数学奥林匹克在中国

Chapter 1 Mathematical Olympiad in China
1.1 International Mathematical Olympiad (IMO) and China Mathematical Contest-Written before the 31st IMO
1.1.1 A Brief Introduction to IMO
1.1.2 A Historic Review of China Mathematical Contest
1.1.3 Activities of China in the IMO and the 31st IMO

Chapter 2 Olympiad's Mathematics
2.1 The Application of Projective Geometry Methods to Problem Proving in Geometry
2.1.1 A Few Concepts in Projective Geometry
2.1.2 Some Examples
2.1 3 Exercises
2.2 A Conjecture Concerning Six Points in a Square
2.3 Modulo-Period Sequence of Numbers
2.3.1 Basic Concepts
2.3.2 Pure Modulo-period Sequence
2.3.3 The Periodicity of Sum Sequence
2.3.4 The Relation between the Period and the Initial Terms
2.4 Iteration of Fractional Linear Function and Consturction of a Class of Function Equation
2.5 Remarks Initiating from a Putnam Mathematics Competition Problem
2.5.1 Introductory Remarks
2.5.2 The Proof of the Problem
2.5.3 Reinforcing the Promble
2.5.4 Application
2.5.5 Mutually Supplementary Sequences and Reversible Sequences
2.6 The Ways of Finding the Best Choise Point
2.6. 1 The Congruent Transformation of Figures
2.6.2 Similarity Transformation of Figures
2.6.3 Partial Adjusting Method
2.6.4 The Contour Line Method
2.6.5 Algebraic Method
2.6.6 Trigonometrical Method
2.6.7 Analytic Method
2.6.8 Solution by Fermat Point Theorem
2.6.9 The Area Method
2.6.10 Physical Method
2.7 The Formulas and Inequalities for the Volumes of n-Simplex
2.8 The Polynomial of Inverse Root and Its Transformation
2.8.1 The Extension of an IMO Problem
2.8.2 The Inverse Root Polynomial
2.8.3 Trigonometric Formula of Recurrence Type
2.8.4 Inverse Root Polynomial Transformation

Chapter 3 Suggestions and Answers of Problems
3.1 Remarks on Proposing Problems for Mathematics Competition
3.2 A Problem ofIMO and a Useful Polynomial
3.2.1 Introduction
3.2.2 The Proof of the Problem
3.2.3 Some Properties of F(x)
3.2.4 Fm(x) and Some IMO Problems
3.2.5 An Existence Problem
3.3 Preliminary Approach to Methods of Proposing Mathematics Competition Problems
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Chapter 4 Comment on the Exam Paper of Mathematical Olympiad Winter Camp in China
Chapter 5 Cluna Mathematical Olympiad from the First to the Lastest