Discrete mathematics and its applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
McGraw-Hill
2019
|
| Ausgabe: | Eigth Edition, International Student Edition |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXI, 942, A-16, B-8, S-98, I-26 Seiten Diagramme |
| ISBN: | 9781260091991 |
Internformat
MARC
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| 250 | |a Eigth Edition, International Student Edition | ||
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Datensatz im Suchindex
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Contents About the Author vi Preface vii Online Resources xvi To the Student xix 1 The Foundations: Logic andProofs. 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Propositional Logic. 1 Applications of Propositional Logic. 17 Propositional Equivalences. 26 Predicates and Quantifiers. 40 Nested Quantifiers. 60 Rules of Inference. 73 Introduction to Proofs. 84 Proof Methods and Strategy. 96 End-of-Chapter Material. 115 2 Basic Structures: Sets, Functions, Sequences, Sums, and Matrices. 121 2.1 2.2 2.3 2.4 2.5 2.6
Sets. 121 Set Operations. 133 Functions. 147 Sequences and Summations. 165 Cardinality of Sets. 179 Matrices. 188 End-of-Chapter Material. 195 3 Algorithms. 201 3.1 Algorithms. 201 3.2 The Growth of Functions. 216 3.3 Complexity of Algorithms. 231 End-of-Chapter Material. 244 4
Number Theory and Cryptography. 251 4.1 4.2 4.3 4.4 4.5 4.6 Divisibility and Modular Arithmetic. 251 Integer Representations and Algorithms. 260 Primes and Greatest Common Divisors. 271 Solving Congruences. 200 Applications of Congruences. 303 Cryptography.310 End-of-Chapter Material. 324 iii
iv Contents 5 Induction and Recursion.331 5,1 5,2 5.3 5.4 5.5 Mathematical Induction. 331 Strong Induction and Well-Ordering. 354 Recursive Definitions and StructuralInduction. 365 Recursive Algorithms. 381 Program Correctness.393 End-of-Chapter Material.398 6 Counting. . 405 6.1 6.2 6.3 6.4 6.5 6.6 The Basics of Counting. 405 The Pigeonhole Principle. 420 Permutations and Combinations. 428 Binomial Coefficients and Identities. 437 Generalized Permutations and
Combinations.445 Generating Permutations and Combinations. 457 End-of-Chapter Material.461 7 Discrete Probability. 7.1 7.2 7.3 7.4 An Introduction to Discrete Probability. 469 Probability Theory. 477 Bayes’ Theorem. 494 Expected Value and Variance. . 503 End-of-Chapter Material. 520 8 Advanced Counting Techniques. 8.1 8.2 8.3 8.4 8.5 8.6 Applications of Recurrence Relations. 527 Solving Linear Recurrence Relations. 540 Divide-and-Conquer Algorithms and Recurrence Relations. 553 Generating Functions. 563 Inclusion-
Exclusion. 579 Applications of Inclusion-Exclusion. 585 End-of-Chapter Material. 592 9 Relations. 599 469 527 9.1 Relations and Their Properties. 599 9.2 n-ary Relations and Their Applications. 611 9.3 Representing Relations. 621 9.4 Closures of Relations. 62g 9.5 Equivalence Relations. 638 9.6 Partial Orderings. 650 End-of-Chapter Material. 665
Contents 10 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 11 11.1 11.2 11.3 11.4 11.5 12 12.1 12.2 12.3 12.4 v Graphs. 673 Graphs and Graph Models. 673 Graph Terminology and Special Types of Graphs. 685 Representing Graphs and Graph Isomorphism. 703 Connectivity.714 Euler and Hamilton Paths.728 Shortest-Path Problems. 743 Planar Graphs. 753 Graph Coloring. 762 End-of-Chapter Material. 771 Trees. 781 Introduction to Trees. 781 Applications of
Trees. 793 Tree Traversal. 808 Spanning Trees. 821 Minimum Spanning Trees. 835 End-of-Chapter Material. 841 Boolean Algebra. 847 Boolean Functions. 847 Representing Boolean Functions. 855 Logic Gates. 858 Minimization of Circuits.864 End-of-Chapter Material. 879 13 Modeling Computation. 885 13.1 13.2 13.3 13.4 13.5 Languages and
Grammars.885 Finite-State Machines with Output. 897 Finite-State Machines with No Output. 904 Language Recognition. 917 Turing Machines. 927 End-of-Chapter Material. 938 Appendices. A-l 1 2 3 Axioms for the Real Numbers and the Positive Integers.A-l Exponential and Logarithmic Functions. A-7 Pseudocode.A-11 Suggested Readings B-l Answers to Odd-Numbered Exercises S-l Index of Biographies 1-1 Index 1-2 |
| adam_txt |
Contents About the Author vi Preface vii Online Resources xvi To the Student xix 1 The Foundations: Logic andProofs. 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Propositional Logic. 1 Applications of Propositional Logic. 17 Propositional Equivalences. 26 Predicates and Quantifiers. 40 Nested Quantifiers. 60 Rules of Inference. 73 Introduction to Proofs. 84 Proof Methods and Strategy. 96 End-of-Chapter Material. 115 2 Basic Structures: Sets, Functions, Sequences, Sums, and Matrices. 121 2.1 2.2 2.3 2.4 2.5 2.6
Sets. 121 Set Operations. 133 Functions. 147 Sequences and Summations. 165 Cardinality of Sets. 179 Matrices. 188 End-of-Chapter Material. 195 3 Algorithms. 201 3.1 Algorithms. 201 3.2 The Growth of Functions. 216 3.3 Complexity of Algorithms. 231 End-of-Chapter Material. 244 4
Number Theory and Cryptography. 251 4.1 4.2 4.3 4.4 4.5 4.6 Divisibility and Modular Arithmetic. 251 Integer Representations and Algorithms. 260 Primes and Greatest Common Divisors. 271 Solving Congruences. 200 Applications of Congruences. 303 Cryptography.310 End-of-Chapter Material. 324 iii
iv Contents 5 Induction and Recursion.331 5,1 5,2 5.3 5.4 5.5 Mathematical Induction. 331 Strong Induction and Well-Ordering. 354 Recursive Definitions and StructuralInduction. 365 Recursive Algorithms. 381 Program Correctness.393 End-of-Chapter Material.398 6 Counting. . 405 6.1 6.2 6.3 6.4 6.5 6.6 The Basics of Counting. 405 The Pigeonhole Principle. 420 Permutations and Combinations. 428 Binomial Coefficients and Identities. 437 Generalized Permutations and
Combinations.445 Generating Permutations and Combinations. 457 End-of-Chapter Material.461 7 Discrete Probability. 7.1 7.2 7.3 7.4 An Introduction to Discrete Probability. 469 Probability Theory. 477 Bayes’ Theorem. 494 Expected Value and Variance. . 503 End-of-Chapter Material. 520 8 Advanced Counting Techniques. 8.1 8.2 8.3 8.4 8.5 8.6 Applications of Recurrence Relations. 527 Solving Linear Recurrence Relations. 540 Divide-and-Conquer Algorithms and Recurrence Relations. 553 Generating Functions. 563 Inclusion-
Exclusion. 579 Applications of Inclusion-Exclusion. 585 End-of-Chapter Material. 592 9 Relations. 599 469 527 9.1 Relations and Their Properties. 599 9.2 n-ary Relations and Their Applications. 611 9.3 Representing Relations. 621 9.4 Closures of Relations. 62g 9.5 Equivalence Relations. 638 9.6 Partial Orderings. 650 End-of-Chapter Material. 665
Contents 10 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 11 11.1 11.2 11.3 11.4 11.5 12 12.1 12.2 12.3 12.4 v Graphs. 673 Graphs and Graph Models. 673 Graph Terminology and Special Types of Graphs. 685 Representing Graphs and Graph Isomorphism. 703 Connectivity.714 Euler and Hamilton Paths.728 Shortest-Path Problems. 743 Planar Graphs. 753 Graph Coloring. 762 End-of-Chapter Material. 771 Trees. 781 Introduction to Trees. 781 Applications of
Trees. 793 Tree Traversal. 808 Spanning Trees. 821 Minimum Spanning Trees. 835 End-of-Chapter Material. 841 Boolean Algebra. 847 Boolean Functions. 847 Representing Boolean Functions. 855 Logic Gates. 858 Minimization of Circuits.864 End-of-Chapter Material. 879 13 Modeling Computation. 885 13.1 13.2 13.3 13.4 13.5 Languages and
Grammars.885 Finite-State Machines with Output. 897 Finite-State Machines with No Output. 904 Language Recognition. 917 Turing Machines. 927 End-of-Chapter Material. 938 Appendices. A-l 1 2 3 Axioms for the Real Numbers and the Positive Integers.A-l Exponential and Logarithmic Functions. A-7 Pseudocode.A-11 Suggested Readings B-l Answers to Odd-Numbered Exercises S-l Index of Biographies 1-1 Index 1-2 |
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| spelling | Rosen, Kenneth H. Verfasser (DE-588)14281430X aut Discrete mathematics and its applications Kenneth H. Rosen Eigth Edition, International Student Edition New York, NY McGraw-Hill 2019 © 2019 XXI, 942, A-16, B-8, S-98, I-26 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Diskrete Mathematik (DE-588)4129143-8 gnd rswk-swf Mathematics Computer science / Mathematics (DE-588)4123623-3 Lehrbuch gnd-content Diskrete Mathematik (DE-588)4129143-8 s DE-604 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=033628157&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Discrete mathematics and its applications |
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| title_full | Discrete mathematics and its applications Kenneth H. Rosen |
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| title_short | Discrete mathematics and its applications |
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