Galois Theory

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CRC Press, Mar 6, 2015 - Mathematics - 344 pages
Since 1973, Galois Theory has been educating undergraduate students on Galois groups and classical Galois theory. In Galois Theory, Fourth Edition, mathematician and popular science author Ian Stewart updates this well-established textbook for today's algebra students. New to the Fourth EditionThe replacement of the topological proof of the fundame
 

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Contents

Historical Introduction
1
1 Classical Algebra
17
2 The Fundamental Theorem of Algebra
35
3 Factorisation of Polynomials
47
4 Field Extensions
63
5 Simple Extensions
71
6 The Degree of an Extension
79
7 RulerandCompass Constructions
87
14 Solubility and Simplicity
161
15 Solution by Radicals
171
16 Abstract Rings and Fields
181
17 Abstract Field Extensions
193
18 The General Polynomial Equation
205
19 Finite Fields
221
20 Regular Polygons
227
21 Circle Division
243

8 The Idea Behind Galois Theory
107
9 Normality and Separability
129
10 Counting Principles
137
11 Field Automorphisms
145
12 The Galois Correspondence
151
13 A Worked Example
155
22 Calculating Galois Groups
267
23 Algebraically Closed Fields
277
24 Transcendental Numbers
285
25 What Did Galois Do or Know?
295
References
309
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About the author (2015)

Ian Stewart is an emeritus professor of mathematics at the University of Warwick and a fellow of the Royal Society. Dr. Stewart has been a recipient of many honors, including the Royal Society's Faraday Medal, the IMA Gold Medal, the AAAS Public Understanding of Science and Technology Award, and the LMS/IMA Zeeman Medal. He has published more than 180 scientific papers and numerous books, including several bestsellers co-authored with Terry Pratchett and Jack Cohen that combine fantasy with nonfiction.

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