ABSTRACT

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

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