LEADER 05241nam 22006134a 450 001 9910458146903321 005 20200520144314.0 010 $a1-281-05068-7 010 $a9786611050689 010 $a0-08-047734-8 035 $a(CKB)1000000000363903 035 $a(EBL)294091 035 $a(OCoLC)437181437 035 $a(SSID)ssj0000294098 035 $a(PQKBManifestationID)11229838 035 $a(PQKBTitleCode)TC0000294098 035 $a(PQKBWorkID)10302959 035 $a(PQKB)10286808 035 $a(MiAaPQ)EBC294091 035 $a(Au-PeEL)EBL294091 035 $a(CaPaEBR)ebr10185897 035 $a(CaONFJC)MIL105068 035 $a(EXLCZ)991000000000363903 100 $a20030630d2004 uy 0 101 0 $aeng 135 $aurcn||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDiscrete mathematics with applications$b[electronic resource] /$fThomas Koshy 210 $aAmsterdam ;$aBoston $cElsevier Academic Press$dc2004 215 $a1 online resource (1079 p.) 300 $aDescription based upon print version of record. 311 $a0-12-421180-1 320 $aIncludes bibliographical references (p. 899-905) and indexes. 327 $aFront Cover; Discrete Mathematics with Applications; Copyright Page; Table of Contents; Preface; A Word to the Student; Chapter 1. The Language of Logic; 1.1 Propositions; 1.2 Logical Equivalences; 1.3 Quantifiers; 1.4 Arguments (optional); 1.5 Proof Methods; Chapter Summary; Review Exercises; Supplementary Exercises; Computer Exercises; Exploratory Writing Projects; Enrichment Readings; Chapter 2. The Language of Sets; 2.1 The Concept of a Set; 2.2 Operations with Sets; 2.3 Computer Operations with Sets (optional); 2.4 The Cardinality of a Set; 2.5 Recursively Defined Sets; Chapter Summary 327 $aReview Exercises Supplementary Exercises; Computer Exercises; Exploratory Writing Projects; Enrichment Readings; Chapter 3. Functions and Matrices; 3.1 The Concept of a Function; 3.2 Special Functions; 3.3 Properties of Functions; 3.4 The Pigeonhole Principle; 3.5 Composition of Functions; 3.6 Sequences and the Summation Notation; 3.7 Matrices; Chapter Summary; Review Exercises; Supplementary Exercises; Computer Exercises; Exploratory Writing Projects; Enrichment Readings; Chapter 4. Induction and Algorithms; 4.1 The Division Algorithm; 4.2 Divisibility Properties; 4.3 Nondecimal Bases 327 $a4.4 Mathematical Induction 4.5 Algorithm Correctness; 4.6 The Growth of Functions; 4.7 Complexities of Algorithms (optional); Chapter Summary; Review Exercises; Supplementary Exercises; Computer Exercises; Exploratory Writing Projects; Enrichment Readings; Chapter 5. Recursion; 5.1 Recursively Defined Functions; 5.2 Solving Recurrence Relations; 5.3 Solving Recurrence Relations Revisited; 5.4 Generating Functions; 5.5 Recursive Algorithms; 5.6 Correctness of Recursive Algorithms; 5.7 Complexities of Recursive Algorithms (optional); Chapter Summary; Review Exercises; Supplementary Exercises 327 $aComputer Exercises Exploratory Writing Projects; Enrichment Readings; Chapter 6. Combinatorics and Discrete Probability; 6.1 The Fundamental Counting Principles; 6.2 Permutations; 6.3 Derangements; 6.4 Combinations; 6.5 Permutations and Combinations with Repetitions; 6.6 The Binomial Theorem; 6.7 The Generalized Inclusion-Exclusion Principle (GIEP) (optional); 6.8 Discrete Probability (optional); 6.9 Additional Topics in Probability (optional); Chapter Summary; Review Exercises; Supplementary Exercises; Computer Exercises; Exploratory Writing Projects; Enrichment Readings; Chapter 7. Relations 327 $a7.1 Boolean Matrices 7.2 Relations and Digraphs; 7.3 Computer Representations of Relations (optional); 7.4 Properties of Relations; 7.5 Operations on Relations; 7.6 The Connectivity Relation (optional); 7.7 Transitive Closure (optional); 7.8 Equivalence Relations; 7.9 Partial and Total Orderings; Chapter Summary; Review Exercises; Supplementary Exercises; Computer Exercises; Exploratory Writing Projects; Enrichment Readings; Chapter 8. Graphs; 8.1 Graphs; 8.2 Computer Representations of Graphs (optional); 8.3 Isomorphic Graphs; 8.4 Paths, Cycles, and Circuits 327 $a8.5 Eulerian and Hamiltonian Graphs 330 $aThis approachable text studies discrete objects and the relationships that bind them. It helps students understand and apply the power of discrete math to digital computer systems and other modern applications. It provides excellent preparation for courses in linear algebra, number theory, and modern/abstract algebra and for computer science courses in data structures, algorithms, programming languages, compilers, databases, and computation.* Covers all recommended topics in a self-contained, comprehensive, and understandable format for students and new professionals * Emphasizes pr 606 $aMathematics 608 $aElectronic books. 615 0$aMathematics. 676 $a510 700 $aKoshy$b Thomas$0601527 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910458146903321 996 $aDiscrete mathematics with applications$91213834 997 $aUNINA