[Book Cover]

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 0-13-096445-X


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Summary

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.

Features


Introduces and explains specific problem-solving 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 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 problem-solving 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 worked-out examples.


Table of Contents
    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.


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