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数学奥林匹克英文版系列 数学奥林匹克在中国PDF|Epub|txt|kindle电子书版本网盘下载
- 刘培杰主编；欧阳维诚，叶思源，冯海晴副主编 著
- 出版社： 哈尔滨：哈尔滨工业大学出版社
- ISBN：7560346854
- 出版时间：2014
- 标注页数：396页
- 文件大小：43MB
- 文件页数：415页
- 主题词：
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图书目录
Chapter 1 Mathematical Olympiad in China1
1.1 International Mathematical Olympiad(IMO)and China Mathematical Contest—Written before the 31st IMO1
1.1.1 A Brief Introduction to IMO2
1.1.2 A Historic Review of China Mathematical Contest4
1.1.3 Activities of China in the IMO and the 31st IMO6
Chapter 2 Olympiad's Mathematics8
2.1 The Application of Projective Geometry Methods to Problem Proving in Geometry8
2.1.1 A Few Concepts in Projective Geometry10
2.1.2 Some Examples15
2.1.3 Exercises22
2.2 A Conjecture Concerning Six Points in a Square24
2.3 Modulo-Period Sequence of Numbers33
2.3.1 Basic Concepts33
2.3.2 Pure Modulo-period Sequence39
2.3.3 The Periodicity of Sum Sequence44
2.3.4 The Relation between the Period and the Initial Terms47
2.4 Iteration of Fractional Linear Function and Consturction of a Class of Function Equation49
2.5 Remarks Initiating from a Putnam Mathematics Competition Problem55
2.5.1 Introductory Remarks55
2.5.2 The Proof of the Problem56
2.5.3 Reinforcing the Promble57
2.5.4 Application60
2.5.5 Mutually Supplementary Sequences and Reversible Sequences64
2.6 The Ways of Finding the Best Choise Point67
2.6.1 The Congruent Transformation of Figures67
2.6.2 Similarity Transformation of Figures69
2.6.3 Partial Adjusting Method70
2.6.4 The Contour Line Method73
2.6.5 Algebraic Method75
2.6.6 Trigonometrical Method77
2.6.7 Analytic Method78
2.6.8 Solution by Fermat Point Theorem79
2.6.9 The Area Method80
2.6.10 Physical Method81
2.7 The Formulas and Inequalities for the Volumes of n-Simplex84
2.8 The Polynomial of Inverse Root and Its Transformation100
2.8.1 The Extension of an IMO Problem100
2.8.2 The Inverse Root Polynomial102
2.8.3 Trigonometric Formula of Recurrence Type105
2.8.4 Inverse Root Polynomial Transformation108
Chapter 3 Suggestions and Answers of Problems116
3.1 Remarks on Proposing Problems for Mathematics Competition116
3.2 A Problem of IMO and a Useful Polynomial131
3.2.1 Introduction131
3.2.2 The Proof of the Problem132
3.2.3 Some Properties of Fm(x)135
3.2.4 Fm(x)and Some IMO Problems138
3.2.5 An Existence Problem142
3.3 Preliminary Approach to Methods of Proposing Mathematics Competition Problems144
3.3.1 Introduction145
3.3.2 Form Changing148
3.3.3 Generalization151
3.3.4 Construction156
Chapter 4 Comment on the Exam Paper of Mathematical Olympiad Winter Camp in China159
4.1 Comment on the Exam Paper of the First Mathematical Winter Camp(1986)159
4.2 Comment on the Exam Paper of the Second Mathematical Winter Camp(1987)172
4.3 Comment on the Exam Paper of the Third Mathematical Winter Camp(1988)178
4.4 Comment on the Exam Paper of the Fourth Mathematical Winter Camp(1989)183
4.5 Comment on the Exam Paper of the Fifth Mathematical Winter Camp(1990)192
Chapter 5 China Mathematical Olympiad from the First to the Lastest205
5.1 China Mathematical Olympiad(1991)205
5.2 China Mathematical Olympiad(1992)212
5.3 China Mathematical Olympiad(1993)220
5.4 China Mathematical Olympiad(1994)225
5.5 China Mathematical Olympiad(1995)235
5.6 China Mathematical Olympiad(1996)241
5.7 China Mathematical Olympiad(1997)247
5.8 China Mathematical Olympiad(1998)258
5.9 China Mathematical Olympiad(1999)265
5.10 China Mathematical Olympiad(2000)275
5.11 China Mathematical Olympiad(2001)282
5.12 China Mathematical Olympiad(2002)293
5.13 China Mathematical Olympiad(2003)304
5.14 China Mathematical Olympiad(2004)316
5.15 China Mathematical Olympiad(2005)323
5.16 China Mathematical Olympiad(2006)333
5.17 China Mathematical Olympiad(2007)342
5.18 China Mathematical Olympiad(2008)351
5.19 China Mathematical Olympiad(2009)360
5.20 China Mathematical Olympiad(2010)369
5.21 China Mathematical Olympiad(2011)375
5.22 China Mathematical Olympiad(2012)381
5.23 China Mathematical Olympiad(2013)388