Modern Algebra With Applications

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The book covers all the group, ring, and field theory that is usually contained in a standard modern algebra course; the exact sections containing this material are indicated in the Table of Contents. It stops short of the Sylow theorems and Galois theory. These topics could only be touched on in a first course, and the author feels that more time should be spent on them if they are to be appreciated. Table of contents : · Introduction· Boolean Algebras· Groups· Quotient Groups· Symmetry Groups in Three Dimensions· Polya-Burnside Methods of Enumeration· Monoids and Machines· Rings and Fields· Polynomial and Euclidean Rings· Quotient Rings· Field Extensions· Latin Squares· Geometrical Constructions· Error-Correcting CodesBibliography and ReferencesAnswers to Odd-Numbered ExercisesGlossary of SymbolsIndex Market Description : Upper undergraduate and graduate level modern algebra courses About Author : William J. Gilbert is a Professor in the Department of Pure Mathematics at the University of Waterloo, Ontario, Canada.