数学奥林匹克在中国
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作者刘培杰 主编
出版社哈尔滨工业大学出版社
ISBN9787560346854
出版时间2014-06
装帧精装
开本16开
纸张胶版纸
定价98元
货号23705767
上书时间2024-07-20
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【内容简介】:
《数学奥林匹克在中国》介绍了从1986年至2013年的国际数学奥林匹克竞赛在中国的发展情况，并着重介绍了从1986年以来历届国际数学奥林匹克竞赛的试题及解答技巧，后介绍了历届中国数学奥林匹克竞赛试题。
《数学奥林匹克在中国》适合准备参加高中数学奥林匹克竞赛的学生及辅导教师和广大数学爱好者参考阅读。
【目录】:
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
……
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
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