Winning soluti***获胜的解决方案 mobi 下载 网盘 caj lrf pdf txt 阿里云

This book is intended to provide students with the appropriate mathematical tools and problem-solving experience to successfully compete in high-level problem solving competiti***. In each section, the authors attempt to "fill in" the appropriate background and then provide the student with a variety of worked examples and exercises to help bridge the gap between what he or she may already know and what is required for high-level competiti***. Answers or sketches of the soluti*** are given for all exercises. The book makes an attempt to introduce each area "gently" assuming little in the way of prior background - and teach the appropriate techniques, rather than simply providing a compilation of high-level problems.

Preface

1 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 Progressi*** and Sums

1.7 Diophantine Equati***

1.8 Quadratic Reciprocity

2 Algebra

2.1 Basic Theorems and Techniques

2.2 Polynomial Equati***

2.3 Algebraic Equati*** and Inequalities

2.4 The Classical Inequalities

3 Combinatorics

3.1 What is Combinatofics?

3.2 Basics of Counting

3.3 Recurrence Relati***

3.4 Generating Functi***

3.5 The Inclusion-Exclusion Principle

3.6 The Pigeon*** Principle

3.7 Combinatorial Averaging

3.8 Some Extremal Problems

Hints and Answers for Selected Exercises

General References

List of Symbols

Index

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书籍介绍

This book provides the mathematical tools and problem-solving experience needed to successfully compete in high-level problem solving competiti***. 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 competiti***. Answers or sketches of the soluti*** are given for all exercises.