Questions related to the teaching and learning of mathematics.

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9
votes
2answers
514 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 ...
17
votes
7answers
5k views

How to show every subgroup of a cyclic group is cyclic?

I'm teaching a group theory course now, and I wanted to give my students a proof that every subgroup of a cyclic group is cyclic. The easiest way I could think to do this is to say that any cyclic ...
14
votes
8answers
749 views

Elevator pitch for a (sub)field of maths?

When I first saw the title of this question, I forgot for a moment I was on meta, and thought it was asking about quick, catchy, attractive, informative one-or-two-liner summaries of various fields of ...
5
votes
2answers
786 views

Alternatives to arxiv

I am an amateur mathematician (but I do have degree's in computer science (with mathematics)). Anyways, I have written this paper, where I have proved that for $\zeta(\rho) = 0$ if $\Im(\rho) \to ...
16
votes
1answer
2k views

GRE past papers

As it is required for most students who wish to do a Ph.D in maths in the US to sit the GRE subject specific mathematics exam, I hope this question will be of interest to the mathematical community ...
25
votes
11answers
4k views

Vivid examples of vector spaces?

When teaching abstract vector spaces for the first time, it is handy to have some really weird examples at hand, or even some really weird non-examples that may illustrate the concept. For example, a ...
8
votes
8answers
8k views

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. ...
11
votes
7answers
2k views

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 ...
1
vote
3answers
474 views

Free introductory resources for learning algebra?

I have a non-mathematician friend who is interested in re-learning algebra. I am more than happy to help, but I am in no position to judge what is a good introductory text --- only to identify when a ...
14
votes
6answers
5k views

Best intuitive metaphors for math concepts (of any level)

Frequently, we introduce a new concept with a formal definition, then immediately say "Intuitively, what this means is..." What are the absolute best metaphors you've seen (for concepts of any level)? ...
11
votes
9answers
939 views

Sources of problems for teaching/tutoring young mathematicians

I am tutoring several talented students, middle school level and early high school level, in mathematics. I am always looking for new sources from which to draw questions. Can anyone recommend books, ...
5
votes
1answer
388 views

undergraduate courses emphasizing theory building?

I was wondering if anyone had any experience with an undergraduate course that emphasized the building of mathematical theories or if they'd ever heard of this being done? How did the class work (did ...
8
votes
9answers
1k views

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 ...
89
votes
9answers
5k views

Why is Euler's Gamma function the “best” extension of the factorial function to the reals?

There are lots (an infinitude) of smooth functions that coincide with f(n)=n! on the integers. Is there a simple reason why Euler's Gamma function $\Gamma (z) = \int_0^\infty t^{z-1} e^t dt$ is ...
19
votes
8answers
10k views

Online Math Degree Programs

Are there any real online mathematics (applied math, statistics, ...) degree programs out there? I'm full-time employed, thus not having the flexibility of attending an on campus program. I also ...
84
votes
19answers
4k views

Good Physical Demonstrations of Abstract Mathematics

I like to use physical demonstrations when teaching mathematics (putting physics in the service of mathematics, for once, instead of the other way around), and it'd be great to get some more ideas to ...
3
votes
5answers
2k views

Where can I find a review of discrete math

I'm looking for course notes and assignments and hopefully some example exams for Discrete Math, I'm taking a placement exam in the subject after having taken it 4 years ago.
13
votes
11answers
7k views

Which 4 maths courses to take as an Economics PhD student?

I am doing a PhD in economics and I have the chance of taking one subject a semester in the maths department (I would like to do more, but "unfortunately" I have to work on my thesis). I want to have ...