© 1990 – Chapman and Hall/CRC
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.
Preface to the First Edition
Preface to the Second Edition
Notes to the Reader
The Life of Galois
Factorization of Polynomials
The Degree of an extension
Ruler and Compasses
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
Calculating Galois Groups
The Fundamental Theorem of Algebra