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Elements of Algebra

Geometry, Numbers, Equations

  • Textbook
  • © 1994

Overview

Authors:
  1. John Stillwell

    1. Department of Mathematics, Monash University, Clayton, Australia

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

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Algebra and Geometry

    • John Stillwell
    Pages 1-17

  3. The Rational Numbers

    • John Stillwell
    Pages 18-37

  4. Numbers in General

    • John Stillwell
    Pages 38-56

  5. Polynomials

    • John Stillwell
    Pages 57-75

  6. Fields

    • John Stillwell
    Pages 76-88

  7. Isomorphisms

    • John Stillwell
    Pages 89-107

  8. Groups

    • John Stillwell
    Pages 108-127

  9. Galois Theory of Unsolvability

    • John Stillwell
    Pages 128-145

  10. Galois Theory of Solvability

    • John Stillwell
    Pages 146-161

  11. Back Matter

    Pages 162-183
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Keywords

About this book

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.

Reviews

"...The book is written in a very clear and pleasing style. Each of the 9 chapters of the book concludes with a section called "Discussions", which contains very interesting and valuable historical information and comments on the topics presented in the respective chapter. We strongly recommend this nice volume not only to beginners but also to experts."--MATHEMATICAL REVIEWS

Authors and Affiliations

  • Department of Mathematics, Monash University, Clayton, Australia

    John Stillwell

Bibliographic Information

  • Book Title: Elements of Algebra

  • Book Subtitle: Geometry, Numbers, Equations

  • Authors: John Stillwell

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-3976-3

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York 1994

  • Hardcover ISBN: 978-0-387-94290-2Published: 19 August 1994

  • Softcover ISBN: 978-1-4419-2839-9Published: 01 December 2010

  • eBook ISBN: 978-1-4757-3976-3Published: 18 April 2013

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: XII, 184

  • Topics: Algebra, Number Theory, Geometry

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