What Are the Best Resources for Winning Gold at the IMC?

[Hurin]

Hi, this is my first year in college, and I want to participate of the IMC (International Mathematics Competition for University Students). Can someone indicate good textbooks, problem books and other related tips to win a gold medal?

-Thanks.

 

[doodle_sack]

This pretty much depends on where you want to start from. I have a huge list (collected from MIT website and from other sources) of books, but it is very hard and misleading to suggest anything before knowing what your background is.

 

[Hurin]

This pretty much depends on where you want to start from. I have a huge list (collected from MIT website and from other sources) of books, but it is very hard and misleading to suggest anything before knowing what your background is.

I'm in my first year. But, could you post your list please.

 

[doodle_sack]

I meant to ask what is your problem-solving skill level, not which year of college you are in. As I said, the list is quite huge and it won't help you even decide which book to start from.

Assuming you have decent problem solving skills and you can ace a random problem from some regional math olympiad, I would suggest the following books:

Algebra
101 Problems in Algebra by Titu Andreescu and Zuming Feng
Intermediate Algebra by Richard Rusczyk and Mathew Crawford
Complex Numbers from A to... Z by Titu Andreescu

Analysis (For Problem Solving)
Counterexamples in Analysis by Bernard R. Gelbaum and John M. H. Olmsted
The Hitchhiker's Guide to Calculus by Michael Spivak
Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus by Michael Spivak
Problems and Theorems in Analysis I, Pólya & Gábor Szegö (Advanced)
Problems and Theorems in Analysis II, Pólya & Gábor Szegö (Advanced)
Problems & Propositions in Analysis, Klambauer & Gabriel

Combinatorics
102 Combinatorial Problems by Titu Andreescu and Zuming Feng
Generatingfunctionology
Mathematics of Choice by Ivan Niven
A Path to Combinatorics for Undergraduates: Counting Strategies by Titu Andreescu and Zuming Feng
Dr. David Patrick's Intermediate Counting & Probability
Enumerative Combinatorics, Volume 1 by Richard Stanley
Enumerative Combinatorics, Volume 2 by Richard Stanley
A First Course in Probability by Sheldon Ross

Geometry
Challenging Problems in Geometry
Geometry Revisited
Geometry of Complex Numbers by Hans Schwerfdtfeger
Geometry: A Comprehensive Course by Dan Pedoe
Non-Euclidean Geometry by H.S.M. Coxeter
Projective Geometry by H.S.M. Coxeter
Geometric Transformations I, Geometric Transformations II, and Geometric Transformations III by I. M. Yaglom.

General Problem Solving
The Art of Problem Solving Volume 2 by Sandor Lehoczky and Richard Rusczyk
The Art and Craft of Problem Solving by Paul Zeitz
How to Solve It by George Polya (This is more of a tactic & strategy oriented book, it will be a gem if you use it the right way)
A Mathematical Mosaic by Putnam Fellow Ravi Vakil
Proofs Without Words, Proofs Without Words II
Sequences, Combinations, Limits
100 Great Problems of Elementary Mathematics by Heinrich Dorrie
Mathematical Olympiad Challenges
Problem Solving Strategies by Arthur Engel
Problem Solving Through Problems by Loren Larson

Please Note: This list is partial and I still don't know your level, the BEST advice would be to find a guy from your university who has olympiad experience (or you can ask your professor) and ask him on how to get started.