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?
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2USA Olympiad preperation books like 102 combinatorial problems and 104 Number Theory problems by Titu Andrescu may be helpful. – Math-Learner Aug 05 '21 at 18:29
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1You can also view this this for a comprehensive list of materials for olympiad combinatorics. – James Moriarty Sep 01 '21 at 18:41
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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!
Oshawott
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1I would add "A walk through combinatorics: an introduction to enumeration and graph theory". While it's not made for olympiad problems as far as I can tell. It covers much of the same material while still managing to be engaging and interesting. – Oussema Aug 06 '21 at 03:41
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1Great recommendations!! There are only two other books I find essential when it comes to contest Math. “Inequialities”, by Cvetkovski, Zdravko (https://www.springer.com/gp/book/9783642237911) and Khurmi’s “Modern Olympiad Number Theory” (which can be found for free on aops: https://artofproblemsolving.com/community/c6h2344755). The first book does not only cover the most common and helpful techniques, but also gives an insight on more complex and advanced ones; from the second book, I will only say that it has been compared to Evan Chen’s work, but in NT ;) – Dr. Mathva Aug 10 '21 at 12:54
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2Also, Evan Chen has a nice list of recommendations in his webpage which include both books and other resources online (such as helpful handouts): https://web.evanchen.cc/recommend.html – Dr. Mathva Aug 10 '21 at 12:55
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@Dr.Mathva I've read the first book. The book was good but I forgot to include that. The second book, I never knew existed. I read first few pages of the book and I think it's worth comparing to EGMO. Thanks for your suggestion, especially the second one. I've added both the in my list. – Oshawott Aug 10 '21 at 14:00