05054nam 2200637 a 450 991084188950332120170815114013.01-280-34418-097866103441850-470-31340-40-471-46989-00-471-46988-2(CKB)1000000000019031(EBL)469017(OCoLC)58480766(SSID)ssj0000303419(PQKBManifestationID)11229862(PQKBTitleCode)TC0000303419(PQKBWorkID)10275206(PQKB)11667410(MiAaPQ)EBC469017(PPN)137764391(EXLCZ)99100000000001903120030411d2004 uy 0engur|n|---|||||txtccrModern algebra with applications[electronic resource] /William J. Gilbert, W. Keith Nicholson2nd ed.Hoboken, N.J. Wiley-Intersciencec20041 online resource (353 p.)Pure and applied mathematicsDescription based upon print version of record.0-471-41451-4 Includes bibliographical references (p. 306-308) and index.MODERN ALGEBRA WITH APPLICATIONS; CONTENTS; Preface to the First Edition; Preface to the Second Edition; List of Symbols; 1 Introduction; Classical Algebra; Modern Algebra; Binary Operations; Algebraic Structures; Extending Number Systems; 2 Boolean Algebras; Algebra of Sets; Number of Elements in a Set; Boolean Algebras; Propositional Logic; Switching Circuits; Divisors; Posets and Lattices; Normal Forms and Simplification of Circuits; Transistor Gates; Representation Theorem; Exercises; 3 Groups; Groups and Symmetries; Subgroups; Cyclic Groups and Dihedral Groups; MorphismsPermutation GroupsEven and Odd Permutations; Cayley's Representation Theorem; Exercises; 4 Quotient Groups; Equivalence Relations; Cosets and Lagrange's Theorem; Normal Subgroups and Quotient Groups; Morphism Theorem; Direct Products; Groups of Low Order; Action of a Group on a Set; Exercises; 5 Symmetry Groups in Three Dimensions; Translations and the Euclidean Group; Matrix Groups; Finite Groups in Two Dimensions; Proper Rotations of Regular Solids; Finite Rotation Groups in Three Dimensions; Crystallographic Groups; Exercises; 6 Pólya-Burnside Method of Enumeration; Burnside's TheoremNecklace ProblemsColoring Polyhedra; Counting Switching Circuits; Exercises; 7 Monoids and Machines; Monoids and Semigroups; Finite-State Machines; Quotient Monoids and the Monoid of a Machine; Exercises; 8 Rings and Fields; Rings; Integral Domains and Fields; Subrings and Morphisms of Rings; New Rings from Old; Field of Fractions; Convolution Fractions; Exercises; 9 Polynomial and Euclidean Rings; Euclidean Rings; Euclidean Algorithm; Unique Factorization; Factoring Real and Complex Polynomials; Factoring Rational and Integral Polynomials; Factoring Polynomials over Finite FieldsLinear Congruences and the Chinese Remainder TheoremExercises; 10 Quotient Rings; Ideals and Quotient Rings; Computations in Quotient Rings; Morphism Theorem; Quotient Polynomial Rings That Are Fields; Exercises; 11 Field Extensions; Field Extensions; Algebraic Numbers; Galois Fields; Primitive Elements; Exercises; 12 Latin Squares; Latin Squares; Orthogonal Latin Squares; Finite Geometries; Magic Squares; Exercises; 13 Geometrical Constructions; Constructible Numbers; Duplicating a Cube; Trisecting an Angle; Squaring the Circle; Constructing Regular PolygonsNonconstructible Number of Degree 4Exercises; 14 Error-Correcting Codes; The Coding Problem; Simple Codes; Polynomial Representation; Matrix Representation; Error Correcting and Decoding; BCH Codes; Exercises; Appendix 1: Proofs; Appendix 2: Integers; Bibliography and References; Answers to Odd-Numbered Exercises; IndexPraise for the first edition ""This book is clearly written and presents a large number of examples illustrating the theory . . . there is no other book of comparable content available. Because of its detailed coverage of applications generally neglected in the literature, it is a desirable if not essential addition to undergraduate mathematics and computer science libraries.""-CHOICE As a cornerstone of mathematical science, the importance of modern algebra and discrete structures to many areas of science and technology is apparent and growing-with extensive use in computing science, Pure and applied mathematics (John Wiley & Sons : Unnumbered)Algebra, AbstractAlgebra, Abstract.512Gilbert William J.1941-42123Nicholson W. Keith104483MiAaPQMiAaPQMiAaPQBOOK9910841889503321Modern algebra with applications4144263UNINA