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| 005 | 20200820105332.0 | ||
| 008 | 080304s2009 njua 001 0 eng | ||
| 020 | _a9788131724972 | ||
| 020 | _a9789332549593 (pbk) | ||
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_a511.6 _222 _bK815 |
| 100 | 1 | _aKolman, Bernard, | |
| 245 | 1 | 0 |
_aDiscrete mathematical structures / _cBernard Kolman, Robert C. Busby, Sharon Cutler Ross. |
| 250 | _a6th ed. (two editions 2009 and 2018) | ||
| 260 |
_aNew Delhi : _bPearson/Prentice Hall, _c2009 |
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| 300 | _avarious pages | ||
| 650 | 0 | _aComputer science--Mathematics | |
| 700 | 1 | _aBusby, Robert C. | |
| 700 | 1 | _aRoss, Sharon Cutler, | |
| 942 | _cBK | ||
| 505 | 0 | _aContents Preface viii A Word to Students xii 1 Fundamentals 1 1.1 Sets and Subsets 2 1.2 Operations on Sets 5 1.3 Sequences 13 1.4 Division in the Integers 20 1.5 Matrices 32 1.6 Mathematical Structures 41 2 Logic 50 2.1 Propositions and Logical Operations 51 2.2 Conditional Statements 57 2.3 Methods of Proof 62 2.4 Mathematical Induction 67 3 Counting 78 3.1 Permutations 79 3.2 Combinations 83 3.3 Pigeonhole Principle 88 3.4 Elements of Probability 91 3.5 Recurrence Relations 100 4 Relations and Digraphs 110 4.1 Product Sets and Partitions 111 4.2 Relations and Digraphs 115 4.3 Paths in Relations and Digraphs 123 4.4 Properties of Relations 129 4.5 Equivalence Relations 136 4.6 Computer Representation of Relations and Digraphs 140 4.7 Operations on Relations 147 4.8 Transitive Closure and Warshall's Algorithm 157 5 Functions 168 5.1 Functions 169 5.2 Functions for Computer Science 178 5.3 Growth of Functions 183 5.4 Permutation Functions 188 6 Order Relations and Structures 200 6.1 Partially Ordered Sets 201 6.2 Extremal Elements of Partially Ordered Sets 211 6.3 Lattices 216 6.4 Finite Boolean Algebras 226 6.5 Functions on Boolean Algebras 233 6.6 Circuit Design 237 7 Trees 254 7.1 Trees 254 7.2 Labeled Trees 259 7.3 Tree Searching 264 7.4 Undirected Trees 273 7.5 Minimal Spanning Trees 280 8 Topics in Graph Theory 290 8.1 Graphs 291 8.2 Euler Paths and Circuits 296 8.3 Hamiltonian Paths and Circuits 304 8.4 Transport Networks 307 8.5 Matching Problems 315 8.6 Coloring Graphs 320 9 Semigroups and Groups 329 9.1 Binary Operations Revisited 330 9.2 Semigroups 334 9.3 Products and Quotients of Semigroups 341 9.4 Groups 347 9.5 Products and Quotients of Groups 358 9.6 Other Mathematical Structures 363 10 Languages and Finite-State Machines 372 10.1 Languages 373 10.2 Representations of Special Grammars and Languages 381 10.3 Finite-State Machines 390 10.4 Monoids, Machines, and Languages 396 10.5 Machines and Regular Languages 401 10.6 Simplification of Machines 407 11 Groups and Coding 416 11.1 Coding of Binary Information and Error Detection 417 11.2 Decoding and Error Correction 428 11.3 Public Key Cryptology 436 | |