My Account \| Help Desk \| Market Place Shopping Cart
	No items in cart. Total: $0.00

College Apparel

Related Topics: Technology

Welcome Aquinas College Students!

Navigate: (use the links to quickly navigate your virtual bookstore)

Aquinas College

Modern Algebra: An Introduction, 4th Edition,9780471321477

Other versions by this Author

Modern Algebra: An Introduction, 4th Edition

Author(s): John R. Durbin
ISBN10: 0471321478
ISBN13: 9780471321477
Format: Hardcover
Publisher(s): Wiley

Upgraded Edition: Click here!

New Price $6.95 List Price ~~$108.00~~ eVIP Price N/A
New Copy: In Stock Usually Ships in 24 Hours.

Take 90 Days to Pay on $250 or more

with Quick, Easy, Secure

Subject to credit approval.

Summary

Table of Contents

This book presents an introduction to modern (abstract) algebra covering the basic ideas of groups, rings, and fields. The first part of the book treats ideas that are important but neither abstract nor complicated, and provides practice in handling mathematical statements - their meaning, quantification, negation, and proof. This edition features a new section to give more substance to the introduction to Galois theory, updated lists of references and discussions of topics such as Fermat's Last Theorem and the finite simple groups.

Introduction

1

(8)

I. Mappings and Operations

9

(20)

Mappings

9

(6)

Composition. Invertible Mappings

15

(4)

Operations

19

(5)

Composition as an Operation

24

(5)

II. Introduction to Groups

29

(20)

Definition and Examples

29

(4)

Permutations

33

(5)

Subgroups

38

(6)

Groups and Symmetry

44

(5)

III. Equivalence. Congruence. Divisibility

49

(21)

Equivalence Relations

49

(5)

Congruence. The Division Algorithm

54

(4)

Integers Modulo n

58

(4)

Greatest Common Divisors. The Euclidean Algorithm

62

(5)

The Fundamental Theorem of Arithmetic

67

(3)

IV. Groups

70

(30)

Elementary Properties

70

(6)

Generators. Direct Products

76

(4)

Cosets

80

(3)

Lagrange's Theorem

83

(5)

Isomorphism

88

(4)

More on Isomorphism

92

(5)

Cayley's Theorem

97

(3)

V. Group Homomorphisms

100

(14)

Homomorphisms of Groups. Kernels

100

(4)

Quotient Groups

104

(5)

The Fundamental Homomorphism Theorem

109

(5)

VI. Introduction to Rings

114

(18)

Definition and Examples

114

(5)

Integral Domains. Subrings

119

(3)

Fields

122

(4)

Isomorphism. Characteristic

126

(6)

VII. The Familiar Number Systems

132

(23)

Ordered Integral Domains

132

(3)

The Integers

135

(2)

Field of Quotients. The Field of Rational Numbers

137

(4)

Ordered Fields. The Field of Real Numbers

141

(4)

The Field of Complex Numbers

145

(4)

Complex Roots of Unity

149

(6)

VIII. Polynomials

155

(19)

Definition and Elementary Properties

155

(5)

The Division Algorithm

160

(4)

Factorization of Polynomials

164

(4)

Unique Factorization Domains

168

(6)

IX. Quotient Rings

174

(15)

Homomorphism of Rings. Ideals

174

(4)

Quotient Rings

178

(2)

Quotient Rings of F[X]

180

(4)

Factorizations and Ideals

184

(5)

X. Field Extensions

189

(8)

Adjoining Roots

189

(4)

Finite Fields

193

(4)

XI. Polynomial Equations

197

(12)

Roots of a Polynomial

197

(1)

Rational Roots. Conjugate Roots

198

(3)

An Introduction to Galois Theory

201

(5)

Solvability by Radicals

206

(3)

XII. Geometric Constructions

209

(8)

Three Famous Problems

209

(4)

Constructible Numbers

213

(1)

Impossible Constructions

214

(3)

XIII. Application of Permutation Groups

217

(13)

Groups Acting on Sets

217

(4)

Burnside's Counting Theorem

221

(6)

Sylow's Theorem

227

(3)

XIV. Symmetry

230

(25)

Finite Symmetry Groups

230

(7)

Infinite Two-dimensional Symmetry Groups

237

(5)

On Crystallographic Groups

242

(8)

The Euclidean Group

250

(5)

XV. Algebraic Coding

255

(15)

Introduction

255

(3)

Linear Codes

258

(4)

Standard Decoding

262

(3)

Error Probability

265

(5)

XVI. Lattices and Boolean Algebras

270

(20)

Partially Ordered Sets

270

(4)

Lattices

274

(4)

Boolean Algebras

278

(4)

Finite Boolean Algebras

282

(5)

Switching

287

(3)

A. Sets

290

(3)

B. Proofs

293

(5)

C. Mathematical Induction

298

(3)

D. Linear Algebra

301

(5)

E. Solutions to Selected Problems

306

(16)

Photo Credit List

322

(1)

Index

323

Check Out These Items!
	eCampus.com Pink Backpack Retail Price ~~$28.95~~ Our Price $10.00		eCampus.com T-Shirt Retail Price ~~$14.99~~ Our Price $2.00		eCampus.com 4GB USB Drive Retail Price ~~$32.95~~ Our Price $25.00


For support, contact our Virtual Bookstore Program Customer Service at: 877.284.6744 or bookstore@ecampus.com

	Buy Textbooks Sell Textbooks College Apparel Shop by School Virtual Bookstores	Order Status Shipping Rates Return Policy Marketplace Info F.A.S.T.	Contact Us Privacy Policy Legal Notices Site Security Employment	Help Desk eCampus Blog Affiliate Program Bulk Orders College Marketing

Need Help? bookstore@ecampus.com Copyright© 1999-2008
.