fabiochiu/medium-articles huggingface dataset:
Mathematics. A form of Apophenia?
By: Atharva Ghatnekar
Tags: Math, Patterns, The Queens Gambit, Mathematics, Psychology

Mathematics. A form of Apophenia?

Photo by Sergio Souza on Unsplash

Lately, I was watching the award-winning drama biopic: A Beautiful Mind, starring Russell Crowe as ‘John Forbes Nash Jr.’, a mathematical genius diagnosed with paranoid schizophrenia. The movie, with its extraordinary plot and execution forced me to learn more about Nash and schizophrenia. As I was surfing through the internet about schizophrenia, I came across a concept called ‘Apophenia’. As I continued searching about apophenia, I realized that the word apophenia was also used in the chart-topping drama series: The Queen’s Gambit. Apparently, in one of the episodes, a reporter asks Beth Harmon, a prodigious chess player whether she has ever heard of ‘apophenia’. Harmon replies to the report’s question saying that she has never heard of apophenia.

Well I too didn’t know the meaning of apophenia so I simply searched up its definition.

Apophenia is the tendency to perceive a connection or meaningful pattern between unrelated or random things.

The reporter then asks Harmon whether she sees unusual patterns on the chess board during her games. Harmon thinks for a while then replies with a no.

Honestly, I found the entire idea of apophenia rather interesting. When I first read about it on the internet and then watched the clip from The Queen’s Gambit where ‘apophenia’ was mentioned for the first time, my mind immediately related it with mathematics (yes, I know, I apologize for this nerdy approach, but I had to).

As a student, I am extremely fond of mathematics. I have always been flabbergasted by its theories, its applications… its omnipresence in nature and even its mysteries. The reason why I instantly related apophenia to math is because I believe that ‘patterns’ make up a major portion of mathematics… may it be observing mathematical patterns and relationships in nature or even using math as a tool to provide structure and framework to the patterns we see everywhere around us.

common example of apophenia

Apophenia, on some sites on the internet has also been defined as a ‘human experience’, wherein people see familiar objects or patterns in unrelated or random things and places. We have all had this moment where we’ve seen animal figures and faces in clouds. We also tend to visualize familiar patterns, symbols or faces on tree barks, or certain textures on the wall or even on a slice of toast. Well all these actually count as ‘everyday examples’ of apophenia.

Wait, hold on. Before I continue sharing my personal opinions and thoughts regarding the link between mathematics and apophenia, let me make it clear that I am not an expert in math and nor do I have any expertise and experience in neurology, psychology, or any other subject or course that studies apophenia in people. I am just as curious as John Nash and Beth Harmon (less actually, both of them were far beyond genius… even though Harmon is a fictional character).
Chapter 13 | Math
By: Kumar Anurag
Tags: Math, C Sharp Language

In this chapter, we will learn some predefined methods of Math in C#.

The following code (wait for it to load) will explain the same.

I hope you enjoyed this lesson. See you in the next one. Bbye!
Philosophical approaches: purity of systems
By: Hüseyin Akbaş
Tags: Purity, Math, System, Philopsophy, Science

Retrieved from https://cdn.thomasnet.com/insights-images/embedded-images/99f2f999-0133-4767-9694-9ce8a8af4147/c0322aaf-472e-4ebb-8773-a820008b95ae/FullHD/Spur,-helical,-and-bevel-gears.jpg

Purity comes when a system is not dependent or vulnerable to another one. Math is, for example, is a consistent and pure system in itself because its terminals works always the same on its own space and for every x, there is a y and this is always the same and true for math as far as I know (Cannot be too sure for each operation since I am no math expert). Since flows include external time sense according to my approaches(https://hakbas.medium.com/philosophical-approaches-verbs-and-nouns-in-human-mind-936512dbea56) and it depends on something which is not in the space of the human mind, they should not be considered as ‘pure concepts or contexts’ as they can be reduced into smaller pieces and they will not create a reliable and pure system on their own. Pure concepts, though, can create impure concepts by relating them to external terminals which can later be resolved into themselves.

Science can be done on the systems that is pure because ‘reliability’ can only be achieved if the system is not dependent on other variables unless it is wanted.
Compound Interest: Winning The War>Battles
By: Sriya Chintalapalli
Tags: Math, Self Improvement, Growth, Love, Mindset

Have you ever heard the saying,

“It’s easy to win the battles, & still lose the war?”

I have.

But how do I/you/anyone win the war — our war? I hypothesize that it’s through — compounding.

For ages, I assumed reaching big, audacious goals could be best done by taking large, intense leaps of self-improvement in the shortest amount of time.

Most of the people around me have too — but often they claim to end up in frustration, self-doubt, or the term I’ve heard way too many times during the pandemic, “burnout.”

I’ve never once faced ‘burnout’ and in solely in the past 4 months I

Was invited to conferences like MIT Tough Tech Summit (for only founders & investors — but was sponsored to attend as an exception).

Sponsored by OpenBCI to build a system to type using my thoughts, brain-controlled prosthetics & VR games as a neurotech developer.

Consulted for an MIT startup on how to increase app adoption by 50% of populations in selected states.

Built a vision for the future of our interface evolution & spoke at India’s largest education conference, WEEXPO India on that. Here’s the talk.

Built AIs that could identify hand motions from EEG recordings, predict visual stimuli from MEG recordings of human brain activity, detect P300 evoked responses + more

Developed XR skills and created an AR Web Browser, VR Pilot training simulation etc.

Developed blockchain skills and built a voting dApp, compensation for content creation dApp. Oh, and my own cryptocurrency.

Released a podcast (here’s the first episode to learn about a game-changing approach to life).

Also attended YC’s Future Female Founder’s, KET’s, & Verizon Media’s Immersion Conference among others.

These are just a few of the fun stuff I’ve been able to get my hands dirty in.

And I believe that a lot of this progress has come from — compounding.

It’s not that I was always able to get things I loved done fast, with limited resources, & remotely.

But overtime — habits, relationships, & experiences have compounded to allow me to do so.

It’s a continuous improvement process. I’m still in it. Will always be.
Weapons of Math Destruction- Como os algoritmos impactam a nossa vida
By: Luiza Vasconcelos
Tags: Racism, Math, Algorithms, Preconceito

Learn more. Medium is an open platform where 170 million readers come to find insightful and dynamic thinking. Here, expert and undiscovered voices alike dive into the heart of any topic and bring new ideas to the surface. Learn more

Make Medium yours. Follow the writers, publications, and topics that matter to you, and you’ll see them on your homepage and in your inbox. Explore
Learn How to Calculate Square Root of 2 in Easiest Method
Tags: Grammar, Math, English

Learn How to Calculate Square Root of 2 in Easiest Method Ellepetter ·Dec 25, 2020

If you have an idea to calculate square root 3 and 5, then it is easier to calculate the square root of 2. There are some simple and easy methods known as — Long Division, Average, and Equation, through which learning the square root of 2 easier. Check the examples also, as we have added how to calculate it easily.

Better, you start reading the article from here in detail and learn.
Math, Physics, and Psychology Syllabus
Tags: Ib Coaching In Delhi, Math, Physics Tutor

The IB has done away with the previous system entirely and comes up with two new courses of Math, both for SL and HL. These are Math AA (Mathematics: analysis and approaches) and Math AI (Mathematics: applications and interpretations). Math AA focuses on algebraic methods, while Math AI integrates technology with its focus on statistics and modeling. The purpose of improvisation in the IBDP Math syllabus is to open up more career opportunities for the students who have a deep passion for Math and also equipped with critical and analytical skills with the problem-solving ability both in the real and abstract worlds.

Physics

IBDP Physics syllabus, as a part of the Nature of Sciences (NOS) in Group 4 of the IBDP, is the most fundamental of the experimental sciences, as it seeks to explain the universe itself from the smallest atomic particle to the inter-galaxy distances. The study involves hands-on activities in the classroom or in the field. Integrating natural phenomena and secondary data sources, the students are able to investigate, research, collect data, improvise results, analyze, critique, and reflect. Observations with imagination take this discipline to a new dimension- the art of Imagineering and this is where in a recent analysis it comes under the study of STEAM instead of STEM.

Psychology

Psychology is a very rigorous structured study of mental processes and behavior. It is trans-disciplinary, adaptive to changes, can encounter challenges, and hence is pretty dynamic.

The relation between the approaches and areas helps in analyzing the key factors underpinning the mental process and diverse behavior. The approaches are Biological, Cognitive, and Socio-cultural approaches to the understanding of behavior. These approaches are applied in the areas or options of study which are Abnormal Psychology, Developmental Psychology, Health Psychology, and Psychology in Relationships.

For More Information:-SEV7N IB RESOURCE CENTRE

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What’s the difference between imagesc and imshow?
By: Technical Source
Tags: Matlabsolution, Math, Matlab Assignment Help, Mathematics

Hi,

When I want to display an image in figure screen, both works the same way. I was wondering what’s the difference between both imagesc and imshow commands?

ANSWER:

Matlabsolutions.com provide latest MatLab Homework Help,MatLab Assignment Help for students, engineers and researchers in Multiple Branches like ECE, EEE, CSE, Mechanical, Civil with 100% output.Matlab Code for B.E, B.Tech,M.E,M.Tech, Ph.D. Scholars with 100% privacy guaranteed. Get MATLAB projects with source code for your learning and research.

imshow has a number of default settings intended for displaying images, such as turning off the axes and locking the aspect ratio, that imagesc does not. imshow also had additional options for customizing how you view the image that are not available or not as easily doable through imagesc. You can see the basic differences by doing something like the following and looking at the two figures side by side.

Read More:

https://www.matlabsolutions.com/resources/what-s-the-difference-between-imagesc-and-imshow-.php
discrete time optimization with non-linear constraints
By: Technical Source
Tags: Matlabsolution, Math, Matlab Assignment Help, Mathematics

Hello,

I have an optimization problem to solve with non-linear constraints. It is a control theory based discrete time model (which i feel fules out using fmincon) over a time horizon say N seconds.

I found a few old posts similar to this, but none I felt had clear answers.

I am going nuts trying to find a way to implement it in matlab. Which Matlab tool would be best suited in this case?

Thanks,

italic EDIT: the system is continuous, but we analyse it in a discrete time domain. Thus, variables have discrete values. There are n_v entities and each of the entity has each parameter described below:

variables: p,v,u; size(p)=size(v)=size(u)=(1,N) vectors

Obj. fn: minimize sum(u(1,:))

ANSWER:

Matlabsolutions.com provide latest MatLab Homework Help,MatLab Assignment Help for students, engineers and researchers in Multiple Branches like ECE, EEE, CSE, Mechanical, Civil with 100% output.Matlab Code for B.E, B.Tech,M.E,M.Tech, Ph.D. Scholars with 100% privacy guaranteed. Get MATLAB projects with source code for your learning and research.

I tried to create an example. Hope this helps.
Guidelines on how to find the best math help
By: Erica Medina
Tags: Math, Maths Tutor, Mathematics, Math Help

Mathematics is considered to be the most difficult subject for most kids in NW Calgary. Most children have nightmares before their math examinations and often it is you, and not your child, who feels terrified and troubled about how to deal with math. The best solution to help your child who is struggling with math is to hire the best math help to support their learning and fill their skill gaps.

When it comes to finding a good math tutor for your child in NW Calgary, their teaching capabilities should not only be measured but also the attitude and interest of the instructor to teach your child should be taken into account as well. Tutoring should be a mutual effort between the tutor and your child.

Fruitful learning can be attained if your child and the tutor are working together. If there is good chemistry between the two, your child will have a better understanding of math and achieve good academic outcomes. A professional math instructor will make a dedicated effort and find innovative ways to make the subject easier to understand.

So how do you find a good math tutor in NW Calgary who can not only help your child do better in math but can also help them feel good about being tutored?

A good tutor needs to be realistic, honest, and practical while at the same time, they must demonstrate optimism, hope, and strong support. A skilled tutor is committed to doing everything possible to help your child understand math concepts, their current lessons, homework problems, and good study skills so their grades have the best chances of improving.

Your child’s tutor should directly involve them in their current lessons by using a customized tutoring approach and with questions and help with specific examples, that they are having concerns with. It is important for the tutor to consistently engage with your child at a one-on-one level to help reduce their frustration with math and improve their interest in lesson plans.

After a few sessions, an experienced tutor will understand and adapt to, your child’s unique learning style and will personalize lessons to fit. The tutor will also talk with your child as needed to give them feedback on their progress.

Your chosen tutor should encourage your child to be independent of them eventually. The best tutors never view themselves as a permanent fixture in your child’s life, but rather as the means to strengthen their confidence, knowledge, skills, and self-esteem so that they will learn to help themselves. The goal is to instill a love for learning that will stick with your child throughout their lives and help them pass their academic tests with flying colors.

For the tutoring to be effective, the tutor and your child must be compatible with each other. Their relationship has to be one of mutual respect. After a few tutoring sessions, your child can determine if both of them are on the same page.

In the end, you need to trust your gut both before and after you choose a good math tutor for your child.
Why you need math tutoring in Windsor
By: Mathnasium Of Lasalle
Tags: Math, Windsor, Education, Mathematics, Canada

Mathematics is one of those subjects that many kids struggle with. While some children are whizzes with numerical equations, for others it seems like the instructors are speaking a foreign language. When you find your child struggling with the concepts of math and math homework assignments it is important that you choose good math tutoring help and guidance in Windsor to support your child’s learning objectives.

A good math tutor will help your child to move ahead in their course with confidence. Mathematics must be fully understood by your child at each and every stage for the next level of learning will be built on the existing foundation of knowledge. If the foundation of your child is shaky, the next level will be even shakier. Once your child begins to lose interest in the subject, they may lose confidence and begin to hate the class. A skilled math tutorcan repair the foundation of knowledge and boost their confidence.

Whether your child is having a minor issue with learning a few concepts or completely struggling, math tutoring in Windsor can help them to achieve their learning goals. When you hire a professional instructor to assist your child’s learning, you are providing them with the tools needed to succeed.

There are numerous benefits to getting help from an expert math tutor in Windsor:

1. Less frustration: Most kids become frustrated when they try to do something that they simply cannot do. Extra academic help from a trained professional math instructor can help your child get over their frustration and excel in school for they now have consistent and customized tutoring help from their math tutor.

2. Better test scores: Getting good grades on academic tests is the goal of every child. If your child does not really thrive well in the subject, it will be hard for them to really do well on their tests. A great math learning service will help your child to give their best performance onin their tests. A dedicated math tutor will conduct regular practice sessions and tests to help your child understand the key concepts of the math topics and help them achieve great learning outcomes.

3. Increase the eagerness to learn: With good math tutoring in Windsor your child can excel in the subject and their confidence will increase. This is usually because there is less frustration and when a child realizes that learning the subject is not impossible and they can do it easily, it makes them realize that with extra help and focus, they can learn anything.

4. More preparation for the future: Many times, arithmetic fundamentals are learned at an early age. And, if your child is unable to pick them early on, this can cause them to struggle later. With help from a math learning service, your child will be better prepared for the future. Focused and customized tutoring makes their education journey as easy as possible.
Dividir Para Conquistar
By: Rebeca Haddad
Tags: Math, Mami

Learn more. Medium is an open platform where 170 million readers come to find insightful and dynamic thinking. Here, expert and undiscovered voices alike dive into the heart of any topic and bring new ideas to the surface. Learn more

Make Medium yours. Follow the writers, publications, and topics that matter to you, and you’ll see them on your homepage and in your inbox. Explore
How to choose a good tutoring centre for your child?
By: Elise Rose
Tags: Math Learning, Math, Maths Tuition, Education

Are you are worried about the slipping grade of your child in math? If so, it is important for you to choose a good children’s tutoring centre to support your child and help them in achieving a good grade in math.

When choosing a math learning centre for your child, we recommend that you follow certain guidelines that will help you choose the best tutor for your child, who is in sync with their unique learning styles and knowledge gaps.

Here are some of the critical questions you should ask before making a final decision:

1. Do the centre’s tutors openly seek feedback? Dedicated math tutors from the best children’s tutoring centres invariably asks your child for feedback to determine if there is any need to modify their teaching style. Tutors who are interested in the feedback of your child are more dutiful and possess a great willingness to help your child by using an individualized learning approach that suits their current skills and learning needs. A great math tutor who has the potential to help your child recognize their concerns and gaps successfully works with your child to push them quickly to the next level.

2. Are the tutors qualified? When choosing a good learning centre for your child it is important that you choose an option that has qualified and experienced tutors who will be working with your child. A qualified tutor will analyze the gaps in your child’s knowledge and will formulate a customized tutoring program that best fits their unique learning skills and abilities.

3. Does the centre have a comprehensive exam revision plan for your child? To assist your child to gain increased confidence or managing upcoming tests, a good children learning centre often has an exam revision plan that helps children to mold their problems solving techniques and boost their confidence so they can finish their tests accurately and in time.

4. One-on-One engagement: A great children’s learning centre uses a one-on-one approach when working with your child. Such an approach helps to build a powerful trust between the tutor and your child. Also, the tutor will be able to provide focused attention to your child and work on their learning gaps. The tutor also encourages your child to ask questions or concerns they have pertaining to the math topics without any fear or embarrassment.

5. Understands the psychology of your child: One of the factors that have to be given the highest priority is that the tutor has to understand the psychology of your child and should motivate an otherwise average student to secure good marks. A dedicated math tutor will be a guide to your child and help them focus their attention on the right targets. The tutor’s experience and motivation combined with their ability to find the weaker aspects of your child’s knowledge will help them achieve the desired results. A great children’s learning centre gives comprehensive help in completing tasks and math homework assignments which your child finds difficult to handle on their own.
Do this 30 minutes a day and improve your Mathematics
By: Naushad Avadia
Tags: Math, Tips, Education, Mathematics, Math Tips

Mathematics is probably the most hated subject but as a student, I never had a problem with Mathematics. While my friends found the subject hard, I found it easy. I didn’t understand why they were finding it hard as a student.

I am a teacher now. After years of experience in teaching, I have found the reasons why students find Mathematics hard and how they can improve it.

Note down all the formulas in a book and memorize them daily:

In Maths, there are a lot of formulas that one needs to memorize. The problem is majority of the students move from one chapter to another and forget the previous ones completely.

Students should make a separate book for noting down all the formulas. They should read it daily for 15 minutes. 15 minutes of full focus only on memorizing the formulas will help in the long run.

2. Read the question properly:

Most of the students don’t read the questions properly. They use the wrong formula due to that and the whole answer goes wrong. For example, the question is about finding the area of the rectangle and the student ends up finding the perimeter of the rectangle. If the student reads the question properly, the chances of such errors will reduce to a great extent.

3. Avoiding silly mistakes by rechecking the sums:

Students sometimes make silly mistakes in addition, subtraction, multiplication or division and end up losing marks due to that. They can avoid this by rechecking the sums and by not getting distracted.

4. Never hurry while using the multiplication sign rule:

Below is the multiplication sign rule.

Whenever a question like this comes up where multiplication sign rule has to be used, students should do it slowly with full concentration. If they try to hurry, whole answer will get wrong. So never hurry.

5. Memorize Multiplication Tables till 20:

Half the students don’t know the multiplication tables till 20 fully. They know most of them but not all of them. They make mistakes in multiplication due to this. They think that they know but they don’t. Students should give oral test of these tables to their parents once a week. It will help a lot in the long term.

6. Practice daily:

All the above steps are useless if students don’t practice. Practice every day for at least 15 minutes. You will make a lot of mistakes in the beginning but you’ll see a marginal improvement in a month and a lot of improvement in a year. If you can practice more, it is even better.

Hope it helps.
Solving a Polar Coordinate Problem in Calculus.
By: Nate Metens
Tags: Math, Polar, College, Mathematics, Calculus

In this calculus post, I am going to work through a fun problem that I received as an undergraduate. The question states:

Use polar coordinates to evaluate the double integral of the function

over the region determined by the equations

First of all, what I did was take the first equation and rewrite it in terms of x and y…

In terms of x:

In terms of y:

Then, I put the equations into Desmos and got the following graph:

Image 1

Using the equation given will make the integrals much harder to solve, therefore, I have shown in the image how we can change our given equation into simpler form (i.e polar coordinates). Instead of

we will use the polar coordinates:

Now that we have drawn our picture and understand the equations given, it is time to put it all together and begin solving the equation:

And we have our answer. The answer is negative because we were given that

And that concludes this cool problem. Thank you for reading.
How Whatsapp make money ?
By: Abhishek Sharma
Tags: Math, Money, Whatsapp Tips And Tricks, Online Earning, WhatsApp

Are you want to earn money with learn mathematics ? if yes then you are on right place. StudyoCity where we will teach you mathematics with regular weekly test
Functions and Relations
By: Naren Blogs
Tags: Math, Function, Study Material, Relations, Mathematics

Functions and Relations

Introduction:

Relation

A Relation is a set of ordered Pairs that satisfy a relationship.

For Example:

PXQ

PXQ = {(2,10), (2,20), (2,35), (4,10), (4,20), (4,35)}

PXQ = {(p, q): p ɛ P, q ɛ Q}

Relation ‘R’ → ALL (p, q) that satisfies ‘R’

R’ = {(p, q): q is a multiple of p, p ɛ P, q ɛ Q}

R’ = {(2, 10), (2, 20), (4, 20)}

This entire circle represents the set of elements in the Cartesian PXQ.

In that case set R’ will be a part of it. We can say that set R’ is a subset of Cartesian product PXQ. That is the basic concept of relation.

A Relation is a set of order pairs that satisfy a Relationship.

We come across various functions. But very few understand what a function is. It’s simply a function is like this box with two pipes.

It gets an input. Some operation takes place inside and it gives an output based on the operation that occurred inside all that matters is what occurs inside.

Let’s understand an example.

Let this be a function box.

The operation it does inside is that it multiplies every input with 5 and gives

an output. This box gets 2 as an input. It will multiply 2 with 5 and give

an output of 10.

Similarly if it gets 3 as an input it will give 3 times 5 and 15 as

the output. If 4 is the input it will give us 20 as the output.

So this box is our function the function is written as F(X ) equals 5(X)

Make sure you understand this well it means that if we

substitute X with any number this function will give us an output 5 times

that number. So F(2 )will be 5(2) which is 10

Function and Relation Examples

Example : Find A X B, A X B and B X A

1) A={2,-2,3} and B={1,-4}

A X B={(2,1), (2,-4), (-2,1), (-2,-4), (3,1) (3,-4)}

A X A={(2,2), (2,-2), (2,3), (-2,2), (-2,-2), (-2,3), (3,2), (3,-2), (3,3)}

B X A {(1,2), (1,-2), (1,3), (-4,2), (-4,-2), (-4,3)}

A X B={(p , p), (p , q), (q , p), (q , q)}

A X A={(p , p), (p , q), (q , p), (q , q)}

B X A={(p , p), (p , q), (q , p), (q , q)}

A X A={} = {(m , m), (m , n), (n , m), (n , n)}

for more example click here

So, These are some of the examples for Functions and Relations. Which are explained in the top of the section. Two numbers go to gather is known as order pair of number. Where a Relation is a set of ordered Pairs that satisfy a relationship.

Welcome to Narenblogs, your number one source for all knowledge based contents . We’re dedicated to giving you the very best contents, with a focus on school study materials, college study materials, programing languages, and more.
My 2nd Grader Got a Zero on His Math Assignment
Tags: Homework, Math, Logical, Perspective, Teachers

I care about my kids and how well they are doing in school. I don’t care as much about the grades they are getting but whether they are learning and doing their best. Earlier this year my 2nd-grade son got a zero on his math assignment. There were 30 problems and he got every single one of them wrong. But after seeing the completed assignment, I’m not worried at all.

Let me back up a little. My 2nd grader is my youngest. He’s pretty smart and from a young age, he has always loved numbers and math. He would tell us to ask him math problems that he could do in his head. He was able to pick up on board games earlier than my other kids because he could do the math in them, such as figuring out the change for a $500 bill in Monopoly. So I was surprised that he got a zero.

In 2nd grade, the math is pretty simple. It consists mostly of addition problems like 4+1 and 2+3. He could do that kind of math before he was even in kindergarten. Here are the 30 addition problems he had to do for his assignment. All of them are “wrong”. Can you see what he was doing?

The first one is pretty easy. 0+1 is 1. Wait, he put a 2 there. What is happening? The next one is also pretty easy. But that one is wrong too? Now he’s putting in decimals in the answer? They don’t do decimals in 2nd grade!

It took me a little while to figure out what he was doing. The trick is seeing where the decimals are in the problems. Yep, it’s those periods after the problem numbers. So problem 1 is really 1.0+1 which equals 2, just like he wrote. If you use the periods as decimals, you’ll see he got them all right. And after we talked about it, we can all laugh at the experience. He knows that he knows his math no matter what he got on that assignment.

But now consider the perspective of the teacher. I don’t know what they could be thinking. They gave him a zero on that assignment, whether they realized what he was doing. They could have thought he was just making up numbers or that my son was goofing off. But he was not being irrational or silly. He was being perfectly logical and knew far more than what the assignment was asking him to do.

This is a great example to me of how different perspectives lead to different answers. When someone says something unexpected that doesn’t match your thinking, do you automatically assume they must be wrong? Or do you stop to think about how they might be right? Maybe you won’t always be able to see their perspective but that openness will teach you other ways of thinking. You’ll be able to consider different ways of solving the problem. Count on a 2nd grader to remind us how important it is to be open to different perspectives.
Interesting
By: Ashley Noel
Tags: Math, Prime Numbers, Counting, Differential Equations, Science

Hi. I'm Ashley. I enjoy reading and writing. I look forward to connecting with other writers on Medium
Equivalents
By: John Gonzalez
Tags: Life Balance, Math, Equivalents, Mathematics

1 framed picture = 100 cell phone photos

1 basketball game played = 25 NBA games watched

1 favorite hoodie = 7 hoodies worn weekly

1 close friend = 50 not-close friends

1 day with loved ones = 100 online purchases

1 minute of alone time = 15 minutes of arguing

1 hour of movement = 3 hours of alone time

1 second of crying = 5 two-hour movies

1 intentional moment = 1/0 unconscious days
Why your C in math class doesn’t matter
By: Cate Rosenberger
Tags: School, Math, College, Highschool, Grades

I’m a 17 year old girl and have parents who want me to do well in school. This is given. Whose parents want them to fail? But the big question is this: as teenagers, are we working hard for ourselves or our parents?

Parents hold high expectations. Whenever you do something that is not enough for them, they will counter your argument with something they did as a kid.

“Sorry mom I got a 70 on my test”

“When I was your age, I always got A’s on every test. Do better.”

Ah yes. The “do better”.

In high school we are forced to take classes we do not enjoy simply just for credit so we are able to graduate. One of those classes is math. I was never great at math. Freshman year however, I absolutely thrived in Geometry. But thats besides the point. I constantly got C’s in all my other math classes. It was the main cause of my stress. Some mornings I would wake up in misery knowing I had math class that day. I was constantly just worrying about my math grade to the point where I lost my motivation to work hard in all my other classes. But now, being a senior in high school I am now realizing that stressing over that was a waste of my time.
IBM SPSS Statistics 26.0 Crack + License Code Full Download
Tags: Mathematics Education, Math, Mathematics

IBM SPSS Statistics 26.0 Crack plus License Code Full Obtain is a certified and really appropriate software program largely used for the event of knowledge assortment of statistics. Practiced groups and individuals linked to calculations and working use this software program to achieve their work simply.

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Cyberflores
By: Rebeca Haddad
Tags: Math, Mami, Geometry

Learn more. Medium is an open platform where 170 million readers come to find insightful and dynamic thinking. Here, expert and undiscovered voices alike dive into the heart of any topic and bring new ideas to the surface. Learn more

Make Medium yours. Follow the writers, publications, and topics that matter to you, and you’ll see them on your homepage and in your inbox. Explore
Numerical Solvers for ODEs
By: Elias Niepötter
Tags: Math, Numerical Analysis, Mathematics, Differential Equations, Science

How to solve ODEs numerically

Ordinary Differential Equations are not only a special set of equations in mathematics. From the perspective of an ongoing engineer, ODEs can be used to describe dynamic systems in our real world. So let’s go with an example.

Equation 1: ODE of a PT1-System

Equation 1 shows an ODE of a PT1-System. This could be e.g. a simple RC-low-pass filter. The analytical solution is:

Equation 2: Analytical Solution of the example

In this case it it quite easy to solve the ODE analytically, but if things get more complicated and an analytical solution is not the way to go, we can solve ODEs numerically. To be more precise: We can approximate the solution.

I won’t go deep into the details here, but the idea is to calculate the gradient at a given point and then approximate a solution (y) at the next point by using this gradient and defined increment. As we decrease the increment we increase the accuracy of our approximation but it takes more computational power to solve the ODE. To calculate the gradient we just have to rearrange Equation 1 and get:

Equation 3: How to calculate the gradient

Now we can calculate the gradient at any given time if we know the current value of y and the time (we assume that u is constant over time). In most cases we have given starting conditions where we know the gradient and the value of y. From this starting point on we have everything to approximate our solution.

Explicit Euler

The explicit Euler method is the most simple way to perform the approximation.

Equation 4: Explicit Euler

The approximation in the k+1-th increment (or step) is calculated by adding the product of the increment h and the gradient f to the current solution. As described before, the gradient is a function of the current value of y and the time. It is assumed that the gradient is constant over time. Figure 1 shows how this affects the solution. The explicit Euler “reacts” too slow and overshoots in this example.

Figure 1: Different numerical solutions compared to the analytical solution of a ODE

Implicit Euler

The implicit Euler uses 2 explicit Eulers to approximate the solution. The first is called the “predictor” and second is called the “corrector”. The approximation of the predictor is used to approximate the solution again with an explicit Euler.

Equation 5: explicit Euler (predictor)

Equation 6: implicit Euler (corrector)

The corrector-approximation tries to correct the predictor-approximation by calculating the gradient at the predicted point instead of the current one. This tends to create the opposite behavior as observed before (Figure 1).

Modified explicit Euler method (aka Heun’s method)

Heun’s method combines both explicit and implicit Euler methods by averaging them. Figure 1 clearly shows how the error of both Euler methods are cancelling out each other.
How I Realized My Need To Learn Math
By: Ata Tekeli
Tags: Technology, Math, Statistics

It took a year of continuous decisions in various technologies to realize that.

It was the moment when I realized that I couldn’t understand what the mathematical equations on a consensus meant. Consequently, I decided to go on a journey where I could enhance my mathematical skills to deepening my understanding of blockchain technology. Now let’s delve into the details

Part I (Continuous lectures and personal conversations with my computer technology professor)

In my first semester, I couldn’t realize what was he up to. Even more, I thought of him as an old man who doesn’t know what he says. But he proved me wrong at the end of the second semester. Furthermore, his deep conversations further sparked my interest when I was in his room on mathematical topics. Consequently, I started to have some look.

Part II (when I couldn’t understand the mathematical equations on Bitcoin Whitepaper)

I decided to go further when I couldn’t understand two mathematical equations in Bitcoin White Paper. It was formulated as a series and it was the moment I asked my friend. He told me that it was decentralization. But it was actually not. I knew what this meant after I’ve learned series in calculus. It meant that: no matter how much the hacker tries, the probability of simultaneously controlling 51% of the nodes will approximate to 0 as long as the chain becomes longer. And that was simply called “Proof of Work”. I was relaxed and gone further on the road to finish calculus.

Part III (when I asked my statistics professor whether blockchain statistics was possible)

And this was the shortest argument I ever had. And he told, “as long as the data exists on technology, so does the statistics of a technology”. So, it was a way to open the door for me to learn statistics. At the end of the semester, I barely learned anything related to statistics and the next term wasn’t different. Until my statistics professor explained to me how I could learn statistics. And it was way more shocking because the only learning method I knew was in the classroom. He simply told me to learn statistical programming with a few programming languages with a statistics book on my other side. Even more, he helped me with how I could start learning statistical programming. He even recommended me to start with R and Python and told me that I’d need statistics much more than an ordinary professor. Consequently, I started to understand the statistics and learning simultaneously.

How did you realize that you need to learn math? Share your moments in the comments section below.
Does Math Have the Power To Heal?
By: Agents Of Change
Tags: Math, Life Lessons, Parenting, Emotions, Mathematics

Does Math Have the Power To Heal?

Photo credit: iStock

By Michael Allwright

I never imagined that math could be such a powerful force for healing childhood wounds. Especially given the scars from mathematics I’ve carried since middle school.

SCARS OF CHILDHOOD

When I was in 7th grade I hated math … or I should say, I hated my math teacher. He was the high school football coach and he “motivated” his students off the field just as he did on the field: intimidation, yelling, and public humiliation. I was the focus of his wrathful attention on more than one occasion because I couldn’t understand what he was teaching.

His tactics of humiliation and public shaming had the opposite effect of his intention if in fact, his intention was to impart an understanding of mathematics.

Math became a trigger for me as a child and young adult. I found myself often demotivated, frustrated, or checked out in math classes. I had the emotional scars of being “not good at math,” and it showed up from balancing my checkbook to learning calculus. Fractions haunted me when building our remote cabin in McCarthy, Alaska.

It took me quite some time to regain my confidence in my math abilities. I had to learn that my experience wasn’t really about me, but how the subject was presented and how I was (or in this case wasn’t) motivated to learn.

Okay, Allwright, sorry about your mean middle school math teacher, but are you going somewhere with this trip down memory lane?
Strange Math
By: Terry Mansfield
Tags: Math, Haiku, Humor, Mathematics, Poetry

Learn more. Medium is an open platform where 170 million readers come to find insightful and dynamic thinking. Here, expert and undiscovered voices alike dive into the heart of any topic and bring new ideas to the surface. Learn more

Make Medium yours. Follow the writers, publications, and topics that matter to you, and you’ll see them on your homepage and in your inbox. Explore
The Vickrey Auction and how a liar helps you tell the Truth
Tags: Game Theory, Math, Computer Science

Let’s assume you love ice cream (a safe assumption), and that there was a neat little parlor in your neighborhood that served the most amazing chocolate ice cream that could ever be conceived. You frequented the place and enjoyed the ice cream and life was bliss until they closed up shop, leaving you devastated.

So imagine your delight when the owner announces he’ll be putting on his apron one last time for a special treat. A treat that will go to the highest bidder. You’re excited about the opportunity, but know that your wallet isn’t the biggest one around, and you need to pay rent so you can actually have a home to eat ice cream in.

You walk into the auction, and they announce that everyone needs to seal their bid in an envelope, and whoever makes the highest bid gets the ice cream. So how much do you bid? If you spend more than $100, you won’t have enough to pay off the loan sharks and this might turn out to be your last ice cream ever. Not a bad way to go, but you’re rational.

And since you are rational, you believe no ice cream is worth $100, and, delicious as it may be, the ice cream is only worth $70 to you. You’re about to put in the $70 bid when something hits you.

What if no one else believes the ice cream is worth $70 — the ignoramuses. What if the next highest bid is only $50? Then you’ve spent a lot more than you needed to and end up feeling shortchanged, even though you were happy paying this amount initially. And besides, everyone else is afraid of overpaying too. So everyone ends up bidding less than they were originally willing to, and the maker of the world’s most delicious ice cream leaves with chump change and a possibly disgruntled buyer.

This is an example of the first-price sealed-bid auction.
The Evils of the Addiction Economy
By: David Bernat
Tags: Scarlett Johansson, Taxes, M A T H, College, Barack Obama

Globally, the total volume of alcohol consumed is up 70% from 1999 to 2017.

In Russia, 1 in 6 citizens are alcoholics. In Belarus, 40 handles of vodka are drunk per capita per year — that’s 2000 drinks, or about 5.5 drinks per day.

Oh, don’t you moralize Americans: you are drinking 3.2 drinks per day. How?

There’s a tear in my beer / Cause I’m crying for you, dear

The heaviest 10% of drinkers drink 3x as much as the other 90% combined! [src]

Ten drinks per day: that is the appetite of 24 million America.

Not the average, not statistics, but 24 million individuals that went to bed last night with ten drinks of alcohol percolating around their blood stream, and who will wake up this morning and do it again. And tomorrow..

I struggle to go to the gym seven days a week — these folks, they don’t miss a day they can’t drink.

Even the vaunted Washington Post can’t fully stand up to the incredible awfulness of those numbers: The drinks are stiff and the article headline is Think you drink a lot? Honestly, I bet most people think they don’t.

Facebook lists me as having 262 friends, and ignoring first-order bias effects, 26 of them had an average of 10 drinks yesterday. Another 26 had 2 drinks.

Maybe that explains all the shit-posts, rants, and trolling. Who knows?

But this is a problem that needs no introduction: most of us have been to that family picnic or that wedding or that college party where a few of our friends or loved ones drank a few more than we would have thought would be good for them. What we may not have known was how extreme the problem was.

Understanding The Very American Tax on Being Bad At Math

Here’s another headline: Americans spend over $1,000 a year on lotto tickets.

Who? I didn’t. I haven’t bought a scratchy or any of those million variants of Mega Millions in years. Anyone buying tickets as an investment plan is crazy!

How the article describes the situation: “Despite the long odds, thousands of Americans will buy tickets for a chance to win. About half of Americans play state lotteries, with total sales topping $71 billion in 2017 (the most recent year on file), according to the U.S. Census Bureau. Consumers each spend an average of about $86 a month on lottery tickets.” $86! Who? I didn’t.

And if only half of Americans play, those Americans are spending $172 a month! What poor bastards are wasting 24 hours of minimum wage labor!

Behold: “Americans earning less than $30,000 admit to spending about 13% of their income on lottery tickets.” Lottery tickets are their investment plans!

To scratch out a living, Merriam-Webster: to earn barely enough money to live.