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This book presents the principles and specific problem-solving methods that can be used to solve a variety of mathematical problems. The book provides clear examples of various problem-solving methods accompanied by numerous exercises and their solutions. KEY TOPICS: Principles of Mathematical Problem Solving introduces and explains specific problem-solving methods (with examples), and gives a set of exercises and complete solutions for each method. The idea is that by studying the principles and applying them to the exercises, the reader will gain problem-solving ability as well as general mathematical insight. Eventually, the reader should be able to produce results that have "the whole air of intuition." Organized according to specific techniques in separate chapters, techniques include induction and the pigeonhole principle, among others. Arranged in order of increasing difficulty, the book presents a wide variety of problem sets designed to illustrate significant mathematical ideas. Each chapter also includes a moderate amount of the "theory" behind each problem-solving principle it presents. MARKET: An essential resource for every student of mathematics and every professional who needs to solve mathematical problems.
Table of contents
2. Direct and Indirect Reasoning.
5. Specialization and Generalization.
8. Various Moduli.
9. Pigeonhole Principle.
10. Two-Way Counting.
11. Inclusion-Exclusion Principle.
12. Algebra of Polynomials.
13. Recurrence Relations and Generating Functions.
14. Maxima and Minima.
15. Means, Inequalities, and Convexity.
16. Mean Value Theorems.
17. Summation by Parts.
19. Deus Ex Machina.
20. More Problems.
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