I like this class!" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5688.0 0.0 0.0 0.0
"how did he get the numbers for the matrix at 9:35?" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 13215.0 0.0 1.0 0.0
"Wow!! Thanks very much MIT!! Really appreciate the amazing sharing of resources and hopefully one day we will get open courses on the key undergraduate and graduate math subjects!" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 12056.0 0.0 0.0 0.0
"no no no sir, thank you" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 14070.0 0.0 0.0 0.0
"he's so cuteeee" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 13125.0 0.0 0.0 0.0
"and its exactly the golden ratio.." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 12370.0 0.0 0.0 0.0
"Thank you MIT. I'm a chemical engineer with over 3 years experience in the industry. Just recently I needed to go back and relearn basis of calculus. This was a great refresher" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9166.0 0.0 0.0 0.0
"what is the reason behind considering second order terms of delta? since it is just an interval." jsqSScywvMc "14. Poisson Process I" "6.041 Probabilistic Systems Analysis and Applied Probability" 15170.0 0.0 1.0 0.0
"In two years of junior college and 4 years of engineering, not once did anyone gave the column picture explanation. Mind blown. Thank you, Dr. Strang." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 6692.0 0.0 0.0 1.0
"Thanks! Thanks! XD" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 9834.0 0.0 0.0 0.0
"fuckin conservatives, they just go round in circles and do nothing as a result" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12907.0 0.0 0.0 0.0
"very informative, thanks." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 15020.0 0.0 0.0 0.0
"Thank you Prof Aureux." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9177.0 0.0 0.0 0.0
"lecturer keeps on saying - ""what is this good for"" and i cannot for the life of me concentrate due to my inner monologue sounding like chris rock and singing - ""absolutely nothing!""" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13774.0 0.0 0.0 0.0
"There is a difference of concepts between Lec1 and Lec2. Does anyone else feel the difference" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 10363.0 0.0 1.0 0.0
"👏👏👏congratulations from Brazil for the class !" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 15720.0 0.0 0.0 0.0
"okkkkk, cameras are rolling, this is lecture 14. What an intro line!" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14133.0 1.0 0.0 0.0
"He should have been awarded with some applause at the end :)" zUEuKrxgHws "Lec 25 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4603.0 0.0 0.0 0.0
"@46:40 correct me if I'm wrong, the function is symmetric across the origin, not across the left and right side as professor Jerison perhaps mistakenly said. Meaning the 1st and 3rd quadrant are symmetric, and the 2nd and 4th quadrant are symmetric." eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1563.0 0.0 1.0 0.0
"Thank you professor Tsitsiklis, It is clear and simple." TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 9321.0 0.0 0.0 0.0
"Is Linear Algebra useless? How would you go about solving a million equations with a million unknowns?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 6751.0 0.0 1.0 0.0
"Why is the volume so low on this video?  I'm pumped up to full and I can barely hear him." TSkDZbGS94k "3. Parametric Inference" "MIT 18.650 Statistics for Applications, Fall 2016" 11891.0 1.0 0.0 0.0
"calls the first row a 'HE'
the second row a 'SHE'
18:35" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 12587.0 0.0 0.0 0.0
"I took linear algebra 30 years ago and I thought it was pretty hard at the time.  Prof. Strang makes it easy!" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 6107.0 0.0 0.0 0.0
"Please can any one let me know which grade syllabus is this one?  Is it Bachelor class?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8200.0 0.0 0.0 0.0
"DR. Strang , thank you for another strong explanation of Distance Matrices and also the failure of the Triangle Inequality in Numerical Linear Algebra. Defining and explaining the Trace is another important part of Numerical linear Algebra." 0Qws8BuK3RQ "34. Distance Matrices, Procrustes Problem" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3274.0 0.0 0.0 1.0
"This lecture in specific was truly beautiful" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 10788.0 0.0 0.0 0.0
"@xo20202004 i also forgot to mention that you can also type in the name of the college eg. harvard, cambridge, StanfordUniversity, UCBerkeley, nptelhrd, calcommunitycontent etc" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2071.0 0.0 0.0 0.0
"Thank you, sir Strang!" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 9529.0 0.0 0.0 0.0
"I wish I knew or cared for the meaning of life for you." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6207.0 0.0 0.0 0.0
"Is the ((A transpose) * A ) always invertible?" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6807.0 0.0 1.0 0.0
"Even a high school student can understand his lectures." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 3583.0 0.0 0.0 0.0
"how do we get 24 p's for the 4x4 
i think i got lost 😅" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 13223.0 0.0 1.0 0.0
"The absolute lack of rigor and the hand-waviness of the lesson makes this video a popular science segment rather than a math lesson.  A nice popular science segment, but I certainly hope MIT students of Physics and engineers are directed to take something with a higher level, significantly so.  Physics undergrads don't need total rigor, but such a total lack of it doesn't develop mathematical thinking." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 9978.0 0.0 0.0 1.0
"""Be... and be new..."" Sounds like a philosophical statement 🧐" XhSk_Lw2X_U "14. Low Rank Changes in A and Its Inverse" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 34.0 0.0 0.0 0.0
"The way the ideas were tied together in the end - simply beautiful." JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 10333.0 0.0 0.0 0.0
"that's just great, the proof removed so many misconceptions!
thanks Philippe Rigollet" a1ZCeFpeW0o "20. Principal Component Analysis (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 14646.0 0.0 0.0 1.0
"i am his virtual student and i am proud of it...in lecture 8 of linear algebra, while writing the summary , he feels something went wrong and the moment he find out he grab his head like a child and said "" not, oh my god"" and correct the error. this shows that he actually get involved with students while doing maths on the board... the ego of being a instructor is missing in this great personality.. we can learn how to teach from him side by side of the mathematics." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 13332.0 0.0 0.0 1.0
"https://youtu.be/elSFjUPrlM4
Please like share and subscribe" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13302.0 0.0 0.0 0.0
"jeeeesssssuuuusssss .... have to watch this video in 2x speed. he talks soooo slowly" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 13721.0 0.0 0.0 0.0
"44:50 : why a11 a21 ... am1 is the first column of matrix A? 
Isn't this equation right? >> T(V1) = AV1 = a11w1 + a21w2 + ... +am1Wm" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1244.0 0.0 1.0 0.0
"It’s such a conundrum. I feel like I needed a teacher like this in my school, yet the kids that are able to get into mit l, who probably have less need for a guy like this, get him as a teacher. 

I struggled with really bad teachers all college. If I knew about these lectures, I would have used them to learn lecture instead of my useless professors that I could hardly understand." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7103.0 0.0 0.0 0.0
"i like his accent :D" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 13415.0 0.0 0.0 0.0
"I think the class starts to get messy from 18:30, with occasional clarity, prof. Strang starts to throw out facts that do not have a clear logical connections. For example, the introduction of upper Hessenberg, tri-diagonal and bi-diagonal, why we look for them and in what way do they help QR methods are not very natural to me." d32WV1rKoVk "12. Computing Eigenvalues and Singular Values" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6050.0 0.0 0.0 0.0
"So Kepler could've done all of newtons work. Nice explanation" 0D4BbCa4gHo "Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8735.0 0.0 0.0 0.0
"What is the formula from the notes 3B for integrals of that kind?!" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11527.0 0.0 1.0 0.0
"16:30 He says that the function ""depend only on one direction of things"". I guess he ment it only depends on one of the variables. However, when 4ac-b^2=0, we are still left with the square on the left side, which contains both x and y. Can someone explain what i'm not seeing?" 3_goGnJm5sA "Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 477.0 0.0 1.0 0.0
"Could i see (A^t)(A) as a dot product of two vectors in the matrix space? " YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3230.0 0.0 1.0 0.0
"c_i,j =Sum (a_i,t b_t,j)    gives the product of matrices. What happens when we put a (definite) integral in place of the sum? Do we get a product of differential manifolds? Putting surfaces?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 12583.0 0.0 1.0 0.0
"Hello guys , i am going to be taking a class in probability and statistics this coming semester , if anyone has followed these videos , do they cover statics as well or they are biased on probability and they touch both subjects well" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 4658.0 0.0 1.0 0.0
"看着他越来越老 唉 时光" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15641.0 0.0 0.0 0.0
"can someone explain exactly what is going on at 22:45. what formula is he using to take that derivative? i thought i understood the chain rule but now i'm not so sure. thanks!" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12619.0 0.0 1.0 1.0
"Merci Denis ! Im a very old Danish lady and i adore your expressions ❤️ Regarding math ofc and youll be proud i understand❤️" phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7658.0 0.0 0.0 0.0
"Do you recommend any book to read about the GLM, especially on the Hypotheses testing part which is not covered in the course ? thank you" lWW54ts9Ubo "24. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 3422.0 0.0 1.0 0.0
"That differential equation analogy was impeccable" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 9881.0 0.0 0.0 0.0
"Can someone help me? I don't have a good foundation for the details in math atm. I get the concepts really well, but I found something that doesn't make sense to me. When he is doing S (1-cos^2x)*sinx*cos^2x*dx = .... he adds the powers of cos^2x 's and makes it cos^4x. I tried pluging in numbers to see if this logic actually added up and it doesn't unless the base of the number with powers is 1. Is this because cos is considered 1 in some way? If I did 10^2 and 10^2... I get 10^4. lets say my formula is (1-10^2)*2*(10^2)*4=. well (1-100)*2*100*4 = -99*2*100*4 = -79200. But if I add those powers like so... (1-10^4)*2*4=-79,992. Doesn't add up. Anyone??? lol asking for a friend who knows what they are doing. I'm gonna go to school for this stuff but need to know what went wrong here. BTW as I said when the bases of the number with power being added are 1 it seems to work out." Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3085.0 0.0 1.0 0.0
"He's great :) " wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4637.0 0.0 0.0 0.0
"simply amazing :)" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14304.0 0.0 0.0 0.0
niceee 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14059.0 0.0 0.0 0.0
"Well, goodbye to my old calculus teacher!!! Welcome MIT!!!!!!!!!!" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 11365.0 0.0 0.0 0.0
"36:49 the precise answer would be n(n²-1)/3.." MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 1046.0 0.0 0.0 0.0
"Props to Saurav Bastola, https://www.youtube.com/channel/UC7hkeE-LRyzietNCecWnHLg for the listed topics.
Lecture 1: Rate of Change

Lecture 2: Limits
Lecture 3: Derivatives
Lecture 4: Chain Rule
Lecture 5: Implicit Differentiation
Lecture 6: Exponential and Log
Lecture 7: Exam 1 Review
Lecture 9: Linear and Quadratic Approximations
Lecture 10: Curve Sketching
Lecture 11: Max-min
Lecture 12: Related Rates
Lecture 13: Newton's Method
Lecture 14: Mean Value Theorem
Lecture 15: Antiderivative
Lecture 16: Differential Equations
Lecture 18: Definite Integrals
Lecture 19: First Fundamental Theorem
Lecture 20: Second Fundamental Theorem
Lecture 21: Applications to Logarithms
Lecture 22: Volumes
Lecture 23: Work, Probability
Lecture 24: Numerical Integration
Lecture 25: Exam 3 Review
Lecture 27: Trig Integrals
Lecture 28: Inverse Substitution
Lecture 29: Partial Fractions
Lecture 30: Integration by Parts
Lecture 31: Parametric Equations
Lecture 32: Polar Coordinates
Lecture 33: Exam 4 Review
Lecture 35: Indeterminate Forms
Lecture 36: Improper Integrals
Lecture 37: Infinite Series
Lecture 38: Taylor's Series
Lecture 39: Final Review" kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8448.0 0.0 0.0 0.0
"Can any1 say how should i download video????

" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3010.0 0.0 0.0 0.0
"So? 

This can mean a lot of things, and one of them is that they couldn´t tape this class and Strang had to repeat it in front of the cameras and they didn´t pay to some people to just sit right there so people like you would stop commenting that fact.

Great classes, I do not speak english as native language, but certainly this is awesome, I really appreciate it

So much Thanks to MIT and Professor Strang!!" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 8816.0 1.0 0.0 0.0
"For those who haven't gone through the lecture....I would say it is the best way this subject can be taught and he explains it very clearly. Not for those who have exam tomorrow." 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 3913.0 0.0 0.0 0.0
"amazing teaching methodology...salute sir!:)" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 12353.0 0.0 0.0 0.0
"In the Fib example, it seems impossible to find a c1 and c2 s.t. c1*x1 + c2*x2 = [1 0]" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 6657.0 0.0 1.0 0.0
"* I can solve Ax=b for all b that is in the column space of A.
* Nullspace is all the vectors x that solve Ax=b where b=0" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 229.0 0.0 0.0 0.0
"@cesfigas 
Ei, sou brasileiro . Vc na certa é português. O que acha de traduzir alguns?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 1810.0 0.0 0.0 0.0
"pls answer anyone" mHfn_7ym6to "8. Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 14192.0 0.0 0.0 0.0
"41:26 differenti-able :D
5/5" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 1152.0 0.0 0.0 0.0
"Does any one know where the solutions to the problem sets (link below) are? If there are no official solutions, does anyone have a solution that can be shared so I can check against my answers?
Link for psets:  https://ocw.mit.edu/courses/mathematics/18-650-statistics-for-applications-fall-2016/assignments/" V4xOdtqic3o "15. Regression (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 3428.0 0.0 0.0 0.0
"@anakore2 there is not! its minus because of the ""-u"" and the ""-1/2"" in (1-u)^-1/2" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1780.0 0.0 1.0 0.0
"*There is no video for Lecture 13 as that was the day for the Midterm Exam.*" 1VhnDdQsELo "14. P and NP, SAT, Poly-Time Reducibility" "MIT 18.404J Theory of Computation, Fall 2020" 240.0 0.0 0.0 0.0
"Thank you so much for the amazing lectures.. MIT!" --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9370.0 0.0 0.0 0.0
"so what ?
" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 14349.0 0.0 0.0 0.0
"why dimension of {0} is 0 ? I think it could be 1. Because there is a vector [0]. You can multiply it by c, it still keep answer to be zero. 
Any explain ?" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 15303.0 0.0 1.0 0.0
"31:59 Basically, the reason why you can solve this problem, you can make a finite automaton which recognizes the language B, is because that finite automaton is going to keep track of the parity of the number of 1's
it's seen before. This has two states, one of them remembering that it's seen an odd number of 1's so far,
the other one remembering it's seen an even number of 1's before. And that's going to be typical for these automata,
finite automata. There's going to be several different possibilities that you may have to keep track of as you're reading the input, and there's going to be a state associated with each one of those possibilities. So if you're designing an automaton, you have to think about-- as you're processing the input-- what things you have to keep track of. And you're going to make a state for each one of those possibilities

41:52 Show finite automata equivalent to Regular Expression." 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 919.0 0.0 0.0 1.0
"Denis Auroux is the prof's name. Thumbs up so everyone can know who he is!" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3347.0 0.0 0.0 0.0
"Does anyone else feel a nice smooth buttery feeling when the chalk glides against the board?
" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 3434.0 1.0 0.0 0.0
"this is so elementary to be taught on 1st year UNIVERSITY , but it's well taught GREAT " kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14876.0 0.0 0.0 0.0
"Thanks to MIT OCW and Prof. Strang from India. This journey of 34 lectures was really amazing !!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9800.0 0.0 0.0 0.0
"how did it go from intro 1 to this? When did he tal about central klimit theorem etc? is he solving exercises? wtf" C_W1adH-NVE "2. Introduction to Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 13217.0 0.0 0.0 0.0
"Why is the volume low af" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11890.0 0.0 0.0 0.0
"Is the camera-man sleeping?" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 6809.0 1.0 0.0 0.0
"A child of five years cannot understand this, the wonderful of language is that you can explain anything even child can sense, I think this the old system of teaching mathematics" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 2103.0 0.0 0.0 0.0
"Is this calculus 4?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6857.0 0.0 0.0 0.0
"Too much suspense! I'm starting the next video now" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 11067.0 0.0 0.0 0.0
"10:14 I don't think the centre of mass of the (N+1)th block would be 1 unit away, unless being considered at infinity." wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 343.0 0.0 1.0 0.0
"Apparently you can 
Not only calculate the transformation coordinate of two vectors by just doing dot product between the two vectors..
But you can also calculate the area and volume..
using determinant" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2516.0 0.0 0.0 1.0
"this is why MIT is world-leading, amazing stuff 
 " QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 14889.0 0.0 0.0 0.0
"This shit is so good" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10925.0 0.0 0.0 0.0
"somethings wrong in the last A=QR?  should the transpose on the q_1 q_2 not on the a_1 a_2??????" 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 14366.0 0.0 1.0 0.0
"I love him with my whole heart." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5732.0 0.0 0.0 0.0
"That guy who asked 'Are we supposed to understand this' just stopped my brain from going under stress, feeling that why ain't i understanding anything" _JXPe2J069c "Lec 21 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9888.0 0.0 0.0 0.0
"awsome lecture, the content just flows into the mind without much effort!" X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 12501.0 0.0 0.0 0.0
"The guy whit the camera was eating donnuts because he forgets to follow the teacher many times :/" twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10135.0 1.0 0.0 0.0
"Great lecture!!
Thank you Prof. Strang!" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 4274.0 0.0 0.0 0.0
"16:16 I guess it should be P(0,2)*int_0^3 f_T1(t)dt (probability of catching 0 fish in 2 hours*the probability of the 1st arrival within 3 hours). Then I get the same results
but somehow if you use P(0,2)*(1-P(0,3)) it's also the same result" XsYXACeIklU "15. Poisson Process II" "6.041 Probabilistic Systems Analysis and Applied Probability" 471.0 0.0 1.0 0.0
"Sir please allow ads to your videos and channel and monetize it that will help better than donation along with donation it will also be sharing knowledge freely" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8700.0 0.0 0.0 0.0
"finally everything in the last couple of lectures is coming together. Im finally understanding!" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 12857.0 0.0 0.0 0.0
"https://www.youtube.com/watch?v=S_Egep9GOpQ&list=PLBnyXcEhKK3CcaTN0gTM9vM70s_kLYuvn&index=6 can someone tell me  how did he get 1/2 and 1/3 in this mit special video" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 13278.0 0.0 1.0 0.0
"Probably not the best instructor. There are a lot of instructors on YouTube who are much much better teachers than him. Imagine the students at MIT have to through this ." vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 8257.0 0.0 0.0 0.0
"@Arstim lol econ" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1593.0 0.0 0.0 0.0
booooooo 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12552.0 0.0 0.0 0.0
"Ok Universities: teaches L'Hospital's Rule immediately after differentiation as a way of solving limits.
MIT: teaches L'Hospital's Rule last." PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8042.0 0.0 0.0 0.0
"Great lecturer, mediocre author." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 4301.0 0.0 0.0 0.0
"""I ADD! 3 times row one to ... (light speed level quick glance) row two !"" This man is the GOAT of linear algebra teaching." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 53.0 0.0 0.0 0.0
"Wish we all had a professor like him" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 11962.0 0.0 0.0 0.0
"if you don't understand this drop to 1260 lmao" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 13553.0 0.0 0.0 0.0
"your lecture is simply excellent, i'm very thankful to have the possibility to see it
thanks to the lecturer and mit from argentina" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 15525.0 0.0 0.0 0.0
"This professor is detailed in his calculations and explains why things work the way they do" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10902.0 0.0 0.0 1.0
"why should E[X] be zero at 21:30? I understand that W can be assumed with mean 0 but why X?" tBUHRpFZy0s "24. Classical Inference II" "6.041 Probabilistic Systems Analysis and Applied Probability" 15356.0 0.0 1.0 0.0
"It would be great if ""man"" and ""mankind"" were just ""humans"" and ""humankind"". It's a super easy change." rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7007.0 0.0 0.0 0.0
"Now I finally understood the linear regression in its matrix form" Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 7950.0 0.0 0.0 0.0
"7:54 yes, sir!!!!!!!!!!!!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1406.0 0.0 0.0 0.0
"미안하다 이거 보여주려고 어그로끌었다.. 선대 수준 ㄹㅇ실화냐? 진짜 세계관최강자들의 싸움이다.. 그 찐따같던 대수학이 맞나? 진짜 선대는 전설이다..진짜옛날에 맨날 선대와 군 봤는데 진짜 내가 다 감격스럽고 null space부터 eigenvector까지 가슴 울리는 장면들이 뇌리에 스치면서 가슴이 웅장해진다.. 그리고 강의에 진짜 언제 이렇게 신급 최강들이 되었을까 옛날생각나고 나 영재고 준비할 때 생각나고 뭔가 슬프기도하고 좋기도 하고 감격도 하고 여러가지 감정이 복잡하네.. 아무튼 길버트는 진짜 강의 중 최강명작임.." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 15677.0 0.0 0.0 0.0
"After passing  the linear algebra course, i was kind of disappointed no need  to see your lecture   again . but for data analysis u came again in a HD resolution. So glad to see you professor ." NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2248.0 0.0 0.0 0.0
"I don't know, why some people unlike this kind of valuable lectures....?" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5326.0 0.0 0.0 0.0
🖕🖕🖕probability🖕🖕🖕 jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15730.0 0.0 0.0 0.0
"I'm confused about the intersection of sub spaces. 
1) If the intersection doesn't contain the origin then you can't multiply by zero and hence doesn't satisfy condition 2
2) v&w may be in both sub spaces and can be added or scalar multiplied in either, but once the subspace is constrained, how do you know this is still true?" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 6310.0 0.0 1.0 0.0
"""I see that this fourth space is getting  second class citizen treatment..it doesn't deserve it""" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 60.0 0.0 0.0 0.0
"All his application lectures seem kind of sloppy" M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 2296.0 0.0 0.0 0.0
"Awesome lecture!" V4xOdtqic3o "15. Regression (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 2759.0 0.0 0.0 0.0
"Thank you, sir.Your temperament and wisdom impress me a lot." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9532.0 0.0 0.0 0.0
"@akhil089 If you have algebra to deal with you might find it helpful! Check it out! ""Speed maths- Multiplying without multiplying"". Click on my username and check the vid. Cheers." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 1772.0 0.0 0.0 0.0
"This automated motion-tracking is very bothering. Why not a wide-angle lens instead ?" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 10468.0 1.0 0.0 0.0
"Thankyou professor" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 9871.0 0.0 0.0 0.0
"It is heart warming to see so many people showing appreciation for this great man. It is has been an honor to watch this man's classes." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 6947.0 0.0 0.0 0.0
"at 38:40 ""has anyone seen this before?""  I mean...HOW DID YOU GET INTO    M  I  T    if you don't know what the Law of Cosines is????" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12448.0 0.0 0.0 0.0
"48:37 A little confusion here. Don't you have to use a lower bound for that junk terms? Big O is an upper bound. And (delta x)^2 cannot be an upperbound for, say, (delta x)^3." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1295.0 0.0 1.0 0.0
"absolutely loved this lecture. so many elegant ideas! witnessing ⟨D⟩ being fed into D felt as mindblowing as learning the Y-combinator" 3PzuSPQPEU4 "8. Undecidability" "MIT 18.404J Theory of Computation, Fall 2020" 12303.0 0.0 0.0 0.0
"Interesting. When I think about the prospect of even the function of a -a^x I don't know how that would even be graphed. Seeing as the fractional powers between the integers would involve roots of negative numbers right? 

Take -2^1/2 for example, which would imply the square root of -2, which is undefined unless we use imaginary, right? 

Thinking about it, I guess you could graph the integer values of x which would generate alternating positive and negative y's right? hmm." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6734.0 0.0 1.0 0.0
"Think think his proof at 22:38 is unclear. cos(t) is not represented by the green line, rather it is the distance from the center of the circle (or tip or the arc) along the radius to the point where the green line meets the radius line. cos(t) approaches 1 as (t) approaches 0, and hence cos(t) - 1 approaches 0." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10450.0 0.0 1.0 0.0
"No obscure boring definition but still looks very clear with live examples, thank you!" TluTv5V0RmE "2. Conditioning and Bayes' Rule" "6.041 Probabilistic Systems Analysis and Applied Probability" 7879.0 0.0 0.0 1.0
"I Really Like The Video Independence, Basis, and Dimension From Your" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 4976.0 0.0 0.0 0.0
"is he french?" tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13630.0 0.0 0.0 0.0
坏！ CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 15619.0 0.0 0.0 0.0
"It is the truth, Calculus is very hard for some people but hat does not mean that you have to find it hard." jBkXbAgMj6s "Lec 24 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6969.0 0.0 0.0 0.0
"10: 37 ""the queue is getting closer and closer to pee"" " 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 338.0 0.0 0.0 0.0
"Thank you so much sir gilbert strang and OCW MIT, for such a wonderful course... Really helpful...
Gilbert sir...You have taught this topic in the best way possible...Thank you" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9378.0 0.0 0.0 0.0
"(Negative due to that positive direction is chosen upwards; speed is the absolute value |v|, meaning it only cares about the magnitude, not the direction, hence it's a scalar." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 223.0 0.0 1.0 0.0
"@virginialikesyou 

This is Denis Auroux. It says the names at the beginning of each lecture! You can search for him in the ""people"" search at mit.edu and shoot him an email - I doubt he'll respond, but he might read it!" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2062.0 0.0 0.0 0.0
"So fucking confused lmaoo" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8758.0 0.0 0.0 0.0
"wow !  This is really a masterpiece." 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 15408.0 0.0 0.0 0.0
"Lecture timeline Links
Lecture 0:00
What's the Inverse of a Product 0:25
Inverse of a Transposed Matrix 4:02
How's A related to U 7:51
3x3 LU Decomposition (without Row Exchange) 13:53
L is product of inverses 16:45
How expensive is Elimination 26:05
LU Decomposition (with Row exchange) 40:18
Permutations for Row exchanges 41:15" MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 7301.0 0.0 0.0 0.0
"Method of Moments starts at 32:36" JTbZP0yt9qc "6. Maximum Likelihood Estimation (cont.) and the Method of Moments" "MIT 18.650 Statistics for Applications, Fall 2016" 7659.0 0.0 0.0 0.0
"Being taught by an instructor who not only has an h-Index of 90 but is also the author of your textbook is a flex you can only have while sitting in an MIT classroom." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 2843.0 0.0 0.0 0.0
"I am not surprised ShaneHayes that you are doing this in school. This is the first lesson in AS level differential calculus taught to 16/17 year olds all over the UK. The delivery is complicated but the ideas are identical
" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5128.0 0.0 0.0 0.0
"USA 🇺🇸 MIT!!
Let's focus on our students, our future." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11116.0 0.0 0.0 0.0
"How does the +1 end up coming in" -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 4861.0 0.0 1.0 0.0
"Thank you Prof Strang.  Wonderful course. Have learned to love Linear Algebra - something I never managed in the 60's.  ;¬D  All the very best" rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9185.0 0.0 0.0 0.0
"это проходится в Росси в 9 классе" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15561.0 0.0 0.0 0.0
"I been studying and working with mathematical statistics for almost 10 years. This is the first time I actually understand (intuitively) what the Bayesian approach is" bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 5164.0 0.0 0.0 0.0
"we are grateful of MITOCW and prof Gilbert Strang, we might not be at MIT but we have the sense of being there and learning whatever you offer. 
you are doing the best thing a human being can do." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 15072.0 0.0 0.0 0.0
"i learned this in highschool" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13413.0 0.0 0.0 0.0
"Question) If we complete the squares of the eq. (at 44:53), I don't think the squares get multiplied by the three pivots(2, 3/2, 4/3)... Can anyone tell me why?" vF7eyJ2g3kU "27. Positive Definite Matrices and Minima" "MIT 18.06 Linear Algebra, Spring 2005" 8477.0 0.0 1.0 0.0
"Nice Video" cjeXg5rJ9D8 "Lecture 13: Limits of Functions" "MIT 18.100A Real Analysis, Fall 2020" 7838.0 0.0 0.0 0.0
"Peter Griffin says: ""This tv show is Fantastic Lois i knew i shouldn't trust this fucked up GPS""
Thanx MIT" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8185.0 0.0 0.0 0.0
"The application of the Fundamental Theorem of Linear Algebra is the constant theme of Professor Strang's lectures:
http://mathworld.wolfram.com/FundamentalTheoremofLinearAlgebra.html

I never heard of this theorem before these lectures, and I'm an Old Bastard. So this has been a fun learning experience!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 9981.0 0.0 0.0 1.0
"I LOVE GILBERT STRANG SIR. I am in high school and love his lectures. All this is taught in a boring way in our class...but STRNG SIR maks this topic epic. Now I love linear algebra!! thanks a lot MIT for helping millions like me" TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 4925.0 0.0 0.0 0.0
"ajea ❤😂" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12318.0 0.0 0.0 0.0
"Thanks Sir. Couldn't get well the big diff between posterior and prior distributions." 1jDBM9UM9xk "21. Bayesian Statistical Inference I" "6.041 Probabilistic Systems Analysis and Applied Probability" 9646.0 0.0 1.0 0.0
"The fuck is that" 4LYom0ekars "4. Forbidding a subgraph III: algebraic constructions" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 10116.0 0.0 0.0 0.0
"Great! What a gifted Professor, thank you Dr. Strang!" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 4370.0 0.0 0.0 0.0
"x+y+3z=5
is the equation of a plane ..
Then you find normal vector from that equation
which is perpendicular to the plane..
So maybe the equation of that normal vector is
x+y+3z=0
Then normal vector to the plane is
N=<1,1,3>
Then do dot product between N and Z
If it is 0 then it is perpendicular to N and thus Z is parallel with the plane x+y+3z=5
People might be mistaken ..
Ah just do dot product between Z and <1,1,3> ..ah it's 0 so it must be perpendicular to the plane x+y+3z=5
And doest not realized <1,1,3> the normal vector of plane x+y+3z=5..
I don't really understand this..
Because what does x+y+3z=0
Represents?
Is it perpendicular to x+y+3z=5?
It must be not true
Because the planes must be parallel to each other because the coefficient of x,y,z are similar
Maybe the way he gets the normal vector is weird but it is what it is" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15454.0 0.0 1.0 0.0
"Video starts at 13:00" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 11234.0 0.0 0.0 0.0
"cleaning blackboards just before they get covered by the other one...






*savage*" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12655.0 1.0 0.0 0.0
"Could someone explain to me why d/dx f(kx) = kf'(kx) around 18:00? " 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3233.0 0.0 1.0 0.0
"This is Pop mathematics. He did not explain why the derivative of the sum of two functions is the sum of the respective derivatives. Given that is correct you assume that the derivative of the product of two functions is the product of the respective derivatives?  Of course not because (f * g)'(x)=f'(x)*g´(x)+f(x)*g'(x),
" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10582.0 0.0 1.0 0.0
"Prof strang brings a smile to my face every lecture. Without fail." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 8285.0 0.0 0.0 0.0
"@deyomash Bullshit" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1824.0 0.0 0.0 0.0
"thankeewwwwwwwww sooooooooo muchhhhhhh for uploading these vedios for free" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14539.0 0.0 0.0 0.0
"48:54 red bull on the desk...." 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1301.0 1.0 0.0 0.0
"it's so weird how some of these MIT students look like normal people. some of the girls are actually hot! i must say i'm shocked, given the stereotype associated with MIT..." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13700.0 0.0 0.0 0.0
"This guy literally helped me pass all my stats courses! He is a bomb... If i ever visit MIT, i will drop by and thank him in person lol" IkbkEtOOC1Y "16. Markov Chains I" "6.041 Probabilistic Systems Analysis and Applied Probability" 10551.0 0.0 0.0 0.0
"He's mentioning Rectifier Linear Unit (ReLU) when he talks about that important function ie: f(x) = max(0, x)" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4640.0 0.0 0.0 0.0
"15:13 I don't want to make that precise - Gilbert Strang -
16:33 Big determinant formula
22:34 Example
24:48 *DEATH PASSING BY*
29:26 Cofactor 3x3
36:00 Cofactor features
39:45 Cofactor formula
43:54 Tri-diagonal matrix Example" 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 450.0 0.0 0.0 0.0
"@sponsoredwalk1 The Khanacademy ones do give you the intuition but the ability to derive them, at least for me, brings this one over the top.

While Mr. Khan is great at giving you intuition, I think it is much better for you to be able to derive the equations in order for you to get the intuition.

Also he doesn't tell you how to derive anything, other than a few instances.(From what I have seen.)" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2026.0 0.0 0.0 1.0
"Teaching like this is exceedingly rare..Gilbert Strang is near unique." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 9022.0 0.0 0.0 0.0
"Does he mean ""a * a^T"" near the end of the video?" xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3452.0 0.0 1.0 0.0
"33:18 Flirting starts at row 2, not the matrix row I mean." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 956.0 0.0 0.0 0.0
"Well that was quite the pleasure! Thank you Professor Strang for your excellent instruction! I had to rewatch some episodes after getting to the halfway point due to a forced break resulting in me forgetting a few points, so really I've now seen 50+ of these. They were always great, though! And I intend to take the Computational Science and Engineering and Differential Equations and Linear Algebra courses, too. Hope they're equally as good!" RWvi4Vx4CDc "34. Final Course Review" "MIT 18.06 Linear Algebra, Spring 2005" 11359.0 0.0 0.0 0.0
"Handwriting ❤️" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4419.0 0.0 0.0 0.0
"so based" tBUHRpFZy0s "24. Classical Inference II" "6.041 Probabilistic Systems Analysis and Applied Probability" 14326.0 0.0 0.0 0.0
"MIT please provide water and sponges for your professor's blackboard cleaning needs wtf" X-ix97pw0xY "21. Generalized Linear Models" "MIT 18.650 Statistics for Applications, Fall 2016" 7537.0 1.0 0.0 0.0
"Thank you, Prof.
Thank you, MIT." 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 9507.0 0.0 0.0 0.0
"It`s kind of funny, the word ""Eigenvector"" is a mix of german with english" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7079.0 0.0 0.0 0.0
"his lectures are extremely trrible i don not u8nderstand how all comments agree that they are great it seems like they are watching kim during the lecture" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 13166.0 0.0 0.0 0.0
"Wait, the people at this university already know this stuff right?!
because I am learning this in high-school... they can't just be going through it in university at MIT!?!??" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11263.0 0.0 0.0 0.0
"He does the lecture off the top of his head, he's great" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 4474.0 0.0 0.0 0.0
same dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 14276.0 0.0 0.0 0.0
"thank you, professor strang" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 14533.0 0.0 0.0 0.0
"he has amazing grasp of the subject" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 13081.0 0.0 0.0 0.0
"Now I really understand what Tschebyschev is actually saying :)" 3eiio3Tw7UQ "19. Weak Law of Large Numbers" "6.041 Probabilistic Systems Analysis and Applied Probability" 7954.0 0.0 0.0 0.0
"Great teacher." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 4339.0 0.0 0.0 0.0
"What a pleasant fellow!
I am very thankful that he enjoys what he does so very much.
Stay awesome man!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 11428.0 0.0 0.0 0.0
"This is the best teacher I ever seen. :D" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 10746.0 0.0 0.0 0.0
"oh thank god for this first 18.06 test Friday " 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 14112.0 0.0 0.0 0.0
"Dear IDidactl, 

Thank you very much for your reply.  I understood now.  Thanks again. 

Are you taking his class as well?" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3323.0 0.0 0.0 0.0
"Very helpful to future students! Great work! Thank you!" m9eHViDPAJQ "4. Pushdown Automata, Conversion of CFG to PDA and Reverse Conversion" "MIT 18.404J Theory of Computation, Fall 2020" 11195.0 0.0 0.0 0.0
"The end portion really educated how matrix algebra theory can be applied to computer vision; really glad he added that in." nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10088.0 0.0 0.0 1.0
"Hi , I need cours about matrices polynomial please ." xsP-S7yKaRA "5. Positive Definite and Semidefinite Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 4707.0 0.0 0.0 0.0
"Thanku Jitendra Singh  Gill Sir, for recommending this video. Very well explained." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9862.0 0.0 0.0 0.0
"Blackboard = best teaching method!" MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2897.0 1.0 0.0 0.0
"ANY 1 FROM INDIA" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2182.0 0.0 0.0 0.0
"Damn, his jokes are just not landing." RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3305.0 0.0 0.0 0.0
"Between Auroux erasing chalkboards and Walter Lewin making dotted lines, MIT is full of chalkboard GODS." ChiM2-MV-qM "Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2889.0 1.0 0.0 0.0
"Thanks for this amazing lecture ." j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 9728.0 0.0 0.0 0.0
"From a pedagogical point of view this lecture ist bad." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3928.0 0.0 0.0 0.0
"I love you professor !!!" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 5848.0 0.0 0.0 0.0
"I find it sad that more people are watching politicians debate than all this amazing free education.  Wake up people, be smarter.  Anything the government gives you was first stolen, then leveraged with the central banks.  Turn off the 'entertainment' and get smart." DUA6lk7X2VY "20. Roth's theorem III: polynomial method and arithmetic regularity" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 5415.0 0.0 0.0 0.0
20220517簽 k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 633.0 0.0 0.0 0.0
"Aha so close to finish course 😏 only twelve lectures remained 🤗" QNpj-gOXW9M "20. Cramer's Rule, Inverse Matrix, and Volume" "MIT 18.06 Linear Algebra, Spring 2005" 2282.0 0.0 0.0 0.0
"""if you cannot explain what you  learnt to a little child in the way that she/he can understand easily, you definitily didint understood what you a trying to explain"". This Professor Understood deepily lenear algebra. Congrates and thanks" Ts3o2I8_Mxc "30. Linear Transformations and Their Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 158.0 0.0 0.0 0.0
"and unacademy says...their content is best...lol" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12375.0 0.0 0.0 0.0
"Guys, remember this is simply revision!

(its a very international university and people know different things so they make sure everyone knows the basics of everything and then they work them hard)

this is to level the playing field, also note that they do this stuff very very quick and so someone who has no experience with them will still struggle (im from the UK btw)" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4392.0 0.0 0.0 0.0
"I think he made an error. He said the determinant of an orthogonal matrix is 1, but actually it is 1 or -1. Then Det(A) = + or - the product of the singular values." rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6016.0 0.0 1.0 0.0
"In Dr. Strang's lecture, every idea rolls out so naturally that you feel the world should have been like that in the first place." Z_5uLqcwDgM "Lecture 10: Survey of Difficulties with Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6610.0 0.0 0.0 0.0
"This man is my hero 🙌🏽✨" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 10871.0 0.0 0.0 0.0
"The geometric proof was great." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 10119.0 0.0 0.0 1.0
"thank you so much!" l4NoMKEHQwM "11. Derived Distributions (ctd.); Covariance" "6.041 Probabilistic Systems Analysis and Applied Probability" 14518.0 0.0 0.0 0.0
"CLEARLY the camera man DOES NOT attend MIT." MK_0QHbUnIA "Lec 37 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2982.0 1.0 0.0 0.0
"That was the kind of lecture that deserved applause!" k3AiUhwHQ28 "25. Stochastic Gradient Descent" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9924.0 0.0 0.0 0.0
"Thanks sir!" KAySmSEGc9U "3. Regular Pumping Lemma, Conversion of FA to Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 9779.0 0.0 0.0 0.0
"Mr. Professor - you are great!" nrDkb2MAwSA "20. Definitions and Inequalities" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 7715.0 0.0 0.0 0.0
"life saving god thank you" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 13789.0 0.0 0.0 0.0
"This simple connected region lecture, helps to find the integration using line integral using green theorem for multiply connected region. " PnPIqh7Frlw "Lec 24: Simply connected regions; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10927.0 0.0 0.0 1.0
"He is a great teacher, thanks" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4500.0 0.0 0.0 0.0
"Great lecture! Invigorating, precise, and enthusiastic!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4267.0 0.0 0.0 0.0
"Trying to get a head start before the semester. Thank you Prof. Strang!!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11098.0 0.0 0.0 0.0
Thanks! k2inA31Gups "18. Bayesian Statistics (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 9825.0 0.0 0.0 0.0
"This professor has saved me a bunch of struggle. I really appreciate it. I don't normally write on YouTube videos but this is an exception. Great stuff, great professor. Can't wait to watch more." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 10894.0 0.0 0.0 0.0
"9:38 - MIT - Massachusetts Institute of Technology
9:40 - MIT - Mexico Institute of Technology" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 1442.0 0.0 0.0 0.0
"41:32 my determination level" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 1154.0 0.0 0.0 0.0
"thanks a lot sir!" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 14572.0 0.0 0.0 0.0
"@MyInfiniteWisdom He is french" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1688.0 0.0 0.0 0.0
"Start at 10:40" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 8880.0 0.0 0.0 0.0
"Really happy this is online! Thank you Professor :)" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 8519.0 0.0 0.0 0.0
"27:36 legend say he's still waiting for his high5 till now" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 823.0 0.0 0.0 0.0
"30:40 that thing won't stop staring at me :O" dK3NEf13nPc "Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 892.0 0.0 0.0 0.0
"@horrabletypoe You think it matters? You really don't have to be overly smart to go to a school as great as MIT. You just have to show them you have the persistence to learn from their staff. Obviously, you cannot be overly stupid either." PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1870.0 0.0 0.0 0.0
"while explaining flux in his 2nd question. the force was only directed towards the z- axis ;
the question is if we look physically doesn't it happens that the flux is zero , as the amount of flux entering is also leaving . please explain" phk05iSMezA "Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15254.0 0.0 1.0 0.0
hello rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 13132.0 0.0 0.0 0.0
"I just found this guy.  Man, he is good." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5606.0 0.0 0.0 0.0
"2:00 hahahaa" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 865.0 0.0 0.0 0.0
"how many of you here are from iit delhi" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 13245.0 0.0 0.0 0.0
"What is the use of this?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11542.0 0.0 0.0 0.0
"good teacher" k095NdrHxY4 "4. Eigenvalues and Eigenvectors" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 12952.0 0.0 0.0 0.0
"36:21 how can sum(x^n) be 1/(1-x), that is obviously too small" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 1037.0 0.0 1.0 0.0
"can anyone provide me notes" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 12610.0 0.0 0.0 0.0
"I did not have 1 degree of separation from that woman." 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 5258.0 0.0 0.0 0.0
"could someone explain how to do the integral at 28:00?" CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 12687.0 0.0 1.0 0.0
"It seems that Prof. Gilbert Strang is a fan of Gauss." Y4f7K9XF04k "7. Eckart-Young: The Closest Rank k Matrix to A" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6981.0 0.0 0.0 0.0
"why can we treat the mean of x equal to 0?" 4HRhg4eUiMo "8. Parametric Hypothesis Testing (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 15291.0 0.0 1.0 0.0
"Omg you know how to teach,wow👏👏👏. You make life with stats so so easy for students." 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 8063.0 0.0 0.0 0.0
"prof.strang teaches you how to think !!! a rare thing in many" cdZnhQjJu4I "21. Eigenvalues and Eigenvectors" "MIT 18.06 Linear Algebra, Spring 2005" 14215.0 0.0 0.0 0.0
"so sweet... i wish my linear algebra prof was actually interested in teaching math" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 14344.0 0.0 0.0 0.0
"Mr. Denis made me able to pass my final Multivariable Calculus exam... He's the boss!!!" RMBGQtwkoyU "Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7712.0 0.0 0.0 0.0
"carai mindblowing essa parada de infinitesimais" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12645.0 0.0 0.0 0.0
"32:41 – that's where the FFT part starts." M0Sa8fLOajA "26. Complex Matrices; Fast Fourier Transform" "MIT 18.06 Linear Algebra, Spring 2005" 938.0 0.0 0.0 0.0
"The best math professor I have ever enxountered" YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 10002.0 0.0 0.0 0.0
"For people who are confused, try studying basics of 3-D geometry. You will easily understand the equation of tangent plane. It is basically asking us to find the equation of a plane whose direction ratios of its normal vector and the a point through which it passes is given." 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 3870.0 0.0 0.0 1.0
"Hot off the presses : We can pair every positive floating point number 
using up only about 20% of the integers 

Algorithm #1 : Convert a float with a zero whole part into an integer

1. Reverse the character sequence representing this float
2. Remove the decimal point to obtain the desired integer

Example :  Convert the float 0.002743 into its integer equivalent
1. Reverse the float string to obtain 347200.0
2. Remove the decimal point to obtain the integer 3472000 
3. Note : All corresponding integers will be terminated by the character  “0”

Algorithm #2 : Convert a float with a non-zero whole part into an integer

1. Count the number of whole digits or NWD (those preceding the decimal point ) 
2. Append a number of  “0” digits equal to NWD to the float. 
3. Append a digit “1”  to the resulting float
4. Remove the decimal point to obtain the desired integer

Example : Convert the float  1230.0098 into its integer equivalent 
1. Count the number of whole digits : NWD = 4
2. Append NWD = 4  “0” digits to obtain 1230.00980000
3. Append a digit “1”  to obtain 1230.009800001
4. Remove the decimal point : this gives us the final integer of 1230009800001

Note : We append a digit “1”  to distinguish the integers derived from floats with 
non-zero whole parts from integers generated by floats with zero whole parts .

This can be done for every  float [whole.fraction]  where whole  >  0  !!! AMAZING!!! 
We just came up with a scheme which pairs each positive float with a positive integer.

Reverse Algorithms : Converting valid syntax integers into floats also exist" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 4792.0 0.0 0.0 0.0
"You know, up till now, I had considered this guy to be a ""definitely good"" teacher, but not much past that...   but under the staggering weight of the sheer amount of unforced, helpful insight he provides in this video, I am forced to reclassify him as one of the best math teachers I've seen. If you are reading this, Prof. Jerison - Thank You, Good Sir. Much obliged. */tips hat*" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12222.0 0.0 0.0 0.0
"Thank you soooo much!! ❤️" a1ZCeFpeW0o "20. Principal Component Analysis (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 9420.0 0.0 0.0 0.0
"He never taught the compression step right? ie., c -> c(hat)" 0h43aV4aH7I "31. Change of Basis; Image Compression" "MIT 18.06 Linear Algebra, Spring 2005" 4590.0 0.0 1.0 0.0
"If the Angle language is German, both Newton and Leibniz were German, which is great for the German people. It means they can solve their own problems on their own land." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6517.0 0.0 0.0 0.0
"Why you always add y' at the end of differentiation of any y?
Please Answer!!" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11938.0 0.0 1.0 0.0
"2020 still there, following every tape and note so far," 0MtwqhIwdrI "17. Orthogonal Matrices and Gram-Schmidt" "MIT 18.06 Linear Algebra, Spring 2005" 627.0 0.0 0.0 0.0
"blackboard duster action highlights - 28:28 and 43:30" 2XraaWefBd8 "Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 12545.0 1.0 0.0 0.0
"49:35 Why is F1 equal to 1? Isn't the first number in the sequence 0?" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 1308.0 0.0 1.0 0.0
"Great videos! the only thing that i'm missing is ""to rise my hand and ask him some questions"".." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 4362.0 0.0 0.0 0.0
"Thanks for the lesson! One thing Idont understand is why exactly does the way we do example to with the greater than one same linear factor in the denominator work? I still dont understand how it was roved to be so from the analogy...Please help. Thanks!" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9721.0 0.0 1.0 0.0
"love this course" TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 13881.0 0.0 0.0 0.0
"36:24 there’s a mistake here. It should lead to integrating [u^(-1/2)]/2" -MI0b4h3rS0 "Lec 15 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1039.0 0.0 1.0 0.0
"What a lecture" 6oV3pKLgW2I "4. Counting" "6.041 Probabilistic Systems Analysis and Applied Probability" 11419.0 0.0 0.0 0.0
"18:31 26:42 oh lololol :D" tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 541.0 0.0 0.0 0.0
"I had 3 semesters math in informatics study. This guy is way better than my prof years ago. He explains it way better" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5460.0 0.0 0.0 0.0
"@jcgarces85 Denis Auroux" 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1900.0 0.0 0.0 0.0
"Of all the lectures in this course, this was the least understood. Formulae outta nowhere!!!" hjZhPczMkL4 "Lec 18 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7994.0 0.0 0.0 0.0
"Subgraph can be a loop or cant be without a loop. Did this answer ur question?" 6-wh6yvk6uc "12. Graphs, Networks, Incidence Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 8921.0 0.0 1.0 0.0
"thank a lot" YzZUIYRCE38 "14. Orthogonal Vectors and Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 14452.0 0.0 0.0 0.0
"He talks about 'a bunch of' this and that. Euler would not have talked in such a loose way." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 4610.0 0.0 0.0 0.0
"@matanorland1 This is not how things work. MIT works like a corporation, and when corporations start new projects, they either allocate money for their development from a bank account or by loans. After the project is developed is must be self-sustained and cannot exist as a burden of other projects. Plus, departments compete within an corporation for funding; it's not free for all." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1937.0 0.0 0.0 0.0
"@ShaneHayes123 do you know about Taylor series or Bernoulli's-L'Hopital's rule? This is only the first lecture. The first several lectures (for example math) in technical universities all over the world is repeat of last school lessons. 23 people is schoolie like you, imho." 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1724.0 0.0 0.0 0.0
"20:00 an example from suspension bridge
50:00 how well Newton's method works" sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 641.0 0.0 0.0 0.0
"Love it!" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 7446.0 0.0 0.0 0.0
"@iDiViNeXx His from Italy" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1882.0 0.0 0.0 0.0
Superb! IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 8966.0 0.0 0.0 0.0
"Liked that teacher! he is funny ^^
great class \o" 4sTKcvYMNxk "Lec 4 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7363.0 0.0 0.0 0.0
"
i really had to stretch my mind here !" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 5.0 0.0 0.0 0.0
"Finally the subtitles are on sync!!
This is great!!" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 3779.0 0.0 0.0 0.0
"""Fundamental Theorem of Linear Algebra"" ~ Wolfram
http://mathworld.wolfram.com/FundamentalTheoremofLinearAlgebra.html

Application of this theorem is the underlying theme of these lectures." TX_vooSnhm8 "29. Singular Value Decomposition" "MIT 18.06 Linear Algebra, Spring 2005" 47.0 0.0 0.0 1.0
"views has been decreasing since lecture 1 ... only the few remain xD" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15046.0 0.0 0.0 0.0
"I thought Multivariable Calculus was Calculus 3?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6088.0 0.0 1.0 0.0
"Fortunate are those who get to study the book directly from the author..." l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 3918.0 0.0 0.0 0.0
"Very helpful to future students! Great work! Thank you!" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 11194.0 0.0 0.0 0.0
"오늘 지수함수 미분 공부했는데... 추천 동영상에 뜨다니 소오름...." 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15683.0 0.0 0.0 0.0
"Is it possible to obtain a course completion certificate in exchange for a final exam to determine the student's level?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6795.0 0.0 0.0 0.0
"Thanks professor Jerison. Great job
Thanks a lot!" wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9762.0 0.0 0.0 0.0
"Why does the nullspace of A is in Rn instead of Rm when the special solution vectors have m components" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 11847.0 0.0 1.0 0.0
"in pset 7 of 18.02sc excercise 3c-3 the formula used  for the solution is without squaring the distance. I think it's wrong at least I'm missing something with respect at min. 41:00 explanation. Pset (solutions) link: http://goo.gl/Qwyivj" 60e4hdCi1D4 "Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13594.0 0.0 1.0 0.0
"Please add subtitles in Turkish. Thank you." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 8199.0 0.0 0.0 0.0
"Thank you,  my university professor did not explain this good. This is called Taylor eqation? Am I right?" eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9491.0 0.0 0.0 0.0
"Clearly Prof.Strang is a master, and his lectures are brilliant. But how do the students learn without Q&A? Is this standard procedure at MIT?" 13r9QY6cmjc "22. Diagonalization and Powers of A" "MIT 18.06 Linear Algebra, Spring 2005" 3156.0 0.0 0.0 0.0
"At 6:30 , if 3 times 2 equals 6 and 6 minus 8 is - 2 why he wrote positive 2? What did I miss here?" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 2696.0 0.0 1.0 0.0
"why does the chalk on the board have cel shading with edge detection? :o" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 15312.0 1.0 0.0 0.0
"i like math series in ocw mit veryy much <3
" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13419.0 0.0 0.0 0.0
Thanks! bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9822.0 0.0 0.0 0.0
"I never really got the whole picture thing even until now. Does it give any conceptual meaning beyond the definitions embodied by it? Or it is merely a memory aid to remember the definitions? The definitions embodied are:
For any m by n matrix A - row space and nullspace are orthogonal complements in Rn, column space and left nullspace are orthogonal complements in Rm.

i.e. does it supply meaning to the 4 subspaces the way a graph would supply meaning to a function? From what I see, no... Or am I missing something?" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 5882.0 0.0 0.0 0.0
"Thank u sir. Hope u read this !!" 3MOahpLxj6A "5. Discrete Random Variables I" "6.041 Probabilistic Systems Analysis and Applied Probability" 9077.0 0.0 0.0 0.0
"Maybe the cameraman can zoom in more, profs handwriting is a bit small" 9_xG0AGRa-w "Lecture 2: Cantor's Theory of Cardinality (Size)" "MIT 18.100A Real Analysis, Fall 2020" 7640.0 1.0 0.0 0.0
"could someone help me in finding the difference between (delta y / delta x) and (dy/dx) please? 
it would be a great help you have done to me  🧡" ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12688.0 0.0 1.0 0.0
"@treeandplant your comment confuses me 0_o" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 2049.0 0.0 0.0 0.0
"Thanks 3brown2blue to make this easier." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9583.0 0.0 0.0 0.0
"Insane :)" WW3ZJHPwvyg "19. Principal Component Analysis" "MIT 18.650 Statistics for Applications, Fall 2016" 6713.0 0.0 0.0 0.0
"hmmm thanks for the explanation. I had to play with examples for some time to get a hang of it." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 13177.0 0.0 0.0 1.0
🍆🍆🍆🍆🍆🍆🍆🍆🍆🍆🍆🍆🍆🍆🍆🍆🍆🍆🍆🍆🍆🍆🍆🍆🍆🍆🍆🍆🍆🍆🍆🦖🐍🦖🐍🦖🐍🦖🐍🦖🐍🦖🐍🦖🐍🦖🐍🦖🐍🦖🐍🦖🐍🦖🐍🦖🐍🦖🐍🦖🐍🦖🐍🦖🐍🦖🐍🦖🐍🦖🐍🦖🐍🦖🐍🦖🐍🦖🐍🦖🐍🦖🐍🦖 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15696.0 0.0 0.0 0.0
"Gilbert Strang,

You are an awsome teacher! Congratulations for the great work done and thanks for the opportunity!

Congratulations to MIT as well." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 4033.0 0.0 0.0 0.0
"density in grams per cubic inches???? Weird! He was really in a rush towards the end though..." 44R5HgbrUmc "Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 12733.0 0.0 0.0 0.0
"Is he taken? I’m in love." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 6774.0 0.0 0.0 0.0
"Its difficulty is irrelevant. If you have to take it, there is not point wondering whether or not it's easy or hard. While there are different universities, the material will always remain the same." QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 7084.0 0.0 0.0 0.0
"hell yeah, hyperbola bitch. btw when kepler found out that reality there was no calculus. smart man, huh?" BGE3wb7H2PA "Lec 33 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13131.0 0.0 0.0 0.0
"This is art! Indeed!" 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 10640.0 0.0 0.0 0.0
"Damn, this is a great lecture....  somehow connect to the least square problem by the interpretation of pure linear algebra without using calculus.   what an enlightenment." Y_Ac6KiQ1t0 "15. Projections onto Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 3308.0 0.0 0.0 1.0
"You mean the area under the CURVE of sinx lol 
the hump exactly proper terminology :p    who says that?!" 1RLctDS2hUQ "Lec 19 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12226.0 0.0 0.0 0.0
"Good lecture.  Horrible camera control." BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 4136.0 1.0 0.0 0.0
"Great thanks Mit OCW, the textbook is also great" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 4346.0 0.0 0.0 0.0
"Mr David sir L'hospitat's rule  holds  provided f(a)=g(a)  is correct  also limit must exists  means both left & right limits must exist not only right limit" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7708.0 0.0 1.0 0.0
"just amazing, thank you ! professor." sRIDVAcoG5A "Lec 13 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13729.0 0.0 0.0 0.0
"Finally Its HAD BEEN DONE" BChhAS1sFvA "Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07" "MIT 18.02 Multivariable Calculus, Fall 2007" 3763.0 0.0 0.0 0.0
"where are lectures 4,5?" 19Ql_Q3l0GA "3. Independence" "6.041 Probabilistic Systems Analysis and Applied Probability" 15217.0 0.0 0.0 0.0
"These whole series is brilliant.  Excellent job by Prof. Tsitsiklis.  My respect and admiration." -qCEoqpwjf4 "6. Discrete Random Variables II" "6.041 Probabilistic Systems Analysis and Applied Probability" 10435.0 0.0 0.0 0.0
"simple and great" YP_B0AapU0c "Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 14301.0 0.0 0.0 0.0
"Look before you ""elope""?" PNTnmH6jsRI "Lec 35 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7415.0 0.0 0.0 0.0
"It is definitely a pun. So hilarious." 23LLB9mNJvc "19. Determinant Formulas and Cofactors" "MIT 18.06 Linear Algebra, Spring 2005" 6943.0 0.0 0.0 0.0
"Thanks MIT !" 9v25gg2qJYE "Lec 6 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9603.0 0.0 0.0 0.0
"What is the overall of the E ? You said that there was two E in these case and I want to know what are those E ?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11531.0 0.0 1.0 0.0
"Thanks for this amazing video... Am a high schooler seeking to study something extra... I am interested, but can anyone suggest me some material, from which I can practice problems as well?" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 9729.0 0.0 0.0 0.0
"Come to visit us in Berkeley!😊" YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3170.0 0.0 0.0 0.0
"Anyone can tell me at the first time of the lecture, is the formular of total differential from the definition?" 23xbkrpQuAo "Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 2484.0 0.0 1.0 0.0
"I love these lectures, but it's really annoying how, in a lot of them, the professor's mic stops working at some point and the subtitles also start to get wonky. Makes it really hard to understand sometimes." srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 5797.0 1.0 0.0 0.0
"Why ||A||2 = max ||Ax||2/||x||2? Can someone help me explain? :(" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11940.0 0.0 1.0 0.0
"I think this course could be part of the Micromaster Credential in Statistics & Data Science because it all these lectures are CRITICAL to understand learning-from-data processes." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6074.0 0.0 0.0 0.0
"Why not introduce Python or R; or is that reserved for the ML + CS courses? Basically why Julia?" rZS2LGiurKY "Lecture 36: Alan Edelman and Julia Language" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11900.0 0.0 0.0 0.0
"""why learn statistics?""
To not be fooled by statisticians." VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 194.0 0.0 0.0 0.0
"6:11
Prof Auroux meets an alien...
""Wow another life form! How fascinating! You must tell me... Do you use the same sign convention for curl??""" tYdoS0tkAHA "Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1376.0 0.0 1.0 0.0
"lovely experiment" CadZXGNauY0 "9. Multiple Continuous Random Variables" "6.041 Probabilistic Systems Analysis and Applied Probability" 13889.0 0.0 0.0 0.0
"What about inverses of non-square matrices?" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 11443.0 0.0 1.0 0.0
"just amazing! I feel a little bit sad because I have no chance to listen this course exactly from him :)" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 13728.0 0.0 0.0 0.0
"34:29~35:13
It is really helpful for me that he explicitly pointed that out." osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 981.0 0.0 0.0 0.0
https://youtu.be/PnH8HbtFMlk PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13299.0 0.0 0.0 0.0
"This teacher is amazing! Not just that he lightened me up with linear algebra but it made me really happy to see there are still people so passionate about their work. I just love it!
" 8o5Cmfpeo6g "6. Column Space and Nullspace" "MIT 18.06 Linear Algebra, Spring 2005" 10932.0 0.0 0.0 0.0
"I really hope Gil gets the time to do his rework of Linear Algebra, I was looking at his new Intro to LA and I love it so much.
He starts off with so many great axioms, and theories, as to why LA is useful in the purpose.
Also gives how to visualize matrices as vectors." 7UJ4CFRGd-U "An Interview with Gilbert Strang on Teaching Linear Algebra" "MIT 18.06 Linear Algebra, Spring 2005" 5921.0 0.0 0.0 1.0
"I have a question if someone could answer it; 
right at the end of the lecture where a second order diff. eqn is converted into a 2x2 matrix called A;
while defining the matrix A, shouldn't element A22 be= -k/b since on rearranging the  given eqn and solving for y'  we get y'= - (1/b) *y""/b -  (k/b)* y; so since the coefficient of y is -k/b ; shouldn't this coefficient correspond to element A22 of the 2x2 Matrix A?" IZqwi0wJovM "23. Differential Equations and exp(At)" "MIT 18.06 Linear Algebra, Spring 2005" 5499.0 0.0 1.0 0.0
"9:42 omit the step of factoring out (-1)^M is not a good way to deliver knowledge." 0_w-R_g5lRA "Lecture 10: The Completeness of the Real Numbers and Basic Properties of Infinite Series" "MIT 18.100A Real Analysis, Fall 2020" 1444.0 0.0 1.0 0.0
"Excellent Lectures ! Thank you, Prof. Auroux." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 3630.0 0.0 0.0 0.0
"I like how this is almost like an intro to Taylor series, as it explains the first (and second) terms of it; so whenever the students later see it, they will be more familiar with it and can understand how it can be expanded even further to approximate functions" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5672.0 0.0 0.0 1.0
"Really an inspiration to me as how the things add up and come together. Great lecture intense easy to follow / understand   " osh80YCg_GM "16. Projection Matrices and Least Squares" "MIT 18.06 Linear Algebra, Spring 2005" 8503.0 0.0 0.0 0.0
"Wow they start by differentiating e^(arctangent(x))d/d. My community college we start with  xd/dx" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12037.0 0.0 0.0 0.0
"powerful lecture" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 14203.0 0.0 0.0 0.0
"Gud Lecture" PnPIqh7Frlw "Lec 24: Simply connected regions; review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4385.0 0.0 0.0 0.0
"love the series, you can tell he is passionate about what he is teaching, thank professor.  Also thank you MIT for uploading this content" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13875.0 0.0 0.0 0.0
"Thanks sir!" oNsscmUwjMU "2. Nondeterminism, Closure Properties, Conversion of Regular Expressions to FA" "MIT 18.404J Theory of Computation, Fall 2020" 9780.0 0.0 0.0 0.0
"could someone tell me at 33:33 how do we get [1000] for particular solution? im so confused. Thank you so much!" l88D4r74gtM "13. Quiz 1 Review" "MIT 18.06 Linear Algebra, Spring 2005" 12692.0 0.0 1.0 0.0
"I'm not saying the Spanish model is the best one, and I'm not saying your model is totally wrong, it has good things, but I think there are better societies almost in any aspect than yours, read for example about countries such as Denmark, Norway etc, I think you'll be pretty surprised." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 6355.0 0.0 0.0 0.0
"I came here just for fun, but end up knowing something new. A new and easy method to multiply matrix. Thank you so much 🥰" J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 5180.0 0.0 0.0 0.0
"god i wish my teachers wrote this big" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 12932.0 0.0 0.0 0.0
"So, the eigenvectors of a circular matrix are roots of unity -> Fourier matrix.  I've used Fourier Transform and DCT in image processing and found it amazing but mysterious: where did it come from?  Now I know.  I also never realized convolution is essentially polynomial multiplication... and circular convolution simply applies a modulus to the powers!  Mind expanding; thanks Prof Strang!" 1pFv7e9xtHo "31. Eigenvectors of Circulant Matrices: Fourier Matrix" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8809.0 0.0 0.0 0.0
"Will the proof of the three consequences (if f'(x)>0, then f is increasing, sort of things) still works when there are some wiggles on the function ? For instance, the picture from geometric proof of MVT at  22:00  shows that f'(c)>0 and f(b)>f(a), but the function is not always increasing in the interval from a to b." 4Q37iOyBq44 "Lec 14 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11948.0 0.0 1.0 0.0
"Please mit ocw release a tensor calculus course, with full lectures and exercises, that would be amazing." Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 8207.0 0.0 0.0 0.0
"One of my favorite MIT professor. May Allah Almighty bless with long life." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 8082.0 0.0 0.0 0.0
"Does anyone know something more concrete about the Srebro results? Have they been verified already? How general are they? 44:54" NcPUI7aPFhA "Lecture 8: Norms of Vectors and Matrices" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 3440.0 0.0 1.0 0.0
"the crackling in this video is annoying" aeXp1zC6Hls "Lec 30 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 14681.0 1.0 0.0 0.0
"why these video lectures are not to be downloaded?
" 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15370.0 0.0 0.0 0.0
"what did the professor smoke at 19:05" z5TPjZrsp2k "Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15133.0 0.0 0.0 0.0
"Is this the last lecture of the series? (Not like I’m gonna get a response lol)" ydyiq1Z22gc "26. Sum-product problem and incidence geometry" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 6880.0 0.0 0.0 0.0
"""I dont think we'd better put that on tape here..."" Take care prof.Strang dont get ""suicided"" LOL" 2IdtqGM6KWU "11. Matrix Spaces; Rank 1; Small World Graphs" "MIT 18.06 Linear Algebra, Spring 2005" 55.0 0.0 0.0 0.0
"We can assign arbitrary values to the Pivot Variables as well, right?" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 11315.0 0.0 1.0 0.0
"excellent :o" UCc9q_cAhho "25. Symmetric Matrices and Positive Definiteness" "MIT 18.06 Linear Algebra, Spring 2005" 12816.0 0.0 0.0 0.0
"Powerful stuff." 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 8234.0 0.0 0.0 0.0
"a new course, we are your students." LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 12287.0 0.0 0.0 0.0
"It would be even better if there are some practical examples" oNsscmUwjMU "2. Nondeterminism, Closure Properties, Conversion of Regular Expressions to FA" "MIT 18.404J Theory of Computation, Fall 2020" 7006.0 0.0 0.0 1.0
"Professor, Can we consider that Σ*1 is equal to Σ^1" 9syvZr-9xwk "1. Introduction, Finite Automata, Regular Expressions" "MIT 18.404J Theory of Computation, Fall 2020" 8403.0 0.0 1.0 0.0
"anyone by chance know what the problem with particle clumping the professor was referring to? Thanks in advance!" ShGBRUx2ub8 "Lec 22 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12381.0 0.0 1.0 0.0
"Yeah, he could have covered the ratio test in just as much time as it took to explain why he wasn't covering the radius of convergence." wOHrNt9ScYs "Lec 38 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 12126.0 0.0 1.0 0.0
"what is his name" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15155.0 0.0 0.0 0.0
"Excellent lectures. I have thoroughly enjoyed this course and learned more than I had expected." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 3664.0 0.0 0.0 0.0
"wtf.. theres Calc AB at MIT?!" YN7k_bXXggY "Lec 12 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15449.0 0.0 0.0 0.0
"Can i have that stellar link here" VPZD_aij8H0 "1. Introduction to Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 3056.0 0.0 0.0 0.0
"im in algebra 1..." bHdzkFrgRcA "Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13568.0 0.0 0.0 0.0
"~21:45 0.52 is zero point five two, not point fifty two.---- basic mathematics." bFZ-0FH5hfs "17. Bayesian Statistics" "MIT 18.650 Statistics for Applications, Fall 2016" 15533.0 0.0 1.0 0.0
"No esta subtitulada...me cuesta entenderlo :( :(
" yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 7871.0 0.0 0.0 0.0
"it's funny but great job by the teacher because these stuff we are doing them at the 3grade of lyceum in greece but they are not explaining them in so much details. This is awesome work. Thanks for sharing the knowlenge." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13694.0 0.0 0.0 0.0
"At 45 min 23 sec,in my perspective,that alone cannot lead to the conclusion that E,your elimination matrix,is the inverse matrix because it can also be the transpose complex conjugate of A!And A can be a unitary matrix.I’m really new in linear algebra,but Im pretty guaranteed that that is not the TRUE way of proving that E is the inverse matrix!" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 2678.0 0.0 1.0 0.0
"The camera crew does not understand what is important and which shots to take and later include in the final video... Way too many close-ups. In general, if the Professor is pointing to something on the blackboard and it is not included in the shot, it's a major fail." Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 10028.0 1.0 0.0 0.0
"44:02 The ""[unintelligible]"" was ""Similarly for the others, but the others turn out to be zero""" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 1226.0 0.0 0.0 0.0
"Slow students." YAo1sd4kuOQ "2. Forbidding a subgraph I: Mantel's theorem and Turán's theorem" "MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019" 8722.0 0.0 0.0 0.0
"when it comes to what's on the exam, suddenly everyone has questions" U1EcnfTKXJ0 "Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15208.0 0.0 0.0 0.0
"Watch at 1.5" BSAA0akmPEU "Lec 9 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11281.0 0.0 0.0 0.0
"I am an engineering student and I have been looking for this for such a long time. Real analysis, functional analysis. I hope in the future there will be complex analysis. This is extremely useful for digital signal processing stuff. One strange thing is that currently all the machine learning stuffs are not design for things that have complex number inside them" LY7YmuDbuW0 "Lecture 1: Sets, Set Operations and Mathematical Induction" "MIT 18.100A Real Analysis, Fall 2020" 5065.0 0.0 0.0 1.0
"very good lecture
" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 15007.0 0.0 0.0 0.0
"i should be giving him my tuition money" 7eZVshlT33Q "Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13456.0 0.0 0.0 0.0
"I even feel that I would like to cry after watching this lecture. The professor explained the thoughts and techniques of maths so clearly that makes me enjoy it very much. I feel just like watching a movie, but the movie let me understand many complex concepts. 
I also found how important a teacher is! How bad some of my teachers are!" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 5387.0 0.0 0.0 1.0
"great series and great lecturer - many thanks Denis and MIT" PxCxlsl_YwY "Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13002.0 0.0 0.0 0.0
"https://crowdfund.mit.edu/project/2286

If you're watching this video then you know how beneficial MIT OCW is! Donate now! It literally took a minute and was so easy and I'm not someone who can be bothered donating to things normally..

But if like me you've ever had trouble learning something at school/uni or needed extra material or just been keen to learn then you may have benefited from all the great lectures + content MIT OCW provides! So give back a little even if it's just a few dollars and share and convince others to give too. :)

If we want humanity to progress then education is key and it's great to see one of the best universities in the world putting up it's resources to benefit everyone! 

Let's keep on learning and growing and making this world a better place as a result :)" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 13258.0 0.0 0.0 0.0
"It's easier thinking a matrix as a linear combination of columns! Tank you, mr Strang." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 7035.0 0.0 0.0 0.0
"when he tipe in te board that s give ma satisfaction" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15205.0 1.0 0.0 0.0
"Did he say R2 in conjunction with space?" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 3378.0 0.0 1.0 0.0
"Professor Auroux turns into a comedian at 20:30" 15HVevXRsBA "Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 8322.0 0.0 0.0 0.0
"Did one of your students build the motiontracking camera?" uoL4lQxfgwg "Lecture 1: Basic Banach Space Theory" "MIT 18.102 Introduction to Functional Analysis, Spring 2021" 3384.0 1.0 0.0 0.0
"The best thing in the first 3 lectures is the new way you look at a matrix multiplication as linear combination of either rows or columns which makes more complicated topics easier to understand." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 10012.0 0.0 0.0 1.0
"May I have the link to the entire series, please" OYcdw5vOgIc "23. Generalized Linear Models (cont.)" "MIT 18.650 Statistics for Applications, Fall 2016" 7632.0 0.0 0.0 0.0
"If only there was a way to back up the video to a previous time and watch it again.
Oh well, maybe that technology will come along one of these days." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6514.0 0.0 0.0 0.0
"I just completed the whole 18.02 course. Thank you Prof. Denis Auroux! Thank you MIT! It helped a lot!" 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 5601.0 0.0 0.0 0.0
"La clase más coñazo de todas" HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7243.0 0.0 0.0 0.0
"The hat problem deserved an all lecture on its own..." EObHWIEKGjA "7. Discrete Random Variables III" "6.041 Probabilistic Systems Analysis and Applied Probability" 10137.0 0.0 0.0 0.0
"Thanks for updates and course" Cx5Z-OslNWE "Course Introduction of 18.065 by Professor Strang" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 9738.0 0.0 0.0 0.0
"When I am listening to my prof, math is a pain in the arse.... 
When I am listen to auroux's  math is interesting and meaningful...." UYe98CcxPbs "Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11601.0 0.0 0.0 0.0
"@lizamarget  yes we do, not everyone gets the chance to study it at 11th grade like you..." ryLdyDrBfvI "Lec 2 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 1931.0 0.0 0.0 0.0
"i had a revision" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13386.0 0.0 0.0 0.0
"Why don't he tell definition of limit and also refer about epsilon-delta staff?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11855.0 0.0 1.0 0.0
"he is a good teacher.." YBajUR3EFSM "Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 13086.0 0.0 0.0 0.0
"Beautiful exposition of  SVD" rYz83XPxiZo "6. Singular Value Decomposition (SVD)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 2817.0 0.0 0.0 0.0
"Why is there no more comments for such a great course? MIT is a great university!" wrEcHhoJxjM "23. Accelerating Gradient Descent (Use Momentum)" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 11893.0 0.0 0.0 0.0
"Ive always been interested in quantum mechanics but to get there you need to start from the bottom. excited to start my journey!" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 7104.0 0.0 0.0 0.0
"What is the application of dot product in multivar calc? Should we expect to use it to think about gradients? Critical points?" 9FLItlbBUPY "Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11522.0 0.0 1.0 1.0
"Strang: That is the first time in the history of linear algebra in which a eingenvalue has a component 3300.
LA: *Oh, not today, no!*" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 8913.0 0.0 0.0 0.0
"I think x=0 does not belong to the domain of f , there is no ln(0)." twzGBqPeW0M "Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6081.0 0.0 1.0 0.0
"I used to think that MIT students were kind of special, so amazingly smart! But I realize that they are just the same any other students at other Universities! Oops..." 5q_3FDOkVRQ "Lec 5 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 6131.0 0.0 0.0 0.0
"Amazing lecture, such a great professor!" j9WZyLZCBzs "1. Probability Models and Axioms" "6.041 Probabilistic Systems Analysis and Applied Probability" 2373.0 0.0 0.0 0.0
"@seisdoesmatter The chalk's really awesome. Looks thicker than ordinary chalk. It seems a bit like the chalk kids use to paint on the pavement!" srxexLishgY "18. Properties of Determinants" "MIT 18.06 Linear Algebra, Spring 2005" 2005.0 1.0 0.0 0.0
❤️ MsIvs_6vC38 "4. Factorization into A = LU" "MIT 18.06 Linear Algebra, Spring 2005" 15607.0 0.0 0.0 0.0
"I never understood Fourier series more clearly" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 5888.0 0.0 0.0 0.0
"its what Chinese learned in high school" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 13716.0 0.0 0.0 0.0
"Who has ever seen a mathematician have a sense of humor. Who has ever seen a young mathematician be a classic." 24v9onS9Kcg "Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 11735.0 0.0 0.0 0.0
"How does Jacobian go with nonlinear transformations? Namely if I have u=g(x,y) v=h(x,y) then will dudv=|J|dxdy be satisfied where J=(dg/dx dg/dy; dh/dx dh/dy) ?  (here d's are actually referring to partial derivatives)" UZb9hZIAvL4 "Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4859.0 0.0 1.0 0.0
"What is the feeling of teaching an empty class?" JibVXBElKL0 "5. Transposes, Permutations, Spaces R^n" "MIT 18.06 Linear Algebra, Spring 2005" 11525.0 0.0 0.0 0.0
"Thanks MIT" eHJuAByQf5A "Lec 7: Exam 1 review | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9597.0 0.0 0.0 0.0
"Hard to follow him because him skipping steps." FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 4427.0 0.0 0.0 0.0
"21:12 ""the three plains meet in one point and that's the solution"". I can't get my head to imagine plains intersecting at a point, they keep drawing lines where they intersect." J7DzL2_Na80 "1. The Geometry of Linear Equations" "MIT 18.06 Linear Algebra, Spring 2005" 673.0 0.0 1.0 0.0
"34:52 freudian slip" Bv9kVDcj7yo "Lec 27 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 989.0 0.0 0.0 0.0
"Which book does they follow?" 7K1sB05pE0A "Lec 1 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 11707.0 0.0 1.0 0.0
"Me when I saw the deduction of F and I: 
""It's not math, it's magic"" lol" VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 7647.0 0.0 0.0 0.0
"Very useful lecture. Thanks a lot" QVKj3LADCnA "2. Elimination with Matrices." "MIT 18.06 Linear Algebra, Spring 2005" 11229.0 0.0 0.0 0.0
"Imagine being late to a class by this legend" MuEW9pG9oxE "Lecture 11: Minimizing ‖x‖ Subject to Ax = b" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6582.0 0.0 0.0 0.0
"It's so weird these videos are from 1999..
I was in elementary school  learning the multiplication table in 1999.. and now I'm using these lectures to help my pass my University midterms.. woah" 9Q1q7s1jTzU "8. Solving Ax = b: Row Reduced Form R" "MIT 18.06 Linear Algebra, Spring 2005" 7072.0 0.0 0.0 0.0
"The link between Orthonormal vectors and Trigonometric functions by the example of Fourier Series! Great example with Great connection between Algebra and Function! at 44:00. Thanks!" lGGDIGizcQ0 "24. Markov Matrices; Fourier Series" "MIT 18.06 Linear Algebra, Spring 2005" 10179.0 0.0 0.0 1.0
"29:48 famous Auroux speed erasing :-)" _CdoRiNSrqI "Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 860.0 0.0 0.0 0.0
"why some of the videos of this course are not being downloaded by Idm while some of them are downloaded by same Idm." eRCN3daFCmU "Lec 10 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 15360.0 0.0 0.0 0.0
"Does anybody else watch the lecture at 2x speed? It's much better." VqP2tREMvt0 "7. Solving Ax = 0: Pivot Variables, Special Solutions" "MIT 18.06 Linear Algebra, Spring 2005" 3429.0 0.0 0.0 0.0
"Thanks so much for putting this online! Helps me to refresh my mind in preparation for Analysis class in university." kCPVBl953eY "Lec 3 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 9787.0 0.0 0.0 0.0
"I am an undergraduate student studying physics and mathematics and these lectures helped me a lot to understand everything. Thank you very much Prof. Jerison and MIT OCW for making this possible." --lPz7VFnKI "Lec 39 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 5067.0 0.0 0.0 0.0
"I requested this video and I am the first person to comment" 3PzuSPQPEU4 "8. Undecidability" "MIT 18.404J Theory of Computation, Fall 2020" 5952.0 0.0 0.0 0.0
"It is snowing at the outside at 4:58. what a wonderful and lovely class." YiqIkSHSmyc "Lecture 1: The Column Space of A Contains All Vectors Ax" "MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018" 6964.0 1.0 0.0 0.0
"Great video.  

I kept wanted to walk away instead of spending 50 minutes on YT, but each new topic was very relevant.   Ended up watching the whole damn thing.  

Thanks

p.s. I agree.  That chalk is pretty sweet.  " tzoYhe3H5dM "Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007" "MIT 18.02 Multivariable Calculus, Fall 2007" 4359.0 0.0 0.0 0.0
"For your (and my) convenicence:
4:40 Independence
18:08 Span
21:26 Basis
36:23 Dimension
Also, check out this amazing video 
https://youtu.be/k7RM-ot2NWY
 if you'd like a graphical idea of the topics in this lecture." yjBerM5jWsc "9. Independence, Basis, and Dimension" "MIT 18.06 Linear Algebra, Spring 2005" 3915.0 0.0 0.0 1.0
"Thank you for sharing this video prof Strang!!! Very helpful! :D" nHlE7EgJFds "10. The Four Fundamental Subspaces" "MIT 18.06 Linear Algebra, Spring 2005" 9259.0 0.0 0.0 0.0
"Seeing this in LOCKDOWN is amazing,..." HgEqXhsIq_g "Lec 29 | MIT 18.01 Single Variable Calculus, Fall 2007" "MIT 18.01 Single Variable Calculus, Fall 2006" 8616.0 0.0 0.0 0.0
"Lecturing capability aside, the thing that amazes me most about this man is his entrancing hand-writing! They just don't make em like they used to!" TSdXJw83kyA "28. Similar Matrices and Jordan Form" "MIT 18.06 Linear Algebra, Spring 2005" 7309.0 0.0 0.0 0.0
"What does he mean ""A projection matrix is the identity matrix where it can be and everywhere else it's the zero matrix""  at 19:20?" Go2aLo7ZOlU "33. Left and Right Inverses; Pseudoinverse" "MIT 18.06 Linear Algebra, Spring 2005" 11488.0 0.0 1.0 0.0
"Every time I listen to one of Dr. Strang’s lectures, I have to crack my Finite Math with Calculus book just to refresh on Gauss’s Theory" FX4C-JpTFgY "3. Multiplication and Inverse Matrices" "MIT 18.06 Linear Algebra, Spring 2005" 3601.0 0.0 0.0 0.0