Undergraduate Math Competitions?

[DWarrior]

Does anyone know how to study for these? It seems like a lot of the concepts would repeat, is there a book that lists all the common theorems/concepts that commonly show up on these competitions?

Does anyone have any advice on how to prepare for these aside from doing random problems?

[Duke]

I have no idea, as you're right that they're going to be widely varied and random, and require you to know obscure things. The main problem is that speed will be a factor.

If you just want to learn a lot of math, and have the ability to derive a large set of problems, thenI'd say move back to number theory and really attack all of the basic concepts of all types of math. If you're clever enough you can derive a lot of it on your own. This takes time, though, and won't help in a competition.

Short answer: I have no idea.

[bigpooch]

If you are writing the Putnam, it helps to do some problems
from previous exams and look at the solutions. It also
helps to know some theory such as elementary number theory,
combinatorics and some abstract algebra. Keep in mind that
often solutions to problems given have short or very elegant
solutions. If you don't see an efficient way to find the
solution, you haven't really "got it". I would suggest
reading ALL solutions to previous problems and trying to
see how the solution would change if the problem were
"slightly altered".

I think for some problems, no amount of study may be able to
help most individuals because they have to see the right
ideas.

[blah_blah]

some books you might want to read include

Larson - Problem Solving Through Problems
Engel - Problem Solving Strategies
Zeitz - The Art and Craft of Problem Solving
[author unknown] - Putnam and Beyond
Kedlaya et al - [collections of Putnam problems with solutions (published by the MAA iirc]