Synopses & Reviews
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, for professional teacher development seminars and workshops, for self-study, or as a resource for training for mathematical competitions.
-----
From a review of the first edition:
This book isb&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 masteryb&. The book is aimed at motivated high school and beginning college students and instructors. It can be used as a text for advanced problem-solving courses, for self-study, or as a resource for teachers and students training for mathematical competitions, and for teacher professional development, seminars, and workshops. bThe Mathematical Gazette
Synopsis
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.
This book] isa ]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 masterya ]. The book isaimed at motivated high school and beginning college students and instructors...I strongly recommend this book for anyone interested in creative problem-solving in mathematicsa ]. It has already taken up a prized position in my personal library, and is bound to provide me with many hours of intellectual pleasure.
a The Mathematical Gazette (Review of the First Edition)
Synopsis
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 were selected from numerous mathematical competitions and journals. The problems are clustered by topic into self-contained sections with solutions provided separately. All sections start with an essay discussing basic facts and one or two representative examples. A list of carefully chosen problems follows and the reader is invited to take them on. Additionally, historical insights and asides are presented to stimulate further inquiry. The emphasis throughout is on encouraging readers to move away from routine exercises and memorized algorithms toward creative solutions to open-ended problems.
Synopsis
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 were selected from numerous mathematical competitions and journals. An important feature of the work is the comprehensive background material provided with each grouping of problems. The problems are clustered by topic into self-contained sections with solutions provided separately. All sections start with an essay discussing basic facts and one or two representative examples. A list of carefully chosen problems follows and the reader is invited to take them on. Additionally, historical insights and asides are presented to stimulate further inquiry. The emphasis throughout is on encouraging readers to move away from routine exercises and memorized algorithms toward creative solutions to open-ended problems. Aimed at motivated high school and beginning college students and instructors, this work can be used as a text for advanced problem- solving courses, for self-study, or as a resource for teachers and students training for mathematical competitions and for teacher professional development, seminars, and workshops.
Table of Contents
Foreword x Preface x PART I: Problems x 1. Geometry and Trigonometry x 2. Algebra and Analysis x 3. Number Theory and Combinatorics x PART II: Solutions x 1. Geometry and Trigonometry x 2. Algebra and Analysis x 3. Number Theory and Combinatorics x Appendix: Definitions and Notation