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Recommended Mathematics Literature

Book Cover Klamkin
Book Cover Aha! Solutions
Book Cover Primer for Math Competitions
Book Cover Problem-Solving Strategies
Book Cover Zeitz
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Andy Liu, Bruce Shawyer. Problems from Murray Klamkin
Martin Erickson. Aha! Solutions
Zvezdelina Stankova, Tom Rike. A Decade of the Berkeley Math Circle
Sam Vandervelde. Circle in a Box
Alexander Zawaira, Gavin Hitchcock. A Primer for Mathematics Competitions
Valentin Boju, Louis Funar. The Math Problems Notebook
Béla Bollobás. The Art of Mathematics: Coffee Time in Memphis
Titu Andreescu, 103 Trigonometry Problems
Titu Andreescu, 104 Number Theory Problems
Titu Andreescu et al. Mathematical Olympiad Challenges
Titu Andreescu et al. Mathematical Olympiad Treasures
Terence Tao. Solving Mathematical Problems: A Personal Perspective
Jiri Herman et al. Equations and Inequalities
Jiri Herman et al. Counting and Configurations
B. J. Venkatachala. Functional Equations: A Problem Solving Approach
Christopher Small. Functional Equations and How to Solve Them
Publications by the UK Mathematics Trust
Dmitry Fomin, et al. Mathematical Circles: Russian Experience
Robert and Ellen Kaplan. Out of the Labyrinth: Setting Mathematics Free
Alfred Posamentier, Problem-Solving Strategies For Efficient and Elegant Solutions
Douglas Faires. First Steps for Math Olympians
Michael Steele. The Cauchy-Schwarz Master Class: An Introduction to the Art of Inequalities
Loren Larson. Problem Solving Through Problems
Bonnie Averbach, Orin Chein. Problem Solving Through Recreational Mathematics
Liong-shin Hahn. New Mexico Mathematics Contest Problem Book
William Briggs. Ants, Bikes, and Clocks: Problem Solving for Undergraduates
Steven Krantz. Techniques of Problem Solving
Wayne Wickelgren. How to Solve Mathematical Problems
Dusan Djukic. The IMO Compendium
Jörg Bewersdorff. Luck, Logic, and White Lies
Steve Olson. Count Down
David Acheson. 1089 and All That: A Journey into Mathematics.
Paul Zeitz. The Art and Craft of Problem Solving
Motivation for literature recommendation

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Of course, it is also recommended that you read books on other disciplines.

Problem Solving

The classic book about solving mathematical problems is: A kind of sequel to Polya's How to Solve It, presenting modern heuristics, especially for bigger problems (math problems, not `just' programming problems) requiring computers: Book Cover Another book that will help you become a good math problem solver, by distinguishing `mere' exercises from (challenging, unpredictable) real problems (the author participated in IMO 1974): Excellent IMO training material: A good initial preparation for IMO-style problem solving: More training material: From a 1988 IMO gold-medal winner, summarizing Polya's method and applying it to 26 diverse contest problems: More aimed at beginners, and especially their teachers: Based on the various (levels of) USA mathematical competitions: Approaching problem solving via puzzles and games: Another general overview with many sample problems: Another classic on mathematical problem solving, adding a psychological perspective:

Collections of Mathematical (Competition) Problems

There are many collections of mathematical (contest) problems (incl. IMO):

Anthologies and Surveys

A delightful book, covering "old" and "new" mathematics, in 16 short well-illustrated chapters: Don't let the title of Gower's Very Short Introduction put you off. It is very well done, even if you (think you) know mathematics well enough: In a rare combination of history, biography and mathematics, the following books presents twelve great theorems: A four-volume collection about and with mathematics, containing many classical essays by famous mathematicians: Another, more recent, collection is: An addictive and brilliant book about mathematics: A very accessible book that emphasizes the "Aha"-feeling when discovering (beautiful) proofs in mathematics based on varied and real mathematical problems: A classic survey of the field of mathematics: A philosophically more advanced survey is:

Number Theory

The bible of number theory is: If you are willing to fill in some gaps and want to delve into important number theory in less than 100 pages, including excercises, then go for: Another extremely useful reference dealing with numbers is: A somewhat excentric collection about all kinds of numbers: A collection of problems, hints, and solutions in number theory:



I am biased about the next book, because I took many (excellent) math courses from Jack van Lint. It has very broad coverage (including Pólya's Counting Theorem): An exceptional title for an exceptional book: An overview of theory combined with a collection of problems, hints, and solutions in combinatorics, combinatorial number theory, and combinatorial geometry: Another collection of problems, hints, and solutions in combinatorics:



Equations and Inequalities

A light introduction to inequalities: An introduction to inequalities aimed at training for math contests: A thoroough and more advanced introduction to inequalities: A systematic approach to solving functional equations: Another systematic approach to solve functional equations, based on problem from Mathematical Olympiads and other contests: An overview of theory combined with a collection of problems, hints, and solutions in equations, identities, and inequalities:



History of Mathematics

Mathematical Circles

Other Recommendations

If you want to bring your school library up to date: Kiran Kedlaya maintains a list of Olympiad Recommended Reading.

`Bedside' Mathematics Literature

Here follow some references to books that may not directly improve performance at the IMO, but that put mathematics and its players into a broader perspective.

Note that Martin Gardner, Ian Stewart (among others) are authors of many interesting mathematics books.

In alphabetic order of (first) author:

For the Very Young

Of interest to parents (e.g. the book shows how very young children can be taught the concepts related to quantity; this is not done by teaching them to count, but by teaching them to grasp quantity as a Gestalt):

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