Questions related to the teaching and learning of mathematics.

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Middle school number theory

Find at least three numbers that satisfy all three conditions: (1) there is a remainder of $1$ when the number is divided by $2$; (2) there is a remainder of $2$ when the number is divided by $3$; ...
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4answers
842 views

Is there a more efficient method of trig mastery than rote memorization?

I would like to get alot better at trig than I am. What is the best/most efficient method? Thanks much in advance Joe
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7answers
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What should the high school math curriculum consist of?

"Life is open book." With the advent of widely accessible, inexpensive (or even free) computational tools and Computer Algebra Systems (TI-89, Wolfram|Alpha, etc.), much of what traditionally ...
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2answers
813 views

Success in maths (soft question)

I would really like to hear from any professional mathematicians who didn't just sail through their university education. If one looks at the pages of many of today's mathematicians, one finds that ...
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9answers
996 views

A Poster About Prime Numbers [closed]

We're going to design a poster about prime numbers, which will appear in a mathematics magazine for middle school students. The poster should be both visually attractive and mathematically rich. Do ...
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4answers
818 views

Why would you expand a square wave in a Fourier series?

The periodic square wave $$ f(x) = \cases{ 1 \text{ if } 0 \le x \le \pi \\ 0 \text { if } -\pi \le x < 0} $$ seems easy enough to work with. Why transform it into a series of sines and cosines? ...
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4answers
528 views

Recommended survey of mathematics [closed]

What do you see as the most explanatory and beautiful survey of mathematics book...For short is there a book like Feynman lectures but for math?I've looked at Elementary Mathematics from an Advanced ...
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6answers
853 views

Am I just bad at math? [closed]

I currently pursuing a degree in computer science. When I started back 4 years ago, I took a test to see how I would place into certain subjects. My math scores were absolutely horrible. I started ...
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5answers
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Motivating linear algebra for economics students?

I'm a tutor for the introductory linear algebra course at my school; this course is required for most upper division economics classes, so a lot of my tutees are economics majors. This is a typical ...
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6answers
208 views

When the approximation $\pi\simeq 3.14$ is NOT sufficent

It's common at schools to use $3.14$ as an appropriate approximation of $\pi$. However, here it's stated that for some purposes, $\pi$ should be approximated to $32$ decimal places. I need an example ...
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4answers
347 views

Is studying mathematics chronologically a good idea or not and why?

In high school nowadays most mathematics you learn is fairly 'old'. You have your geometry, all of which (taught in high school) was known to the Greeks more than 2 thousand years ago. You have ...
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4answers
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Self-Paced Graduate Math Courses for Independent Study

Does anyone know of any graduate math courses that are self-paced, for independent study? I am a high school math teacher at a charter school in Texas. While I am quite happy with where I am right ...
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3answers
433 views

Popular general-interest math courses

I'm hoping the userbase here doesn't mind if I do a little crowd-sourcing. I'm curious to find out about popular general-interest mathematics or statistics classes that are offered universities that ...
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2answers
507 views

Is “problem solving” a subject to be taught?

Note: This question has been cross-posted to MathOverflow: see here. I am witnessing a new curriculum change in my country (Iran). It includes the change of all the mathematics textbooks at all ...
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2answers
196 views

How to introduce category theory to a high school audience?

I am a mathematician with background in Category Theory. I have been asked to give a 20 minute talk about my area of research to an audience of talented high school students and school mathematicians ...
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3answers
382 views

A question from an engineering undergraduate

My question primarily concerns the necessary transition from an undergraduate program in electrical engineering to graduate program in applied mathematics or pure mathematics. I'm an electrical ...
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0answers
325 views

How to be a bird

Freeman Dyson has famously characterized two styles of mathematics, that of the bird and that of the frog. I was asked recently the following question, which I don't know how to answer: If, in ...
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6answers
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Should I do all the exercises in a textbook?

The problem sets that you usually get in a university course is a small fraction of the exercises in your textbook. Which raises a question: do you need to solve all the exercises from your textbook? ...
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5answers
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Mathematics, Philosophy and writing.

Do you know of any famous mathematicians who were also philosophers? I have heard of Descartes, Plato and Leibniz. Are there other good examples, especially more modern examples? Also welcome are ...
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2answers
401 views

How to explain the commutativity of multiplication to middle school students?

It's easy for natural numbers: $3\times 5=5\times 3$ ***** ***** ***** but how do you explain that $x.y=y.x$ for any real numbers $x$ and $y$. Moreover, in $\Bbb{N}$, do you prefer to define ...
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2answers
507 views

Is there any way to read articles without subscription?

This is not mathematician question but I think it's related. How I can get access to some of "Software: Practice and Experience" articles without subscription? Any advice is welcome. Sorry if I'm ...
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3answers
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how to explain prime numbers to children

My little cousin (12year) asked me about how emails are encrypted and I want to answers her in such a way she understands it. This is diffuct, but I am happy with teaching the definition of a prime ...
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3answers
278 views

Links to Online Videos of Good-Quality Lectures by Mathematicians

I am not trying to do anything new here, but I would like to start an activity that has been going on at Math Overflow. Hopefully, people here at the Math StackExchange can also enjoy the good stuff. ...
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5answers
295 views

High-School Level Introduction to Dynamical Systems

In one month I'll be giving a talk to motivated high schools students on a topic of my choice from dynamical systems and/or ergodic theory. I'm having trouble coming up with a topic compelling enough ...
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6answers
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Up-to-date advice on the best way to take notes (maths)

I have read some old discussions about this topic and would like to get some up-to-date advice if possible. I'm going to start university next year (maths), and I know how important is to have a set ...
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2answers
183 views

Good Reference for Justifying (less well-known fields of) Math?

How do we as mathematicians justify the study of math to students? Or, indeed, how do we justify it to the general public? How do you justify your particular field? I'm particularly interested in ...
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1answer
544 views

Undergrad Student Trying to Figure Out What to Study

this is my first time on stack exchange and I am seeking advice for my future studies. Some background first; I am a undergraduate student pursuing a degree in mathematics and I hope to pursue ...
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2answers
503 views

How to assess a non-natively english speaking high-schooler's mathematical ability?

I'm a math PhD who has been asked to interview a high school student and determine what he/she is interested in and how strong the student is. Usually I would want them to talk as much as possible ...
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1answer
152 views

A graph of all of mathematics

In mathematics, one often makes (proves) statements on the basis of: Previously proven statements Axioms I like to think of these dependencies as a directed graph, with edges from the accepted ...
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1answer
136 views

How and what to teach on a first year elementary number theory course?

In the late 80’s and early 90’s there was the idea of ‘calculus reform’ and some emphasis and syllabus changed. The order of doing things in calculus also changed with the advantage of technology. ...
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1answer
244 views

General question: What one can do to help students one is grading?

Due to unknown reason I was assigned as a grader this semester for a certain proof writing class in my universtiy. The class size is 65 and students took it usually comes from a computer science ...
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1answer
349 views

Where can I find the 1960s New Math syllabus?

I've been looking everywhere for even a short summary of the content of the 1960s New Mathematics Math education reform in the US but I cannot ;-; Does anyone know?
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1answer
246 views

Publishing mathematics

How or where does one express work they've done to others? What does it mean formally to 'publish' mathematical work you've done? How do you know if your work is any good? Or if someone has already ...
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1answer
240 views

Journals or Magazines on Study Skills or How to Study Math

I am trying to find only journals or trustworthy magazines which can help math students to study math more efficiently and productively. I am not asking about books in this thread. In particular, I am ...
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1answer
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Education: Reading Proofs

I am finishing my undergraduate degree and one thing I've noticed is how little weight has been placed upon the ability to read proofs, in basically all of my math courses. In first year calculus you ...
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The use for solving quadradic equations for high school students

I have a little brother who is in high school and he just learnt the quadratic formula for finding roots of second degree polynomials. He asked me what why we learn this and how this could apply to a ...
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1answer
143 views

Is there any curriculum based on recreational mathematics?

I'm a high school physics teacher. Next year, I'll be teaching mathematics for middle school students so I was wondering if there's a curriculum based on recreational mathematics which not only ...
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5answers
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Why does $n^0 = 1$?

Why is it that $n^0 = 1$? I understand how $n^2 = n*n$ and how $n^1 = n$ but I can't understand why $n^0 = 1$.
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Should I try to change the way Abstract Algebra is taught at my university? If so, how?

[This (soft) question should be Community Wiki.] Background: A year ago, I did a one-semester long course on Abstract Algebra at my university. When we started, I was excited, because I knew the ...
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4answers
776 views

How To Reach The “Next Level” of Mathematics

I am a junior-high pre-algebra student. I feel that my class is holding me back, so I wanted to learn "higher-level math". So what should I learn now? What do you believe is a "next step"?
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Where to go after calculus?

Ok this is a bit of an unanswerable question, but hopefully someone will answer. As I have been going through college & high school there has been a kind of "path" through which you learn math. ...
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4answers
350 views

What's the deal with integration?

So at uni we learned tricks and techniques for integration until cows came home. But to what end? Any/All definite integrals can be evaluated using numerical methods. Most integrals in application can ...
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4answers
956 views

Learning math: still paper and pen

Is it, from an educational perspective, still sound advice to recommend people to use paper/a notebook (of the traditional sort, not the device) and pen/pencil? I wonder if computers are a ...
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7answers
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Educational Math Software

What is the the most educational software for high school and college math? Not the one that just gives you the answer, but has any of the following: Edit: Software mentioned in answer added in ...
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5answers
139 views

Sources for mathematics outside the mathematics world

In this question I would like to ask you about material showing the uses (or occurrences) of mathematics in the everyday world. The aim is to encourage with it a group of young undergraduate ...
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5answers
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Are there any memorization techniques that exist for math students?

I just watched this video on Ted.com entitled: Joshua Foer: Feats of memory anyone can do and it got me thinking about memory from a programmers perspective, and since programming and mathematics ...
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3answers
420 views

Mathematics Style Guide - l vs 1 vs |

I had a quick look around here and google before, and didn't find any answer to this particular question, and it's beginning to really irritate me now, so I'm asking here: How is one supposed to ...
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6answers
644 views

What we're never taught explicitly

I would like to make a complaint really. School math(s) can be the most boring way to learn: sitting down and rote learning binomial expansion or the volume of a cylinder is just not interesting. It ...
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3answers
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Why is 1 raised to infinity Not defined and not “1” [duplicate]

$1$ square is $1$, so is raised $1$ to $123434234$. My maths teacher claims that $1$ raised to infinity is not $1$, but not defined. Is there any reason for this? I know that any number raised to ...
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Reviews/comparison of Python vs Matlab for teaching Linear Algebra

I am wondering about advantages of using Python for teaching introductory linear algebra. I have been using Matlab and I became interested in Python mainly because of several resources, e.g., ...