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020 _a9781264258819
_q(electronic bk.)
020 _z9781264258802
035 _a(MiAaPQ)EBC6798110
035 _a(Au-PeEL)EBL6798110
035 _a(OCoLC)1285170988
040 _aMiAaPQ
_beng
_erda
_epn
_cMiAaPQ
_dMiAaPQ
050 4 _aBC135 .L577 2022
082 0 _a512.02
100 1 _aLipschutz, Seymour.
245 1 0 _aSchaum's Outline of Discrete Mathematics, Fourth Edition.
250 _a4th ed.
264 1 _aNew York :
_bMcGraw-Hill Education,
_c2021.
264 4 _c�2022.
300 _a1 online resource (727 pages)
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
505 0 _aCover -- Title Page -- Copyright Page -- Preface -- Contents -- CHAPTER 1 Set Theory -- 1.1 Introduction -- 1.2 Sets and Elements, Subsets -- 1.3 Venn Diagrams -- 1.4 Set Operations -- 1.5 Algebra of Sets, Duality -- 1.6 Finite Sets, Counting Principle -- 1.7 Classes of Sets, Power Sets, Partitions -- 1.8 Mathematical Induction -- Solved Problems -- Supplementary Problems -- CHAPTER 2 Relations -- 2.1 Introduction -- 2.2 Product Sets -- 2.3 Relations -- 2.4 Pictorial Representatives of Relations -- 2.5 Composition of Relations -- 2.6 Types of Relations -- 2.7 Closure Properties -- 2.8 Equivalence Relations -- 2.9 Partial Ordering Relations -- Solved Problems -- Supplementary Problems -- CHAPTER 3 Functions and Algorithms -- 3.1 Introduction -- 3.2 Functions -- 3.3 One-to-One, Onto, and Invertible Functions -- 3.4 Mathematical Functions, Exponential and Logarithmic Functions -- 3.5 Sequences, Indexed Classes of Sets -- 3.6 Recursively Defined Functions -- 3.7 Cardinality -- 3.8 Algorithms and Functions -- 3.9 Complexity of Algorithms -- Solved Problems -- Supplementary Problems -- CHAPTER 4 Logic and Propositional Calculus -- 4.1 Introduction -- 4.2 Propositions and Compound Statements -- 4.3 Basic Logical Operations -- 4.4 Propositions and Truth Tables -- 4.5 Tautologies and Contradictions -- 4.6 Logical Equivalence -- 4.7 Algebra of Propositions -- 4.8 Conditional and Biconditional Statements -- 4.9 Arguments -- 4.10 Propositional Functions, Quantifiers -- 4.11 Negation of Quantified Statements -- Solved Problems -- Supplementary Problems -- CHAPTER 5 Counting: Permutations and Combinations -- 5.1 Introduction -- 5.2 Basic Counting Principles -- 5.3 Mathematical Functions -- 5.4 Permutations -- 5.5 Combinations -- 5.6 The Pigeonhole Principle -- 5.7 The Inclusion-Exclusion Principle -- 5.8 Tree Diagrams -- Solved Problems.
505 8 _aSupplementary Problems -- CHAPTER 6 Advanced Counting Techniques, Recursion -- 6.1 Introduction -- 6.2 Combinations with Repetitions -- 6.3 Ordered and Unordered Partitions -- 6.4 Inclusion-Exclusion Principle Revisited -- 6.5 Pigeonhole Principle Revisited -- 6.6 Recurrence Relations -- 6.7 Linear Recurrence Relations with Constant Coefficients -- 6.8 Solving Second-Order Homogeneous Linear Recurrence Relations -- 6.9 Solving General Homogeneous Linear Recurrence Relations -- Solved Problems -- Supplementary Problems -- CHAPTER 7 Discrete Probability Theory -- 7.1 Introduction -- 7.2 Sample Space and Events -- 7.3 Finite Probability Spaces -- 7.4 Conditional Probability -- 7.5 Independent Events -- 7.6 Independent Repeated Trials, Binomial Distribution -- 7.7 Random Variables -- 7.8 Chebyshev's Inequality, Law of Large Numbers -- Solved Problems -- Supplementary Problems -- CHAPTER 8 Graph Theory -- 8.1 Introduction, Data Structures -- 8.2 Graphs and Multigraphs -- 8.3 Subgraphs, Isomorphic and Homeomorphic Graphs -- 8.4 Paths, Connectivity -- 8.5 Traversable and Eulerian Graphs, Bridges of K�onigsberg -- 8.6 Labeled and Weighted Graphs -- 8.7 Complete, Regular, and Bipartite Graphs -- 8.8 Tree Graphs -- 8.9 Planar Graphs -- 8.10 Graph Colorings -- 8.11 Representing Graphs in Computer Memory -- 8.12 Graph Algorithms -- 8.13 Traveling-Salesman Problem -- Solved Problems -- Supplementary Problems -- CHAPTER 9 Directed Graphs -- 9.1 Introduction -- 9.2 Directed Graphs -- 9.3 Basic Definitions -- 9.4 Rooted Trees -- 9.5 Sequential Representation of Directed Graphs -- 9.6 Warshall's Algorithm, Shortest Paths -- 9.7 Linked Representation of Directed Graphs -- 9.8 Graph Algorithms: Depth-First and Breadth-First Searches -- 9.9 Directed Cycle-Free Graphs, Topological Sort -- 9.10 Pruning Algorithm for Shortest Path -- Solved Problems.
505 8 _aSupplementary Problems -- CHAPTER 10 Binary Trees -- 10.1 Introduction -- 10.2 Binary Trees -- 10.3 Complete and Extended Binary Trees -- 10.4 Representing Binary Trees in Memory -- 10.5 Traversing Binary Trees -- 10.6 Binary Search Trees -- 10.7 Priority Queues, Heaps -- 10.8 Path Lengths, Huffman's Algorithm -- 10.9 General (Ordered Rooted) Trees Revisited -- Solved Problems -- Supplementary Problems -- CHAPTER 11 Properties of the Integers -- 11.1 Introduction -- 11.2 Order and Inequalities, Absolute Value -- 11.3 Mathematical Induction -- 11.4 Division Algorithm -- 11.5 Divisibility, Primes -- 11.6 Greatest Common Divisor, Euclidean Algorithm -- 11.7 Fundamental Theorem of Arithmetic -- 11.8 Congruence Relation -- 11.9 Congruence Equations -- Solved Problems -- Supplementary Problems -- CHAPTER 12 Languages, Automata, Grammars -- 12.1 Introduction -- 12.2 Alphabet, Words, Free Semigroup -- 12.3 Languages -- 12.4 Regular Expressions, Regular Languages -- 12.5 Finite State Automata -- 12.6 Grammars -- Solved Problems -- Supplementary Problems -- CHAPTER 13 Finite State Machines and Turing Machines -- 13.1 Introduction -- 13.2 Finite State Machines -- 13.3 G�odel Numbers -- 13.4 Turing Machines -- 13.5 Computable Functions -- Solved Problems -- Supplementary Problems -- CHAPTER 14 Ordered Sets and Lattices -- 14.1 Introduction -- 14.2 Ordered Sets -- 14.3 Hasse Diagrams of Partially Ordered Sets -- 14.4 Consistent Enumeration -- 14.5 Supremum and Infimum -- 14.6 Isomorphic (Similar) Ordered Sets -- 14.7 Well-Ordered Sets -- 14.8 Lattices -- 14.9 Bounded Lattices -- 14.10 Distributive Lattices -- 14.11 Complements, Complemented Lattices -- Solved Problems -- Supplementary Problems -- CHAPTER 15 Boolean Algebra -- 15.1 Introduction -- 15.2 Basic Definitions -- 15.3 Duality -- 15.4 Basic Theorems -- 15.5 Boolean Algebras as Lattices.
505 8 _a15.6 Representation Theorem -- 15.7 Sum-of-Products Form for Sets -- 15.8 Sum-of-Products Form for Boolean Algebras -- 15.9 Minimal Boolean Expressions, Prime Implicants -- 15.10 Logic Gates and Circuits -- 15.11 Truth Tables, Boolean Functions -- 15.12 Karnaugh Maps -- Solved Problems -- Supplementary Problems -- APPENDIX A Vectors and Matrices -- A.1 Introduction -- A.2 Vectors -- A.3 Matrices -- A.4 Matrix Addition and Scalar Multiplication -- A.5 Matrix Multiplication -- A.6 Transpose -- A.7 Square Matrices -- A.8 Invertible (Nonsingular) Matrices, Inverses -- A.9 Determinants -- A.10 Elementary Row Operations, Gaussian Elimination (Optional) -- A.11 Boolean (Zero-One) Matrices -- Solved Problems -- Supplementary Problems -- APPENDIX B Algebraic Systems -- B.1 Introduction -- B.2 Operations -- B.3 Semigroups -- B.4 Groups -- B.5 Subgroups, Normal Subgroups, and Homomorphisms -- B.6 Rings, Integral Domains, and Fields -- B.7 Polynomials Over a Field -- Solved Problems -- Supplementary Problems -- Index.
588 _aDescription based on publisher supplied metadata and other sources.
590 _aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650 0 _aLogic, Symbolic and mathematical.
655 4 _aElectronic books.
700 1 _aLipson, Marc.
776 0 8 _iPrint version:
_aLipschutz, Seymour
_tSchaum's Outline of Discrete Mathematics, Fourth Edition
_dNew York : McGraw-Hill Education,c2021
_z9781264258802
797 2 _aProQuest (Firm)
856 4 0 _uhttps://ebookcentral-proquest-com.mlisicats.remotexs.co/lib/ppks/detail.action?docID=6798110
_zClick to View
942 _2lcc
_cEB
999 _c298
_d298