Contemporary Abstract Algebra

ISBN-10: 0547165099
ISBN-13: 9780547165097
Edition: 7th 2010
Authors: Joseph Gallian
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Description: The seventh edition of Contemporary Abstract Algebra, by Joseph A. Gallian, Provides a solid introduction to the traditional topics in abstract algebra while conveying that it is a contemporary subject used daily by working mathematicians, computer  More...

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Book details

List price: $223.95
Edition: 7th
Copyright year: 2010
Publisher: Brooks/Cole
Publication date: 1/8/2009
Binding: Hardcover
Pages: 656
Size: 6.75" wide x 9.50" long x 1.00" tall
Weight: 2.442
Language: English

The seventh edition of Contemporary Abstract Algebra, by Joseph A. Gallian, Provides a solid introduction to the traditional topics in abstract algebra while conveying that it is a contemporary subject used daily by working mathematicians, computer scientist, and chemists. The text includes numerous theoretical and computational exercises, figures, and tables to teach you how to work out problems, as well as to write proofs. Additionally, the author provides biographies, poems, song Lyrics, historical notes, and much more to make reading the text an interesting, accessible and enjoyable experience. Contemporary Abstract Algebra will keep you engaged and gives you a great introduction to an important subject.

Preface
Integers and Equivalence Relations
Preliminaries
Properties of Integers
Madular Arithmetic
Mathematical Induction
Equivalence Relations
Functions (Mappings)
Exercises
Computer Exercises
Groups
Introduction to Groups
Symmetries of a Square
The Dihedral Groups
Exercises
Biography of Niels Abel
Groups
Definition and Examples of Groupso40
Elementary Properties of Groups
Historical Note
Exercises
Computer Exercises
Finite Groups; Subgroups
Terminology and Notation
Subgroup Tests
Examples of Subgroups
Exercises
Computer Exercises
Cyclic Groups
Properties of Cycle Groups
Classification of Subgroups of Cyclic Groups
Exercises
Computer Exercises
Biography of J. J. Sylvester
Supplementary Exercises for Chapters1-4
Permutation Groups
Difinition and Notation
Cycle Nation
Properties of Permutations
A Check Digit Scheme Based on D5
Exercises
Computer Exercises
Biography of Augustin Cauchy
Isomorphisms
Motivation
Dfinition and Examples
Cayley�s Theorem
Properties of Isomorphisms
Automorphisms
Exercises
Computer Exercise
Biography of Arthur Cayley
Cosets and Lagrange�s Theorem
Properties of Cosets
Lagrange�s Theorem and Consequences
An Application of Cosets of Permutation Groups
The Rotation Group of a Cube and a Soccer Ball
Exercises
Computer Exercise
Biography of Joseph Lagrange
External Direct Products
Definition and Examples
Properties of External Direct Products
The Group of Units Modulo n as an External Direct Products
Applications
Exercises
Computer Exercises
Biorgaphy of Leonard Adleman
Supplementary Exercises for Chapters 5-8
Normal Subgroups and Factor Groups
Normal Subgroups
Factor Groups
Applicatons of Factor Groups
Internal Direct Products
Exercises
Biography of Evariste Galois
Group Homomorphisms
Difinition and Examples
Properties Of Homomorphisms
The First Isomorphism Theorem
Exercises
Computer Exercise
Biography of Camille Jordan
Fundamental Theorem of Finite Abelian Groups
The Fundamental Theorem
The Isomorphism Classes of Abelian Groups
Proof of the Fundamental Theorem
Exercises
Computer Exercises
Supplementary Exercises for Chapter 9-11
Rings
Introduction to Rings
Motivation and Definition
Examples of Rings
Properties of Rings
Subrings
Exercises
Computer Exercises
Biography of I. N. Herstein
Integral Domains
Definition and Examples
Fields
Characteristic of a Ring
Exercises
Computer Exercises
Biography of Nathan Jacobson
Ideals and Factor Rings
Ideals
Factor Rings
Prime Ideals and Maximal Ideals
Exercises
Computer Exercises
Biography of Richard Dedekind
Biography of Emmy Noether
Supplementary Exercises for Chapters 12-14
Ring Homomorphisms
Definition and Example
Properties of Ring Homomorphisms
The Field of Quotients
Exercises
Polynomial Rings
Notation and Terminology
The Division Algorithm and Consequences
Exercises
Biography of Sounders Mac Lane
Factorization of Polynomials
Reducibility Tests
Irreducibility Tests
Unique Factorization in Z[x]
Weird Dice: An Application of Unique Factorization
Exercises
Computer Exercises
Biography of Serge Lang
Divisibility in Integral Domains
Irreducibles, Primes
Historical Discussion of Fermat�s Last Theorem
Unique Factorization Domains
Euclidean Domains
Exercises
Comupter Exercise
Biography of Sophie Germain
Biography of Andrew Wiles
Supplementary Exercises for Chapters 15-18
Fields
Vector Spaces
Definition and Examples
Subspaces
Linear Independence
Exercises
Biography of Emil Artin
Biography of Olga Taussky-Todd
Extension Fields
The Fundamental Theorem of Field theory
Splitting Fields
Zeros of an Irreducible Polynomial
Exercises
Biography of Leopold Kronecker
Algebraci Extensions
Characterization of Extensions
Finite Extensions
Properties of Algebraic Extensions
Exercises
Biography of Irving Kaplansky
Finite Fields
Classification of Finite Fields
Struction of Finite Fields
Subfields of a Finite Field
Exercises
Computer Exercises
Biography of L. E. Dickson
Geometric Constructions
Historical Discussion of Geometric Constructions
Constructible Numbers
Angle-Trisectors and Circle-Squarers
Exercises
Supplementary Exercises for Chapters
Special Topics
Sylow Theorems
Conjugacy Classes
The Class Equation
The Probability That Two Elements Commute
The Sylow Theorems
Applications of Sylow Theorems
Exercises
Computer Exercise
Biography of Ludwig Sylow
Finite Simple Groups
Historical Background
Nonsimplicity Tests
The Simplicity of A5
The Fields Medal
The Cole Prize
Execises
Computer Exercises
Biography of Michael Aschbacher
Biography of Daniel Gorenstein
Biography of John Thompson
Generators and Relations
Motivation
Definitions and Notation
Free Group
Generators and Relations
Classification of Groups of Order Up to 15
Characterization of Dihedral Group
Realizing the Dihedral Groups with Mirrors
Exercises
Biography of Marshall Hall, Jr.
Symmetry Groups
Isometries
Classification of Finite Plane Symmetry Group
Classification of Finite Groups of Rotations in R3
Exercises
Frieze Groups and Crystallographic Groups
The Frieze Groups
The Crystallographic Groups
Identification of Plane Periodic Patterns
Exercises
Biography of M. C. Escher
Biography of George Polya
Biography of John H. Conway
Symmetry and Counting
Motivation
Burnside�s Theorem
Applications
Group Action
Exercises
Biography of William Burnside
Cayley Digraphs of Groups
Motivaton
The Cayley Digraph of a Group
Hamiltonian Circuits and Paths
Some Apllications
Exercises
Biography of William Rowan Hamilton
Biography of Paul Erdos
Indtoduction to Algebraic Coding Theory
Motivation
Liner Codes
Parity-Check Matrix Decoding
Coset Decoding
Hestorical Note: The Ubiquitous Reed-Solomon Codes
Exercises
Biography of Richard W. Hamming
Biography of Jessie Mac Williams
Biography of Vera Pless
An Introduction to Galois Theory
Fundamental Theorem of Galois Theory
Solvability of Polynomials by Radicals
Insolvability of a Quintic
Exercises
Biography of Philip Hall
Cyclotomic Extensions
Motivation
Cyclotomic Polynomials
The Constructible Regular n-Gons
Exercises
Computer Exercis
Biography of Carl Friedrich Gauss
Biography of Manjul Bhargava
Supplementary Exercises for Chapters 24-33
Selected Answers
Text Credits
Photo Credits
Index of Mathematicians
Index of Terms

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