Mathematics has so many divisions, but you do not have to be
expert in all parts for Mathematical Olympiads. If you check the past papers of
any Mathematical Olympiad, especially International Mathematical Olympiad, then
you’ll see that it basically covers Number
Theory, Algebra, Geometry, Combinatorics and Inequality. To solve the
problems you’ve to increase your problem solving skills, know some tricks and enhance
the capability of doing problems using the best method.
I’m giving you some book suggestion to start your preparation
for Mathematical Olympiad. Books are given in order of difficulty. So, if you
are a beginner, you should start with the first book of each part.
Number
theory
(i) Beginning Number Theory
(ii) Number Theory
(iii) Adler’s Number Theory
(iv) A Pathway into Number Theory
(v) Elementary Number Theory
(vi) A Primer of Analytic Number Theory
Algebra
(i)
Concrete Abstract Algebra
Geometry
(i)
Plane Euclidean Geometry Theory & Problems
(ii) Geometry Revisited
(iii) Geometry Unbound
(iv) Complex number & Geometry
(v) The Algebra of Geometry
(vi) Transformation Geometry
Combinatorics
(i) Combinatorics
(ii) Principles and Techniques in Combinatorics
(iii) A Path to Combinatorics for Undergraduates
Inequality
(i) Inequalities
(ii) Algebra Inequalities
(iii) Secrets in Inequality