Galois Theory / Edition 3

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Overview

Ian Stewart's Galois Theory has been in print for 30 years. Resoundingly popular, it still serves its purpose exceedingly well. But mathematics education has changed considerably since 1973, when theory took precedence over examples, and the time has come to bring this presentation in line with more modern approaches. To this end, the story now begins with polynomials over the complex numbers, and the central quest is to understand when such polynomials have solutions that can be expressed by radicals. Reorganization of the material places the concrete before the abstract, thus motivating the general theory, but the substance of the book remains the same.

The third edition preserves and extends the most popular feature of the previous editions -- a wealth of historical storytelling, with the tale of Evariste Galois and his fatal duel as its centerpiece. To provide further motivation, Stewart has also added some of the more technical history. Several newer proofs replace some that were rather obscure or indirect, and some classical topics have been revived. Galois theory is a showpiece of mathematical unification and of "technology transfer" to a range of modern applications. While sacrificing nothing to mathematical rigor, there is simply no more engaging, no more accessible, no more outstanding introduction to the intriguing concepts of abstract algebra than Galois Theory.

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Editorial Reviews

Booknews
Beautifully produced text for advanced undergraduates, in which a master expositor takes obvious delight in introducing young mathematicians to the classical aspects of one of the glories of their field. Expanded revision of the edition of 1973. Keeps in nice focus the motivating historical roots of the theory, and treats explicitly its relation to some classic ruler-and-compass construction problems. Nineteen brief chapters, many exercises, with selected solutions and references. A slim treasure. Paper edition unseen, $22.50. NW Annotation c. Book News, Inc., Portland, OR booknews.com
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Product Details

  • ISBN-13: 9781584883937
  • Publisher: Taylor & Francis
  • Publication date: 8/28/2003
  • Series: Chapman Hall/CRC Mathematics Series , #24
  • Edition description: REV
  • Edition number: 3
  • Pages: 328
  • Sales rank: 1,449,668
  • Product dimensions: 9.20 (w) x 6.00 (h) x 0.80 (d)

Table of Contents

Preface to the First Edition
Preface to the Second Edition
Preface to the Third Edition
Illustration Acknowledgments
Historical Introduction
1 Classical Algebra 1
2 The Fundamental Theorem of Algebra 17
3 Factorization of Polynomials 31
4 Field Extensions 49
5 Simple Extensions 57
6 The Degree of an Extension 67
7 Ruler-and-Compass Constructions 75
8 The Idea Behind Galois Theory 85
9 Normality and Separability 107
10 Counting Principles 117
11 Field Automorphisms 125
12 The Galois Correspondence 133
13 A Worked Example 137
14 Solubility and Simplicity 143
15 Solution by Radicals 153
16 Abstract Rings and Fields 163
17 Abstract Field Extensions 177
18 The General Polynomial 191
19 Regular Polygons 209
20 Finite Fields 227
21 Circle Division 233
22 Calculating Galois Groups 251
23 Algebraically Closed Fields 261
24 Transcendental Numbers 269
References 279
Index 283
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