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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: 3RD 06
Copyright: 2006
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: 3RD 06
Copyright: 2006
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

Other Editions for First Course in Abstract Algebra

Cover of First Course in Abstract Algebra 2nd edition

First Course in Abstract Algebra - 2nd edition

ISBN13: 978-0130115843
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