Questions related to the teaching and learning of mathematics.

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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 ...
11
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1answer
788 views

What is the expected mathematical repertoire of a Ph.D. program applicant?

I am an undergraduate (currently a sophomore) studying to prepare for applying to a Ph.D. program in mathematics. I have thus far structured my course selection upon the advice of a friend I met ...
11
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1answer
249 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 ...
11
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1answer
210 views

How can I raise my intuition in solving mathematical problem?

I am an undergraduate student studying some elementary calculus and statistics. In my honor calculus class, my professor gave one of final exam problem: $$\lim_{n \to \infty} \int_{[0,1]^{n}} ...
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1answer
207 views

Studies on lack of mathematical education

I am looking for studies which compare students who did not receive mathematical education beyond basic mthematics and those that learned maths upto introductory calculus, with the assumption that ...
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14answers
2k views

False beliefs in mathematics (conceptual errors made despite, or because of, mathematical education)

Over on mathoverflow, there is a popular CW question titled: Examples of common false beliefs in mathematics. I thought it would be nice to have a parallel question on this site to serve as a ...
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5answers
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Common misconceptions about math

YARFMO (Yet another reposting from Mathoverflow) ;-) The more you know about math the more you find conceptions previously thought correct to be false: 1.) math is not as exact as many believe - in ...
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7answers
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practical uses of matrix multiplication

The use of matrix multiplication is usually given with graphics initially (scalings, translations, rotations, etc). Then there are more in-depth examples such as counting the number of walks between ...
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4answers
534 views

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
857 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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2answers
824 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
1k 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 ...
10
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4answers
833 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
569 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
871 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
3k views

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
225 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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5answers
297 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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1answer
552 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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4answers
401 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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3answers
440 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
528 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 ...
10
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2answers
204 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
412 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 ...
10
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1answer
146 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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0answers
330 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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3answers
248 views

Examples of useful, insightful, and interesting hand-waving

It seems to me that some hand-waving (by which I mean some arguments that aim at giving some form of intuition on the problem even at expenses of complete rigour [and not mnemonics for high-schoolers ...
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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
412 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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6answers
2k views

What is the best base to use?

When I typed this question in google I found this link: http://octomatics.org/ Just from the graphic point of view: this system seems to be easier (when he explains that you can overlap the line). He ...
9
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2answers
515 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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4answers
1k 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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3answers
2k views

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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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
287 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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6answers
1k views

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 ...
9
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2answers
186 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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2answers
505 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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3answers
79 views

Video Lessons in Complex Analysis

Does anybody have some link for good video lessons of a complete course in Complex Analysis? Grateful.
9
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1answer
158 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
247 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
355 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?
9
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1answer
248 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 ...
9
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1answer
78 views

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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5answers
207 views

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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5answers
297 views

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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4answers
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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
799 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"?