Doubts about preparing for the IMO.

Question

Would any of the following books be any good for preparing for IMO?

Schilling - Measures, Integrals and Martingales

Rudin- Real and Complex Analysis

E.J. Barbeau - Polynomials

F.Klein - Idk any good ones of F.Klein?

And any other books you may suggest. Also, I've already read EGMO and

1. I suck at geo
2. I only learnt how to bash from it.

Answer 1

I wouldn't really recommend those, except for maybe some books on elementary Analysis as there are occasionally some sequences problems that come up for which a knowledge of analysis is useful.

Some books I would absolutely recommend are:

Combinatorial problems in mathematical competitions (Zhang)

Solving problems in geometry (Han Wang)

Graph Theory (Zhongyi) - good for some combinatorics problems

104 Number Theory Problems (USA IMO prep book)

Good luck!!

Answer 2

From my own experience the by far most valuable preparation for competitions such as the IMO is to look at past problems. IMO problems are generally designed to have a relatively low threshold regarding to required knowledge: It is all about knowing the ideas how to use the few theorems and techniques. (An exception can be sometimes made in the field of Geometry and inequalities, where knowing a lot of exotic theorems can sometimes help: But usually this then is not the expected solution.)

Because of the specific way the problem selection process for the IMO works there are shortlists of around 8 problems ordered by difficulty of each of the four core disciplines for each year. They are all featured (including solutions) in the

IMO Compendium, a huge and yellow book.

In my opinion, one of the most effective ways of preparing is to simply pick out problems from the short list (the younger, the better: The IMO was way different 50 years ago.) Usually, you will not be able to solve them. But don't be afraid: Then look at the solutions (or at least a part of it) and try to understand how they work, and especially, how one would come up with it. If they utilize theoretical background you don't understand, try to understand in the context of the solution of the exercise.

And, I believe the most important thing during this is: Have fun! Having fun while preparing for a competition makes it so much easier. :)