Questions related to the teaching and learning of mathematics.

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41
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14answers
8k views

How to effectively and efficiently learn mathematics

How do you effectively study mathematics? How does one read a maths book instead or just staring at it for hours? (Apologies in advance if the question is ill-posed or too subjective in its current ...
22
votes
9answers
6k views

What is the (mathematical) point of geometric constructions?

The ancient discipline of construction by straightedge and compass is both fascinating and entertaining. But what is its significance in a mathematical sense? It is still taught in high school ...
4
votes
2answers
244 views

Is there a online reference that chains mathematical knowledge from simple to complex?

I'm a very, very logical person -- but I've never taken any math classes; really, I know. So, on that note -- how do I teach myself math? As my question might suggest, I see the answer as being an ...
28
votes
5answers
3k views

How to pick a thesis advisor?

This sort of question is probably in bad taste for math.stackexchange, but is probably in high demand. (I tried to start a site on Area 51 to house questions like this, but my request was closed due ...
10
votes
3answers
422 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 ...
58
votes
6answers
3k views

How Do You Actually Do Your Mathematics?

Better yet, what I'm asking is how do you actually write your mathematics? I think I need to give brief background: Through most of my childhood, I'd considered myself pretty good at math, up ...
14
votes
8answers
1k views

Elementary Papers at ArXiv

Inspired by this question, at MO i am asking this question. Can anyone list some elementary articles at ArXiv which can be understood by High-School/Undergrad Students. I am asking this because, i ...
39
votes
8answers
5k views

When to learn category theory?

I'm a undergraduate who wishes to learn category theory but I only have basic knowledge of linear algebra and set theory, I've also had a short course on number theory which used some basic concepts ...
4
votes
3answers
464 views

The elementary coordinate geometry of polynomials? Of rational expressions? Of radicals?

With a few colleagues, we're trying to design an (intermediate) algebra course (US terminology) where we stress the interplay between algebra and geometry. The algebraic topics we would like to cover ...
34
votes
21answers
2k views

Mathematics problems for very young children?

This is a tall order, but since this site is for everything mathematical, here goes: What are some nice games/puzzles/problems/problem-like activities that would be appropriate for a three-five year ...
3
votes
3answers
330 views

Is there any physical analogy to explain multiplication by zero?

This is targeted for elementary kids. One way to think is that add any number to itself zero times... Just wondering if there is a better way...
13
votes
3answers
874 views

Guidelines for learning about Ramanujan's work?

It is well known that one of the first books Ramanujan studied was "Synopsis of Pure and Applied Mathematics" and that it shaped the way Ramanujan thought and wrote about mathematics. Being interested ...
3
votes
5answers
300 views

how to explain that Prob[heads, tails] = 2 * Prob[heads, heads] to a student?

I throw two coins (simultaneously). A student (very much a beginner in both math and probability theory) thought that the following 3 outcomes are equally likely: "two heads", "two tails", "a head and ...
3
votes
4answers
322 views

Preparing for the Mathematical Contest in Modeling

The Mathematical Contest in Modeling (MCM) is coming up in a couple of weeks. With the idea that the competition is ultimately about teaching students to become better at mathematical modeling, I was ...
3
votes
1answer
296 views

Best Practices for Learning Mathematics (especially in the classroom)

What study practices have led you to the best success in learning mathematics (or applied math, or theoretical CS) in the classroom (undergraduate/lower graduate level), especially in courses that ...
17
votes
5answers
800 views

Fun math outreach/social activities

What are some great math social activities for students? I'm looking for things that bring people together with a "light" mathematical touch. The goal is to create a stronger mathematical community in ...
4
votes
3answers
496 views

Need good material on multifractal analysis

I'm searching for some good reading material on multifractal analysis. Preferably something accessible that doesn't put the stress too much on mathematical proofs but rather on applications. As long ...
22
votes
5answers
2k views

Math GRE Subject Exam

I am studying for the GRE Mathematics subject exam [1]. I am looking for tips regarding how to more effectively study for it. Does anyone know of any good study materials or have any tips in general? ...
1
vote
1answer
229 views

How do you generate mathematical formulas programmatically using a server side language [closed]

We would like to generate simple mathematical formulas on the fly (e.g. $\sin^2 \theta$). The above function seems to be a MathJaX representation. Most of the solutions depend on writing mathematical ...
14
votes
2answers
2k views

Summer programs to gain research experience as an undergraduate, outside the United States?

There are many summer programs in the United States, targeted at good, motivated undergraduate students majoring in mathematics. Most programs, however (if not all), demand that the applicant is ...
39
votes
9answers
11k views

What is the meaning of the third derivative of a function at a point

(Originally asked on MO by AJAY.) What is the geometric, physical, or other meaning of the third derivative of a function at a point? If you have interesting things to say about the meaning of the ...
5
votes
1answer
611 views

Geometry or Topology

So, I am a graduate student who is certain that he does not want to do analysis (I think...). What are the most exciting fields in mathematics right now? It seems to me that very generally, they are ...
3
votes
2answers
438 views

about math in general

I wanted to ask these questions here, feeling that this place place is without doubt is better than anywhere else, feeling hesitant and shy to ask such question. For several reasons, the environment ...
2
votes
2answers
307 views

I would like to buy references in order to review and study mathematics

I am an ESL learner and most of the time I am able to understand English but In my courses, we don't study mathematics, and I think that it is a mistake or wrong. 1-What are really the best sources ...
4
votes
1answer
314 views

Mathematics Graduate Student Summer Opportunities

I am currently a mathematics graduate student at Western Kentucky University in Bowling Green, KY. I am looking for some kind of summer opportunity to participate in during summer 2011. Does anyone ...
8
votes
5answers
1k views

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 ...
1
vote
4answers
341 views

Which discussion board is good for homework questions?

I'm a CompSci university student and i want some help for my math questions. Therefore i am looking for a good discussion board for math homework questions. I don't know any (good), because I come ...
5
votes
7answers
2k views

Best Cities for Mathematical Study

This may sound silly, but... Suppose an aspiring amateur mathematician wanted to plan to move to another city... What are some cities that are home to some of the largest number of the brightest ...
10
votes
13answers
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 ...
2
votes
2answers
393 views

Is most of the GM-AM Inequality in its codicil?

Let’s define the codicil of the Geometric Mean – Arithmetic Mean Inequality to be the statement that if the means are equal, then all the terms are equal. Then: I conjecture that most of the GM-AM ...
10
votes
4answers
3k views

Is “locally linear” an appropriate description of a differentiable function?

In this answer on meta, Pete L. Clark said: I think the question concerns the idea that a differentiable curve becomes more and more like a straight line segment the closer one zooms in on its ...
8
votes
2answers
494 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 ...
13
votes
8answers
672 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 ...
-2
votes
1answer
758 views

Define “higher-level mathematics” [closed]

I've recently volunteered as a tutor for "higher-level mathematics" as a Calculus student because I'm required by my school to achieve at least twenty volunteer hours for service learning. When ...
5
votes
2answers
712 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 ...
15
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 ...
22
votes
11answers
3k 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
6k 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. ...
10
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
458 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
4k 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
839 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
375 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
7answers
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 ...
84
votes
9answers
4k 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
8k 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 ...
82
votes
19answers
3k 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 ...
2
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
5k 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 ...