# Tagged Questions

**23**

votes

**3**answers

1k views

### Nearly all math classes are lecture+problem set based; this seems particularly true at the graduate level. What are some concrete examples of techniques other than the “standard math class” used at the *Graduate* level?

In the fall, I am teaching one undergraduate and one graduate course, and in planning these courses I have been thinking about alternatives to the "standard math class". I have found it much easier ...

**15**

votes

**3**answers

959 views

### Research level applications of “row rank = column rank”?

No less an authority than Gilbert Strang frames "row rank equals column rank" (and a couple of other facts) as "The Fundamental Theorem of Linear Algebra."
I'd simply like to assemble (for teaching ...

**11**

votes

**9**answers

1k views

### math circles video lectures for school children?

Hello,
I am from India. I find the mathoverflow amazing.
I have a question: Are there any good quality video lectures on school math topics?
There are a lot of high quality lectures available on ...

**14**

votes

**12**answers

2k views

### Excellent uses of induction and recursion

Can you make an example of a great proof by induction or construction by recursion?
Given that you already have your own idea of what "great" means, here it can also be taken to mean that the chosen ...

**12**

votes

**17**answers

2k views

### Short Course Suggestions For High School Students

I am planning to teach a course for talented high school students at a summer camp and I need suggestions for possible topics. The students usually have different backgrounds but most of them are ...

**40**

votes

**44**answers

13k views

### An example of a beautiful proof that would be accessible at the high school level?

The background of my question comes from an observation that what we teach in schools does not always reflect what we practice. Beauty is part of what drives mathematicians, but we rarely talk about ...

**8**

votes

**9**answers

2k views

### Mathematical Advice for Interested Highschool Students

This may not be a research level math question, but I believe it is still relevant to Math Overflow.
What general resources exist for students in highschool who are very interested in ...

**31**

votes

**18**answers

9k views

### Interesting Calculus Questions/Exercises

I am in the process of redesigning the calculus course that I have taught five or six times. What I would like to know is if anyone has some really good examples or exercises that I could either do ...

**6**

votes

**8**answers

1k views

### Undergraduate Probability Topics

I am teaching undergraduate probability this semester, and I am looking for some suggestions about inspiring applications that could be reasonably covered over the course of two one-hour lectures or ...

**16**

votes

**13**answers

2k views

### What are your favorite puzzles/toys for introducing new mathematical concepts to students?

We all know that the Rubik's Cube provides a nice concrete introduction to group theory. I'm wondering what other similar gadgets are out there that you've found useful for introducing new math to ...

**7**

votes

**2**answers

1k views

### Vinogradov's Elements of Number Theory

I can't be the only person here who has fond memories of the problems in Vinogradov's Elements of Number Theory. (For people who have not read it - the text itself is just a concise basic number ...

**8**

votes

**3**answers

1k views

### The harmonic (series) beetle: live illustrations of mathematical theorems

In my analysis class I use the following problem to illustrate the divergence
of the harmonic series (consider this as a hint for solving it).
Exercise.
A beetle creeps along a 1-meter infinitely ...

**31**

votes

**19**answers

5k views

### Fun applications of representations of finite groups

Are there some fun applications of the theory of representations of finite groups? I would like to have some examples that could be explained to a student who knows what is a finite group but does not ...