First Steps for Math Olympians: Using the American Mathematics Competitions 数学奥林匹亚第一步：美国数学竞争

A major aspect of mathematical training and its benefit to society is the ability to use logic to solve problems. The American Mathematics Competitions (AMC) have been given for more than fifty years to millions of high school students. This book considers the basic ideas behind the solutions to the majority of these problems, and presents examples and exercises from past exams to illustrate the concepts. Anyone taking the AMC exams or helping students prepare for them will find many useful ideas here. But people generally interested in logical problem solving should also find the problems and their solutions interesting.
　　This book will promote interest in mathematics by providing students with the tools to attack problems that occur on mathematical problem-solving exams, and specifically to level the playing field for those who do not have access to the enrichment programs that are common at the top academic high schools. The book can be used either for self-study or to give people who want to help students prepare for mathematics exams easy access to topic-oriented material and samples of problems based on that material. This is useful for teachers who want to hold special sessions for students, but it is equally valuable for parents who have children with mathematical interest and ability.
　　As students' problem solving abilities improve, they will be able to comprehend more difficult concepts requiring greater mathematical ingenuity. They will be taking their first steps towards becoming math Olympians!　
作者简介：
　　J. Douglas Faires received his BS in mathematics from Youngstown Uni-versity in 1963. He earned his PhD in mathematics from the University of South Carolina in 1970. Faires has been a Professor at Youngstown State University since 1980. He has been actively involved in the MAA for many years. For example, he was Governor of the Ohio Section from 1997-2000. He is currently a member of the MAA's Strategic Planning Committee for the AMC. Faires is a past President of Pi Mu Epsilon and he was a member of the Council for many years. He has been the National Director of the AMC-10 Competition of the American Mathematics Competitions since 1999. Faires has been the recipient of many awards and honors. He was named the Outstanding College-University Teacher of Mathematics by the Ohio Section of the MAA in 1996; he has also received five Distinguished Professorship awards from Youngstown State University and an honorary Doctor of Science degree in May 2006. Faires has authored and coauthored numerous books including Numerical Analysis (now in its eighth edition!),Numerical Methods (third edition), and Precalculus (fourth edition).

J. Douglas Faires received his Ph.D from the University of South Carolina in 1970. He has been the National Director of the AMC-10 Competition of the American Mathematics Competitions (sponsored by the Mathematical Association of America) since 1999.

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Any high school student preparing for the American Mathematics Competitions should get their hands on a copy of this book! A major aspect of mathematical training and its benefit to society is the ability to use logic to solve problems. The American Mathematics Competitions (AMC) have been given for more than fifty years to millions of high school students. This book considers the basic ideas behind the solutions to the majority of these problems, and presents examples and exercises from past exams to illustrate the concepts. Anyone taking the AMC exams or helping students prepare for them will find many useful ideas here. But people generally interested in logical problem solving should also find the problems and their solutions interesting. This book will promote interest in mathematics by providing students with the tools to attack problems that occur on mathematical problem-solving exams, and specifically to level the playing field for those who do not have access to the enrichment programs that are common at the top academic high schools. The book can be used either for self-study or to give people who want to help students prepare for mathematics exams easy access to topic-oriented material and samples of problems based on that material. This is useful for teachers who want to hold special sessions for students, but it is equally valuable for parents who have children with mathematical interest and ability. As students' problem solving abilities improve, they will be able to comprehend more difficult concepts requiring greater mathematical ingenuity. They will be taking their first steps towards becoming math Olympians!

Preface
1　Arithmetic Ratios
　1.1 Introduction
　1.2 Time and Distance Problems
　1.3 Least Common Multiples
　1.4 Ratio Problems
　Examples for Chapter 1
　Exercises for Chapter 1
2　Polynomials and their Zeros
　2.1 Introduction
　2.2 Lines
　2.3 Quadratic Polynomials
　2.4 General Polynomials
　Examples for Chapter 2
　Exercises for Chapter 2
3　Exponentials and Radicals
　3.1 Introduction
　3.2 Exponents andBases
　3.3 Exponential Functions
　3.4 Basic Rules of Exponents
　3.5 The Binomial Theorem
　Examples for Chapter 3
　Exercises for Chapter 3
4 Defined Functions and Operations
　4.1 Introduction
　4.2 Binary Operations
　4.3 Functions
　Examples for Chapter 4
　Exercises for Chapter 4
5　Triangle Geometry
　5.1 Introduction
　5.2 Definitions
　5.3 Basic Right Triangle Results
　5.4 Areas of Triangles
　5.5 Geometric Results about Triangles
Examples for Chapter 5
　Exercises for Chapter 5
6　Circle Geometry
　6.1 Introduction
　6.2 Definitions
　6.3 Basic Results of Circle Geometry
　6.4 Results Involving the Central Angle
　Examples for Chapter 6
Exercises for Chapter 6
7 Polygons
　7.1 Introduction
　7.2 Definitions
　7.3 Results about Quadrilaterals
　7.4 Results about General Polygons
　Examples for Chapter 7
　Exercises for Chapter 7
8 Counting
　8.1 Introduction
　8.2 Permutations
　8.3 Combinations
　8.4 Counting Factors
　Examples for Chapter 8
　Exercises for Chapter 8
9　Probability
10　Prime Decomposition
11　Number Theory
12　Sequemces and Series
13　Statistics
14　Trigonometry
15　Three-Dimensional Geometry
16　Functions
17　Logarithms
18　Complex Numbers
Solutions to Exercoses
Epilogue
Sources of the Exercises
Index
About the Author