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Abstract Algebra and Famous Impossibilities 1991. Corr. 2nd Edition
Contributor(s): Jones, Arthur (Author), Morris, Sidney A. (Author), Pearson, Kenneth R. (Author)

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 ISBN: 0387976612     ISBN-13: 9780387976617
Publisher: Springer
OUR PRICE: $66.49  

Binding Type: Paperback - See All Available Formats & Editions
Published: September 1991
* Out of Print *

Annotation: The famous problems of squaring the circle, doubling the cube, and trisecting the angle have captured the imagination of both professional and amateur mathematician for over two thousand years. These problems, however, have not yielded 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. This text aims to develop the abstract algebra.

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Additional Information
BISAC Categories:
- Mathematics | Number Theory
- Mathematics | Algebra - General
Dewey: 512.02
LCCN: 91024830
Series: Applied Mathematical Sciences (Springer)
Physical Information: 0.43" H x 6.14" W x 9.21" L (0.64 lbs) 189 pages
Features: Bibliography, Illustrated, Index
 
Descriptions, Reviews, Etc.
Publisher Description:
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.
 
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