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First Course in Abstract Algebra

First Course in Abstract Algebra - 3rd edition

ISBN13: 978-0131862678

Cover of First Course in Abstract Algebra 3RD 06 (ISBN 978-0131862678)
ISBN13: 978-0131862678
ISBN10: 0131862677
Cover type: Print On Demand
Edition/Copyright: 3RD 06
Publisher: Prentice Hall, Inc.
Published: 2006
International: No
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First Course in Abstract Algebra - 3RD 06 edition

ISBN13: 978-0131862678

Joseph J. Rotman

ISBN13: 978-0131862678
ISBN10: 0131862677
Cover type: Print On Demand
Edition/Copyright: 3RD 06
Publisher: Prentice Hall, Inc.

Published: 2006
International: No
Summary

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.

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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