Preparing for Mathematics Olympiad I am preparing for Mathematics Olympiad , can any one suggest me some books to prepare for olympiad ? The topics that usually come up involve: 


*

*congruence modulo $n$, 

*inequalities ,

*number system, elementary number theory, etc.


Please help me!
Thanks
Kushashwa
 A: Buy AoPS books starting from pre algebra and work your way to precalculus... Then just buy practice amc, aime, and usamo tests from the MAA website:
Also I recommend reading the book polynomials by Barbeau as well as Art and Craft of Problem Solving.
For a lighter read go through the Barron's E-Z series in each math subject before touching the AoPS volume. This will make your transition from learning topics to learning to problem solve a lot easier.
A: These following books are good:


*

*Problem Solving Strategies by Arthur Engel

*Mathematical Circles by Dmitri Fomin et al

*The USSR Olympiad Problem Book by D. O. Shklarsky et al

*Others books By Titu Andreescu and Isaak Yaglom
A: I'd recommend that you visit the Art of Problem Solving's (AoPS) website: I've linked you to their "resource" page with articles you can download (they are freely accessible.) The website is a "hub" for very motivated students of mathematics, many of whom engage in competition math. The site hosts mathematics resources, curricula, on-line forums, and a "bookstore". So feel free to explore the vast site.
Given the topics you specifically mention, I'll link you to some pdf notes on Number Theory; it's about 40-some odd pages, covering the topics you mention, and more.  I'll also link you to a pdf entitled Olympiad Number Theory: an Abstract Perspective. You'll find at least two (freely accessible) notes in pdf on inequalities available for downloading, at the linked page at the top. Here's one of those: Inequalities.
Enjoy!
