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A thousand can be written as 1,000 as well as 1000 and a million as 1,000,000 or 1000000. Visit WebsitePoints: 13. Differential geometry: a field of mathematics that uses the methods of differential and integral calculus as well as linear and multilinear algebra to study the geometry of curves and surfaces. In mathematics, the Riemann hypothesis, proposed by Bernhard Riemann 1859, is a conjecture that the non trivial zeros of the Riemann zeta function all have real part 1/2. The methods used for calculating the mean, median, and mode are different from those used for ungrouped data e. Prodigy is a free, curriculum aligned, fantasy based math game for kids to practice essential math skills. From this, the x momentum equation becomes. Locally convex spaces, weak topologies. All concentrations share core courses. The points on the graph of a function f have the form x, fx, soonce you know the first coordinate, the second is determined. Mathematics majors learn the internal workings of this language, its central concepts and their interconnections. 29 students do not play basketball or baseball. For stock investments, two kinds of yields are generally watched yield on cost, and current yield. For example, a = 3 and b = 11. May be taken for credit six times with consent of adviser as topics vary. Spatial right hemisphere, in which children show deficits in the spatial representation of number. 3 Existence and Uniqueness Having seen some definitions, we’re ready to develop the main tool we need for secret sharing: the existence and uniqueness theorem for polynomials passing through a given set of points. Your answer should be given as a word or as a whole number. Mobile App Development Courses50+ Courses★★★★★. Thanks for your input, Milind. Score 600 https://domyhomeworkfor.me/ on SAT Reading. Want to browse local tutors near you in more subjects. This proposition cannot at all be shown from concepts, but rests immediately on intuition and indeed on pure intuition a priori because it is apodictically demonstrably certain. Suppose we imagine that 11 is the largest prime. Once you’ve tried out the four practice questions above, it’s time to compare your answers and see whether you understand not just how to find the mean of data but also how to use what you know about the mean to more effectively approach any math questions that deal with averages. Your first 30 minutes with a Chegg tutor is free. 6, 2017—Vanderbilt students Lauren Branscombe, Joshua Fleck and David Zhang have been recognized in this year’s Goldwater Scholars competition. A right angle is an angle whose measure is exactly 90° or π2. ” “Twenty years from now you will be more disappointed by the things youdidn’t do than by the ones you did do.
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Moreover, we are never certain that the interpretive project is accurate and complete, and that other problems are not lurking ahead. Suppose that a student is taking three technology related classes. “Mathematics is the gate and key to science. Answer: B Quantity B is greater. The initiative also seeks to establish consistent educational standards across the states as well as ensure that students graduating from high school are prepared to enter credit bearing courses at two or four year college programs or to enter the workforce. ” Donald Newman 1930 2007 quoted in A Beautiful Mind by S. In a similar fashion, mathematicians can prove that the angles of a triangle add up to 180 degrees, or that there is no largest prime number—and they don’t need physical triangles or pebbles for counting to make the case, just a nimble brain. “I like to learn multiplication and division,” said Christina Gabrieli, a third grader at Dexter Southfield, a private school in Brookline. Availability: Ready to ship. Two additional developments around 1980 once again accelerated the ability to compute π. We have three modes trimodal in this set which are 0. Lambert also worked on geometry and cartography, created map projections, and foreshadowed the discovery of non Euclidean spaces. Data is presented in RST with the help of an information system, which may be complete, incomplete or non deterministic. The 4th number in 1, 2, 3, 5, 6, 7, 9 is 5. Each hypothesis specifies completely the probability distribution of a certain random variable, X. Submit questions about how to become an IB World School or enquire about our professional development opportunities. I cannot understand why we are asking 3rd graders to solve problems this way. Note: Please review CPS’ Minimum HS Graduation Requirements policy for in depth details. ” Popular Mechanics, March 1949, p. For each of the following scenarios, determine if it is a compound interest problem, a savings annuity problem, a payout annuity problem, or a loans problem. The last step in the verbal description table was to cube the result. I think one of the most vibrant is the questionof what distances and shapes can be constructed just by folding alone,without doing any measuring. Hungarian Problem Book III 1929 1943 Andy Liu MAA,20017.
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This is exactly what I’ve experienced over the years. The Pythagorean theorem. Content and quantity in relation to the applied programme specific requirements see below. Such numbers must end in 1, 5, or 6 as these are the only numbers whose products produce 1, 5, or 6 in the units place. Further, let us apply the Turkey rule to find the outlier. The author recommended that teachers focus on first leading students in enjoying the illustrations and text and then making connections to math content areas when reviewing the text. Non linear first order equations, including Hamilton Jacobi theory. 65–81; Butterworth, Varma, and Laurillard, 2011; Iuculano, Tang, Hall, and Butterworth, 2008; Kucian and von Aster, 2015; Landerl, Bevan, and Butterworth, 2004; Rousselle and Noel, 2007. Greater focus on fewer topics. The cone, sphere and flat disc were used to represent small, medium and large measures of grain. Generally, yield is calculated by dividing the dividends or interest received on a set period of time by either the amount originally invested or by its current price. Some graphs may also have a legend that specifies what various colors represent, such as in a stacked bar graph. Exercise 4 asks you to prove it using elementary means. We just don’t want there to be any more than one ordered pair with 2 as a first component. Therefore, 4, 6, and 9 are composite numbers since they each have more than 2 factors. Example 3: A marathon race was completed by 5 participants. What is the average temperature in degrees Fahrenheit. Prerequisites: MATH 31CH or MATH 109. Proper understanding of given situations and contexts can often provide a person with the tools necessary to determine what statistically relevant method to use. During the 2019 2020 academic year, University of Georgia handed out 71 bachelor’s degrees in mathematics. Feel free to send suggestions. With what kind of mathematical problem can learners discover a certain mathematical idea e. Working in a mathematics career can require skills in problem solving and numerical aptitude, but today’s competitive marketplace asks for hard skills beyond just being good with numbers. It can be made to hold by changing the meaning of √ so that this no longer represents the principal square root see above but selects a branch for the square root that contains 1 ⋅ − 1. Lang from one uncut square of Korean hanji paper. That was extremely useful. Most math of radicals is to change them to their simplest form to reduce complexity. Beberman also urged a conceptual overhaul of math education. The final aspect is that relearning one’s field allows one to revisit the proofs of the central theorems of that subject.
He was one of the central forces behind systematizing probability theory, laying the groundwork for what is now termed Bayesian statistics. Published: Jan 15, 2021. There is no general consensus about its exact scope or epistemological status. We have multiplication and division in the formula, and the standard form exponents make these two operations very easy to calculate. How’s your head after that paragraph. The sim command produce a tilde like binary relation symbol that is often used in mathematical expressions, and the double tilde is obtained with approx. Determine whether these statements are true or false. Learn how to pick the right recovery. New Process for 20E Transfer Equivalency. By the implicit function theorem, is smooth, and by differentiating the above equation in time using 3 we see that. Applied math is slightly different, but you’ll still need to immerse your head in a world of numbers to make yourself valuable in the applied mathematics market. Completing a practice test or two ahead of time will make it so that you’re already comfortable with the directions going into the exam.
References and Citations
While students are only required to obtain 3 credits of math, they are strongly encouraged to take a fourth credit and maintain one math course each year. In a study of a frozen meal diet plan, the treatment group would receive the diet food, and the control could be given standard frozen meals stripped of their original packaging. Centers and Institutes. Methods for factoring large whole numbers are of great importance in public key cryptography, and on such methods rests the security or lack thereof of data transmitted over the Internet. Although the strains caused by gravitational waves are miniscule, they can be measured directly using techniques of laser interferometry. Your email address will not be published. Top 5 sectors our students work in. You may cancel at any time. Your email address will not be published. Sqrt 2 has no minus under the square root the minus is outside the root, is not divided by zero, so it is real. This method works in any instance where a percentage and its value are given. That these sorts of precise distinctions can be made is not immediately obvious to young children; for this reason, it is important that teachers design activities to demonstrate this. Culture is part of the unholy trinity—culture, chaos, and cock up—which roam through our versions of history, substituting for traditional theories of causation.
Learning Areas – Bachelor of Secondary Education Honours
Angles can be measured in both degrees and radians. Area of a Trapezoid: A=½base₁+base₂height. They each try to summarize a dataset with a single number to represent a typical data point from the dataset. 25×2−20x+4=5×2−25x⋅2+22=5x−22. In the 19th century, when the study of mathematics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear cut relation to quantity and measurement, mathematicians and philosophers began to propose a variety of new definitions. Then I said, Awesome. Concerning the Goldbach conjecture, Helfgott proved in 2014 that every odd number larger than 5 is the sum of three primes. In a study about anti depression medicine, you would not want the psychological evaluator to know whether the patient is in the treatment or control group either, as it might influence their evaluation, so the experiment should be conducted as a double blind study. You are commenting using your Twitter account. Com and the editor of “Run Strong,” he has written for Runner’s World, Men’s Fitness, Competitor, and a variety of other publications. As a class activity, present theorems and conjectures and ask students to first list all conditions of the statement and then produce non examples for each. However, supplemental self study is recommended. On top of that, 50% of Americans eventually develop math anxiety. Copyright © Old Dominion University • Updated 8/15/2021. We have taken the value of a that is 1 and the values of x are 2, 1, 0, 1, 2. Web of Science Emerging Source Citation Index ESCI: Clarivate Analytics.
Simplify 2 + 3–4
Enter your mobile number or email address below and we’ll send you a link to download the free Kindle App. However, to succeed in the Math Lab program students must have motivation and self discipline. As nouns the difference between conjecture and speculation. Prove that for all integers ngeq1. The basic arithmetical operations are addition, subtraction, multiplication and division. “We work in more general terms on more abstract problems, whereas in the sciences, like the wet lab sciences, you’re working specifically with materials or chemicals or life’s biological systems. As the focus on children’s literature as a resource and tool for mathematics learning became more prominent, authors identified additional rationales for using these books and functions of these books. 9 x − 3x − 3 x−3 = lim x − 3 f ′ 3 = lim x→3 x→3 =0 This was a nice exercise, but it’s tedious to compute derivatives over and over again for every input. You’ll need to make complicated mathematical calculations to understand the relationships between cosmic bodies. That is, instead of writing f x, one writes f x. 1, while taking advantage of the weaker ellipticity condition 3. I used this for a research paper so if anything is wrong in this research i’m in big trouble. It involves applying mathematical models in order to map out the mathematical core of a practical problem. Summer: 8 weeks 8 hours of lecture per week. For website help or updates, please email Accessibility. It is normal for two different individuals to have different number of questions asked, and still be placed in the same placement domain, and recommended for the same preparatory courses. North Central College is exactly that kind of program, offering insightful, devoted instruction from experienced faculty who will pay attention to your interests and help you find a path that fits. The correct answer is D. Thanks to Theodore Slaman and Jon Wilkening for mathematical consultation. For example, √2 is irrational but not transcendental because it is the solution to the polynomial x2 = 2. 9 for fourth graders between the top 10% and the top 1% Table 3. Copyright © 2022 Student Progress. Gottlieb Daimler John Dalton James Dwight Dana Charles Darwin Humphry Davy Peter Debye Max Delbruck Jean Andre Deluc Democritus René Descartes Rudolf Christian Karl Diesel Diophantus Paul Dirac Prokop Divis Theodosius Dobzhansky Frank Drake K. 9500 Gilman Drive, La Jolla, CA 92093 0112. If you do the math, you’ll see that it’s not such a bargain. How roman numeral symbols originated.
Learn Math in the Blogosphere: 10 Top Math Blogs
This will give you the total amount of your total gain or loss on your bond investment. For the sake of example, we’ll say that Stock A makes up 20 percent of the portfolio, Stock B makes up 10 percent, and Stock C makes up 70 percent. In the next example, we’ll see how a mapping is used to create a list of ordered pairs. Two languages who could not be further apart. If you are a person who is creative with their words, try making an acronym out of the first letters of your important concepts, like PEMDAS in math Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Lower level of the modal class l = 30. The product rule can be used in reverse to simplify trickier radicals. SC Uniform Grading Scale. No tricks, just hard words you might encounter in. School and District Reports. ” means “Can 20 be divided by 3. To order a copy or learn more about the text, visit The Heart of Mathematics web pages at or at Springer Verlag or call Key College at 888 877 7240 or 510 595 7000. Company ABC’s dividend yield is 5% 1 ÷ 20, while XYZ’s dividend yield is only 2. This idea is expanded in our pages on managing your money. Foreign languages tests have four answer choices. We also offer private tutoring, semi private and traditional classes, and online prep to fit any schedule and learning style. June 2020April 2020March 2020February 2020January 2020December 2019November 2019October 2019September 2019August 2019July 2019June 2019April 2019March 2019February 2019November 2018September 2018August 2018July 2018June 2018May 2018April 2018March 2018February 2018January 2018December 2017November 2017October 2017September 2017August 2017July 2017June 2017May 2017April 2017March 2017February 2017January 2017December 2016November 2016October 2016September 2016August 2016July 2016June 2016May 2016April 2016March 2016February 2016January 2016December 2015November 2015September 2015August 2015June 2015February 2015January 2015December 2014October 2014June 2014. Then each of the following equations holds. Try it risk free for 30 days. The formula is straightforward, being the number of products that pass through a step of the process without error on the first attempt, divided by the total number of products being tested. ” “The full beauty of the subject of generating functions emerges only from tuning in on both channels: the discrete and the continuous. Note that the reason I’ve always heard of for movie. Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences. But first, students can estimate how far they’ll jump. I also used the IBID one, which is quite cool, stresses trigonometry a bit and focuses also on partial fractions very useful in calculus. No matter how a ratio is written, it is important that it be simplified down to the smallest whole numbers possible, just as with any fraction. And they’d say, ‘That’s not how they teach it here. Its adjective is mathēmatikós μαθηματικός, meaning “related to learning” or “studious,” which likewise further came to mean “mathematical. Grading/Final exam status: Letter grade. Having no remainder means that n can in fact be divided by 2.


Are you thinking of studying Mathematics at Cambridge? Join us for the King's Mathematics Open Morning, followed by the Mathematics Faculty Open Afternoon on Saturday 30 April.
Prospective mathematicians arrive at 10.00 / 10.15 am and spend the morning at King's. You will have a talk and Q&A with an academic in Mathematics, a chance to meet current King's undergraduates studying Maths, and a tour of the College, as well as brunch in the College Hall.
In the afternoon we take you over to the New Museums Site where you can attend the Mathematics Faculty Open Afternoon (a series of taster lectures and information about STEP). The afternoon programme and further information is available on the Mathematics Faculty website. The event ends at 16.40.
Please sign up for the day's events using the online booking form.


Hi all, I can recommend one online school with math tutors. I recommend you Brighterly online school, in this online school tutors will help your child learn new topics or tighten up difficult math topics. You can find out you just need to visit math site, I am sure that the tutors from this online school will help your child get great grades in math.
I think I have helped you with your question.
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The Math Hunter: improve your math skills!
The Math Hunter is a iOS game for practicing basic Math skills: addition, subtraction, multiplication and division. The game allows you practice several operations together or independent as well as complex equations like 7 * (54 / 6).
The fun part is you need to help an archer protect the blooming forest against monsters. You have a few ways to defeat monsters as shooting at them with the bow or blowing up with bombs. In order to do anything you need to use your math skills.
The game has nice, nonviolent graphic style and good sound effects.
Follow us on twitter: https://twitter.com/TheMathHunter
I will glad to hear your feedback: info[at]themathhunter.com
Last edited by The Math Hunter; 07-17-2014 at 02:37 PM. Reason: make the link to app store more visible
- 07-17-2014, 02:31 PM #2
Re: The Math Hunter: improve your math skills!
Welcome and thank you for sharing your app with iMore, hopefully a lot of our members will check it out and give plenty of feed back.
Please take a moment and read:App and Developer Forum Rules & Guidelines - Mobile Nations Forums
Thank you again and best of luck with your app.
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Real solutions equal
Hope that helps!
To solve an equation using the x-intercept method, we must graph the corresponding function and locate x-values of the x-intercepts.
The given polynomial equation is
The graph of the corresponding function
Is shown in the attachment.
The x-intercepts are:(1,0), (3,0), (6,0)
Therefore the solutions are,
hey there : ) your answer would be a.


A single conservative force acts on a 5.00-kg particle within a system due to its interaction with the rest of the system. The equation Fx = 2x + 4 describes the force, where Fx is in newtons and x is in meters. As the particle moves along the x axis from x = 1.00 m to x = 5.00 m, calculate
(a) the work done by this force on the particle
(b) the change in the potential energy of the system
(c) the kinetic energy the particle has at x = 5.00 m if its speed is 3.00 m/s at x = 1.00 m
A 4.00-kg particle is subject to a net force that varies with position as shown in the figure. The particle starts from rest at x 5 0. What is its speed at (a) x = 5.00 m, (b) x = 10.0 m, and (c) x = 15.0 m?
(a) A 3.00-kg object has a velocity (6.00 i - 2.00 j) m/s. What is its kinetic energy at this moment?
(b) What is the net work done on the object if its velocity changes to (8.00 i + 4.00 j) m/s?
When a 4.00-kg object is hung vertically on a certain light spring that obeys Hooke’s law, the spring stretches 2.50 cm. If the 4.00-kg object is removed, (a) how far will the spring stretch if a 1.50-kg block is hung on it? (b) How much work must an external agent do to stretch the same spring 4.00 cm from its unstretched position?
A uniform chain of length 8.00 m initially lies stretched out on a horizontal table. Assuming the coefficient of static friction between chain and table is 0.600, show that the chain will begin to slide off the table if at least 3.00 m of it hangs over the edge of the table.


IUPUI High School Math Contest
2016 High School Math Contest
How the contest enhances student engagement
- The High School Math Contest is an opportunity for teachers to supplement their lesson plans and provide students with creative and competitive outlets.
- Student participants study patterns, analyze relationships, draft and refine their solutions, and submit their work.
How the contest works
- Contest questions and poster to advertise the contest are emailed to Indiana high schools
- Questions cover 9-12th grade math problem-solving skills and one question essay
- Students work on the questions independently and mail in their solutions
- IUPUI faculty and graduate students volunteer over 100 hours to judge all entries based on the following criteria:
- A student's method of finding the solution
- Correctness of solution
- Elegance of solution
- Winners and participants are invited to campus for the award ceremony every April
- This contest is open to Indiana high school students (grades 9 - 12)
- The 2017 High School Math contest will be announced January 2017
PrizesIn order to receive the scholarship, the winner must be directly admitted to the Purdue School of Science at IUPUI, major in any discipline in the School of Science, and attend full-time. These scholarships are renewable for four years, subject to certain requirements.
- 1st Place (1 winner)
- $300 and a full four-year academic tuition scholarship to the School of Science at IUPUI
- 2nd Place (5 winners)
- $150 and a $2,000 scholarship to the School of Science at IUPUI
- 3rd Place: (10 winners)
- $100 and a $2,000 scholarship to the School of Science at IUPUI
- Request more information for the 2017 math contest or call (317) 274-6917


Some confusion about time-complexity and A*.
According to A* Wiki the time-complexity is exponential in the depth of the solution (shortest path):
The time complexity of A* depends on the heuristic. In the worst case of an unbounded search space, the number of nodes expanded is exponential in the depth of the solution (the shortest path) d: $O(b^d)$, where $b$ is the branching factor (the average number of successors per state).
The comment to this accepted answer points out that it makes more sense to give the complexity in termes of the size of the graph and therefore it should be $O((|V| + |E|) \cdot log |V|)$
Obviously, if the heuristic assigns a value of 0 to every node, A* becomes Dijkstra's algorithm and any uniform cost heuristic will essentially disable the heuristic.
If we assume the heuristic to be $O(1)$ (and consistent), it would make sense that the worst case is essentially degrading A* to Dijkstra's algorithm which has complexity
with a min-priority queue implementation (Fibonacci heap).
Am I wrong?
Any book etc I have been looking at always gives the complexity in terms of the depth of the solution


NCERT Class XI Mathematics Book Click Here for Class XI All NCERT Books NextNCERT Class VIII Maths Chapter 2 Linear Equations in One Variable». NCERT Solutions for class 11 Maths provided by Vedantu here have been solved by our best Mathematics teachers, who have many years of experience in the field of CBSE Board education. The class 11 Maths NCERT solutions systematically cover the solutions for all the exercise. Mathematics for Class 11 by R D Sharma Session: fyadocoodenes.tk: R.D. Sharma: Books.
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Ganit. NCERT/CBSE class 11 Mathematics book Ganit · Mathematics. NCERT/ CBSE class 11 Mathematics book Mathematics · Reyazi. NCERT/CBSE class 11 . If you are a CBSE student, then go for NCERT books. NCERT books are supreme when it comes to appearing for Government level exams also. IN THIS APP YOU WILL GET ALL CHAPTERS OF SCIENCE 11TH CLASS CBSE SYLLABUS.(NCERT). Read more. Collapse.
Anyone can understand the concepts. The ICSE books have vast information on the topics.
But the illustrations, examples, and explanations are more in ICSE books. Both the books give enough knowledge to the students. While preparing for an examination, the ones who study from ICSE books have to refer for side books to know more information and different types of questions.
Using many reference books will confuse the person as every book will explain the concept in a different way. NCERT books help to clear most of these exams. It takes more time to study from ICSE books due to vast information.
The idea of set fills in as a major piece of the present-day Mathematics. Today this idea is being utilized in pretty much every Chapter of science. Sets are utilized to characterize the ideas of relations and capacities.
The investigation of geometry, sequences, probability, and so forth requires the learning of sets. In this Chapter, consistent way to deal with set hypothesis is clarified. The term set falls in the classification of unclear terms in science. Additionally, to be a component of a set is likewise unclear term. In any case, a set is defined as characterized accumulation of all items.
NCERT Solutions for Class 11 Maths
Relations and Functions will explain you how to link pairs of objects from two sets and then derive relations between the two objects in the pair. What you will learn finally is about special relations which will qualify to be functions. The concept of function is very important in mathematics since it captures the idea of a mathematically precise correspondence between one quantity with the other.
The idea of Functions is exceptionally principal in Modern Mathematics. In this chapter, we will generalize the concepts of trigonometric ratios to trigonometric functions and will study the properties. The study of trigonometry at first began in India.
The early hints of scientific enlistment can be found in Euclid's proof that number of primes is endless. There is only one exercise in this chapter and is very interesting if you are curious enough to solve the questions of Mathematical Induction.
To permit the square root of negative numbers, the real number framework is stretched out to complex numbers. Truth be told, Greeks were the first to perceive the way that square root of a negative number does not exist in the real number system. This chapter has three exercises in total where you will consider how the inequalities emerge in everyday practice.
At whatever point we compare two quantities, they are bound to be unequal than equivalent. Linear inequalities is a very important and interesting chapter if you study in depth.
NCERT Solutions for CBSE Class 11 Mathematics: All Chapters
Permutation is a kind of arrangement in an unequivocal request of various particular of n different items taking r at once. Combination — The number of ways for choosing r things out of n distinctive things is called combination. There are total 4 exercises in this chapter with 31 questions based on the concepts of Permutations and Combinations.
This equation or expansion is called Binomial hypothesis. Chapter 9 called Sequences and Series has four exercises in total where you will learn important topics like Arithmetic Progression, Geometric Progression, General Term of a G.
P, Sum to n terms of a G. P and other important topics.
Historically, Aryabhata was the primary mathematician to give the equation for the sum of the square of the first n natural numbers, the whole of 3D squares of first n normal numbers, and so forth. In this chapter, you will study some important topics like Slope of a line, Angle between two lines, Collinearity between two points, horizontal and vertical lines and much more.
There are total three exercises in this chapter.
French mathematician Rene Descartes was the primary mathematician who utilized variable based math for the investigation of geometry. Utilizing Cartesian directions, he spoke to lines and bends by mathematical condition.
Conic Sections will broaden your concepts of sections of a cone and also, you will study about circle, ellipse, parabola and hyperbola and other important topics. The curves like circles, oval, parabolas and hyperbolas are called conic segments or all the more normally conics.
Earlier, the ideas of plane organize geometry were started by French mathematician Rene Descartes and furthermore by Fermat in the start of seventeenth century.
UP Board Class 11 Maths Book Solutions PDF गणित
In this Chapter, with a total of three exercises, we will study about the coordinate geometry in the 3 — D space. This chapter is an introduction to a very important area called Calculus for the students.
Calculus is that branch of mathematics which is associated with the study of change in the value of a function as the points of the domain change. If we mug up the facts, Brahmagupta's Yuktibhasha is viewed as the main book on analytics. Bhaskar's chip away at analytics goes before much before the season of Leibjitz and Newton.
Bhaskara — II utilized standards of differential Calculus in issues on Astronomy. In Math, mostly two sorts of reasoning happen.
One is inductive reasoning which is examined in Chapter 4 — Mathematical Induction and the other is deductive reasoning which we expect to consider in depth in this Chapter.
In this chapter, you will be studying important topics like Measures of dispersion, range, mean deviation, Mean deviation for ungrouped data, 1 Standard deviation and much more. We will do the next dimension of measurements in this chapter than whatever we have studied in classes 8, 9 and Probability is the word we utilize computing the level of the conviction of occasions in perfect conditions. An experiment implies an activity which can deliver some very much characterized results.
The traditional approach is given out by Blaise Pascal and the main approach is given by a Russian mathematician A Kolmogorov in For all those students who require additional guidance with their studies, Vedantu has got their back. System of Particles and Rotational Motion Chapter 8: Gravitation Chapter 9: Mechanical Properties of Solids Chapter Mechanical Properties of Fluids Chapter Thermal Properties of Matter Chapter Thermodynamics Chapter Kinetic Theory Chapter Oscillations and Waves Oscillations Waves Chapter Some Basic Concepts of Chemistry Chapter 2: Structure of Atom Chapter 3: Classification of Elements and Periodicity in Properties Chapter 4: Chemical Bonding and Molecular Structure Chapter 5: Thermodynamics Chapter 7: Equilibrium Chapter 8: Redox Reactions Chapter 9: Hydrogen Chapter The s — Block Elements Chapter Hydrocarbons Chapter The Living World Chapter 2: Biological Classification Chapter 3: Plant Kingdom Chapter 4: Animal Kingdom Chapter 5: Morphology of Flowering Plants Chapter 6: Anatomy of Flowering Plants Chapter 7: Structural Organisation in Animals Chapter 8: The Unit of Life Chapter 9: Biomolecules Chapter Cell Cycle and Cell Division Chapter One is inductive reasoning which is examined in Chapter 4 — Mathematical Induction and the other is deductive reasoning which we expect to consider in depth in this Chapter.
Mock Tests. RD Sharma Class 11 Solutions. Next Next post: Statistics Chapter Permutation is a kind of arrangement in an unequivocal request of various particular of n different items taking r at once. So students need not worry about the given content for the solutions.
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This applet calculates the Mandelbrot set using a modified and inferior version of the boundary trace algorithm. (see "Future Features" below) Transparent pixels (gray in the hotjava default) are members of the Mandelbrot set, which is defined as all complex c such that the transformation z -> z^2 +c starting with z=0 does not go to infinity. The color of points not in the set is determined by the number of iterations of the tranform before the value of z reaches a threshold value. (see "Future Features" below).
The number of iterations determines how many times the tranform is applied. If z is still lower than a threshold, the point is considered to be in the set. To get full detail at any zoom, the number of iterations would have to be infinite. This would take too long though. 50 or 60 iterations is fine for a few zooms. 120 is a lot of detail. More is slower, but also more detail.
The applet reports on the status line how many point it actually calculated. This number should always be smaller than the maximum. Sections of the set with large blocks of solid color will be calculated faster than intricate border areas.
Being the first Java app I've written, I'm too embarrassed by the messiness of the code to give it out. Maybe after I clean it up.
<app class="Mandel" (the name of the class) src="http://www.netgen.com/~mkgray/java/" iterations=20 (the number of iterations for orbits) realcenter=0 (the real coordinate of the center in the complex plane) imagcenter=0 (the imaginary coordinate of the center in the complex plane) scale=.01 (the scale per pixel) size=200 (the size of the resultant image) >


The simplicity of the branching of representations of the groups GL(n, q) under the parabolic restrictions
- 21 Downloads
We present a direct proof of the simplicity of the branching of representations of the groups GL(n, q) under the parabolic restrictions. The proof consists of three steps. First, we reduce the problem to the statement that a certain pair of finite groups is a Gelfand pair. Then, we obtain a criterion for establishing this fact, which generalizes the classical Gelfand’s criterion. Finally, we check the obtained criterion with the help of some matrix computations. Bibliography: 7 titles.
KeywordsRussia Finite Group Direct Proof Mathematical Institute Matrix Computation
Unable to display preview. Download preview PDF.
- 1.A. Aizenbud and D. Gourevitch, “Multiplicity free Jacquet modules,” to appear in Canad. Math. Bull., arXiv:0910.3659v1.Google Scholar
- 2.I. M. Gelfand and D. A. Kajdan, “Representations of the group GL(n, K) where K is a local field,” in: Lie Groups and Their Representations, Akad. Kiadó, Budapest (1975), pp. 95–118.Google Scholar
- 7.A. V. Zelevinsky, “Representations of finite classical groups. A Hopf algebra approach,” Lect. Notes Math., 869, Springer-Verlag, Berlin-New York 1981).Google Scholar


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Course Level: Beginner
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This course provides a comprehensive introduction to fundamental concepts in calculus and their applications, covering all of Calculus 1 and some of Calculus 2. The course starts with functions and limits, followed by differential calculus, and then moves on to integral calculus and a brief discussion of differential equations. It includes a sample exam based on the AP Calculus AB course. Problem sessions, exercises and auto-graded quizzes are provided for self-paced assessment. Earn a certificate by watching all lesson and problem session videos and completing the quizzes with a passing grade.
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10 km long 3 phase line delievers 1 MW at 0.8 p.f lagging....the series impedence of the line is 0.5+j0.56 ohm per km per phase ...sending end voltage is 11 kV ....find line current .....recieving end voltage and transmission efficiency.
plz solve in step by step...and clearify in very simple
(hint ans: 71.5A. 10.1kV. 093 )


Quadrance polygons, association schemes and strongly regular graphs
Quadrance between two points and is the number . In this paper, we present some interesting results arise from this notation. In Section 1, we will study geometry over finite fields under quadrance notations. The main purpose of Section 1 is to answer the question, for which , we have a polygon such that for . In Section 2, using tools developed in Section 1, we define a family of association schemes over finite field space where is a prime power. These schemes give rise to a graph with vertices the points of , and where is an edge of if and only if is a nonzero square number in . In Section 3, we will show that is a strongly regular graph and propose a conjecture about the maximal clique of .
1 Universal geometry over finite fields
Suppose that is an odd prime power, and that is the finite field with elements. To avoid lengthly calculations (but mostly repetition), we assume that is of form for some integer throughout Sections 1-3. In Section 4, we will present companion results for case . The following definitions follow  where the importance of the notation of quadrance is developed.
The quadrance between the points , and is the number
A circle in a finite field with center and quadrance is set of all points in such that
Recall that a (multiplicative) character of is a homomorphism from , the multiplicative group of the non-zero elements of , to the multiplicative group of complex numbers with modulus . The identically function is the principal character of and is denoted . Since for every we have for every character . A character is of order if and is the smallest positive integer with this property. By convention, we extend a character to the whole of by putting . The quadratic (residue) character is defined by . Equivalently, is on square, at and otherwise. It is easy to see that . Let and be the numbers of in such that , , and , respectively. We have the following lemma.
Let be an odd prime power of the form for some integer . Then , and .
Proof We have
But we have
Thus, or . Similarly, consider the sum
This gives or . Similarly, consider the sum
we have . And consider the sum
we have . This concludes the proof.
From Lemma 1, we can count the number of points in any circle in .
Let be a circle with nonzero quadrance in . Then has exactly points.
Proof Without lose of generality, we may assume that is centered at the origin. Let be the quadrance of . We will prove the lemma for the case as other cases are similar. The number of points in is
We have if and only if . Since is not a square in . We have the numbers of with is . For each with , we have corresponding points . Besides, we have 4 other points and . Hence, . This concludes the proof of the lemma.
Let denote the circle centered at with quadrance .
Let in and let be two distinct points in such that . Then only depends on and . Precisely, define
Then the number of intersection points is , where
Proof Suppose that and for some then . Suppose that where for some . Then we have and . This implies that . But we have so
If is non-square number in then it is clear that there does not exist such , or . Otherwise, let and for then
Solving for with respect to we have
If then we have only one for each , but if then we have two pairs . This implies (1), completing the proof.
The function defined above has an interesting property.
Given in , there exists at least values of such that is square (maybe zero).
Proof There are two cases.
Suppose that is square in . Then for some . We have
From Lemma 1, we have values of () such that is square. For each , we have two values of . Besides, we may choose from so we have three more values of . Thus, the number of such that is square (maybe zero) is .
Suppose that is non square in . Then for some . We have
From Lemma 1, we have values of () such that is square. For each , we have two values of . These are all possiblities for . Thus the number of such that is square (maybe zero) is .
This concludes the proof of the lemma.
If then for any and , there exists a polygon in such that for all (note that ).
Proof It suffices to prove for . For any , we need to show that there exists a quadrangle such that for . From Lemma 4, there are at least values of such that is square and at least values of such that is square. We have only possible values for so by the pigeonhole principal, there must be some value such that both and are square. Choose any two points with . From Lemma 3 , and are square in so there exists such that , , and . Thus we can choose . This concludes the proof.
2 Quadrance Association Schemes
We now have enough tools to construct an association scheme on . Let us recall the formal definition of an association scheme from .
An association scheme with associate classes on a finite set is a partition of into sets (called associate classes) such that
is symmetric for , i.e. ;
for all in there is an integer such that, for all in
The numbers are called the intersection numbers. The number is called the valency of the -th associate class.
Our association schemes are defined by quadrances between elements of . To meet the condition (i) in Definition 3, we need if and only if for all , which is equivalent to (mod ). The following theorem gives us an association scheme on .
Let , and partition into subsets (indexed by elements of ; for example ) such that for in , if and only if . This partition gives us an association scheme on . Furthermore, for , let . Then the intersection numbers of the scheme are
Proof The conditions (i) and (ii) of Definition 3 are easy to check. We will check (iii). Suppose that we have where and for some . Then . For , it is clearly that , i.e. . We have
We call this scheme the quadrance association scheme. This scheme can be used to obtain some other schemes. Precisely, we have the following theorem.
For any , there exists an association scheme with associate classes on .
Proof If then for some positive integer . There exists a primitive element of , says . Let and let be set of all nonzero powers in . We have , and write . Set for . We partition into sets by
Here are the associate classes of the quadrance association scheme. We check that this partition gives us an association scheme. The conditions (i) and (ii) of Definition 3 are easy to check. We will check (iii). For , iff . Similarly as in proof of Theorem 2, we have that
is the same for any .
For , suppose that . Then for some . The number of ’s in such that and is
From Theorem 2, depends only on whether is nonzero square, zero or nonsquare. Thus, we only need to look at this condition. For , we have
So that is a square (nonzero/zero) or non square if and only if so is . Hence, if we replace by in (4) then ). This implies that is the same for any , completing the proof.
3 Quadrance Graphs
3.1 Strongly Regular Graphs
Remind that . In Theorem 3, we saw that for any , there exists an association scheme with associate classes on . Now is an odd prime power so and we can compose the quadrance association scheme into an association scheme with three associative classes. It is not hard to see (from the construction in Theorem 3) that the association scheme with 3 associative classes is a partition where
Consider a graph of with vertices the points of , and where is an edge of graph if and only if is in . For , define
We have the following theorem.
Let be any two points in .
If then .
If then .
Proof a) Suppose that . Then for some .
We count the number of points in . Let be any point in then there exists such that and . Without loss of generality, we can divide both by and assume that . We have
There are three separate cases.
Suppose that is nonsquare. Then from Lemma 3 , there does not exist such that and .
Suppose that . We have three subcases.
If then and . But it contradicts to the condition .
If then and . Thus, we have pairs for . From Lemma 3, each pair gives us one point .
If then and . Similarly, we have points .
Suppose that is a nonzero square. Then either both and are nonzero square or both and are nonsquare.
Suppose that and are nonsquare. Similarly, we have values of and values of . Thus, we also have points .
Therefore, the number of points such that and is
But any point is counted four times (for the four pairs and ), so .
b) Suppose that . Then for some . We count the number of points in . Let be any point in then there exists such that and . Without loss of generality, we can divide both by and assume that . We have
There are three separate cases.
Suppose that is nonsquare. Then from Lemma 3, there does not exist such that and .
Suppose that . This is impossible as is not a square number in .
Suppose that is a nonzero square. Again, there are two subcases.
Suppose that is nonsquare and is nonzero square. Similarly, we have values of and values of . Thus, we also have points .
Therefore, the number of points such that and is . But any point is counted four times (for the four pairs and ) so . This completes the proof of the theorem.
From Theorem 4, we have is a strongly regular graph with parameters ; that is is -regular, any two adjacent vertices have common neighbours and any two non-adjacent vertices have common neighbours. For any two vertices and , there are precisely vertices joined to and not joined to . We call quadrance graph.
3.2 Maximal complete subgraphs
Let be the vertex set of a subgraph of and be the number of edges joining vertices in . In Section 3.1, we see that the graph is a strongly regular graph with parameters . The well-known Paley graph has the same parameter. Thus, we can follow Bollobas’s proof for Paley graphs (see , page 321-322) to show that
Let be a set of vertices of the Quadrance graph . Then
Proof We may assume that . Let be the number of unordered triples with and . By Theorem 4, for each pair of adjacent vertices of there are such triples and for each pair of non-adjacent vertices of there are such triples. Thus, we have
Let be the average degree in the induced subgraph . There are edges joining to . So on average, a vertex of is joined to vertices in , and a vertex in is joined to vertices in . Thus, we have
Multiplying by and rearranging, we have
This completes the proof.
If spans a complete subgraphs or an empty subgraphs of and then
Hence . It is easy to see that the equality holds when is a set of points in a line. Inspections for support for the converse statement. We propose the following conjecture.
If spans a complete subgraphs or an empty subgraphs of order of then is a line in .
4 Companion Results
In this section, we suppose that . We present companion results of previous sections in this case. Some proofs of the results in this section require extra works but they are basically similar to proofs in previous sections. Therefore, we obmit the details. The following lemma is an analogue to Lemma 1.
Let be an odd prime power. Then , and .
Using Lemma 5, we have the following result, which is an analogue to Lemma 2.
Let be a circle with nonzero quadrance in . Then has exactly points.
Lemma 4 still holds in this case. From Lemma 2 and Lemma 6, it is clear that the circle is a single point when for some integer . But for , the circle consists of points. This property causes some troubles in calculations (see ) which can be resolved by redefine the circle . We redefine and . We have the following lemmas.
For any in . Suppose that are two distinct points in with . Then the circle intersects if and only if . Furthermore, if then two circles intersect at only one point.
Let then there exists such that and are square in .
Proof There are three cases.
Suppose that is square in . Then is square in . Thus, we can choose .
Suppose that is square in . We have
Since is square in


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Math Problem Solver Math Problem Solver Mathematics is a subject that is included in every stream of education and its problems gets tougher as student moves further in his studies. Thatâ€™s why proper assistance in solving math problems is required by most of the students because they know it is a kind of practical subject in which they can score maximum. But this is not an easy task to do, This subject requires regular math practice. At present, several online math tutoring services provide math problem solvers on the internet platform for the students so that students can take help in math anytime they want. Math problem solver simplifies all the math related queries of the student and provides all the related steps to that problem which can be useful while solving other similar kind of problems. As we all know mathematics is categorized in several of its branches which have distinct types of queries and due to this online math tutoring websites have math problem solver for each of the mathematical branch. Let us talk about algebra solver that solves all the complex queries of students related to the algebra. Know More About Significant Figures Calculator Math.Tutorvista.com
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Algebra is an art of forming mathematical expressions with variables and integer constant which are related through arithmetic operators. These relations are made according to any real life situation which is explained in words to the students. While taking lessons from online tutors, students are free to ask their doubts without hesitation and they can review the lessons as many times they want. Algebra solver uses some of the features provided by tutoring service for better explanation of math principles with good interactive communication on the internet platform. These features are video aids, online test, and various worksheets for practice, online live chat, and video conferencing. Let us take an example of an algebra problem and see how algebra solver helps to solve the equation for students: X2 + 9x = 2x Here X is a variable which is to be replaced by an integer value to solve the above equation: X2 = 2x â€“ 9x X2 = - 7x Dividing both terms by x X = -7 Now for check your answer. Put this value of X in the given equation: X2 + 9x = 2x (-7)2 + 9(7) = 2( -7) 49 -63 = -14 -14 =-14 LHS = RHS equation satisfied so the answer of the equation is correct. How I Do My Homework? If you are asking this question to yourself then don't worry free math help will help you to solve your problem. The free online math help used for solving the math problem on internet. The website is designed with the purpose that the student can solve their problem at their home.Sometime the students shy away from asking about their problems directly from school teachers. Learn More Prime Factorization Calculator
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Mathematics is a subject that is included in every stream of education and its problems gets tougher as student moves further in his studies...


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Academic Component- This component provides engaging and differentiated instruction using multi-sensory techniques and materials that strengthen language arts and mathematics foundational skills; fostering
confidence and achievement in mathematics and reading literacy
Music Component - Our music component includes three courses: music theory, music electives and ensembles. CAFÉ students prepare for an examination in music theory developed
by the Maryland State Board of Music Teachers Examination.
Life Skills - CAFE seeks to prepare students to examine their world critically
and respond to its challenges with creativity. Students are encouraged to assume leadership;
to value the opportunity for service; and, to accept, understand and appreciate the diversity
of their community and the world. Throughout the school year, CAFE students typically participate
in special life-skills related programs and workshops.


Alison Etheridge is Professor of Probability at the University of Oxford where she holds a joint appointment in the Departments of Mathematics and Statistics and a Fellowship at Magdalen College. She was an undergraduate at New College, and divided her graduate study between Oxford and McGill. She then held research fellowships in Oxford and Cambridge and positions in Berkeley, Edinburgh and Queen Mary University of London before returning to Oxford in 1997.
Over the course of her career, her interests have ranged from abstract mathematical problems to concrete applications as reflected in her four books which range from a research monograph on mathematical objects called superprocesses to an exploration (co-authored with Mark Davis) of the percolation of ideas from the groundbreaking thesis of Bachelier in 1900 to modern mathematical finance.
Much of her recent research is concerned with mathematical models of population genetics, where she has been particularly involved in efforts to understand the effects of spatial structure of populations on their patterns of genetic variation.
Professor of Probability, Mathematical Institute, University of Oxford Professor of Probability, Department of Statistics, University of Oxford
Interest and expertise
Statistics and Operational Research, Pure mathematics
Organismal biology, evolution and ecology
Probability theory, Population genetics, Mathematical models


A reference for engineers and students, this volume devotes more than 300 pages to theoretical and experimental considerations. It progresses from elementary materials to methods used in the design of NACA low-drag airfoils, and it presents techniques for using wing-section data to predict wing characteristics. Requires differential and integral calculus and elementary mechanics. 1949 edition.
Corrected reprint of the 1st (1949) edition, with a new preface by the authors.
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TRIGGER WARNING FOR MOM: There is a picture of a snake on this post.
There are several different ways that this phrase can be taken. One way that it is commonly used: when people talk about jettisoning some extra weight in their life. This could be a toxic relationship, clutter, or other problems which add to their selves.
However, I’d like to talk about the mathematical thing. Don’t worry, it will not be heavily mathematical.
When I was in kindergarten or first grade, one way that my teacher described subtraction (definitely not in these words, but follow along): “Consider that you are on the 11th floor of a building, and want to go to the seventh floor. How many floors must you go down? This is a way to visualize 11-7=4.)
I’m probably badly misremembering this, and it’s not exactly what I had in mind. I just wanted to mention it.
There are two contexts where I regularly use addition by subtraction, or vice-versa. The G-word and book-keeping.
On the G-word, there tend to be good problems and bad problems. I have rubrics for math problems which are sometimes additive (i.e. each component is worth a certain amount of points), and sometimes they are subtractive (i.e. I list a number of errors and a number of penalty points for each).
I find that for people who apparently did well, I start from the max points and subtract according to the errors. Whereas if someone has mostly an answer full of dreck, I try to add points from zero.
At the end of the G-word for exams, I turn into a specific type of snake, as shown below.
The exams have five problems, with their scores to add. If all of the numbers are fairly close to the maximum, in order to add them I instead do what is similar to the Common Core method of subtraction: consider the max score (usually 100), and then add the LOST points and subtract that from 100. For example, 17+19+18+20+13 = 100-(3+1+2+0+7) = 87.
On the other hand, if someone doesn’t do so well, I add the points from zero by normal addition.
In book-keeping, I find that instead of carrying when the Cents of the larger number are smaller than the Cents of the smaller number, I add a number of cents to both numbers before subtracting. For example, $402.33 – $98.69 = $(402.33+1.31)-(98.69+1.31) = $303.64. It’s useful to add zero in some cases–this was a tenet of “Hands-On Equations” that we did in fifth grade.
I’ve touched mostly on the mathematical idea of addition by subtraction. I welcome comments on non-mathematical addition by subtraction (or vice-versa)!
Today is the four-hundred and thirty-first day of Mission 441. Ten days remain.


Moments of coinless quantum walks on lattices
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The properties of the coinless quantum-walk model have not been as thoroughly analyzed as those of the coined model. Both evolve in discrete time steps, but the former uses a smaller Hilbert space, which is spanned merely by the site basis. Besides, the evolution operator can be obtained using a process of lattice tessellation, which is very appealing. The moments of the probability distribution play an important role in the context of quantum walks. The ballistic behavior of the mean square displacement indicates that quantum-walk-based algorithms are faster than random-walk-based ones. In this paper, we obtain analytical expressions for the moments of the coinless model on d-dimensional lattices by employing the methods of Fourier transforms and generating functions. The mean square displacement for large times is explicitly calculated for the one- and two-dimensional lattices, and using optimization methods, the parameter values that give the largest spread are calculated and compared with the equivalent ones of the coined model. Although we have employed asymptotic methods, our approximations are accurate even for small numbers of time steps.
KeywordsCoinless quantum walks Moments Mean square displacement Standard deviation
RAMS acknowledges financial support from Capes-Faperj E-45/2013. RP thanks Faperj (Grant No. E-26/102.350/2013) and CNPq (Grant Nos. 304709/2011-5, 474143/2013-9, and 400216/2014-0). SB acknowledges financial support from the US National Science Foundation through Grant DMR-1207431.
- 4.Ambainis, A., Bach, E., Nayak, A., Vishwanath, A., Watrous, J.: One-dimensional quantum walks. In: Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing. STOC ’01, pp. 37–49. ACM, New York, NY, USA (2001)Google Scholar
- 5.Nayak, A., Vishwanath, A.: Quantum Walk on the Line (2000). arXiv:quant-ph/0010117v1
- 14.Falk, M.: Quantum search on the spatial grid (2013). arXiv:quant-ph/1303.4127
- 16.Ambainis, A., Portugal, R., Nahimov, N.: Spatial search on grids with minimum memory. arXiv:quant-ph/1312.0172
- 17.Portugal, R., Boettcher, S., Falkner, S.: One-dimensional coinless quantum walks (2014). arXiv:1408.5166v2 [quant-ph]


The purpose of this paper is to extend the Buneman construction of partially labelled trees to the general case. This extension is related with the characterization of median graphs by Mulder and Schrijver. In the first section, we construct a graph G(H) associated with a copair hypergraph H on a finite set X and define the notion of a median graph with latent vertices (called X-median graph). The latent vertices (i.e. the vertices who are not labelled by elements of X) are obtained by iterating the median operation from actual (labelled) vertices. In the second section, we prove that the graph G(H) is an X-median graph. Then, in the last section, we study some special cases, the Buneman result is reobtained and the hypergraphs whose associated graphs are Hasse diagrams of distributive lattices are characterized. © 1989.
Barthelemy, J. P. (1989). From copair hypergraphs to median graphs with latent vertices. Discrete Mathematics, 76(1), 9–28. https://doi.org/10.1016/0012-365X(89)90283-5


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Generate a vector like 1,2,2,3,3,3,4,4,4,4
Fix the last element of a cell array
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Generalised Hamming Number
Pandigital number n°2 (Inspired by Project Euler 32)
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Zero Area Triangles in Delaunay Triangulation
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Boris Blagojevic on 31 May 2021
i am using delaunayTriangulation in my Application. To be specific, i am triangulating between two Lines L1 and L2, which are a distance d apart. All Points on L1 and L2 are less or equal than d apart.
Applying the delaunayTriangulation, i ended up with multiple triangles which are on either L1 or L2. These triangles are obviously colinear, have zero area and are not very useful.
Tri = delaunayTriangulation([L1;L2]);
Triangle1 = Tri.Points(Tri.ConnectivityList(1,:),:);
for i = 1 : 3
See the attached .mats and the code snippet.
I know how the algorithm works and why this happens. Yet, my point of view, it would be desirable to include some option in the delaunayTriangulation, which allows one to prevent the creation of colinear triangles - like it is possible with the polyshape class. There might be other opinions on this, which i would be delighted to hear.
Is there some easy way of doing this with this class?
Or does anybody have an implementation of the algorithm that allows non-colinear delaunay Triangulation?
darova on 1 Jun 2021
What about initmesh?
t = linspace(0,2*pi-0.1,20); % unclosed contour (without selfintersection)
[x1,y1] = pol2cart(t,2); % big circle
[x2,y2] = pol2cart(t,0.7); % small circle
x2 = x2 + 2; % move small circle
m1 = length(x1);
m2 = length(x2);
m = max(m1,m2);
gd = zeros(2+m*2,2); % preallocate matrix for geometry description
gd(1:(2+2*m1),1) = [2; m1; x1(:); y1(:)]; % assign data for big circle
gd(1:(2+2*m2),2) = [2; m2; x2(:); y2(:)]; % assign data for small circle
sf = 'C1-C2'; % solid formula: substract small circle from big circle
ns = char('C1','C2')'; % C1 - big circle, C2 - small circle
dl = decsg(gd,sf,ns); % decomposite solid geometry
[p,e,t] = initmesh(dl); % initialize mesh
pdemesh(p,e,t) % show mesh
more info: initmesh
preparation data: LINK
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Class 1 engaged in mathematics
Class 1 engaged in mathematics; a significant part of human logic and thoughts. Mathematics provides an effective means to create mental discipline and increases logical reasoning. It is found in many fields and disciplines as the concepts and procedures are used to solve engineering, science, and economics problems. Mathematical knowledge also plays an essential role in understanding the concept of other subjects like social studies, music and art. Lastly, mathematics makes our life orderly and prevents chaos. Certain qualities that are nurtured by mathematics are the power of reasoning, creativity, abstract or spatial thinking, critical thinking, problem-solving ability, and even effective communication skills.


Using the approximation
For small x, find a simple algebraic relationship between FKA(t) and FNA(t)
Comment briefly on the relationship you have found.
^ ^ ^
F KA (t) = 1 - ∏ (1 - λj) where λj =
^ ^ ^ ^ ^
FNA (t) = 1 - where Λ(t) = ∑ λj and λj =
Please see the attached file.
Using the approximation ex = 1 + x (approx).
For small x, find a simple algebraic ...
The solution answers the question(s) below.


Evaluate the number of possible combinations of roots for a given polynomial equation. For example for quadratic, you can have:
- 2 imaginary roots (conjugate)
- two real distinct roots
- or 1 repeated root.
In this case, we have only 3 possible combinations For cubic you can have:
- 3 distinct real roots
- 3 repeated real roots
- 2 repeated and 1 distinct real roots
- 2 distinct imaginary (conjugate) and 1 real
- 1 repeated imaginary (conjugate) and 1 real and in this case we have 5 possible combinations:
can you find a formula that gives the total number combinations, for example, 3 for quadratics and 5 for cubic equations, for any given polynomial of degree n?


Authors: ALİ HAMZA TANRIKULU, YALÇIN MENGİ, AHMED KAMİL TANRIKULU
Abstract: In this study, a boundary element formulation having nonlocal boundary conditions is presented for the dynamic analysis of a two-phase composite. Nonlocal boundary conditions, used in the formulation, make it possible to analyze a three-phase composite. The formulation is performed in Fourier transform space using a constant element model. Based on the formulation presented in this study, two general purpose computer programs are developed, namely, CD2NL (for two-dimensional analysis) and CD3NL (for three-dimensional analysis). The programs perform the analysis in Fourier transform space and can also be used for static analysis by assigning a small value to the frequency. The results of some benchmark problems obtained using the programs are compared with those in the literature.
Keywords: Boundary Element Method, Two-Phase Composite, Three-Phase Composite, Nonlocal Boundary Conditions, Fourier Transform Space.
Full Text: PDF


Let $S(x)$ be the area of the yellow curvilinear triangle. I'd like to find a graph for which $S(x)=H(x)$ where $H $ is some prescribed function (small, smooth, vanishing near the endpoints to any order you wish, etc.). Is it always possible or there are some non-obvious hidden restrictions?
The question comes from the infamous t-section problem (if you know the areas of all sections of a symmetric convex body by the hyperplanes at some fixed small distance $t$ from the origin (so small that all sections are non-empty), can you recover the body?). The problem is open even on the plane. I do not say that this toy question is directly relevant here but an answer to it will certainly make a few things clearer for me.


Symmetry between mathematical constructions is a very desired phenomena in mathematics in general, and in algebraic geometry in particular. For line arrangements, symmetry between topological characterizations and the combinatorics of the arrangement has often been studied, and the first counterexample where symmetry breaks is in dimension 13. In the first part of this paper, we shall prove that two arrangements of smooth compact manifolds of any dimension that are connected through smooth functions are homeomorphic. In the second part, we prove this in the affine case in dimension 4.
- Smooth manifold
All Science Journal Classification (ASJC) codes
- Computer Science (miscellaneous)
- Chemistry (miscellaneous)
- Physics and Astronomy (miscellaneous)


This function has been removed as of Datameer v6.3
Computes the Jaccard distance of all values in a group. The Jaccard distance between two sets is the ratio of the size of their intersection to the size of their union. For example, the Jaccard distance between two species is 1-(number of regions where both species are present)/(number of regions where at least one species is present).
This is an aggregate function.
Given the following data:
First create a group using GROUPBY(#RawData!Groups)
Then use the GROUP_JACCARD_DIST(#RawData!Letters), and the result is the Jaccard distance of the group created from the column in relation to the GROUPBY() column.


There’s still plenty of time to enter the Create Your Own Math Exploration Contest from Ascend Math. Ascend Education is giving educators and their students a chance to come up with their own ideas for online explorations for any math objective grade 3-Algebra II. The educator submitting the exploration voted best will receive a $500 cash prize. The second prize winner will receive $250 and the third $100. Three honorable mentions will receive $50 each. Educators interested in submitting will find complete information and examples of online explorations on the Ascend Math website. All entries must be submitted by May 8, 2015. The winners will be notified by email.
Recently, the Washington Post reported that for the first time ever, the majority of public school students are from low income families, that is students qualifying for free or reduced lunch. The article goes on to explain how this changes the way teachers have to deal with students. They now need to look at these students individually each day. “When did this student eat last?” “Is this student healthy today?” “Is something making this student especially fearful today?” These questions are now a part of most teachers’ daily routine. When everything is pretty much okay with students, they can be taught and dealt with collectively. When things are not okay, individual attention is necessary.
The same is true when students, for any reason, fall behind. Just as educators cannot form a collective opinion of what is going on in the personal lives of disadvantaged students, they cannot make a collective decision on what academically struggling students require to progress. Each student in need of intervention is individual and their personal needs or skill gaps must be seen to. According to the Washington Post article this need has greatly expanded. “The shift to a majority-poor student population means that in public schools, a growing number of children start kindergarten already trailing their more privileged peers and rarely, if ever, catch up.”
These students can and do catch up when their instruction is individualized to their needs. Providing individual instruction to a few students is extremely challenging. Multiply the need by more than half the students in the class without help and it quickly becomes an impossible situation. Intervention programs must be created to relieve teachers of part of this burden. Programs like Ascend Math provide truly individualized assessment and instruction, reaching down to the student’s lowest math skill gaps. Only in this way can one teacher help a large number of individual students.
To learn more about Ascend Math I encourage you to attend one of our brief weekly webinars.
Our records show that math intervention and enhancement students working in Ascend Math are making fantastic progress this year. We offer this Valentine’s Day math fun for them and you.
1. The oldest known valentine still in existence today was a poem written in 1415 by Charles, Duke of Orleans, to his wife while he was imprisoned in the Tower of London following his capture at the Battle of Agincourt. (The greeting is now part of the manuscript collection of the British Library in London, England.) How many years have passed since that first valentine?
2. According to the Hallmark Corporation, 132 million Valentine’s Day cards are exchanged annually, making Valentine’s Day the second-most popular greeting-card-giving occasion. This total does not include packaged kids valentines for classroom exchanges. Packages of 25 Valentines are on sale for $5.00 each. How many could be purchased for $20?
3. According to a nationwide survey conducted by the National Confectioners Association (NCA) Americans overwhelmingly prefer chocolate over flowers on Valentine’s Day by a margin of 69 to 31%. When asked what was their most popular flavor in a box of Valentine’s Day chocolates here’s how they voted:
34% Caramel 24% Chocolate-covered nuts 13% Cream filled 13% Chocolate filled
What percentage said something other than these top choices? What do you think was the next most popular chocolate?
In honor of Black History Month we’ve provided a few fun and challenging math problems. Try these out.
1. On 25 March 1965, Martin Luther King led thousands of nonviolent demonstrators on a 5-day, 54-mile march from Selma, Alabama to the steps of the capitol in Montgomery, Alabama. According to the American College of Sports Medicine the average step length of an adult is 2.6 feet or about 31 inches. There are 5,280 feet in a mile.
Can you determine how many steps were taken by someone marching the entire distance from Selma to Montgomery Alabama? (To estimate there are about 2000 steps in a mile)
2. A court order restricted the number of marchers to 300 when passing over a stretch of two-lane highway. However, on the final day of the march, when the road reached four lanes the number of demonstrators swelled to 25,000.
What was the percentage of increase?
3. An African-American and son of a former slave, Benjamin Banneker rose to fame as a brilliant scientist, scholar and mathematician. He wrote and collected mathematical puzzles written in verse. Here is one that can be a lot of fun to try and figure out. See how close you can come to answering the question “How many leaps did the hound have to make to catch the hare?
When fleecy skies have Cloth’d the ground
With a white mantle all around
Then with a grey hound Snowy fair
In milk white fields we Cours’d a Hare
Just in the midst of a Champaign
We set her up, away she ran,
The Hound I think was from her then
Just thirty leaps or three times ten
Oh it was pleasant for to see
How the Hare did run so timorously
But yet so very Swift that I
Did think she did not run but Fly
When the Dog was almost at her heels
She quickly turn’d, and down the fields
She ran again with full Career
And ‘gain she turn’d to the place she were
At every turn she gain’d of ground
As many yards as the greyhound
Could leap at thrice, and She did make,
Just Six, if I do not mistake
Four times She Leap’d for the Dogs three
But two of the Dogs leaps did agree
With three of hers, nor pray declare
How many leaps he took to Catch the Hare.
Just Seventy two I did Suppose,
An Answer false from thence arose,
I Doubled the Sum of Seventy two,
But still I found that would not do,
I mix’d the Numbers of them both,
Which Shew’d so plain that I’ll make Oath,
Eight hundred leaps the Dog to make,
And Sixty four, the Hare to take.
For hints on solving this complex verse problem see John F. Mahoney’s excellent discussion of this and other Banneker puzzles
Share these five engaging Super Bowl math problems with your math intervention or enhancement students.
A super bowl quarterback can throw a fully inflated football 55 yards in the air. If he has his equipment manager deflate the balls by 16% (or 2 pounds per square inch) and that causes a 10% increase in distance how much further will he throw the ball?
If the score is the Patriots at 27 and the Seahawks at 14, what combination of touchdowns (7 points) or field goals (3 points) would the Seahawks have to make in order to tie or win the game?
If Marshawn Lynch of the Seattle Seahawks, rushes for 127 yards on 22 carries against the New England Patriots in Super Bowl XLIX, how many yards per carry would he have averaged?
Oh by the way, what Super Bowl number is that?
Dash off the answer!
A super bowl wide receiver runs a 40 yard dash in 4.5 seconds. Assuming he runs a hundred yards at the same pace, how much longer would it take him?
The more complete quarterback
Tom Brady completed 65% of his passes while Russell Wilson completes 70% they each throw 40 passes. How many passes will Tom Brady complete, how many will Russell Wilson complete? Bonus: what is the total of incomplete passes for both quarterbacks?
A few months ago, Amy Boyd of Holabird STEM program in Baltimore County Schools spoke to a group of math educators attending the NCTM regional conference in Richmond, VA. Holabird STEM program is an Ascend Math Gold Medal leader for 2014.
Prior to using Ascend, 97% of their students tested at least one grade below grade level, with about 70% of those students testing three or more grades below their current academic grade. The math intervention program they ran last year using Ascend Math helped these students make tremendous gains. More than 60% of students gained two or more grade levels in math.
Please watch this brief video.
More than a year ago, we made the conscious decision to add a greater level of interactivity to the online lessons in Ascend Math. Ascend Math was already among the most interactive math intervention resources available. We saw the opportunity to go further. The reasons are firmly based in research.
The Role of Interactivity in Web-Based Material examined students divided into three groups experiencing the same web content with varying degrees of interactivity. This study found those students working most interactively with a web program attained significantly higher pre to post test gains. The students also reported a greater sense of satisfaction and spent nearly double the amount of time on task compared to the next highest group.
Educators and students using Ascend Math agree that increased interactivity aids learning. In a recent survey, educators using Ascend Math had the following to say:
“They like the interactivity. The students are surprised when they see their name in the captions.”
“Students enjoy the interaction. The interactivity makes this program unique.”
“I think it helps them to remain focused on what objective is being taught”
The Ascend Math website includes several examples of our interactive student experience. Please visit. http://ascendmath.com/student_experience/index.html
Crosby Middle School was the First Prize Winner in the Ascend Math Reel Success Video contest. All the schools entering videos use Ascend Math with their math intervention students. For example, 60% of tier 3 intervention students at Crosby Middle School grew one or more grade levels the first two months of this school year.
You can find all the winners at http://ascendmath.com/math_reel_success.html
Wondering what tech trends you might see in classrooms in 2015? The Washington Post released an article you may be interested in. They even ask for feedback on which ones might be reality and which are wishful thinking.
Students using Ascend Math love to track their own progress using the Ascend Climber. They can choose their own avatar and watch as the Climber ascends the mountain with each lesson they pass. Take a look at this special Holiday version of the climber http://22.214.171.124/Ascend4/holidayClimber.html


It is shown that the nonstandard representatives of Schwartz distributions, as introduced by K. D. Stroyan and W. A. J. Luxemburg in their book Introduction to the theory of infinitesimals , are locally equal to a finite-order derivative of a finite-valued and S-continuous function. By ‘equality’, we mean a pointwise equality, not an equality in a distributional sense. This proves a conjecture by M. Oberguggenberger in Z. Anal. Anwendungen 10 (1991), 263–264. Moreover, the representatives of the zero-distribution are locally equal to a finite-order derivative of a function assuming only infinitesimal values. These results also unify the nonstandard theory of distributions by K. D. Stroyan and W. A. J. Luxemburg with the theory by R. F. Hoskins and J. Sousa Pinto in Portugal. Math. 48 (1991), 195–216.
Cite this article
Hans Vernaeve, The local structure of nonstandard representatives of distributions. Port. Math. 65 (2008), no. 3, pp. 321–337DOI 10.4171/PM/1815


By John Taylor
The concept of proof is relevant to arithmetic but it's some of the most tough elements of the topic to coach and grasp. particularly, undergraduate arithmetic scholars usually adventure problems in figuring out and developing proofs.
Understanding Mathematical Proof describes the character of mathematical facts, explores some of the suggestions that mathematicians undertake to turn out their effects, and provides suggestion and techniques for developing proofs. it is going to increase scholars’ skill to appreciate proofs and build right proofs in their own.
The first bankruptcy of the textual content introduces the type of reasoning that mathematicians use whilst writing their proofs and provides a few instance proofs to set the scene. The e-book then describes uncomplicated common sense to allow an figuring out of the constitution of either person mathematical statements and entire mathematical proofs. It additionally explains the notions of units and capabilities and dissects numerous proofs with the intention to exposing the various underlying gains universal to such a lot mathematical proofs. the rest of the ebook delves extra into kinds of evidence, together with direct facts, facts utilizing contrapositive, evidence by means of contradiction, and mathematical induction. The authors additionally talk about lifestyles and distinctiveness proofs and the function of counter examples.
Read Online or Download Understanding mathematical proof PDF
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Extra info for Understanding mathematical proof
There are other ways of expressing conjunction in English other than using the word ‘and’. Consider the following propositions. 1. Sue went to the party last night but Jamie didn’t. 2. Hamid passed the module whereas Mike did not. 3. Jim played football although he was suﬀering from a cold. In each case, the proposition is true only when both of its component simple propositions are true; hence, each proposition is the conjunction of its two components. The English sentences each have slightly diﬀerent nuances compared with the corresponding sentences using ‘and’ to form the conjunction.
Simply as a device to emphasise that the top level structure is a disjunction rather than a conditional. In this case, we would apply the convention that disjunctions are interpreted as inclusive unless they are explicitly denoted as exclusive and symbolise the sentence as ¬Q ∨ (P ⇒ R). Either of these is a reasonable interpretation of the English language sentence and we leave the reader to decide which is their preferred interpretation. This again emphasises that natural language may sometimes be ambiguous and open to more than one interpretation.
To see this, suppose we replace the term ‘odd’ with ‘prime’ and, to be consistent, we also replace the term ‘even’ (meaning ‘not odd’) with ‘composite’ (meaning ‘not prime’). Then the reasoning is the following. The square of any composite integer is also composite. 1234567893 is prime. Therefore (1234567893)2 is prime. In this case the ﬁrst two statements are true as before but the ﬁnal statement is false. An obvious requirement of any piece of valid reasoning must be that, if the initial (above the line) statements are true, then the (below the line) conclusion must also be true.


Hey, first post and all so maybe someone can help me out with a question from my Number Theory class. It's in the Congruences chapter.
Prove that if n is congruent to 4 (mod 9), then n cannot be written as the sum of 3 cubes.
Thanks in advance for the help!
Edit: I'm not sure if it's a typo when you wrote that a sum of cubes can't be congruent to 4 mod 9... of course if we have four cubes then we can just choose 1+1+1+1.


Abstract: The Gompertz distribution has many applications, particularly in medical and actuarial studies. However, there has been little recent work on the Gompertz in comparison with its early investigation. The problem of analyzing and estimating parameters of bivariate Gompertz distribution with shared frailty is of interest and the focus of this paper. We propose maximum likelihood estimation procedure for a bivariate survival model in which dependence is generated by a gamma distribution. We assume that the bivariate survival times follow bivariate Gompertz distribution and distribution of censoring variable is independent of the two life times. A search of the literature suggests there is currently no bivariate Gompertz distribution with shared frailty.
Keywords: Bivariate Gompertz distribution, censored sample, fisher information, gamma frailty, maximum likelihood estimators (MLE), survival times


First, here is the worksheet for yesterday's discussion:
This is the first worksheet of the final unit of the trimester. No, they have not had anything about derivatives, Riemann sums, or partial fractions in class. And yet, this is what happened:
Every group was able to estimate the area under the curve in #5, an every group came to the conclusion that in order to write the sum using "sigma notation", a choice needed to be made about "which end of the base" (left or right) to use to calculate the height of the rectangles. Every group was able to find the partial fraction decomposition in #6.
When the students actually do the prep work and actively participate in the discussions, this is what happens.