This book consists of three parts： fundamental knowledge， basic methods and typical problems. These three parts introduce the fundamental knowledge of solving combinatorial problems， the important solutions to combinatorial problems and some typical problems with often-used solutions in the high school mathematical competition respectively.In each chapter there are necessary examples and exercises with solutions. These examples and exercises are of the same level of difficulty as the China Mathematical League Competitions which are selected from mathematical competitions at home and abroad in recent years. Some test questions are created by the author himself and a few easy questions in China Mathematical Olympiad （CMO） and IMO are also included. In this book， the author pay attention to leading readers to explore， analyze and summarize the ideas and methods of solving combinatorial problems. The readers' mathematical concepts and abilities will be improved remarkably after acquiring knowledge from this book.
Introduction Preface PART ONE Fundamental Knowledge Chapter 1 Principles and Formulas of Counting Exercise 1 Chapter 2 Pigeonhole Principle and Mean Value Principle Exercise 2 Chapter 3 The Generating Functions Exercise 3 Chapter 4 Recurrence Sequence of Numbers Exercise 4 PART TWO Basic Method Chapter 5 Classification and Method of Fractional Steps Exercise 5 Chapter 6 Correspondent Method Exercise 6 Chapter 7 Counting in Two Ways Exercise 7 Chapter 8 Recurrence Method Exercise 8 Chapter 9 Coloring Method and Evaluation Method Exercise 9 Chapter 10 Reduction to Absurdity and the Extreme Principle Exercise 10 Chapter 11 Local Adjustment Method Exercise 11 Chapter 12 Construction Method Exercise 12 PART THREE Typical Problems Chapter 13 Combinatorial Counting Problems Exercise 13 Chapter 14 Existence Problems and the Proofs of Inequalities in Combinatorial Problems Exercise 14 Chapter 15 Combinatorial Extremum Problems Exercise 15 Solutions to Exercises
鄂公網(wǎng)安備 42010302001612號 