Customer Reviews

Galois Theory (Chapman and Hall mathematics series)

5 star:		(9)
4 star:		(2)
3 star:		(4)
2 star:		(1)
1 star:		(2)

 

 

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.

I just wanted to point out the following:

* The reviews dated prior to the year 2003 refer to earlier editions of the book. The current (3rd) edition was rewritten extensively.

* A list of corrections is available on the Internet. The review guidelines discourage posting URLs, but an internet search with the keywords "stewart galois theory errata" should find the location. You need a postscript reader to view the errata, but a free one is available online.

A lovely book that takes time to show off the applications of Galois theory. The expanded sections in the second edition really make a beautiful job of giving a historical and mathematically meaningful context to the central concepts.

However the main body of the work is a quite traditional textbook account that explorers the abstract idea of Galois groups over general fields - leaving the reader to inject the meaning and context. Someone, somewhere is capable of making the central concepts of Galois theory as natural and obvious to the reader as it was to Galois. But this isn't the book.

I do like Stewart's book. Very much, indeed. I like the approach of starting in the complex case, with very little abstract algebra assumed. Especially since the subject is so much dependent on its own ideas and concepts, it's good that the reader is not blocked by too many abstractions in the beginning. The book also provides a very intuitive feeling for the ideas, before tackling the actual problems. And this is above all an introductory text, rather than a text to learn the details from.

What takes down the rating to only three stars are the typos. Loads of them. Not that they make the book impossible to read (a good math student should notice most of them at first glance) but they disturb the flow of reading, and they somehow tear down the author's authority, so that the reader gets unsure. And that is very bad, for a book aimed primarily for the not-so-advanced student.

Some reviews mention typos. This book has so many typos that it is certainly not useful as a tool to learn Galois Theory. I had this book for a class in Galois Theory and there is at least one mistake for every page. (some mistakes more than typos in fact)

I cannot be more sure when I say "do not purchase this book" If you do, you will regret it. Sorry I can't type more, but I have a final in my Galois Theory class that I have to study for... the book is NOT helping.

Cheers

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.

Good book, with a solid foundation in Galois Theory. Two major problems: the author introduces the theory over the complex field, when he really should start out in the abtract case. Worse, the book has many, many typos. They are all over the place. Someone really dropped the ball on corrections. So while this is a good intro, you need to constantly be on the look out for errors.

I will be using this book as the textbook of an undergraduate course in field extensions and Galois theory because of its simplicity and clear explanations. There are lots of exercise questions after each chapter which is another good thing. I don't like the dagger-star notation for the Galois correspondence however it is not too bad.

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.

If you buy this book, be sure to find the half a dozen(!) pages of errata. Then reserve a few hours to go through almost every page to correct the many mistakes. Be warned! This book could have been very nice if it weren't for the many mistakes.