Synopses & Reviews
"The new book on basic Galois theory by Jean-Pierre Escofier is refreshingly different from the many books on the same subject already on the market. The book covers the standard basic material -- symmetric polynomials, field extensions, normal and Galois extensions, the Galois correspondence, cyclotomic extensions, solvable groups, finite fields and separable and non-separable extensions. However, it also contains the following original features: a sketch of the early history of the subject from a very human viewpoint, containing a large number of excerpts from original works and a discussion of the problems of notation, discovery, mathematical habits and disputes of former times, a complete chapter on explicit constructions with ruler and compass, a chapter on the life of Evariste Galois and a chapter on recent developments which attempts to give an idea of what researchers in Galois theory are working on today. The book requires only standard algebra (groups, rings, fields) as background, and is eminently suitable for an undergraduate text on Galois theory. It contains a large number of useful exercises, mostly with their solutions. Because of its exciting and very human approach, it should attract even students who are not mathematics majors to the beautiful subject of Galois theory. "
J.-P. Escofier Galois Theory "Escofier's treatment, at a level suitable for advanced, senior undergraduates or first-year graduate students, centers on finite extensions of number fields, incorporating numerous examples and leaving aside finite fields and the entire concept of separability for the final chapters . . . copious, well-chosen exercises . . . are presented with their solutions . . . The prose is . . . spare and enthusiastic, and the proofs are both instructive and efficient . . . Escofier has written an excellent text, offering a relatively elementary introduction to a beautiful subject in a book sufficiently broad to present a contemporary viewpoint and intuition but sufficiently restrained so as not to overwhelm the reader."--AMERICAN MATHEMATICAL SOCIETY
This book offers the fundamentals of Galois Theory, including a set of copious, well-chosen exercises that form an important part of the presentation. The pace is gentle and incorporates interesting historical material, including aspects on the life of Galois. Computed examples, recent developments, and extensions of results into other related areas round out the presentation.
Table of Contents
Historical Aspects of the Resolution of Algebraic Equations.- Resolution of Quadratic, Cubic and Quartic Equations.- Symmetric Polynomials.- Field Extensions.- Constructions with Straightedge and Compass.- K-Homomorphism.- Normal Extensions.- Galois Groups.- Roots of Unity.- Cyclic Extensions.- Solvable Groups.- Solvability of Equations by Radicals.- The Life of Evariste Galois.- Finite Fields.- Separable Extension.- Recent Developments.- Bibliography.- Index.