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Universitext

Abstract Algebra and Famous Impossibilities

Authors: Jones, Arthur, Morris, Sidney A., Pearson, Kenneth R.

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  • ISBN 978-1-4419-8552-1
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About this Textbook

The famous problems of squaring the circle, doubling the cube and trisecting an angle captured the imagination of both professional and amateur mathematicians for over two thousand years. Despite the enormous effort and ingenious attempts by these men and women, the problems would not yield to purely geometrical methods. It was only the development. of abstract algebra in the nineteenth century which enabled mathematicians to arrive at the surprising conclusion that these constructions are not possible. In this book we develop enough abstract algebra to prove that these constructions are impossible. Our approach introduces all the relevant concepts about fields in a way which is more concrete than usual and which avoids the use of quotient structures (and even of the Euclidean algorithm for finding the greatest common divisor of two polynomials). Having the geometrical questions as a specific goal provides motivation for the introduction of the algebraic concepts and we have found that students respond very favourably. We have used this text to teach second-year students at La Trobe University over a period of many years, each time refining the material in the light of student performance.

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $44.99
price for USA in USD (gross)
  • ISBN 978-1-4419-8552-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-0-387-97661-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Abstract Algebra and Famous Impossibilities
Authors
Series Title
Universitext
Copyright
1991
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York, Inc.
eBook ISBN
978-1-4419-8552-1
DOI
10.1007/978-1-4419-8552-1
Softcover ISBN
978-0-387-97661-7
Series ISSN
0172-5939
Edition Number
1
Number of Pages
X, 189
Topics