Galois Theory / Edition 1

by L. Schneps, Jean-Pierre Escofier

Overview

The new book on basic Galois theory by Jean-Pierre Escofier is refresh ingly different from the many books on the same subject already on the market. The book covers the standard basic material: symmetric polyno mials, field extensions, normal and Galois extensions, the Galois corr espondence, 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 subj ect from a very human viewpoint, containing a large number of excerpts from original works and a discussion of the problems of notation, dis covery, mathematical habits and disputes of former times, a complete c hapter 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 wor king on today.

Product Details

ISBN-13:	9780387987651
Publisher:	Springer New York
Publication date:	12/21/2000
Series:	Graduate Texts in Mathematics Series , #204
Edition description:	2001
Pages:	283
Product dimensions:	0.75(w) x 6.14(h) x 9.21(d)

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.

Editorial Reviews

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

From the Publisher