ProofWiki:Books/Ian Stewart/Galois Theory, 3rd Edition

Ian Stewart: Galois Theory, 3rd Edition

Published 2004, Chapman & Hall / CRC.

ISBN 1-58488-393-6

Subject Matter

• Galois Theory

Contents

Preface to the First Edition

Preface to the Second Edition

Preface to the Third Edition

Illustration Acknowledgments

Historical Introduction

1 Classical Algebra

2 The Fundamental Theorem of Algebra

3 Factorization of Polynomials

4 Field Extensions

5 Simple Extensions

6 The Degree of an Extension

7 Ruler-and-Compass Constructions

8 The Idea Behind Galois Theory

9 Normality and Separability

10 Counting Principles

11 Field Automorphisms

12 The Galois Correspondence

13 A Worked Example

14 Solubility and Simplicity

15 Solution by Radicals

16 Abstract Rings and Fields

17 Abstract Field Extensions

18 The General Polynomial

19 Regular Polygons

20 Finite Fields

21 Circle Division

22 Calculating Galois Groups

23 Algebraically Closed Fields

24 Transcendental Numbers

References

Index