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Problem-Solving Through Problems

  • Loren C. Larson

Part of the Problem Books in Mathematics book series (PBM)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Loren C. Larson
    Pages 1-57
  3. Loren C. Larson
    Pages 84-119
  4. Loren C. Larson
    Pages 120-153
  5. Loren C. Larson
    Pages 154-191
  6. Loren C. Larson
    Pages 192-240
  7. Loren C. Larson
    Pages 241-279
  8. Loren C. Larson
    Pages 280-316
  9. Back Matter
    Pages 317-333

About this book

Introduction

The purpose of this book is to isolate and draw attention to the most important problem-solving techniques typically encountered in undergradu­ ate mathematics and to illustrate their use by interesting examples and problems not easily found in other sources. Each section features a single idea, the power and versatility of which is demonstrated in the examples and reinforced in the problems. The book serves as an introduction and guide to the problems literature (e.g., as found in the problems sections of undergraduate mathematics journals) and as an easily accessed reference of essential knowledge for students and teachers of mathematics. The book is both an anthology of problems and a manual of instruction. It contains over 700 problems, over one-third of which are worked in detail. Each problem is chosen for its natural appeal and beauty, but primarily to provide the context for illustrating a given problem-solving method. The aim throughout is to show how a basic set of simple techniques can be applied in diverse ways to solve an enormous variety of problems. Whenever possible, problems within sections are chosen to cut across expected course boundaries and to thereby strengthen the evidence that a single intuition is capable of broad application. Each section concludes with "Additional Examples" that point to other contexts where the technique is appropriate.

Keywords

Arithmetic Cauchy-Schwarz Inequality Derivative Division Problem solving Schwarz inequality calculus fundamental theorem mean value theorem pigeonhole principle

Authors and affiliations

  • Loren C. Larson
    • 1
  1. 1.Department of MathematicsSt. Olaf CollegeNorthfieldUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-5498-0
  • Copyright Information Springer-Verlag New York 1983
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-96171-2
  • Online ISBN 978-1-4612-5498-0
  • Series Print ISSN 0941-3502
  • Buy this book on publisher's site
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