Galois Theory, Third Edition

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CRC Press, Jul 28, 2003 - Mathematics - 328 pages
Ian Stewart's Galois Theory has been in print for 30 years. Resoundingly popular, it still serves its purpose exceedingly well. Yet 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.
 

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Contents

Chapter 1 Classical Algebra
1
Chapter 2 The Fundamental Theorem of Algebra
18
Chapter 3 Factorization of Polynomials
33
Chapter 4 Field Extensions
51
Chapter 5 Simple Extensions
60
Chapter 6 The Degree of an Extension
69
Chapter 7 RulerandCompass Constructions
78
Chapter 8 The Idea Behind Galois Theory
88
Chapter 15 Solution by Radicals
157
Chapter 16 Abstract Rings and Fields
167
Chapter 17 Abstract Field Extensions
180
Chapter 18 The General Polynomial
193
Chapter 19 Regular Polygons
211
Chapter 20 Finite Fields
231
Chapter 21 Circle Division
237
Chapter 22 Calculating Galois Groups
257

Chapter 9 Normality and Separability
111
Chapter 10 Counting Principles
121
Chapter 11 Field Automorphisms
129
Chapter 12 The Galois Correspondence
135
Chapter 13 A Worked Example
139
Chapter 14 Solubility and Simplicity
147
Chapter 23 Algebraically Closed Fields
268
Chapter 24 Transcendental Numbers
276
References
287
Index
290
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About the author (2003)

Ian Stewart is Professor of Mathematics at Warwick University, Coventry, UK, a Fellow of the Royal Society and a Fellow of the AAAS.

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