An introduction to discrete mathematics and its applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Reading, Mass. [u.a.]
Addison-Wesley
1986
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 486 S. Ill. |
| ISBN: | 0201149478 |
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MARC
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| 100 | 1 | |a Kalmanson, Kenneth |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An introduction to discrete mathematics and its applications |c Kenneth Kalmanson |
| 264 | 1 | |a Reading, Mass. [u.a.] |b Addison-Wesley |c 1986 | |
| 300 | |a X, 486 S. |b Ill. | ||
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Chapter 1 SETS, NUMBERS, AND
ALGORITHMS 1
1.1 Defining Sets and Subsets 2
1.2 Sets and Functions 9
1.3 Sums and Algorithms 16
1.4 Integers and Algorithms 24
1.5 Rational and Real Numbers 31
1.6 Other Systems of Numeration 39
1.7 Binary Arithmetic and Two s Complements 47
1.8 Modular Arithmetic 54
Computer Programming Exercises 63
Chapter 2 SETS, LOGIC, AND COMPUTER
ARITHMETIC 65
2.1 Examples, Counterexamples, and Mathematical Induction 66
2.2 Set Operations 73
2.3 The Algebra of Set Operations 82
2.4 Truth Sets and Truth Tables 88
vii
viii CONTENTS
2.5 Laws of Logic and Rules of Reasoning 96
2.6 Logic Gates and Computer Arithmetic 103
Computer Programming Exercises 112
Chapter 3 COUNTING 115
3.1 The Multiplication Principle and Permutations 116
3.2 Combinations and Binomial Coefficients 124
3.3 Repetitions and Partitions 130
3.4 Inclusion Exclusion 136
3.5 Applications of Counting from Probability to
Pigeonholes 143
3.6 Recurrence Models 150
3.7 Closed Forms and Analysis of Algorithms 158
3.8 Divide And Conquer Relations 167
Computer Programming Exercises 173
Chapter 4 INTRODUCTION TO GRAPH
THEORY 175
4.1 Graphs and Walks 176
4.2 Classification of Graphs 187
4.3 Planar Graphs and Euler s Formula 197
4.4 Graph Coloring 205
4.5 Multigraphs and Matrices 212
4.6 Matrix Multiplication and Connectedness 220
Computer Programming Exercises 229
Chapter 5 TREES AND ALGORITHMS 231
5.1 Weighted Graphs and the Connector Problem 232
5.2 The Shortest Path Problem 242
5.3 Rooted Trees and Polish Notation 250
5.4 Binary Search Trees 261
Computer Programming Exercises 267
CONTENTS ix
Chapter 6 DIRECTED GRAPHS AND
NETWORKS 269
6.1 Digraphs 270
6.2 Orientable Graphs and Topological Sorting 279
6.3 Activity Analysis and Longest Paths 288
6.4 Transport Networks 296
6.5 Maximal Matchings 307
Computer Programming Exercises 313
Chapter 7 APPLIED MODERN ALGEBRA 315
7.1 Relations 316
7.2 Equivalence Relations and Partitions 326
7.3 Partial Orderings and Dilworth s Theorem 336
7.4 Lattices 342
7.5 Boolean Algebras 351
7.6 Minimization and Switching Circuits 360
7.7 Groups 370
7.8 Group Codes 377
Computer Programming Exercises 383
Chapter 8 FURTHER TOPICS IN COUNTING
AND RECURSION 385
8.1 Homogeneous Linear Recurrence Relations 386
8.2 The Nonhomogeneous Case 393
8.3 Generating Functions and Recurrence Relations 398
8.4 Generating Functions and Counting 410
Computer Programming Exercises 419
Appendix PROGRAMS IN BASIC AND
EXERCISES 421
Al BASIC Statements 422 A6 PRIMETEST 427
A2 More BASIC Statements 423 A7 SIEVE 428
A3 FIBONACCI 425 A8 PARTITION 429
A4 NESTED POLY 1 426 A9 SETS AND BINARY 430
A5 NESTED POLY 2 426 A10 N FACTORIAL 431
x CONTENTS
All BINOMIAL 431 A19 EULER T/C 440
A12 BIRTHDAY 432 A20 MIN COST TREE 442
A13 BUBLSORT 433 A21 DFS SPAN TREE 445
A14 MATRIX ARRAY 434 A22 TOPL SORT 446
A15 MATRIX ADD 434 A23 TRANS TEST 448
A16 MATMULT 435 A24 SYMTRANSTEST 449
A17 VERTEX DEG 437 A25 LOGIC TABLE 450
A18 PATH MATRIX 438
Bibliography 453
Answers to Selected Exercises 455
Index 483
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T16:47:54Z |
| institution | BVB |
| isbn | 0201149478 |
| language | English |
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| publishDate | 1986 |
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| publisher | Addison-Wesley |
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| spelling | Kalmanson, Kenneth Verfasser aut An introduction to discrete mathematics and its applications Kenneth Kalmanson Reading, Mass. [u.a.] Addison-Wesley 1986 X, 486 S. Ill. txt rdacontent n rdamedia nc rdacarrier Informatique - Mathématiques Informatik Mathematik Computer science Mathematics Diskrete Mathematik (DE-588)4129143-8 gnd rswk-swf Diskrete Mathematik (DE-588)4129143-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004164664&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kalmanson, Kenneth An introduction to discrete mathematics and its applications Informatique - Mathématiques Informatik Mathematik Computer science Mathematics Diskrete Mathematik (DE-588)4129143-8 gnd |
| subject_GND | (DE-588)4129143-8 |
| title | An introduction to discrete mathematics and its applications |
| title_auth | An introduction to discrete mathematics and its applications |
| title_exact_search | An introduction to discrete mathematics and its applications |
| title_full | An introduction to discrete mathematics and its applications Kenneth Kalmanson |
| title_fullStr | An introduction to discrete mathematics and its applications Kenneth Kalmanson |
| title_full_unstemmed | An introduction to discrete mathematics and its applications Kenneth Kalmanson |
| title_short | An introduction to discrete mathematics and its applications |
| title_sort | an introduction to discrete mathematics and its applications |
| topic | Informatique - Mathématiques Informatik Mathematik Computer science Mathematics Diskrete Mathematik (DE-588)4129143-8 gnd |
| topic_facet | Informatique - Mathématiques Informatik Mathematik Computer science Mathematics Diskrete Mathematik |
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