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Problem-Solving Through Problems

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  • © 1983
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Overview

Authors:
  1. Loren C. Larson

    1. Department of Mathematics, St. Olaf College, Northfield, USA

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

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xi
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  2. Heuristics

    • Loren C. Larson
    Pages 1-57
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  3. Two Important Principles: Induction and Pigeonhole

    • Loren C. Larson
    Pages 58-83
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  4. Arithmetic

    • Loren C. Larson
    Pages 84-119
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  5. Algebra

    • Loren C. Larson
    Pages 120-153
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  6. Summation of Series

    • Loren C. Larson
    Pages 154-191
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  7. Intermediate Real Analysis

    • Loren C. Larson
    Pages 192-240
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  8. Inequalities

    • Loren C. Larson
    Pages 241-279
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  9. Geometry

    • Loren C. Larson
    Pages 280-316
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  10. Back Matter

    Pages 317-333
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Keywords

About this book

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.

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)

Authors and Affiliations

  • Department of Mathematics, St. Olaf College, Northfield, USA

    Loren C. Larson

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

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1983

  • Softcover ISBN: 978-0-387-96171-2Published: 17 July 1985

  • eBook ISBN: 978-1-4612-5498-0Published: 06 December 2012

  • Series ISSN: 0941-3502

  • Series E-ISSN: 2197-8506

  • Edition Number: 1

  • Number of Pages: XI, 352

  • Number of Illustrations: 11 b/w illustrations

  • Topics: Analysis, Mathematics, general

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