ENGLISH

First course in abstract algebra: with applications

By Joseph J. Rotman

Book information

Publisher
Prentice Hall
Year
2005
ISBN
9780131862678, 0131862677
LCC
QA162 .R68 2006
Open Library ID
OL3428809M
Language
english
Format
PDF
Filesize
4 MB (4504596 bytes)
Edition
3
Pages
629\629
Topic
Mathematics Algebra
Library
Kolxo3
Time added
2009-07-20 03:45:11

Description

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.

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