I want to prepare for the maths olympiad and I was wondering if you can recommend me some books about combinatorics, number theory and geometry at a beginner and intermediate level. I would appreciate your help.
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Bill Dubuque
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http://www.artofproblemsolving.com/wiki/index.php?title=Olympiad_books – Roman83 Jul 22 '16 at 06:28
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1A great book to learn problem solving is 'Art and craft of problem solving' by Paul Zeitz. – Jul 27 '16 at 23:36
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If you're looking for a good Geometry book, you can check out Evan Chen's book, Euclidean Geometry In Mathematical Olympiads. There are no prerequisites to the book; all you need to do is know how to read proofs. A PDF of the book is $28:
http://www.maa.org/press/ebooks/euclidean-geometry-in-mathematical-olympiads
As a sample, here's a free PDF of chapter 2:
http://www.maa.org/sites/default/files/pdf/ebooks/pdf/EGMO_chapter2.pdf
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Unfortunately the MAA webpages seem to have disappeared so here is the updated link: https://web.evanchen.cc/geombook.html – Ilikemath Nov 11 '24 at 21:10
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An elementary intro to combinatorics, with exercises: https://www.amazon.com/Discrete-Mathematics-Highschooler-Alexander-Sadovsky/dp/1453869670/ref=sr_1_fkmr0_1?ie=UTF8&qid=1469170334&sr=8-1-fkmr0&keywords=sadovsky+discrete+math+for+highschooler
Instructional videos on combinatorics: https://www.youtube.com/watch?v=QrfA8mKOIjI
Books specifically on contest problems: https://www.amazon.com/William-Lowell-Mathematical-Competition-1985-2000/dp/088385807X/ref=sr_1_1?s=books&ie=UTF8&qid=1469170542&sr=1-1&keywords=putnam+problems
avs
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One of my favorite mathematical olympiad books is this one: https://www.amazon.es/Mathematical-Olympiad-Challenges-Titu-Andreescu/dp/0817645284 by Andreescu and Gelca. It's more on the itermediate level. It is sort of a compilation on useful techniques with sample problems. I suggest you give it a go.
Sak
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Some of my personal favorites for each category. Where I have attached no link you can easily find them online and for books by Andreescu generally on amazon.
Combinatorics
- A Path to Combinatorics for Undergraduates - Titu Andreescu, Zuming Feng
- Olympiad Combinatorics - Pranav A. Sriram (free pdf)
Number Theory
- Number Theory Structures, Examples, and Problems - Titu Andreescu, Dorin Andrica
- Modern Olympiad Number Theory - Aditya Khurmi (free pdf)
Geometry
- Euclidean Geometry In Mathematical Olympiads - Even Chen
- 103 Trigonometry Problems - Titu Andreescu, Zuming Feng
Ilikemath
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