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** ** 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.**

### Details & Specs

The following ISBNs are associated with this title:

ISBN - 10:0131862677

ISBN - 13:9780131862678

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### Customer Reviews of A First Course in Abstract Algebra

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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