First Course in Abstract Algebra, A

ISBN: 0131862677

Author: Rotman, Joseph

Condition: New

This text introduces students to the algebraic concepts of group and rings, providing a comprehensive discussion of theory as well as a significant number of applications for each.

• Induction | Binomial Coefficients | Greatest Common Divisors | The Fundamental Theorem of Arithmetic | Congruences | Dates and Days | Some Set Theory | Permutations | Groups | Subgroups and Lagrange's Theorem | Homomorphisms | Quotient Groups | Group Actions | Counting with Groups | First Properties | Fields | Polynomials | Homomorphisms | Greatest Common Divisors | Unique Factorization | Irreducibility | Quotient Rings and Finite Fields | Officers, Magic, Fertilizer, and Horizons | Vector Spaces | Euclidean Constructions | Linear Transformations | Determinants | Codes | Canonical Forms | Classical Formulas | Insolvability of the General Quintic | Epilog | Finite Abelian Groups | The Sylow Theorems | Ornamental Symmetry | Prime Ideals and Maximal Ideals | Unique Factorization | Noetherian Rings | Varieties | Grobner Bases | Hints for Selected Exercises | Bibliography | Index