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.
Techniques for solving problems from the American Mathematics Competitions, essential reading for anyone interested in logical problem solving.
'Within each chapter, three well-chosen examples illustrate a variety of problem-solving strategies and applications of concepts. The examples are followed by ten exercises, graduated in difficulty so that nearly every student reader will be able to solve at least one problem easily and nearly every reader will struggle with at least one. The thoughtful choice of examples and exercises is one of the book's strengths, providing a wealth of opportunity for students to become experienced problem solvers within a remarkably small number of pages.' David Wells, Penn State University 'Professor Faires has prepared an impressive problem solving primer. The book presents a wide variety of problems and problem solving strategies, and illustrates how the American Mathematics Competitions can be used to develop many important mathematical techniques.' Richard Gibbs, Fort Lewis College