Overview

The pioneering work of Abel and Galois in the early nineteenth century demonstrated that the long-standing quest for a solution of quintic equations by radicals was fruitless: no formula can be found. The techniques they used were, in the end, more important than the resolution of a somewhat esoteric problem, for they were the genesis of modern abstract algebra.

This book provides a gentle introduction to Galois theory suitable for third- and fourth-year undergraduates and beginning graduates. The approach is unashamedly unhistorical: it uses the language and techniques of abstract algebra to express complex arguments in contemporary terms. Thus the insolubility of the quintic by radicals is linked to the fact that the alternating group of degree 5 is simple - which is assuredly not the way Galois would have expressed the connection.

Topics covered include:

rings and fields

integral domains and polynomials

field extensions and splitting fields

applications to geometry

finite fields

the Galois group

equations

Group theory features in many of the arguments, and is fully explained in the text. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided.

Full Product Details

9781848008854

Table of Contents

Reviews

From the reviews: <p> Howiea (TM)s book ... provides a rigorous and thorough introduction to Galois theory. ... this book would be an excellent choice for anyone with at least some backgound in abstract algebra who seeks an introduction to the study of Galois theory. Summing Up: Highly recommended. Upper-division undergraduates; graduate students. (D. S. Larson, CHOICE, Vol. 43 (10), June, 2006) <p> The book can serve as a useful introduction to the theory of fields and their extensions. The relevant background material on groups and rings is covered. The text is interspersed with many worked examples, as well as more than 100 exercises, for which solutions are provided at the end. (Chandan Singh Dalawat, Mathematical Reviews, Issue 2006 g) <p> The latest addition to Springera (TM)s Undergraduate Mathematics Series is John Howiea (TM)s Fields and Galois Theory. a ] Howie is a fine writer, and the book is very self-contained. a ] I know that many of my students would appreciate Howiea (TM)s approach much more as it is not as overwhelming. This book also has a large number of good exercises, all of which have solutions in the back of the book. All in all, Howie has done a fine job writing a book on field theory a ] . (Darren Glass, MathDL, February, 2006) <p> The author wrote this book to provide the reader with a treatment of classical Galois theory. a ] The book is well written. It contains many examples and over 100 exercises with solutions in the back of the book. Sprinkled throughout the book are interesting commentaries and historical comments. The book is suitable as a textbook for upper level undergraduate or beginning graduate students. (John N. Mordeson, ZentralblattMATH, Vol. 1103 (5), 2007) <p> To write such a book on a widely known but genuinely non-trivial topic is a challenge. a ] J. M. Howie did exactly what it takes. And he did it with such vigour and skill that the outcome is indeed absorbing and astounding. a ] Every paragraph has been scheduled with utmost care and the proofs are crystal clear. a ] the reader will never feel forlorn amidst brilliant theorems, which makes the book such a good read. (J. Lang, Internationale Mathematische Nachrichten, Issue 206, 2007)

Author Information

Tab Content 6

Customer Reviews

Recent Reviews

Countries Available