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Summary
Summary
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!
Reviews 1
Choice Review
Faires (Youngstown State Univ.) has prepared First Steps for Math Olympians as a guidebook for teachers who are helping high school students prepare for the American Mathematics Competitions (AMC). The book breaks the competitions down into 18 subjects and uses problems from past competitions as examples and exercises to illustrate each topic. Perhaps most useful to students taking the tests is the fact that these sample problems are arranged by subject. Also useful are the brief descriptions of the topics preceding the problems in each section. These descriptions serve as reminders of each area and may be useful as a reference while working on the exercises in each section. The preface describes the history of the AMC and Faires's lengthy involvement in the competitions, which lends authority to the choice and arrangement of topics. This book should be included in the library of anyone involved in preparing high school students to take the AMC. ^BSumming Up: Highly recommended. General readers; high-school teachers of mathematics. J. T. Noonan Mount Vernon Nazarene University
Table of Contents
| Preface |
| 1 Arithmetic ratios |
| 2 Polynomials and their zeros |
| 3 Exponentials and radicals |
| 4 Defined functions and operations |
| 5 Triangle geometry |
| 6 Circle geometry |
| 7 Polygons |
| 8 Counting |
| 9 Probability |
| 10 Prime decomposition |
| 11 Number theory |
| 12 Sequences and series |
| 13 Statistics |
| 14 Trigonometry |
| 15 Three-dimensional geometry |
| 16 Functions |
| 17 Logarithms |
| 18 Complex numbers |
| Solutions to exercises |
| Epilogue |
| Sources of the exercises |
| Index |
| About the author |
