Modern Algebra: An Introduction, 6th Edition 0006 Edition

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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. Contents of the book : IntroductionI. Mappings and Operations1 Mappings2 Composition3Operations4 Composition as an Operation II. Introduction to Groups5 Definition and Examples6 Permutations7 Subgroups8 Groups and Symmetry III. Equivalence. Congruence. Divisibility9 Equivalence Relations10 Congruence. The Division Algorithm11 Integers Modulo n12 Greatest Common Divisors. The Euclidean Algorithm13 Factorization. Euler's Phi-Function IV. Groups14 Elementary Properties15 Generators. Direct Products16 Cosets17 Lagrange's Theorem. Cyclic Groups18 Isomorphism19 More on Isomorphism20 Cayley's TheoremAppendix: RSA Algorithm V. Group Homomorphisms21 Homomorphisms of Groups. Kernels22 Quotient Groups23 The Fundamental Homomorphism Theorm VI. Introduction to Rings24 Definition and Examples25 Integral Domains. Subrings26 Fields27 Isomorphism. Characteristic VII. The Familiar Number Systems28 Ordered Integral Domains29 The Integers30 Field of Quotients. The Field of Rational Numbers31 Ordered Fields. The Field of Real Numbers32 The Field of Complex Numbers33 Complex Roots of Unity VIII. Polynomials34 Definition and Elementary Properties35 The Division Algorithm36 Factorization of Polynomials37 Unique Factorization Domains IX. Quotient Rings38 Homomorphisms of Rings. Ideals39 Quotient Rings40 Quotient Rings of F[X]41 Factorization and Ideals X. Galois Theory: Overview42 Simple Extensions. Degree43 Roots of Polynomials44 Fundamental Theorem: Introduction XI. Galois Theory45 Galois Groups46 Splitting Fields. Galois Groups47 Separability and Normality48 Fundamental Theorem of Galois Theory49 Solvability by Radicals50 Finite Fields XII. Geometric Constructions51 Three Famous Problems52 Constructible Numbers53 Impossible Constructions XIII. Solvable and Alternating Groups54 Isomorphis Theorems. Solvable Groups55 Alternation Groups XIV. Applications of Permutation Groups56 Groups Acting on Sets57 Burnside's Counting Theorem58 Sylow's Theorem XV. Symmetry59 Finite Symmetry Groups60 Infinite Two-dimensional Symmetry Groups61 On Crystallographic Groups62 The Euclidean Group XVI. Lattices and Boolean Algebras63 Partially Ordered Sets64 Lattices65 Boolean Algebras66 Finite Boolean Algebras A. SetsB. ProofsC. Mathematical InductionD. Linear AlgebraE. Solutions to Selected ProblemsPhoto Credit ListIndex of NotationIndex