ISBN: 9780131862678 | 0131862677

Edition: 3rdFormat: Paperback

Publisher: Pearson

Pub. Date: 9/28/2005

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This text introduces readers to the algebraic concepts of group and rings, providing a comprehensive discussion of theory as well as a significant number of applications for each. Number Theory:Induction; Binomial Coefficients; Greatest Common Divisors; The Fundamental Theorem of Arithmetic Congruences; Dates and Days.Groups I:Some Set Theory; Permutations; Groups; Subgroups and Lagrange's Theorem; Homomorphisms; Quotient Groups; Group Actions; Counting with Groups.Commutative Rings I:First Properties; Fields; Polynomials; Homomorphisms; Greatest Common Divisors; Unique Factorization; Irreducibility; Quotient Rings and Finite Fields; Officers, Magic, Fertilizer, and Horizons.Linear Algebra:Vector Spaces; Euclidean Constructions; Linear Transformations; Determinants; Codes; Canonical Forms.Fields:Classical Formulas; Insolvability of the General Quintic; Epilog.Groups II:Finite Abelian Groups; The Sylow Theorems; Ornamental Symmetry.Commutative Rings III:Prime Ideals and Maximal Ideals; Unique Factorization; Noetherian Rings; Varieties; Grobner Bases. For all readers interested in abstract algebra.