AMS Chelsea Publishing 1971; 248 pp; hardcover Volume: 268 Reprint/Revision History: first AMS printing 1998 ISBN10: 0821813757 ISBN13: 9780821813751 List Price: US$38 Member Price: US$34.20 Order Code: CHEL/268.H
Temporarily out of stock. Expected date of availability is October 12, 2015.
 This book is strongly recommended to beginning graduate students who already have some background in abstract algebra, including elementary properties of groups, rings, and fields. The exposition and proofs are intended to present Galois theory as simply as possible. The large number of partially or fully solved examples is a special feature of the book. Reviews "This book is strongly recommended to beginning graduate students who already have some background in abstract algebra. The exposition and proofs are intended to present Galois theory in as simple a manner as possible ... The large number of partially or fully solved examples is its special feature."  Mathematical Reviews "Excellent for undergraduate independent study since it demands reader participation."  American Mathematical Monthly Table of Contents  Prerequisites: 1.1 Group theory; 1.2 Permutations and permutation groups; 1.3 Fields; 1.4 Rings and polynomials; 1.5 Some elementary theory of equations; 1.6 Vector spaces
 Fields: 2.1 Degree of an algebraic extension; 2.2 Isomorphisms of fields; 2.3 Automorphisms of fields; 2.4 Fixed fields
 Fundamental theorem: 3.1 Splitting fields; 3.2 Normal extensions and groups of automorphisms; 3.3 Conjugate fields and elements; 3.4 Fundamental theorem
 Applications: 4.1 Solvability of equations; 4.2 Solvable equations have solvable groups; 4.3 General equation of degree \(n\); 4.4 Roots of unity and cyclic equations; 4.5 How to solve a solvable equation; 4.6 Rulerandcompass constructions; 4.7 Lagrange's theorem; 4.8 Resolvent of a polynomial; 4.9 Calculation of the Galois group; 4.10 Matrix solutions of equations; 4.11 Finite fields; 4.12 More applications
 Bibliography
 Index
