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Galois Theory, Third Edition

By Ian Stewart

Chapman and Hall/CRC – 2003 – 328 pages

Purchasing Options:

  • Add to CartPaperback: $67.95
    978-1-58488-393-7
    July 27th 2003

Description

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.

Reviews

"This edition preserves and even extends one of the most popular features of the original edition: the historical introduction and the story of the fatal duel of Evariste Galois. … These historical notes should be of interest to students as well as mathematicians in general. … [A]fter more than 30 years, Ian Stewart's Galois Theory remains a valuable textbook for algebra undergraduate students."

- Zentralblatt MATH, 1049

"The penultimate chapter is about algebraically closed fields and the last chapter, on transcendental numbers, contains 'what-every-mathematician-should-see-at-least-once', the proof of transcendence of pi. … The book is designed for the second and third year undergraduate courses. I will certainly use it."

- EMS Newsletter

Contents

Historical Introduction

Classical Algebra

The Fundamental Theorem of Algebra

Factorization of Polynomials

Field Extensions

Simple Extensions

The Degree of an Extension

Ruler-and-Compass Constructions

The Idea Behind Galois Theory

Normality and Separability

Counting Principles

Field Automorphisms

The Galois Correspondence

A Worked Example

Solubility and Simplicity

Solution by Radicals

Abstract Rings and Fields

Abstract Field Extensions

The General Polynomial

Regular Polygons

Finite Fields

Circle Division

Calculating Galois Groups

Algebraically Closed Fields

Transcendental Numbers

References

Index

Name: Galois Theory, Third Edition (Paperback)Chapman and Hall/CRC 
Description: By Ian Stewart. 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...
Categories: Algebra, Mathematics & Statistics, Number Theory