First Steps for Math Olympians: Using the American Mathematics Competitions

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MAA, Dec 21, 2006 - Mathematics - 307 pages
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A major aspect of mathematical training and its benefit to society is the ability to use logic to solve problems. The American Mathematics Competitions have been given for more than fifty years to millions of 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 preparing for the Mathematical Olympiads will find many useful ideas here, but people generally interested in logical problem solving should also find the problems and their solutions stimulating. The book can be used either for self-study or as topic-oriented material and samples of problems for practice exams. Useful reading for anyone who enjoys solving mathematical problems, and equally valuable for educators or parents who have children with mathematical interest and ability.
 

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Contents

Arithmetic Ratios
1
Polynomials and their Zeros
9
Exponentials and Radicals
19
Triangle Geometry
37
Circle Geometry
55
Polygons
71
Counting
85
Probability
97
Statistics
135
Trigonometry
143
ThreeDimensional Geometry
155
Functions
167
Logarithms
179
Complex Numbers
187
Solutions to Exercises
197
Epilogue
291

Prime Decomposition
109
Number Theory
115
Sequences and Series
127
About the Author
307
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