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Galois Theory, by Ian Stewart
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Galois theory is a showpiece of mathematical unification, bringing together several different branches of the subject and creating a power� ful machine for the study of problems of considerable historical and mathematical importance. This book is an attempt to present the theory in such a light, and in a manner suitable for second- and third-year undergraduates. The central theme is the application of the Galois group to the quintic equation. As well as the traditional approach by way of the 'general' polynomial equation I have included a direct approach which demon� strates the insolubility by radicals of a specific quintic polynomial with integer coefficients, which I feel is a more convincing result. The abstract Galois theory is set in the context of arbitrary field extensions, rather than just subfields of the complex numbers; the resulting gain in generality more than compensates for the extra work required. Other topics covered are the problems of duplicating the cube, trisecting the angle, and squaring the circle; the construction of regular polygons; the solution of cubic and quartic equations; the structure of finite fields; and the 'fundamental theorem of algbra'. The last is proved by almost purely algebraic methods, and provides an interesting application of Sylow theory. In order to make the treatment as self-contained as possible, and to bring together all the relevant material in a single volume, I have included several digressions.
- Published on: 2013-10-04
- Released on: 2013-10-04
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x .54" w x 6.10" l, .74 pounds
- Binding: Paperback
- 236 pages
Review
This edition preserves and even extends one of the most popular features of the original edition: the historical introduction and the story of the fatal duel of Evariste Galois. … These historical notes should be of interest to students as well as mathematicians in general. … [A]fter more than 30 years, Ian Stewart's Galois Theory remains a valuable textbook for algebra undergraduate students.
- Zentralblatt MATH, 1049
Most helpful customer reviews
19 of 20 people found the following review helpful.
Different Editions and an Errata
By a reader
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.
12 of 12 people found the following review helpful.
Accessible intro to field extensions and Galois theory
By A Customer
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.
20 of 22 people found the following review helpful.
Textbook plus Popularisation
By T. F. Mabbott
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.
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