| 000 | 06725nam a22002057a 4500 | ||
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| 999 |
_c8015 _d8015 |
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| 005 | 20231113092301.0 | ||
| 008 | 231113b ||||| |||| 00| 0 eng d | ||
| 020 | _a9781264258802 | ||
| 040 | _cKCST | ||
| 082 |
_a004.0151 _bLi Di |
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| 100 |
_aLipschutz, Seymour _94863 |
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| 245 |
_a Discrete mathematics / _cSeymour Lipschutz, Marc Lipson |
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| 250 | _a4th | ||
| 260 |
_aNew York: _bMcGraw-Hill; _c2022. |
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| 300 | _a472 p. | ||
| 505 | _a Cover 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 Supplementary 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?nigsberg 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 Supplementary 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?del 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 15.6 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 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| 650 |
_aDiscrete mathematics _97887 |
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| 700 |
_aLipson, Marc _94866 |
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| 942 |
_2ddc _cBO |
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