This book provides the mathematical tools and problem-solving experience needed to successfully compete in high-level problem solving competitions. Each section presents important background information and then provides a variety of worked examples and exercises to help bridge the gap between what the reader may already know and what is required for high-level competitions. Answers or sketches of the solutions are given for all exercises.
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Most Helpful Customer Reviews
9 of 10 people found the following review helpful:
5.0 out of 5 stars
Excellent Book on Problem Solving,
By A Customer
This review is from: Winning Solutions (Problem Books in Mathematics) (Paperback)
This is an awesome book on problem solving. While it is true that you should have a couple of seperate references to comprehend fully the mathematics the author uses, I'm sure it's because he assumes a working knowledge on much of the material (contrary to the preface that states that it is a transition from regular high school material---Well, this it is not!). Many exercises and Olympiad questions covering the material presented in each chapter are given. Hints and solutions to the exercises(but not Olympiad questions--whose answer you can find on many sites) are given. There are alot of interesting topics covered (numbers, combinatorics, algebra, induction, pigeonhole, etc) in ways that I hadn't seen them presented. This is an excellent buy for those interested in solving tough and interesting mathematics problems.
10 of 12 people found the following review helpful:
4.0 out of 5 stars
Well thought out, though at times hard to follow,
By A Customer
This review is from: Winning Solutions (Problem Books in Mathematics) (Paperback)
This book traverses through many (though not all) of the subjects encountered in olympiad-style problems. One notable exception is the lack of geometry information.
The book is very much proof oriented. While this gives the problem solver deeper insight into the mathematics involved, some of the proofs are unessasarily hard to understand. Minor modifications would have made the author's logic more apparent.
Included problems well supplement the problem-solver, but require him to explore outside the bounds of what is explained in the text.
This book is definately not for the casual reader, but is a must for training high-school and early college students. Expect at least a semester of course work.
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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pigeonhole principle, recurrence relations, combinatorial averaging, olympiad problems, alternating subsets, ballot condition, complete solution set, multipartite graph, classical inequalities, inversion table, quadratic reciprocity, using mathematical induction Key Phrases - Capitalized Phrases (CAPs): (learn more)
The Classical Inequalities, Well-Ordering Principle, Euclid's Lemma, Binomial Theorem, Euler's Theorem, Some Extremal Problems, Chinese Remainder Theorem, Combinatorics Example, The Inclusion-Exclusion Principle, Principle of Mathematical Induction, Rational Root Theorem, Fundamental Theorem of Algebra, Uniqueness Theorem, The Product Rule, Numbers Example, Leonhard Euler, Basics of Counting, Division Algorithm Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
pigeonhole principle, recurrence relations, combinatorial averaging, olympiad problems, alternating subsets, ballot condition, complete solution set, multipartite graph, classical inequalities, inversion table, quadratic reciprocity, using mathematical induction Key Phrases - Capitalized Phrases (CAPs): (learn more)
The Classical Inequalities, Well-Ordering Principle, Euclid's Lemma, Binomial Theorem, Euler's Theorem, Some Extremal Problems, Chinese Remainder Theorem, Combinatorics Example, The Inclusion-Exclusion Principle, Principle of Mathematical Induction, Rational Root Theorem, Fundamental Theorem of Algebra, Uniqueness Theorem, The Product Rule, Numbers Example, Leonhard Euler, Basics of Counting, Division Algorithm Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
19
books
cite this book:
See all 19 books citing this book
- The IMO Compendium: A Collection of Problems Suggested for The International Mathematical Olympiads: 1959-2004 (Problem Books in Mathematics) by Duan Djuki in Back Matter (1), and Back Matter (2)
- Problem-Solving Strategies (Problem Books in Mathematics) by Arthur Engel in Back Matter (1), and Back Matter (2)
- Exercises in Classical Ring Theory (Problem Books in Mathematics) by T.Y. Lam in Back Matter
- Berkeley Problems in Mathematics by Paulo Ney de Souza in Back Matter
- Problems and Theorems in Classical Set Theory (Problem Books in Mathematics) by Peter Komjath in Back Matter
See all 19 books citing this book
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