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Modern Algebra: An Introduction, 6th Edition

by: Durbin, John R.

Modern Algebra: An Introduction, 6th Edition

by: Durbin, John R.

ISBN 13:
9780470384435
ISBN 10:
0470384433
Edition: 6th
Format: Hardcover
Copyright: 12/31/2008
Publisher: Wiley

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Summary

Engineers and computer scientists who need a basic understanding of algebra will benefit from this accessible book. The sixth edition includes many carefully worked examples and proofs to guide them through abstract algebra successfully. It introduces the most important kinds of algebraic structures, and helps them improve their ability to understand and work with abstract ideas. New and revised exercise sets are integrated throughout the first four chapters. A more in-depth discussion is also included on Galois Theory. The first six chapters provide engineers and computer scientists with the core of the subject and then the book explores the concepts in more detail.

Introduction	p. 1
Mappings and Operations	p. 9
Mappings	p. 9
Composition. Invertible Mappings	p. 15
Operations	p. 19
Composition as an Operation	p. 25
Introduction to Groups	p. 30
Definition and Examples	p. 30
Permutations	p. 34
Subgroups	p. 41
Groups and Symmetry	p. 47
Equivalence. Congruence. Divisibility	p. 52
Equivalence Relations	p. 52
Congruence. The Division Algorithm	p. 57
Integers Modulo n	p. 61
Greatest Common Divisors. The Euclidean Algorithm	p. 65
Factorization. Euler's Phi-Function	p. 70
Groups	p. 75
Elementary Properties	p. 75
Generators. Direct Products	p. 81
Cosets	p. 85
Lagrange's Theorem. Cyclic Groups	p. 88
Isomorphism	p. 93
More on Isomorphism	p. 98
Cayley's Theorem	p. 102
RSA Algorithm	p. 105
Group Homomorphisms	p. 106
Homomorphisms of Groups. Kernels	p. 106
Quotient Groups	p. 110
The Fundamental Homomorphism Theorem	p. 114
Introduction to Rings	p. 120
Definition and Examples	p. 120
Integral Domains. Subrings	p. 125
Fields	p. 128
Isomorphism. Characteristic	p. 131
The Familiar Number Systems	p. 137
Ordered Integral Domains	p. 137
The Integers	p. 140
Field of Quotients. The Field of Rational Numbers	p. 142
Ordered Fields. The Field of Real Numbers	p. 146
The Field of Complex Numbers	p. 149
Complex Roots of Unity	p. 154
Polynomials	p. 160
Definition and Elementary Properties	p. 160
Appendix to Section 34	p. 162
The Division Algorithm	p. 165
Factorization of Polynomials	p. 169
Unique Factorization Domains	p. 173
Quotient Rings	p. 178
Homomorphisms of Rings. Ideals	p. 178
Quotient Rings	p. 182
Quotient Rings of F[X]	p. 184
Factorization and Ideals	p. 187
Galois Theory: Overview	p. 193
Simple Extensions. Degree	p. 194
Roots of Polynomials	p. 198
Fundamental Theorem: Introduction	p. 203
Galois Theory	p. 207
Algebraic Extensions	p. 207
Splitting Fields. Galois Groups	p. 210
Separability and Normality	p. 214
Fundamental Theorem of Galois Theory	p. 218
Solvability by Radicals	p. 219
Finite Fields	p. 223
Geometric Constructions	p. 229
Three Famous Problems	p. 229
Constructible Numbers	p. 233
Impossible Constructions	p. 234
Solvable and Alternating Groups	p. 237
Isomorphism Theorems and Solvable Groups	p. 237
Alternating Groups	p. 240
Applications of Permutation Groups	p. 243
Groups Acting on Sets	p. 243
Burnside's Counting Theorem	p. 247
Sylow's Theorem	p. 252
Symmetry	p. 256
Finite Symmetry Groups	p. 256
Infinite Two-Dimensional Symmetry Groups	p. 263
On Crystallographic Groups	p. 267
The Euclidean Group	p. 274
Lattices and Boolean Algebras	p. 279
Partially Ordered Sets	p. 279
Lattices	p. 283
Boolean Algebras	p. 287
Finite Boolean Algebras	p. 291
Sets	p. 296
Proofs	p. 299
Mathematical Induction	p. 304
Linear Algebra	p. 307
Solutions to Selected Problems	p. 312
Photo Credit List	p. 326
Index of Notation	p. 327
Index	p. 330
Table of Contents provided by Ingram. All Rights Reserved.

Amazon no longer offers textbook rentals. We do!

Modern Algebra: An Introduction, 6th Edition

Modern Algebra: An Introduction, 6th Edition

9780470384435

0470384433

Summary

Author Biography

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Modern Algebra: An Introduction, 6th Edition

Modern Algebra: An Introduction, 6th Edition

9780470384435

0470384433

Summary

Author Biography

Table of Contents

Supplemental Materials

Write a Review

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