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.
目錄:
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.