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First Course in Abstract Algebra, A, 3rd edition

  • Joseph J. Rotman
First Course in Abstract Algebra, A

ISBN-13: 9780131862678

Includes: Paperback

3rd edition

Published byPearson (September 28th 2005) - Copyright © 2006

Free delivery
$119.99 $95.99
Free delivery
$119.99 $95.99

What's included

  • Paperback

    You'll get a bound printed text.

Overview

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 Ideals and Maximal Ideals; Unique Factorization; Noetherian Rings; Varieties; Grobner Bases.

 

MARKET: For all readers interested in abstract algebra.

Table of contents

Chapter 1: Number Theory

Induction

Binomial Coefficients

Greatest Common Divisors

The Fundamental Theorem of Arithmetic

Congruences

Dates and Days

 

Chapter 2: Groups I

Some Set Theory

Permutations

Groups

Subgroups and Lagrange's Theorem

Homomorphisms

Quotient Groups

Group Actions

Counting with Groups

 

Chapter 3: Commutative Rings I

First Properties

Fields

Polynomials

Homomorphisms

Greatest Common Divisors

Unique Factorization

Irreducibility

Quotient Rings and Finite Fields

Officers, Magic, Fertilizer, and Horizons

 

Chapter 4: Linear Algebra

Vector Spaces

Euclidean Constructions

Linear Transformations

Determinants

Codes

Canonical Forms

 

Chapter 5: Fields

Classical Formulas

Insolvability of the General Quintic

Epilog

 

Chapter 6: Groups II

Finite Abelian Groups

The Sylow Theorems

Ornamental Symmetry

 

Chapter 7: Commutative Rings III

Prime Ideals and Maximal Ideals

Unique Factorization

Noetherian Rings

Varieties

Grobner Bases

 

Hints for Selected Exercises

Bibliography

Index

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