From the rear cover
The pioneering work of Abel and Galois in the early nineteenth century demonstrated that the long-standing quest for a solution of quintic equations by radicals was fruitless: no formula can be found. The techniques they used were, in the end, more important than the resolution of a somewhat esoteric problem, for they were the genesis of modern abstract algebra.
This book provides a gentle introduction to Galois theory suitable for third- and fourth-year undergraduates and beginning graduates. The approach is unashamedly unhistorical: it uses the language and techniques of abstract algebra to express complex arguments in contemporary terms. Thus the insolubility of the quintic by radicals is linked to the fact that the alternating group of degree 5 is simple - which is assuredly not the way Galois would have expressed the connection.
Topics covered include:
rings and fields
integral domains and polynomials
field extensions and splitting fields
applications to geometry
finite fields
the Galois group
equations
Group theory features in many of the arguments, and is fully explained in the text. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided.
Details
- Title Fields and Galois Theory
- Author John M. Howie
- Binding Paperback
- Edition International ed
- Pages 226
- Volumes 1
- Language ENG
- Publisher Springer, London
- Date 2005-12-19
- Illustrated Yes
- Features Bibliography, Illustrated, Index, Table of Contents
- ISBN 9781852339869 / 1852339861
- Weight 0.87 lbs (0.39 kg)
- Dimensions 9.26 x 7.08 x 0.52 in (23.52 x 17.98 x 1.32 cm)
- Dewey Decimal Code 512.74
Media reviews
Citations
- Choice, 06/01/2006, Page 1860
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