Every time someone has a math problem they post a new thread for it, it clutters up this subsection of the forum, and real enlightenment rarely takes place since only one or two people ever give their problem-solving insights. This thread is intended to change that by providing a centralized discussion of any aspect of mathematics that anyone is having trouble with, is interested in, or just wants to bone up on after being out of practice for a spell.

To start things off, I'll post one of the first complex analysis problems I ever did; this is a relatively simple problem, and in fact it is possible for anyone who knows integral calculus to solve it. I realize that most of your problems won't be this advanced, but I want to see who's up to it:

Prove that ∫ (e^imθ)*(e^-inθ) dθ

evaluated from 0 to 2π is equal to 2π when m = n, and 0 when m =/= n, where m and n are integers. Hint: e^iθ = sin θ + i cos θ. You can thank Leonhard Euler for that one.

I'm not really expecting anybody to solve that given the general age group here, but those of you who know your calculus and have chutzpah may want to give it a go, as this type of problem will allow you to cut your teeth on more abstract, higher-level math.

I know there are other math nerds out there, so come on in and we can collectively sharpen our MAD SKILLZ! (Xenogears reference ftw)

Edited in an attempt to make the problem slightly more readable; the forum doesn't allow superscripts, apparently.

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