ABSTRACT

Since 1973, Galois theory has been educating undergraduate students on Galois groups and classical Galois theory. In Galois Theory, Fifth Edition, mathematician and popular science author Ian Stewart updates this well-established textbook for today’s algebra students.

New to the Fifth Edition

  • Reorganised and revised Chapters 7 and 13
  • New exercises and examples
  • Expanded, updated references
  • Further historical material on figures besides Galois: Omar Khayyam, Vandermonde, Ruffini, and Abel
  • A new final chapter discussing other directions in which Galois theory has developed: the inverse Galois problem, differential Galois theory, and a (very) brief introduction to p-adic Galois representations

This bestseller continues to deliver a rigorous, yet engaging, treatment of the subject while keeping pace with current educational requirements. More than 200 exercises and a wealth of historical notes augment the proofs, formulas, and theorems.

chapter Chapter 1|18 pages

Classical Algebra

chapter Chapter 2|12 pages

The Fundamental Theorem of Algebra

chapter Chapter 3|18 pages

Factorisation of Polynomials

chapter Chapter 4|10 pages

Field Extensions

chapter Chapter 5|10 pages

Simple Extensions

chapter Chapter 6|10 pages

The Degree of an Extension

chapter Chapter 7|22 pages

Ruler-and-Compass Constructions

chapter Chapter 8|22 pages

The Idea behind Galois Theory

chapter Chapter 9|8 pages

Normality and Separability

chapter Chapter 10|8 pages

Counting Principles

chapter Chapter 11|6 pages

Field Automorphisms

chapter Chapter 12|4 pages

The Galois Correspondence

chapter Chapter 13|12 pages

Worked Examples

chapter Chapter 14|10 pages

Solubility and Simplicity

chapter Chapter 15|10 pages

Solution by Radicals

chapter Chapter 16|14 pages

Abstract Rings and Fields

chapter Chapter 17|20 pages

Abstract Field Extensions and Galois Groups

chapter Chapter 18|18 pages

The General Polynomial Equation

chapter Chapter 19|8 pages

Finite Fields

chapter Chapter 20|16 pages

Regular Polygons

chapter Chapter 21|26 pages

Circle Division

chapter Chapter 22|10 pages

Calculating Galois Groups

chapter Chapter 23|8 pages

Algebraically Closed Fields

chapter Chapter 24|10 pages

Transcendental Numbers

chapter Chapter 25|16 pages

What Did Galois Do or Know?

chapter Chapter 26|10 pages

Further Directions