Winning solutions获胜的解决方案

作者简介

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.

书籍目录

Preface1  Numbers  1.1  The Natural Numbers  1.2  Mathematical Induction  1.3  Congruence  1.4  Rational and Irrational Numbers  1.5  Complex Numbers  1.6  Progressions and Sums  1.7  Diophantine Equations  1.8  Quadratic Reciprocity2  Algebra  2.1   Basic Theorems and Techniques  2.2  Polynomial Equations  2.3  Algebraic Equations and Inequalities  2.4  The Classical Inequalities3 Combinatorics  3.1  What is Combinatofics?  3.2  Basics of Counting  3.3  Recurrence Relations  3.4  Generating Functions  3.5  The Inclusion-Exclusion Principle  3.6  The Pigeonhole Principle  3.7  Combinatorial Averaging  3.8  Some Extremal ProblemsHints and Answers for Selected ExercisesGeneral ReferencesList of SymbolsIndex

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