Foundations of discrete mathematics with algorithms and programming:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton
CRC Press, Taylor & Francis Group
[2019]
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xvi, 518 Seiten Illustrationen |
| ISBN: | 9780815378488 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | Contents Preface xi 1 Sets, Relations and Functions 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 Introduction ................................................................. Functions........................... Equivalence Relations ................... ... ........ Finite and Infinite Sets . . . . . . . . . . ... . ·■. Cardinal Numbers of Sets. ..... ........................ Power Set of a Set ............ ..................... ··.·.. . . . . Exercises .......................................................... Partially Ordered Sets . . . ... . . . ; .... . . Lattices ... . . . ......................... .. . . . . . . . . Boolean Algebras . . . . . ... ... . . . . . . . 1.10.1 Introduction . . ..... .......... . 1.10.2 Examples of Boolean Algebras . . . . . . . . 1.11 Atoms in a Lattice............... ... . . . .N . . . . . . 1.12 Exercises ....................................................................... 2 Combinatorics 1 2 5 9 11 14 17 19 20 25 .34 34 34 38 42 47 2.1 2.2 2.3 What Is Combinatorics? . . .... . . . . . . ... 48 Elementary Counting Principles . . .... —51 Permutations and Combinations . ... . . . . . . . 64 2.3.1 Sums and Products . . . ............ ... . . . . 79 2.4 Binomial Theorem . . . . . . . . . . . . . . . . . .83 2.5 Multinomial Coefficients . . ... .... ... . · · 91 2.6 Stirling Numbers................... . ... . . ... . . .103 2.7 Stirling Number of the Second Kind {£} . . і . . .113 vii
CONTENTS viii 2.8 2.9 Bell Numbers ..............................................................125 The Principle of Inclusion ... . . . . .................127 2.9.1 Applications of Inclusion and Exclusion Principle ............................ 132 2.9.2 Application of Inclusion and Exclusion Principle to Elementary Number Theory . . 137 2.9.3 Applications to Permanents .... ..... 143 2.10 Generating Functions .... .... . . . . . . . . . 152 2.10.1 Solving Recurrence Relations Using Generating Function Techniques ....... 157 2.10.2 Catalan Numbers 160 2.11 Generating Subsets . . ...................... ...................... 166 2.12 Exercises . .... ...... . . ..... . . . . . . 175 3 Basics of Number Theory 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 4 Introduction to Graph Theory : 4.1 4.2 4.3 4.4 4.5 4.6 4.7 183 Introduction . . . . . . . . ՛.·■.: ..... . ... . . . 184 Divisibility. . .......... ..................................184 gcd and lem of Two Integers . . ... . . ............... 186 Primes.............................. ... . . . . . . . . ..... 189 Exercises............ ... 193 Congruences............ . ... ... . ... . . . . . . . . . 194 Complete System of Residues . . . ....... . . 197 Linear Congruences............ ... . . . . . . . . .... 202 Lattice Points Visible from the Origin...... . ..... 206 Exercises. . . . . ...... . . . . . . . . . . . . . 209 Some Arithmetical Functions . . ... . . ... . . 210 Exercises . . . . ... ................... . . ........ 218 The Big О Notation .................. 218 225 The Idea of a Graph . . . . . . .....
... . . . . . 225 An Informal and Intuitive . .... ....... . . 234 Multigraph or Undirected Graph . . ... . 239 Some Special Graphs . . . . ... . . . ..... . . 244 Graphs and Subgraphs . . . . ...... ...... 264 Walks, Paths, Cycles .................................................... 271 Connectedness............ ................................................... 275
CONTENTS ix 4.8 Graphs and Puzzles............ . . . . . . . . . . ·. . 283 4.8.1 An Application........................................... . 288 4.8.2 Two Friendship Theorems . . .... . . . . 289 4.8.3 Pandava Princes Problem and 3 Houses, 3 Utilities Problem . ...........................................292 4.9 Ramsey Numbers.............................. 293 4.10 Graph Algebra . . . ........................................ 308 4.11 Exercises................................................. .................. . 314 5 Introduction to Algorithms 5.1 5.2 5.3 5.4 5.5 5.6 5.7 Algorithms. . ............... ... . ............... ...............326 Complexity of Algorithms ... . . ............................330 An Overview of a Classical Computer . . . . . ... 353 Introduction to Programming .................................. 360 5.4.1 Parameter Passing ...........................................373 5.4.2 Recursion . . . . . . . ................... . .... 381 Introduction to Data Structures................................. 387 5.5.1 Access Restricted Lists ........... . 406 Examples of Algorithms . . . ... . . ... . ... 416 Exercises....................................... 439 6 Introduction to Logic 6.1 6.2 6.3 6.4 325 447 Introduction . ............................... 447 Algebra of Propositions ..................................... 448 Proofs in Mathematics . ......................... ... . 454 6.3.1 Universal and Existential Quantifiers .... 457 Probability ................................................................... 458 Appendices Answers to Even-Numbered Exercises 477
A Answers to Chapter 1 479 В Answers to Chapter 2 483 C Answers to Chapter 3 487 D Answers to Chapter 4 491
x CONTENTS E Answers to Chapter 5 497 F Answers to Chapter 6 503 Index 507
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| id | DE-604.BV045491425 |
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| indexdate | 2024-07-10T08:19:32Z |
| institution | BVB |
| isbn | 9780815378488 |
| language | English |
| lccn | 018018635 |
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| spelling | Sridharan, Sriraman Verfasser aut Foundations of discrete mathematics with algorithms and programming Sriraman Sridharan, R. Balakrishnan Boca Raton CRC Press, Taylor & Francis Group [2019] © 2019 xvi, 518 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Computer science Mathematics Algorithmus (DE-588)4001183-5 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Informatik (DE-588)4026894-9 gnd rswk-swf Informatik (DE-588)4026894-9 s Mathematik (DE-588)4037944-9 s DE-604 Algorithmus (DE-588)4001183-5 s Balakrishnan, Rangaswami Verfasser (DE-588)143438018 aut Erscheint auch als Online-Ausgabe 9781351019149 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030876283&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sridharan, Sriraman Balakrishnan, Rangaswami Foundations of discrete mathematics with algorithms and programming Computer science Mathematics Algorithmus (DE-588)4001183-5 gnd Mathematik (DE-588)4037944-9 gnd Informatik (DE-588)4026894-9 gnd |
| subject_GND | (DE-588)4001183-5 (DE-588)4037944-9 (DE-588)4026894-9 |
| title | Foundations of discrete mathematics with algorithms and programming |
| title_auth | Foundations of discrete mathematics with algorithms and programming |
| title_exact_search | Foundations of discrete mathematics with algorithms and programming |
| title_full | Foundations of discrete mathematics with algorithms and programming Sriraman Sridharan, R. Balakrishnan |
| title_fullStr | Foundations of discrete mathematics with algorithms and programming Sriraman Sridharan, R. Balakrishnan |
| title_full_unstemmed | Foundations of discrete mathematics with algorithms and programming Sriraman Sridharan, R. Balakrishnan |
| title_short | Foundations of discrete mathematics with algorithms and programming |
| title_sort | foundations of discrete mathematics with algorithms and programming |
| topic | Computer science Mathematics Algorithmus (DE-588)4001183-5 gnd Mathematik (DE-588)4037944-9 gnd Informatik (DE-588)4026894-9 gnd |
| topic_facet | Computer science Mathematics Algorithmus Mathematik Informatik |
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