Contemporary Abstract Algebra (Paperback) by Joseph A. Gallian

Book Summary of Contemporary Abstract Algebra

This is the first volume of the book Algebra planned by the authors to provide adequate

 preparation in algebra to prospective teachers and researchers in mathematics and related 

areas. Beginning with groups of symmetries of plane configurations. It studies groups

 (with operators) and their homomorphisms, presentations of groups by generators and relations ,

 direct and semidirect products, Sylow's theorems, soluble, nilpotent and Abelian groups. The

volume ends with Jordan's classification of finite subgroups of the group of orthogonal 

transformations of R'.

An attractive feature of the book is its richness in purposeful examples and instructive exercise

 with a focus on the roots of algebra in number theory, geometry and theory of equations.

Table of Contents
Perface
Part 1 Integers and Equivalence Relations

• Chapter: Preliminaries

Part 2 Groups

• Chapter 1 Introduction to Groups
• Chapter 2 Groups
• Chapter 3 Finite Groups; Subgroups
• Chapter 4 Cyclic Groups
• Chapter 5 Permutation Groups
• Chapter 6 Isomorphisms
• Chapter 7 Cosets and Lagrange's Theorem
• Chapter 8 External Direct Products
• Chapter 9 Normal Subgroups and Factor Groups
• Chapter 10 Group Homomorphisms
• Chapter 11 Fundamental Theorem of Finite Abelian

Part 3 Rings

• Chapter 12 Introduction to Rings
• Chapter 13 Integral Domains
• Chapter 14 Ideals and Factor Rings
• Chapter 15 Ring Homomorphisms
• Chapter 16 Polynomial Rings
• Chapter 17 Factorization of Polynomials
• Chapter 18 Divisibility in Integral Domains

Part 4 Fields

• Chapter 19 Vector Spaces
• Chapter 20 Extension Fields
• Chapter 21 Algebraic Extensions
• Chapter 22 Finite Fields
• Chapter 23 Geometric Constructions

Part 5 Special Topics

• Chapter 24 Sylow Theorems
• Chapter 25 Finite Simple Groups
• Chapter 26 Generators and Relations
• Chapter 27 Symmetry Groups
• Chapter 28 Frieze Groups and Crystallographic Groups
• Chapter 29 Symmetry and Counting
• Chapter 30 Cayley Digraphs of Groups
• Chapter 31 Introduction to Algebraic Coding Theory
• Chapter 32 An Introduction to Galois Theory
• Chapter 33 Cyclotomic Extensions

Selected Answers
Text Credits
Photo Credits
Notations
Index of Mathematicians
Index of Terms

Details of Book: Contemporary Abstract Algebra

Book:	Contemporary Abstract Algebra
Author:	Joseph A. Gallian
ISBN:	8173192693
ISBN-13:	9788173192692 ,  978-8173192692
Binding:	Paperback
Publishing Date:	1999
Publisher:	Narosa Publishing House
Edition:	4thEdition
Number of Pages:	581
Language:	English