Modern Algebra: An IntroductionEngineers 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. |
Contents
| 1 | |
I Mappings and Operations | 9 |
II Introduction to Groups | 30 |
III Equivalence Congruence Divisibility | 52 |
IV Groups | 75 |
V Group Homomorphisms | 106 |
VI Introduction to Rings | 120 |
VII The Familiar Number Systems | 137 |
XIV Applications of Permutation Groups | 243 |
XV Symmetry | 256 |
XVI Lattices and Boolean Algebras | 279 |
A Sets | 296 |
B Proofs | 299 |
C Mathematical Induction | 304 |
D Linear Algebra | 307 |
E Solutions to Selected Problems | 312 |
VIII Polynomials | 160 |
IX Quotient Rings | 178 |
Overview | 193 |
XI Galois Theory | 207 |
XII Geometric Constructions | 229 |
XIII Solvable and Alternating Groups | 237 |
F Algebraic Coding | 325 |
G Switching | 325 |
Photo Credit List | 326 |
Index of Notation | 327 |
Index | 330 |
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Common terms and phrases
Abelian addition algebra applied associative Assume Boolean algebra called chapter classes closed common commutative complete condition Consider constructible contains corresponding cosets cyclic defined definition denote Determine Division divisor element equal equation equivalence Example exists extension fact factor field Figure Find finite given gives group G homomorphism ideal ideas implies important integral domain inverse irreducible isomorphic lattice least Lemma linear mapping mathematics matrix mean multiplication nonzero normal Notice numbers one-to-one operation permutation plane polynomial positive integer prime Problem proof proof of Theorem properties Prove quotient real numbers reflection relation representatives respect ring root rotation satisfies Section simple solution solvable space splitting field statement subfield subgroup subset Suggestion symmetry Theorem theory true unique unity vector Verify write zero