LEADER 03814nam 2200661Ia 450 001 9910139338903321 005 20241009130400.0 010 $a9786613813626 010 $a9781282242500 010 $a1282242504 010 $a9781118033180 010 $a1118033183 010 $a9781118031438 010 $a1118031431 035 $a(CKB)2560000000060930 035 $a(EBL)661625 035 $a(OCoLC)705538692 035 $a(SSID)ssj0000484550 035 $a(PQKBManifestationID)11318009 035 $a(PQKBTitleCode)TC0000484550 035 $a(PQKBWorkID)10594357 035 $a(PQKB)11093704 035 $a(MiAaPQ)EBC661625 035 $a(Perlego)2768387 035 $a(EXLCZ)992560000000060930 100 $a19930526d1994 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFundamental structures of algebra and discrete mathematics /$fStephan Foldes 210 $aNew York $cWiley$dc1994 215 $a1 online resource (362 p.) 300 $a"A Wiley-Interscience publication." 311 08$a9780471571803 311 08$a0471571806 320 $aIncludes bibliographical references and indexes. 327 $aFundamental 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 Algorithm 327 $aBibliographyV. 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 Polynomials 327 $a3. 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 THEOREMS 330 $aIntroduces 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. 606 $aAlgebra 606 $aMathematics 606 $aÀlgebra$2thub 608 $aLlibres electrònics$2thub 615 0$aAlgebra. 615 0$aMathematics. 615 7$aÀlgebra 676 $a512/.02 700 $aFoldes$b Stephan$f1951-$0521673 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910139338903321 996 $aFundamental structures of algebra and discrete mathematics$9837663 997 $aUNINA LEADER 02395oas 2200985 a 450 001 9910134712703321 005 20260203110115.0 011 $a1471-2334 035 $a(DE-599)ZDB2041550-3 035 $a(OCoLC)47657386 035 $a(CONSER) 2002243090 035 $a(CKB)111000136906036 035 $a(DE-599)2041550-3 035 $a(EXLCZ)99111000136906036 100 $a20010726a20019999 sy 101 0 $aeng 135 $aurcn||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aBMC infectious diseases 210 $aLondon $cBioMed Central$d[2001]- 300 $aRefereed/Peer-reviewed 300 $aTitle from BioMed Central archive volume screen (viewed Feb. 15, 2002). 517 3 $aBioMed Central infectious diseases 517 3 $aInfectious diseases 531 10$aBMC Infect Dis 606 $aCommunicable diseases$vPeriodicals 606 $aCommunicable Diseases 606 $aSexually Transmitted Diseases 606 $aCommunicable Diseases$2ebps 606 $aCommunicable diseases$2fast$3(OCoLC)fst00869883 608 $aPeriodical. 608 $aFulltext. 608 $aInternet Resources. 608 $aPeriodicals. 608 $aPeriodicals.$2fast 615 0$aCommunicable diseases 615 12$aCommunicable Diseases. 615 22$aSexually Transmitted Diseases. 615 7$aCommunicable Diseases. 615 7$aCommunicable diseases. 801 0$bCOU 801 1$bCOU 801 2$bOCLCQ 801 2$bNLM 801 2$bCUS 801 2$bCAS 801 2$bWAU 801 2$bNLM 801 2$bOCLCQ 801 2$bCUS 801 2$bOCLCQ 801 2$bHEBIS 801 2$bUKMGB 801 2$bOCLCQ 801 2$bGBVCP 801 2$bOCLCQ 801 2$bTWT 801 2$bOCLCF 801 2$bOCLCO 801 2$bEUW 801 2$bOCLCO 801 2$bOCLCQ 801 2$bOCLCO 801 2$bOCLCQ 801 2$bCASUM 801 2$bOCLCO 801 2$bOCLCA 801 2$bWT2 801 2$bGWDNB 801 2$bNLE 801 2$bOCLCA 801 2$bOCLCQ 801 2$bAU@ 801 2$bOCLCA 801 2$bDLC 801 2$bOCLCQ 801 2$bSRU 801 2$bBWN 801 2$bOCLCQ 906 $aJOURNAL 912 $a9910134712703321 996 $aBMC infectious diseases$92266971 997 $aUNINA