03573nam 2200565Ia 450 991013933890332120200520144314.01-282-24250-497866138136261-118-03318-31-118-03143-1(CKB)2560000000060930(EBL)661625(OCoLC)705538692(SSID)ssj0000484550(PQKBManifestationID)11318009(PQKBTitleCode)TC0000484550(PQKBWorkID)10594357(PQKB)11093704(MiAaPQ)EBC661625(EXLCZ)99256000000006093019930526d1994 uy 0engur|n|---|||||txtccrFundamental structures of algebra and discrete mathematics /Stephan FoldesNew York Wileyc19941 online resource (362 p.)"A Wiley-Interscience publication."0-471-57180-6 Includes bibliographical references and indexes.Fundamental Structures of Algebra and Discrete Mathematics; Contents; ILLUSTRATIONS; PREFACE; I. SETS; 1. Elementary Constructions and Axioms; 2. Cardinal and Ordinal Numbers; 3. Intersections; Bibliography; II. ORDERED SETS; 1. Relations, Orders, and Zorn's Lemma; 2. Lattices and Closures; 3. Covering Relations; 4. Intersecting Convex Sets; Bibliography; III. GROUPS; 1. Binary Operations, Homomorphisms, and Congruences; 2. Permutation Groups; 3. Integers and Cyclic Groups; 4. Alternating Groups; Bibliography; IV. RINGS; 1. Ideals; 2. Polynomials; 3. Factorization and the Euclidean AlgorithmBibliographyV. FIELDS; 1. Rational and Real Numbers; 2. Galois Groups and Imaginary Roots; Bibliography; VI. VECTOR SPACES; 1. Bases; 2. Linear Maps and Equations; 3. Affine and Projective Geometry; 4. Hyperplanes in Linear Programming; 5. Time and Speed in Special Relativity; Bibliography; VII. GRAPHS; 1. Trees and Median Graphs; 2. Games; 3. Chromatic Polynomials; Bibliography; VIII. LATTICES; 1. Complements and Distributivity; 2. Boolean Algebra; 3. Modular and Geometric Lattices; Bibliography; IX. MATROIDS; 1. Linear and Abstract Independence; 2. Minors and Tutte Polynomials3. Greedy Optimization ProceduresBibliography; X. TOPOLOGICAL SPACES; 1. Filters; 2. Closure, Convergence, and Continuity; 3. Distances and Entourages; Bibliography; XI. UNIVERSAL ALGEBRAS; 1. Homomorphisms and Congruences; 2. Algebra of Syntax; 3. Truth and Formal Proof; Bibliography; XII. CATEGORIES; Bibliography; INDEX OF DEFINITIONS; INDEX OF NOTATION; INDEX OF THEOREMSIntroduces and clarifies the basic theories of 12 structural concepts, offering a fundamental theory of groups, rings and other algebraic structures. Identifies essentials and describes interrelationships between particular theories. Selected classical theorems and results relevant to current research are proved rigorously within the theory of each structure. Throughout the text the reader is frequently prompted to perform integrated exercises of verification and to explore examples.AlgebraMathematicsAlgebra.Mathematics.512/.02Foldes Stephan1951-521673MiAaPQMiAaPQMiAaPQBOOK9910139338903321Fundamental structures of algebra and discrete mathematics837663UNINA