**57**

votes

**15**answers

8k views

### What's a nice argument that shows the volume of the unit ball in $\mathbb R^n$ approaches 0?

Before you close for "homework problem", please note the tags.
Last week, I gave my calculus 1 class the assignment to calculate the $n$-volume of the $n$-ball. They had finished up talking about ...

**58**

votes

**16**answers

5k views

### One-step problems in geometry

I'm collecting advanced exercises in geometry. Ideally, each exercise should be solved by one trick and this trick should be useful elsewhere (say it gives an essential idea in some theory).
If you ...

**5**

votes

**4**answers

1k views

### Choice of adviser

Not sure how to tag this one so feel free to edit and add tags.
When I initially started graduate school my choice for an area of study was quite nebulous. I had only figured out enough to know that ...

**8**

votes

**10**answers

10k views

### Math journal for high school students?

I recently discovered The College Mathematics Journal and enjoyed reading through some of the articles on fun applications of mathematics. I'd like to send some of the articles to my younger sister, a ...

**114**

votes

**37**answers

104k views

### Too old for advanced mathematics? [closed]

Kind of an odd question, perhaps, so I apologize in advance if it is inappropriate for this forum. I've never taken a mathematics course since high school, and didn't complete college. However, ...

**18**

votes

**10**answers

73k views

### What are the qualities of a good (math) teacher? [closed]

In forming your answer you may treat the qualifier math or maths as optional, since part of the question is whether there is anything peculiar to the subject of mathematics that demands anything ...

**15**

votes

**7**answers

4k views

### How have mathematicians been raised? [closed]

Many of us have -- or at some point want to have -- children, and wonder how we can do our best to fulfill the "nurture" component of helping them develop mathematical talent... not because we want ...

**29**

votes

**11**answers

3k views

### Are there elementary-school curricula that capture the joy of mathematics?

UPDATE: Wow, thank you everyone for the great insights!
A couple of months ago I stumbled across Paul Lockhart's essay A Mathematician's Lament and it made perfect sense to me. I'm not meaning to ...

**11**

votes

**3**answers

1k views

### Is formal proof (formalized mathematics) interesting to practicing mathematicians? To educators? [closed]

Formalizing mathematical proofs so that they can be checked for correctness and manipulated by computer is a recurrent proposal, most notably stated in the QED manifesto (1994). The December 2008 ...

**17**

votes

**5**answers

4k views

### Pacing for learning new material

I'm beginning to run into work where I have to do a significant amount of learning of math by myself, with a book rather than with a teacher. Now, I do know that doing problems tends to be the best ...

**52**

votes

**9**answers

12k views

### Relating Category Theory to Programming Language Theory

I'm wondering what the relation of category theory to programming language theory is.
I've been reading some books on category theory and topos theory, but if someone happens to know what the ...

**42**

votes

**42**answers

12k views

### What should be offered in undergraduate mathematics that's currently not (or isn't usually)? [closed]

What's one class that mathematics that should be offered to undergraduates that isn't usually? One answer per post.
Ex: Just to throw some ideas out there
Mathematical Physics (for math students, not ...

**3**

votes

**11**answers

4k views

### Your experience of Computer Science/Programming in Mathematics Education? [closed]

This is a survey question, which seeks to produce a list of answers from the audience of mathematicians.
Motivation: I'm doing research in mathematics education. I'm particularly interested in ...

**2**

votes

**2**answers

901 views

### An “Elementary” Math Question Generalized (Ring Theory Perhaps)

The following question is posed in the book "The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics"
"Prove that if integers a_1, ..., a_n are all distinct, then the ...

**140**

votes

**30**answers

50k views

### Real-world applications of mathematics, by arxiv subject area?

What are the most important applications outside of mathematics of each of the major fields of mathematics? For concreteness, let's divide up mathematics according to arxiv mathematics categories, ...

**2**

votes

**2**answers

293 views

### Characterizing triangles unembeddedly

The mathedu mailing list has a recent longish thread at
http://www.nabble.com/Why-do-we-do-proofs--to25809591.html
which discussed among other things whether we should teach triangles as labeled or ...