Discrete mathematics: [467 fully solved problems, complete reviews of computer arithmetic and cryptology, covers all course fundamentals - complements any class]
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
McGraw-Hill
[2022]
|
| Ausgabe: | fourth edition |
| Schriftenreihe: | Schaum's outline series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 472 Seiten |
| ISBN: | 9781264258802 |
Internformat
MARC
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| 245 | 1 | 0 | |a Discrete mathematics |b [467 fully solved problems, complete reviews of computer arithmetic and cryptology, covers all course fundamentals - complements any class] |c Seymour Lipschutz ; Marc Lars Lipson |
| 246 | 1 | 3 | |a Schaum's outline of discrete mathematics |
| 250 | |a fourth edition | ||
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Datensatz im Suchindex
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| adam_text | CHAPTER 1 CHAPTER 2 CHAPTER 3 Set Theory 1 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 1 1 3 4 7 8 10 12 12 18 Relations 23 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 23 23 24 25 27 28 30 31 33 34 40 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 vii 43 43 43 46 47 50 52 55 56 57 60 66
CONTENTS viii CHAPTER 4 Logic and Propositional Calculus 70 „„ 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 CHAPTER 5 Solved Problems Supplementary Problems 75 Z$ 7 79 $2 86 Counting: Permutations and Combinations 88 88 88 89 91 93 94 95 95 96 103 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 107 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 7.2 7.3 7.4 7.5 7.6 7.7 Introduction Sample Space and Events Finite Probability Spaces Conditional Probability Independent Events Independent Repeated Trials, Binomial Distribution Random Variables 107 107 108 108 110 111 113 114 116 118 121 123 123 123 126 127 129 130 131
CONTENTS 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 Königsberg 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 ix 136 137 149 154 154 156 158 159 160 162 162 164 166 168 171 173 176 178 191 201 201 201 202 204 206 209 211 213 216 218 221 228 235 235 235 237 239 240 242 244 248 251 252 259
CONTENTS x CHAPTER 11 Properties of the Integers Introduction Order and Inequalities, Absolute Value Mathematical Induction Division Algorithm Divisibility, Primes Greatest Common Divisor, Euclidean Algorithm Fundamental Theorem of Arithmetic Congruence Relation Congruence Equations Solved Problems Supplementary Problems 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 CHÁPTE? 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 Ի) Finite State Machines and Turing Machines 13.1 Introduction 13.2 Finite State Machines 13.3 Gödel 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 264 264 265 266 267 269 270 273 274 278 283 299 303 303 303 304 305 306 310 314 319 323 323 323 326 326 330 331 334 337 337 337 340 342 342 344 344 346 348 44Q Ј^У 350 Ղհ 1 jj 1 360
CONTENTS 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.l 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.ll Boolean (Zero-One) Matrices Solved Problems Supplementary Problems APPENDIX В Algebraic Systems B.l 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 xi 368 368 368 369 370 370 371 371 372 375 377 381 383 389 403 409 409 409 410 411 412 414 414 415 416 418 422 423 429 432 432 432 435 438 440 443 446 450 461 467
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| adam_txt |
CHAPTER 1 CHAPTER 2 CHAPTER 3 Set Theory 1 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 1 1 3 4 7 8 10 12 12 18 Relations 23 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 23 23 24 25 27 28 30 31 33 34 40 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 vii 43 43 43 46 47 50 52 55 56 57 60 66
CONTENTS viii CHAPTER 4 Logic and Propositional Calculus 70 „„ 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 CHAPTER 5 Solved Problems Supplementary Problems 75 Z$ '7 79 $2 86 Counting: Permutations and Combinations 88 88 88 89 91 93 94 95 95 96 103 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 107 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 7.2 7.3 7.4 7.5 7.6 7.7 Introduction Sample Space and Events Finite Probability Spaces Conditional Probability Independent Events Independent Repeated Trials, Binomial Distribution Random Variables 107 107 108 108 110 111 113 114 116 118 121 123 123 123 126 127 129 130 131
CONTENTS 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 Königsberg 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 ix 136 137 149 154 154 156 158 159 160 162 162 164 166 168 171 173 176 178 191 201 201 201 202 204 206 209 211 213 216 218 221 228 235 235 235 237 239 240 242 244 248 251 252 259
CONTENTS x CHAPTER 11 Properties of the Integers Introduction Order and Inequalities, Absolute Value Mathematical Induction Division Algorithm Divisibility, Primes Greatest Common Divisor, Euclidean Algorithm Fundamental Theorem of Arithmetic Congruence Relation Congruence Equations Solved Problems Supplementary Problems 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 CHÁPTE? 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 Ի) Finite State Machines and Turing Machines 13.1 Introduction 13.2 Finite State Machines 13.3 Gödel 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 264 264 265 266 267 269 270 273 274 278 283 299 303 303 303 304 305 306 310 314 319 323 323 323 326 326 330 331 334 337 337 337 340 342 342 344 344 346 348 44Q Ј^У 350 Ղհ 1 jj 1 360
CONTENTS 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.l 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.ll Boolean (Zero-One) Matrices Solved Problems Supplementary Problems APPENDIX В Algebraic Systems B.l 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 xi 368 368 368 369 370 370 371 371 372 375 377 381 383 389 403 409 409 409 410 411 412 414 414 415 416 418 422 423 429 432 432 432 435 438 440 443 446 450 461 467 |
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| index_date | 2024-07-03T19:56:19Z |
| indexdate | 2024-07-10T09:33:02Z |
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| isbn | 9781264258802 |
| language | English |
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| spelling | Lipschutz, Seymour Verfasser (DE-588)140841733 aut Discrete mathematics [467 fully solved problems, complete reviews of computer arithmetic and cryptology, covers all course fundamentals - complements any class] Seymour Lipschutz ; Marc Lars Lipson Schaum's outline of discrete mathematics fourth edition New York McGraw-Hill [2022] © 2022 XI, 472 Seiten txt rdacontent n rdamedia nc rdacarrier Schaum's outline series Algebra, Abstract Outlines, syllabi, etc Combinatorial analysis Outlines, syllabi, etc Logic, Symbolic and mathematical Outlines, syllabi, etc Diskrete Mathematik (DE-588)4129143-8 gnd rswk-swf Diskrete Mathematik (DE-588)4129143-8 s DE-604 Lipson, Marc Verfasser (DE-588)123331730 aut Erscheint auch als Onlineausgabe 978-1-264-25881-9 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033628181&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lipschutz, Seymour Lipson, Marc Discrete mathematics [467 fully solved problems, complete reviews of computer arithmetic and cryptology, covers all course fundamentals - complements any class] Algebra, Abstract Outlines, syllabi, etc Combinatorial analysis Outlines, syllabi, etc Logic, Symbolic and mathematical Outlines, syllabi, etc Diskrete Mathematik (DE-588)4129143-8 gnd |
| subject_GND | (DE-588)4129143-8 |
| title | Discrete mathematics [467 fully solved problems, complete reviews of computer arithmetic and cryptology, covers all course fundamentals - complements any class] |
| title_alt | Schaum's outline of discrete mathematics |
| title_auth | Discrete mathematics [467 fully solved problems, complete reviews of computer arithmetic and cryptology, covers all course fundamentals - complements any class] |
| title_exact_search | Discrete mathematics [467 fully solved problems, complete reviews of computer arithmetic and cryptology, covers all course fundamentals - complements any class] |
| title_exact_search_txtP | Discrete mathematics [467 fully solved problems, complete reviews of computer arithmetic and cryptology, covers all course fundamentals - complements any class] |
| title_full | Discrete mathematics [467 fully solved problems, complete reviews of computer arithmetic and cryptology, covers all course fundamentals - complements any class] Seymour Lipschutz ; Marc Lars Lipson |
| title_fullStr | Discrete mathematics [467 fully solved problems, complete reviews of computer arithmetic and cryptology, covers all course fundamentals - complements any class] Seymour Lipschutz ; Marc Lars Lipson |
| title_full_unstemmed | Discrete mathematics [467 fully solved problems, complete reviews of computer arithmetic and cryptology, covers all course fundamentals - complements any class] Seymour Lipschutz ; Marc Lars Lipson |
| title_short | Discrete mathematics |
| title_sort | discrete mathematics 467 fully solved problems complete reviews of computer arithmetic and cryptology covers all course fundamentals complements any class |
| title_sub | [467 fully solved problems, complete reviews of computer arithmetic and cryptology, covers all course fundamentals - complements any class] |
| topic | Algebra, Abstract Outlines, syllabi, etc Combinatorial analysis Outlines, syllabi, etc Logic, Symbolic and mathematical Outlines, syllabi, etc Diskrete Mathematik (DE-588)4129143-8 gnd |
| topic_facet | Algebra, Abstract Outlines, syllabi, etc Combinatorial analysis Outlines, syllabi, etc Logic, Symbolic and mathematical Outlines, syllabi, etc Diskrete Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033628181&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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