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Edition: 2nd 1998 (Revised)
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This text offers a clear, efficient exposition of Galois Theory with complete proofs and exercises. Topics include: cubic and quartic formulas; Fundamental Theory of Galois Theory; insolvability of the quintic; Galois's Great Theorem (solvability by radicals of a polynomial is equivalent to solvability of its Galois Group); and computation of Galois groups of cubics and quartics. There are appendices on group theory, ruler-compass constructions, and the early history of Galois Theory. This book provides a concise introduction to Galois Theory 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. The book 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; this analogy can serve as a guide by helping readers organize the various field theoretic definitions and constructions. The exposition has been reorganized so that the discussion of solvability by radicals now appears later and several new theorems not found in the first edition are included (e.g., Casus Irreducibilis).
List price: $59.99
Copyright year: 1998
Publication date: 7/27/2001
Size: 6.50" wide x 9.50" long x 0.75" tall
|Preface to the Second Edition|
|Preface to the First Edition|
|To the Reader|
|Domains and Fields|
|Homomorphisms and Ideals|
|Polynomial Rings over Fields|
|Prime Ideals and Maximal Ideals|
|The Galois Group|
|Roots of Unity|
|Solvability by Radicals|
|Independence of Characters|
|The Fundamental Theorem of Galois Theory|
|Galois's Great Theorem|
|Galois Groups of Quadratics, Cubics, and Quartics|
|Group Theory Dictionary|
|Group Theory Used in the Text|
|Old-fashioned Galois Theory|