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Galois Theory

DOI link for Galois Theory

Galois Theory book

Galois Theory

DOI link for Galois Theory

Galois Theory book

ByIan Stewart
Edition 2nd Edition
First Published 1990
eBook Published 15 May 1990
Pub. location New York
Imprint Chapman and Hall/CRC
DOI https://doi.org/10.4324/9780203489307
Pages 232 pages
eBook ISBN 9780429205484
SubjectsMathematics & Statistics
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Stewart, I. (1990). Galois Theory. New York: Chapman and Hall/CRC, https://doi.org/10.4324/9780203489307

Galois theory is a fascinating mixture of classical and modern mathematics, and in fact provided much of the seed from which abstract algebra has grown. It is a showpiece of mathematical unification and of "technology transfer" to a range of modern applications.

Galois Theory, Second Edition is a revision of a well-established and popular te

TABLE OF CONTENTS

chapter 1|17 pages

Classical Algebra

chapter 2|15 pages

The Fundamental Theorem of Algebra

chapter 3|18 pages

Factorization of Polynomials

chapter 4|9 pages

Field Extensions

chapter 5|9 pages

Simple Extensions

chapter 6|9 pages

The Degree of an Extension

chapter 7|10 pages

Ruler-and-Compass Constructions

chapter 8|23 pages

The Idea Behind Galois Theory

chapter 9|10 pages

Normality and Separability

chapter 10|8 pages

Counting Principles

chapter 11|6 pages

Field Automorphisms

chapter 12|4 pages

The Galois Correspondence

chapter 13|8 pages

A Worked Example

chapter 14|10 pages

Solubility and Simplicity

chapter 15|10 pages

Solution by Radicals

chapter 16|13 pages

Abstract Rings and Fields

chapter 17|13 pages

Abstract Field Extensions

chapter 18|18 pages

The General Polynomial

chapter 19|20 pages

Regular Polygons

chapter 20|6 pages

Finite Fields

chapter 21|20 pages

Circle Division

chapter 22|11 pages

Calculating Galois Groups

chapter 23|8 pages

Algebraically Closed Fields

chapter 24|11 pages

Transcendental Numbers

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