
Principles of Mathematical Problem Solving, 1/e
Martin J. Erickson, Truman State University
Joe Flowers, Truman State University
Published August, 1998 by Prentice Hall Engineering/Science/Mathematics
Copyright 1999, 252 pp.
Cloth
ISBN 013096445X

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Mathematical Problem SolvingMathematics

For introductory undergraduate courses in mathematics and
problemsolving, 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 problemsolving methods
that can be used to solve a variety of mathematical problems. The
book provides clear examples of various problemsolving methods accompanied
by numerous exercises and their solutions.
Introduces and explains specific problemsolving methods
(with examples) and then gives a set of exercises and complete
solutions for each method.
 Each chapter includes an additional set of problems to
challenge the reader.
 By studying the principles and applying them to the exercises,
the reader will gain problemsolving 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 problemsolving techniques
in separate chapters. These techniques include:
 Induction (chapter 4)
 Pigeonhole principle (chapter 9)
Chapters and exercises are arranged in order of increasing
difficulty.
Presents a wide variety of problems—some old favorites
and some new gems.
 Problem sets illustrate significant mathematical ideas
and have elegant but not tedious solutions.
 Some chapters also include a moderate amount of “theory”
in order to provide context.
Includes hundreds of workedout examples.
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. TwoWay Counting.
11. InclusionExclusion 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.
