Synopses & Reviews
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.
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
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.