Mathematical olympiad challenges

Titu Andreescu, Răzvan Gelca (auth.)9780817645281, 0817645284

This signficantly revised and expanded second edition of Mathematical Olympiad Challenges is a rich collection of problems put together by two experienced and well-known professors and coaches of the U.S. International Mathematical Olympiad Team. Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory from numerous mathematical competitions and journals have been selected and updated. The problems are clustered by topic into self-contained sections with solutions provided separately. Historical insights and asides are presented to stimulate further inquiry. The emphasis throughout is on creative solutions to open-ended problems.

New to the second edition:

* Completely rewritten discussions precede each of the 30 units, adopting a more user-friendly style with more accessible and inviting examples

* Many new or expanded examples, problems, and solutions

* Additional references and reader suggestions have been incorporated

Featuring enhanced motivation for advanced high school and beginning college students, as well as instructors and Olympiad coaches, this text can be used for creative problem-solving courses, professional teacher development seminars and workshops, self-study, or as a training resource for mathematical competitions.

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This [book] is…much more than just another collection of interesting, challenging problems, but is instead organized specifically for learning. The book expertly weaves together related problems, so that insights gradually become techniques, tricks slowly become methods, and methods eventually evolve into mastery…. The book is aimed at motivated high school and beginning college students and instructors…I strongly recommend this book for anyone interested in creative problem-solving in mathematics…. It has already taken up a prized position in my personal library, and is bound to provide me with many hours of intellectual pleasure.

—The Mathematical Gazette (Review of the First Edition)

Table of contents :
Front Matter….Pages i-xvii
Geometry and Trigonometry….Pages 3-37
Algebra and Analysis….Pages 39-68
Number Theory and Combinatorics….Pages 69-101
Geometry and Trigonometry….Pages 105-170
Algebra and Analysis….Pages 171-221
Number Theory and Combinatorics….Pages 223-276
Back Matter….Pages 277-283