Math Contest – Recommended Textbooks Apart from AoPs

Question

I am looking for textbooks on math contests that give the theory associated with the topics
(such as graph theory,geometry,Trig,combinatorics,etc) before giving a large volley of problems to solve(apart from AoPs). I am a high schooler and complete beginner to these.
Is there a textbook that discusses theory as good as Arthur Engel has done for problem solving in the book Problem Solving Strategies?

Answer 1

Here are the books I recommend every mathlete from my personal experience:

Geometry and Trigonometry:

• Euclidean Geometry in Mathematical Olympiads by Evan Chen: This is the most recommended book for Olympiad geometry. The book goes through many important concepts and also gives insights of solving problems.
• Geometry Revisited by H.S.M Coxeter: An awesome classic. Some IMO medalists still recommend this book above EGMO.
• Geometry Unbound by Kiran S. Kedlaya: If you've completed all necessary concepts in geometry and want to solve some good problems, this is the book you're looking for.
• 103 Trigonometry Problems by Titu Andreescu: A good problem book for Olympiad trigonometry.

Inequalities:

• Secrets in Inequalities volume 1 and 2 by Pham Kim Hung: The best inequality book. But not recommended for a complete beginner as the problems here are very high level.
• Inequalities a Mathematical Olympiad Approach by Rogelio: A good book for Olympiad inequalities. Also suitable for beginners.
• Inequalities- Theorems, Techniques and Selected Problems by Cvetcovski (suggested by Dr. Mathva)
• Inequalities an Approach Through Problems by B J Venkatachala

Functional Equations:

• Functional Equations and How to Solve Them by Christopher G. Small
• Functional Equations a Problem Solving Approach by B J Venkatachala

Algebra:

• 101 Problems in Algebra by Titu Andreescu

Number Theory:

• Modern Olympiad Number Theory by Aditya Khurmi (suggested by Dr. Mathva)

• Olympiad Number Theory Through Challenging Problems by Justin Stevens

• Number Theory a Problem Solving Approach by Titu Andreescu

• 104 Number Theory Problems by Titu Andreescu

Combinatorics:

• A Path to Combinatorics for Undergraduates by Titu Andreescu
• 102 Combinatorial Problems by Titu Andreescu
• Problem Solving Methods in Combinatorics by Pablo Soberón
• Graph Theory by Xiong Bin

Problem Solving:

• The Arts and Crafts of Problem Solving by Paul Zeitz: The best problem solving book. Also a good resource for recreational mathematics problems.
• How to Solve It by George Polya.

Again, I mention these are my recommendations. Others suggestion may differ from this (you may add your suggestions in the comments). And there might be some books I forgot to include. May your math journey be enjoyable. Happy problem solving!