First Course in Abstract Algebra, A, 3rd edition

Published by Pearson (September 28, 2005) © 2006

  • Joseph J. Rotman
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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.
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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