ABSTRACT

Since 1973, Galois Theory has been educating undergraduate students on Galois groups and classical Galois theory. In Galois Theory, Fourth Edition, mathematician and popular science author Ian Stewart updates this well-established textbook for today's algebra students. New to the Fourth EditionThe replacement of the topological proof of the fundame

chapter |16 pages

Historical Introduction

chapter 1|18 pages

Classical Algebra

chapter 2|12 pages

The Fundamental Theorem of Algebra

chapter 3|16 pages

Factorisation of Polynomials

chapter 4|8 pages

Field Extensions

chapter 5|8 pages

Simple Extensions

chapter 6|8 pages

The Degree of an Extension

chapter 7|20 pages

Ruler-and-Compass Constructions

chapter 8|22 pages

The Idea Behind Galois Theory

chapter 9|8 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|6 pages

A Worked Example

chapter 14|10 pages

Solubility and Simplicity

chapter 15|10 pages

Solution by Radicals

chapter 16|12 pages

Abstract Rings and Fields

chapter 17|12 pages

Abstract Field Extensions

chapter 18|16 pages

The General Polynomial Equation

chapter 19|6 pages

Finite Fields

chapter 20|16 pages

Regular Polygons

chapter 21|24 pages

Circle Division

chapter 22|10 pages

Calculating Galois Groups

chapter 23|8 pages

Algebraically Closed Fields

chapter 24|10 pages

Transcendental Numbers

chapter 25|14 pages

What Did Galois Do or Know?