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© 1983

Problem-Solving Through Problems

Book

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

  1. 1.Department of MathematicsSt. Olaf CollegeNorthfieldUSA

Bibliographic information

  • Book Title Problem-Solving Through Problems
  • Authors Loren C. Larson
  • Series Title Problem Books in Mathematics
  • 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
  • Hardcover ISBN 978-0-387-90803-8
  • Softcover ISBN 978-0-387-96171-2
  • eBook ISBN 978-1-4612-5498-0
  • Series ISSN 0941-3502
  • Edition Number 1
  • Number of Pages XI, 352
  • Number of Illustrations 11 b/w illustrations, 0 illustrations in colour
  • Topics Analysis
    Mathematics, general
  • Buy this book on publisher's site
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Reviews

From the reviews:

"This is a very welcome addition. The main message of the book is that the only way to learn to solve problems is to solve problems! I found this book very helpful. I am quite sure the book will be in constant use and I have no hesitation in recommending it." (The Mathematical Gazette)