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Abstract Algebra A Concrete Introduction

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ISBN-10: 020143721X

ISBN-13: 9780201437218

Edition: 2001

Authors: Robert H. Redfield

List price: $117.80
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Description:

This is a new text for the Abstract Algebra course. The author has written this text with a unique, yet historical, approach: solvability by radicals. This approach depends on a fields-first organization. However, professors wishing to commence their course with group theory will find that the Table of Contents is highly flexible, and contains a generous amount of group coverage.
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Book details

List price: $117.80
Copyright year: 2001
Publisher: Addison Wesley
Publication date: 10/18/2000
Binding: Paperback
Pages: 480
Size: 7.50" wide x 9.25" long x 0.75" tall
Weight: 1.980
Language: English

Introduction
Historical Note: Al-Khwarizmi
Preliminaries
Properties of the Integers
Historical Note: Augustus de Morgan
Solving Cubic and Quartic Polynomial Equations
Historical Note: How the Cubic and Quartic Equations Were Solved
Complex Numbers
Historical Note: Highlights in the Development of the Complex Numbers
Some Other Examples
Historical Note: William Rowan Hamilton
Algebraic Extension Fields
Fields
Solvability by Radicals
Historical Note: Niels Henrik Abel
Rings
Ways in Which Polynomials Are Like the Integers
Historical Note: Julia Robinson
Principal Ideals
Historical Note: Emmy Noether
Algebraic Elements
Eisenstein's Irreducibility Criterion
Historical Note: Gotthold Eisenstein
Extension Fields as Vector Spaces
Automorphisms to Fields
Historical Note: Evariste Galois
Counting Automorphisms
Historical Note: Richard Dedekind
Elementary Group Theory
Groups
Historical Note: Walther von Dyck
Permutation Groups
Group Homomorphisms
Historical Note: Arthur Cayley
Subgroups
Subgroups Generated by Subsets
Cosets
Finite Groups and Lagrange's Theorem
Historical Note: Joseph Louis Lagrange
Equivalence Relations and Cauchy's Theorem
Historical Note: Augustin-Louis Cauchy
Normal Subgroups and Quotient Groups
Historical Note: Otto Holder
The Homomorphism Theorem for Groups
Historical Note: B. L. van der Waerden
Polynomial Equations Not Solvable by Radicals
Galois Groups of Radical Extensions
Solvable Groups and Commutator Subgroups
Historical Note: William Burnside
Solvable Galois Groups
Polynomial Equations Not Solvable by Radicals
Historical Note: Paolo Ruffini
Finite Groups
Finite External Direct Products of Groups
Historical Note: J. H. M. Wedderburn
Finite Internal Direct Products of Groups
Abelian Groups with Prime Power Order
The Fundamental Theorem of Finite Abelian Groups
Historical Note: Leopold Kronecker
Dihedral Groups
Historical Note: Felix Klein
Cauchy's Theorem
The Sylow Theorems
Historical Note: Peter Ludvig Sylow
Groups of Order Less Than 16
Groups of Even Permutations
Historical Note: Camille Jordan
Semidirect Products
The Greek Alphabet
Proving Theorems
Historical Note: George Boole
Vector Spaces Over Fields
Constructions with Straightedge and Compass
Answers to Odd-Numbered Computational Exercises
Bibliography
Photo Credits
Notation Index
Subject Index