Galois Theory / Edition 1

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Overview

Galois theory is one of the jewels of mathematics. Its intrinsic beauty, dramatic history, and deep connections to other areas of mathematics give Galois theory an unequaled richness. David Cox's Galois Theory helps readers understand not only the elegance of the ideas but also where they came from and how they relate to the overall sweep of mathematics. Galois Theory covers classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields. The book also delves into more novel topics, including Abel's theory of Abelian equations, the problem of expressing real roots by real radicals (the casus irreducibilis), and the Galois theory of origami. With intriguing Mathematical and Historical Notes that clarify the ideas and their history in detail, Galois Theory brings one of the most colorful and influential theories in algebra to life for professional algebraists and students alike.
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Editorial Reviews

From the Publisher
“There is barely a better introduction to the subject, in all its theoretical and practical aspects, than the book under review.” (Zentralblatt MATH, 1 December 2012)
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Product Details

Meet the Author

DAVID A. COX, PhD, is Professor in the Department of Mathematics at Amherst College. He has published extensively in his areas of research interest, which include algebraic geometry, number theory, and the history of mathematics. Dr. Cox is consulting editor for Wiley's Pure and Applied Mathematics book series and the author of Primes of the Form x2 + ny2 (Wiley).

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Table of Contents

Ch. 1 Cubic equations 3
Ch. 2 Symmetric polynomials 25
Ch. 3 Roots of polynomials 55
Ch. 4 Extension fields 73
Ch. 5 Normal and separable extensions 101
Ch. 6 The Galois group 125
Ch. 7 The Galois correspondence 147
Ch. 8 Solvability by radicals 191
Ch. 9 Cyclotomic extensions 229
Ch. 10 Geometric constructions 255
Ch. 11 Finite fields 289
Ch. 12 Lagrange, Galois, and Kronecker 313
Ch. 13 Computing Galois groups 357
Ch. 14 Solvable permutation groups 407
Ch. 15 The lemniscate 457
App. A Abstract algebra 509
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