Winning solutions获胜的解决方案 下载 pdf 百度网盘 epub 免费 2025 电子版 mobi 在线

This book is intended to provide students with the appropriate mathematical tools and problem-solving experience to successfully compete in high-level problem solving competitions. 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 competitions. Answers or sketches of the solutions 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 Progressions and Sums

1.7 Diophantine Equations

1.8 Quadratic Reciprocity

2 Algebra

2.1 Basic Theorems and Techniques

2.2 Polynomial Equations

2.3 Algebraic Equations and Inequalities

2.4 The Classical Inequalities

3 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 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 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.