Galois Theory

by Ian Stewart

Book Overview

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...

• Format: Paperback
• Language: English
• ISBN: 103210158X
• ISBN13: 9781032101583
• Release Date: September 2022
• Publisher: CRC Press
• Length: 386 Pages
• Weight: 1.19 lbs.
• Dimensions: 0.8" x 6.1" x 9.2"

Customer Reviews

great for independent study undergrad

I learned Galois Theory from this book as an undergrad in an independent study. Stewart hits the insoluability of the quintic and compass-straight edge constructions. There are a lot of steps to getting to the end, and he puts them out there without robbing the reader of the chance to be a part of the proof.

Great Exposition of Galois Theory

This is the book for Galois Theory. I've read most of the others and they go deeper into the formalization of the theory, but this book outlines it in an eminently readable format, with only the basics of Modern Algebra as a prereq. If you were to buy one book on Galois theory, this is the one (Tignol's book is a close second, but focuses more on the historical development of the theory).

Accessible intro to field extensions and Galois theory

This book is aimed at upperlevel undergraduates, presumably math majors. I'd say that's about right; it assumes the reader is familar with the basics of groups, and the proofs strike a good balance between rigor and informality. The book is also accessible to people who have been out of school a while, but are still interested in math. I had to read it more than once to get comfortable with some of the ideas, but Stewart does a good job of providing examples that are understandable given some familiarity with college algebra. I had some heard about the proofs of the impossibility of trisecting the angle, but had little concept of how that was done. This book made it clear. I had also heard that there was no general formala for solving quintic polynomials, but I was surprised to learn that the solutions couldn't even be expressed by radical equations. I was pleased to be able to follow the proofs. After reading / working my way through the book at least twice, I feel comfortable enough to tackle more ambitious works. Michio Kuga's "Galois' Dream" adds many new concepts, and illustrates Galois Theory in a different application. Seeing Galois theory in another context has been helpful in understanding what is necessary to being able to use it.

Best introduction to Galois theory around

At some point many mathematics majors learn that "you can't solve the quintic" and "you can't trisect an angle". The next they hear of it is in an abstract algebra course where the formalism is so overwhelming there is often very little appreciation for how Galois theory addresses these issues.This book fills that gap. It introduces the abstract notions from a historical point of view which often gives a good complement to the usual treatment and makes the abstract definitions make more sense.Some people have noticed a few minor errors in the proofs however, so beware.