Galois Theory (Universitext)

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J***VERKAUFSKATEGORIE*** 0 e This text offers a clear, efficient exposition of Galois Theory with exercises and complete proofs. Topics include: Cardano's formulas; the Fundamental Theorem; Galois' Great Theorem (solvability for radicals of a polynomial is equivalent to solvability of its Galois Group); and computation of Galois group of cubics and quartics. There are appendices on group theory and on ruler-compass constructions. Developed on the basis of a second-semester graduate algebra course, following a course on group theory, this book will provide a concise introduction to Galois Theory suitable for graduate students, either as a text for a course or for study outside the classroom.

Galois Theory (Universitext) Review

From the definition of a conmutative ring to the fundamental theorem to solvability of equations by radicals in 65 pages, 80 theorems and 106 exercises. The exposition, wich follows the now classical tradition of "Artin's" Galois theory, is quite efficient, packing much material in a limited number of pages. The greatest asset of this book is its nice selection of topics, focusing on the fundamental theorem of Galois theory and its application to solbability of equations by radicals, but pausing to make excursions to finite fields or to work out explicitly some iluminating examples. The style is no-nonsense, crisp but nop hurried. The final 40 pages consist of appendices discussing group theory, ruler an compass constructions and old-fashioned Galois theory. This latter appendix deserves special mention, since it is not customary for a textbook of this size and scope to include such a detailed sketch of the historical motivations behind the theory it describes. One can only agree with the author when he wonders how such thoughts occurred to Galois in the late 1820's, and be grateful to him for providing his reader with material for an answer.

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