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Elements of Algebra

Geometry, Numbers, Equations

  • John Stillwell
Textbook

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xi
  2. John Stillwell
    Pages 1-17
  3. John Stillwell
    Pages 18-37
  4. John Stillwell
    Pages 38-56
  5. John Stillwell
    Pages 57-75
  6. John Stillwell
    Pages 76-88
  7. John Stillwell
    Pages 89-107
  8. John Stillwell
    Pages 108-127
  9. John Stillwell
    Pages 128-145
  10. John Stillwell
    Pages 146-161
  11. Back Matter
    Pages 162-183

About this book

Introduction

Algebra is abstract mathematics - let us make no bones about it - yet it is also applied mathematics in its best and purest form. It is not abstraction for its own sake, but abstraction for the sake of efficiency, power and insight. Algebra emerged from the struggle to solve concrete, physical problems in geometry, and succeeded after 2000 years of failure by other forms of mathematics. It did this by exposing the mathematical structure of geometry, and by providing the tools to analyse it. This is typical of the way algebra is applied; it is the best and purest form of application because it reveals the simplest and most universal mathematical structures. The present book aims to foster a proper appreciation of algebra by showing abstraction at work on concrete problems, the classical problems of construction by straightedge and compass. These problems originated in the time of Euclid, when geometry and number theory were paramount, and were not solved until th the 19 century, with the advent of abstract algebra. As we now know, alge­ bra brings about a unification of geometry, number theory and indeed most branches of mathematics. This is not really surprising when one has a historical understanding of the subject, which I also hope to impart.

Keywords

Galois theory Grad algebra number theory

Authors and affiliations

  • John Stillwell
    • 1
  1. 1.Department of MathematicsMonash UniversityClaytonAustralia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-3976-3
  • Copyright Information Springer-Verlag New York 1994
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-2839-9
  • Online ISBN 978-1-4757-3976-3
  • Series Print ISSN 0172-6056
  • Series Online ISSN 2197-5604
  • Buy this book on publisher's site