ERICKSON
PRINS MATH PROB SOLVG _c
Published on 1. September 1998
Book
Paperback/Softback
272 pages
978-0-13-096445-8 (ISBN)
Description
For introductory undergraduate courses in mathematics and problem-solving, students preparing for such academic contests as the William Lowell Putnam Mathematical Competition, and advanced high school students studying for the American Mathematical Olympiad. 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.
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Content
1. Data.
2. Direct and Indirect Reasoning.
3. Contradiction.
4. Induction.
5. Specialization and Generalization.
6. Symmetry.
7. Parity.
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.
18. Estimation.
19. Deus Ex Machina.
20. More Problems.
Glossary.
Bibliography.
Index.
2. Direct and Indirect Reasoning.
3. Contradiction.
4. Induction.
5. Specialization and Generalization.
6. Symmetry.
7. Parity.
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.
18. Estimation.
19. Deus Ex Machina.
20. More Problems.
Glossary.
Bibliography.
Index.