First Course In Abstract Algebra, A

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. KEY TOPICS: 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...