Introductory discrete mathematics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Englewood Cliffs, NJ
Prentice Hall
1991
|
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 236 S. |
| ISBN: | 0130399426 |
Internformat
MARC
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| 100 | 1 | |a Balakrishnan, V. K. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introductory discrete mathematics |c V. K. Balakrishnan |
| 264 | 1 | |a Englewood Cliffs, NJ |b Prentice Hall |c 1991 | |
| 300 | |a XIV, 236 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
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Datensatz im Suchindex
| _version_ | 1804144576415399936 |
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| adam_text | Contents
Preface xiii
vQ) Set Theoiy and Logic 1
0.1 Introduction to Set Theory 1
0.2 Functions and Relations 7
0.3 Inductive Proofs and Recursive Definitions 17
0.4 The Language of Logic 22
0.5 Notes and References 25
0.6 Exercises 26
vii
ii Combinatorics 35
1.1 Two Basic Counting Rules 55
1.2 Permutations 38
1.3 Combinations 42
1.4 More on Permutations and Combinations 48
1.5 The Pigeonhole Principle 53
1.6 The Inclusion-Exclusion Principle 59
1.7 Summary of Results in Combinatorics 69
1.8 Notes and References 71
1.9 Exercises 72
^ Generating Functions 80
2.1 Introduction 80
2.2 Ordinary Generating Functions 83
2.3 Exponential Generating Functions 86
2.4 Notes and References 90
2.5 Exercises 90
Q) Recurrence Relations 94
3.1 Introduction 94
3.2 Homogeneous Recurrence Relations 97
3.3 Inhomogeneous Recurrence Relations 102
3.4 Recurrence Relations and Generating Functions
105
3.5 Analysis of Algorithms 108
3.6 Notes and References 116
3.7 Exercises 116
4i Graphs and Digraphs 120
4.1 Introduction 720
4.2 Adjacency Matrices and Incidence Matrices 125
4.3 Joining in Graphs 129
4.4 Reaching in Digraphs 132
4.5 Testing Connectedness 133
4.6 Strong Orientation of Graphs 135
4.7 Notes and References 135
4.8 Exercises 136
S) More on Graphs and Digraphs 140
5.1 Eulerian Paths and Eulerian Circuits 140
5.2 Coding and de Bruijn Digraphs 144
5.3 Hamiltonian Paths and Hamiltonian Cycles 149
5.4 Applications of Hamiltonian Cycles 153
5.5 Vertex Coloring and Planarity of Graphs 155
5.6 Notes and References 161
5.7 Exercises 162
(o) Trees and Their Applications 164
6.1 Definitions and Properties 164
6.2 Spanning Trees 167
6.3 Binary Trees 170
6.4 Notes and References 177
6.5 Exercises 778
u Spanning Tree Problems 180
7.1 More on Spanning Trees 180
7.2 Kruskal s Greedy Algorithm 184
7.3 Prim s Greedy Algorithm 187
7.4 Comparison of the Two Algorithms 193
7.5 Notes and References 193
7.6 Exercises 193
© Shortest Path Problems 196
8.1 Introduction 196
8.2 Dijkstra s Algorithm 197
8.3 Floyd-Warshall Algorithm 202
8.4 Comparison of the Two Algorithms 204
8.5 Notes and References 205
8.6 Exercises 205
Alplpdondlik What Is NP-Completeness 207
A.I Problems and Their Instances 207
A.2 The Size of an Instance 208
A.3 Algorithm to Solve a Problem 209
A.4 Complexity of an Algorithm 209
A.5 The Big Oh or the O() Notation 210
A.6 Easy Problems and Difficult Problems 211
A.7 The Class P and the Class NP 212
A.8 Polynomial Transformations and NP-Completeness
214
A.9 Coping with Hard Problems 217
Bibliography 219
Answers to Selected Exercises 224
Index 231
|
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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T23:05:45Z |
| institution | BVB |
| isbn | 0130399426 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021721810 |
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| physical | XIV, 236 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
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| publisher | Prentice Hall |
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| spelling | Balakrishnan, V. K. Verfasser aut Introductory discrete mathematics V. K. Balakrishnan Englewood Cliffs, NJ Prentice Hall 1991 XIV, 236 S. txt rdacontent n rdamedia nc rdacarrier HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021721810&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Balakrishnan, V. K. Introductory discrete mathematics |
| title | Introductory discrete mathematics |
| title_auth | Introductory discrete mathematics |
| title_exact_search | Introductory discrete mathematics |
| title_full | Introductory discrete mathematics V. K. Balakrishnan |
| title_fullStr | Introductory discrete mathematics V. K. Balakrishnan |
| title_full_unstemmed | Introductory discrete mathematics V. K. Balakrishnan |
| title_short | Introductory discrete mathematics |
| title_sort | introductory discrete mathematics |
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