Galois Theory

by Joseph J. Rotman

A clear, efficient exposition of this topic with complete proofs and exercises, covering cubic and quartic formulas; fundamental theory of Galois theory; insolvability of the quintic; Galoiss Great Theorem; and computation of Galois groups of cubics and quartics. Suitable for first-year graduate students, either as a text for a course or for study outside the classroom, this new edition has been completely rewritten in an attempt to make proofs clearer by providing more details. It now begins with a short section on symmetry groups of polygons in the plane, for there is an analogy between polygons and their symmetry groups and polynomials and their Galois groups - an analogy which serves to help readers organise the various field theoretic definitions and constructions. The text is rounded off by appendices on group theory, ruler-compass constructions, and the early history of Galois Theory. The exposition has been redesigned so that the discussion of solvability by radicals now appears later and several new theorems not found in the first edition are included.

Genres: Mathematics, Science, Textbooks, Algebra

157 pages, Paperback

First published January 1, 1994

Reviews

[Michael]

This is fine, for a terse and unmotivated exposition of Galois Theory. But then, what's the point? If you like your Galois Theory terse and unmotivated, buy Grove's Algebra for half the price of this book, and have at Chapter 3, plus get a complete graduate course in algebra with the deal. I think the only thing you will be missing would be the cubic and quartic formulas. Just grab those online somewhere; you can actually find some really cool derivations of them.

[curtis · Rating 4 out of 5]

not the best introduction to the subject, but there are some particularly cute things i like about it, including the opening chapter and the epilogue on historical galois theory

[Robert · Rating 4 out of 5]

I am actually not sure if this is the best introduction to this topic.

It's probably a little bit too light if you're looking to go more in depth, but it's ok as an introduction.

[César Carranza · Rating 5 out of 5]

Una explicación muy clara, si es que es eso posible, de la teoría, bastante útil en la carrera))