Contemporary Abstract Algebra

ISBN-10: 0618122141

ISBN-13: 9780618122141

Edition: 5th 2002

List price: $89.56
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Description: Joseph Gallian is a well-known active researcher and award-winning teacher. His Contemporary Abstract Algebra, 6/e, includes challenging topics in abstract algebra as well as numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings that give the subject a current feel and makes the content interesting and relevant for students.

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Book details

List price: $89.56
Edition: 5th
Copyright year: 2002
Publisher: CENGAGE Learning
Publication date: 7/30/2001
Binding: Paperback
Pages: 576
Size: 6.75" wide x 9.50" long x 1.00" tall
Weight: 2.244
Language: English

Integers and Equivalence Relations
Preliminaries Properties of Integers Modular Arithmetic Mathematical Induction Equivalence Relations Functions (Mappings) Computer Exercises
Introduction to Groups Symmetries of a Square The Dihedral Groups Biography of
Groups Definition and Examples of Groups Elementary Properties of Groups Historical Note Computer Exercises
Finite Groups; Subgroups Terminology and Notation Subgroup Tests Examples of Subgroups Computer Exercises
Cyclic Groups Properties of Cyclic Groups Classification of Subgroups of Cyclic Groups Computer Exercises Biography of
Supplementary Exercises for Chapters 1–4
Permutation Groups Definition and Notation Cycle Notation Properties of Permutations A Check-Digit Scheme Based on D5 Computer Exercises Biography of
Isomorphisms Motivation Definition and Examples Cayley's Theorem Properties of Isomorphisms Automorphisms Biography of
Cosets and Lagrange's Theorem Properties of Cosets Lagrange's Theorem and Consequences An Application of Cosets to Permutation Groups The Rotation Group of a Cube and a Soccer Ball Biography of
External Direct Products Definition and Examples Properties of External Direct Products The Group of Units Modulo n as an External Direct Product Applications Computer Exercises Biography of
Supplementary Exercises for Chapters 5–8
Normal Subgroups and Factor Groups Normal Subgroups Factor Groups Applications of Factor Groups Internal Direct Products Biography of
Group Homomorphisms Definition and Examples Properties of Homomorphisms
The First Isomorphism Theorem Biography Camille Jordan
Fundamental Theorem of Finite Abelian Groups
The Fundamental Theorem Isomorphism Classes of Abelian Groups Proof of the Fundamental
Theorem Computer Exercises Supplementary Exercises for Chapters 9–11
Introduction to Rings Motivation and Definition Examples of Rings Properties of Rings Subrings Computer Exercises Biography of
Integral Domains Definition and Examples Fields Characteristic of a Ring Computer Exercises Biography of
Ideals and Factor Rings Ideals Factor Rings Prime Ideals and Maximal Ideals Biography of Richard Dedekind Biography of
Supplementary Exercises for Chapters 12–14
Ring Homomorphisms Definition and Examples Properties of Ring Homomorphisms The Field of Quotients
Polynomial Rings Notation and Terminology The Division Algorithm and Consequences Biography of
Factorization of Polynomials Reducibility Tests Irreducibility Tests Unique Factorization in Z[x] Weird Dice: An Application of Unique Factorization Computer Exercises
Divisibility in Integral Domains Irreducibles, Primes Historical Discussion of Fermat's Last Theorem Unique Factorization Domains Euclidean Domains Biography of Sophie Germain Biography of
Supplementary Exercises for Chapters 15–18
Vector Spaces Definition and Examples Subspaces Linear Independence Biography of Emil Artin Biography of
Extension Fields The Fundamental Theorem of Field Theory Splitting Fields Zeros of an Irreducible Polynomial Biography of
Algebraic Extensions Characterization of Extensions Finite Extensions Properties of Algebraic Extensions Biography of
Finite Fields Classification of Finite Fields Structure of Finite Fields Subfields of a Finite Field Biography of
Geometric Constructions Historical Discussion of Geometric
Constructions Constructible Numbers Angle-Trisectors and Circle-Squarers
Supplementary Exercises for Chapters 19–23
Special Topics
Sylow Theorems Conjugacy Classes The Class Equation The Probability That Two Elements Commute The Sylow Theorems Applications of Sylow Theorems Biography of
Finite Simple Groups Historical Background Nonsimplicity Tests The Simplicity of A5 The Fields Medal The Cole Prize Computer Exercises Biography of Michael Aschbacher Biography of Daniel Gorenstein Biography of
Generators and Relations Motivation Definitions and Notation Free Group Generators and Relations Classification of Groups of Order up to 15 Characterization of Dihedral Groups Realizing the Dihedral Groups with Mirrors Biography of
Symmetry Groups Isometries Classification of Finite Plane Symmetry Groups Classification of Finite Group Rotations in R3
Frieze Groups and Crystallographic Groups The Frieze Groups The Crystallographic Groups Identification of Plane Periodic Patterns Biography of M.C. Escher Biography of George Poacute;lya Biography of
Symmetry and Counting Motivation Burnside's Theorem Applications Group Action Biography of
Cayley Digraphs of Groups Motivation The Cayley Digraph of a Group Hamiltonian Circuits and Paths Some Applications Biography William Rowan Hamilton Biography of
Introduction to Algebraic Coding Theory Motivation Linear Codes Parity-Check Matrix Decoding Coset Decoding Historical Note: Reed-Solomon Codes Biography of Richard W. Hamming Biography Jessie MacWilliams Biography of
An Introduction to Galois Theory Fundamental Theorem of Galois Theory Solvability of Polynomials by Radicals Insolvability of a Quintic Biography
Cyclotomic Extensions Motivation Cyclotomic Polynomials
The Constructible Regular n-gons Computer Exercise Biography Carl
Friedrich Gauss Supplementary Exercises Chapters 24–33
Table of Contents provided by Publisher. All Rights Reserved.
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