Galois Theory, Second Edition

By Ian Stewart

© 1990 – Chapman and Hall/CRC

232 pages

Comp Exam Copy

About the Book

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 text. The author's treatment is rigorous, but motivated by discussion and examples. He further lightens the study with entertaining historical notes - including a detailed description of Évariste Galois' turbulent life. The application of the Galois group to the quintic equation stands as a central theme of the book. Other topics include the problems of trisecting the angle, duplicating the cube, squaring the circle, solving cubic and quartic equations, and the construction of regular polygons

For this edition, the author added an introductory overview, a chapter on the calculation of Galois groups, further clarification of proofs, extra motivating examples, and modified exercises. Photographs from Galois' manuscripts and other illustrations enhance the engaging historical context offered in the first edition.

Written in a lively, highly readable style while sacrificing nothing to mathematical rigor, Galois Theory remains accessible to intermediate undergraduate students and an outstanding introduction to some of the intriguing concepts of abstract algebra.

Table of Contents

Preface to the First Edition

Preface to the Second Edition

Notes to the Reader

Historical Introduction

The Life of Galois

Overview

Background

Factorization of Polynomials

Field Extensions

The Degree of an extension

Ruler and Compasses

Transcendental Numbers

The Idea behind Galois Theory

Normality and Separability

Field Degrees and Group Order

Monomorphisms, Automorphisms, and Normal Closures

The Galois Correspondence

A Specific Example

Soluble and Simple Groups

Solution of Equation by Radicals

The General Polynomial Equation

Finite Fields

Regular Polygons

Calculating Galois Groups

The Fundamental Theorem of Algebra

Selected Solutions

References

Index

Symbol Index

Subject Categories

BISAC Subject Codes/Headings:
MAT002000
MATHEMATICS / Algebra / General
MAT022000
MATHEMATICS / Number Theory