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Kolman B., Busby R.C., Cutler S.C. — Discrete Mathematical Structures
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Название: Discrete Mathematical StructuresАвторы: Kolman B., Busby R.C., Cutler S.C.Аннотация: More than any other book in this field, this book ties together discrete topics with a theme. Written at an appropriate level of understanding for those new to the world of abstract mathematics, it limits depth of coverage and areas covered to topics of genuine use in computer science. Chapter topics include fundamentals, logic, counting, relations and digraphs, trees, topics in graph theory, languages and finite-state machines, and groups and coding. For individuals interested in computer science and other related fields — looking for an introduction to discrete mathematics, or a bridge to more advanced material on the subject.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: Fourth EditionГод издания: 2001Количество страниц: 505Добавлена в каталог: 18.04.2008Операции: Положить на полку |
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Matrix 30 Matrix, (i, j) entry of 30 Matrix, (i, j)th element of 30 Matrix, Boolean 34 Matrix, Boolean, complement of 142 Matrix, column of 30 Matrix, diagonal 30 Matrix, element of 30 Matrix, identity 33 Matrix, main diagonal of 30 Matrix, of a relation 11 Matrix, parity check 409 Matrix, regular 448 Matrix, row of 30 Matrix, square 30 Matrix, symmetric 34 Matrix, transition 447 Matrix, transpose of 34 Matrix, zero 31 Max Flow Min Cut Theorem 304 Maximal compatibility block 443 Maximal element of a poset 202 Maximal matching 307 Maximum likelihood decoding function 414 Maximum likelihood technique 414 Meet of two elements in a lattice 207 Meet of two matrices 34 Message 401 Minimal element of a poset 202 Minimal spanning tree 272 Minimum distance of an encoding function 405 Minterm 231 Mod-2 Boolean product 408 Mod-2 sum 407 Mod-n function 27 170—171 Modular lattice 217 Modulus 129 modus ponens 59 Monoid 325 Monoid of a machine 381 Monoid, free 382 Monoid, idempotent element in 331 Monoid, submonoid 326 Moore machine 377 Moore machine, acceptance state of 377 Moore machine, language of 384 Moore machine, quotient 379 Moore machine, starting state of 377 Multiple, common 26 Multiple, least common 26 Multiplication principle of counting 73 Multiplication table 341 Mutually exclusive events 88 Natural homomorphism 335 Negation of a statement 47 Negation, properties of 55 Neighbor, nearest, of a set of vertices 272 Neighbor, nearest, of a vertex 272 Network 297 Network, cut in 304 Network, flow in 297 Noise 402 Nondistributive lattice 214 Nonterminal symbol 359 Normal production 363 Normal subgroup 351 Notation, Backus — Naur 366 Notation, complete 247 Notation, infix 259 Notation, n-tree 247 Notation, postfix 259 Notation, prefix 257 O (big oh) 176 Odd permutation 185 Offspring of a vertex in a tree 246 One-to-one correspondence between A and B 165 One-to-one function 164 Onto function 164 Operation 39 319 Operation on a set 319 Operation, associative 39 322 Operation, binary 39 Operation, commutative 39 321 Operation, idempotent property of binary 322 Operation, table 321 Operation, unary 39 OR gate 227 Order of a group 341 Order of an element in a group 451 Order, lexicographic 193 Order, linear 192 Order, lower 177 Order, partial 191 Order, product partial 193 Order, same 176 Ordered pair 103 Ordered tree 247 Out-degree of a vertex 113 Outcome(s) 86 Outcome(s), equally likely 91 Output of a machine 375 Palindrome 82 Parent 246 Parity check code 403 Parity check matrix 409 Parse tree 363 Parsing a sentence 363 Partial order 191 Partial order, dual 192 Partial order, product 193 Partially ordered set 191 Partition 105 Partition, block of 105 Partition, cell of 105 Pascal's triangle 82 Path(s) in a graph 281 Path(s) in relations 115 Path(s), composition of 119 Path(s), Euler 284 Path(s), Hamiltonian 293 Path(s), interior vertices of 153 Path(s), length of 115 Path(s), simple 264 282 Permutation(s) 67 Permutation(s) of n objects taken r at a time, number of 75 Permutation(s) with limited repeats 77 Permutation(s), cyclic 182 Permutation(s), even 185 Permutation(s), function 180 Permutation(s), odd 185 Permutation(s), product of 182 Phrase structure grammar 358 Phrase structure grammar, derivation m 359 Phrase structure grammar, language of 360 Phrase structure grammar, nonterminal symbol of 359 Phrase structure grammar, production of 358 Phrase structure grammar, production relation of 358 Phrase structure grammar, regular 363 Phrase structure grammar, terminal symbol of 359 Phrase structure grammar, Type n, (n = 0, 1, 2, 3) 363 Pigeonhole Principle 83 Pigeonhole principle, extended 85 Planar graph 312 POINTER 133 Pointer, left 252 Pointer, right 252 Polish form 257 Polish form, reverse 259 Polynomial, Boolean 226 Polynomial, chromatic 313 Poset(s) 191 Poset(s), dual 192 Poset(s), greatest element of 203 Poset(s), Hasse diagram of 196 Poset(s), isomorphic 198 Poset(s), least element of 203 Poset(s), linearly ordered 192 Poset(s), maximal element 202 Poset(s), minimal element of 202 Poset(s), unit element of 204 Poset(s), zero element of 204 Positional tree 251 Positional tree, binary 251 Postfix form 259 Postorder search 258 Power set of a set 3 Predicate 49 Prefix form 257 Premises 58 Preorder search of a tree 255 Prim's algorithm 268—269 273 Prime number 22 Prime, relatively 24 127 Principle of correspondence 198 Principle of Mathematical Induction 64 Principle, addition 9 Principle, extended pigeonhole 85 Principle, multiplication, of counting 73 Principle, pigeonhole 83 print statement 435 Probabilistic 86 Probability of an event 88 Probability, elementary 90 Probability, space, axioms for 89 Probability, transition 447 Product in a semigroup 324 Product of two groups 349 Product of two matrices 32 Product of two permutations 182 Product of two semigroups 331 Product, Boolean, of two matrices 35 Product, cartesian 103 104 Product, mod-2 Boolean 408 Product, partial order 193 209 Product, set 103 Production 358 Production relation 358 Production, left 358 Production, normal 366 Production, recursive 366 Production, right 358 Proof by contradiction 60 Proof, constructive 83 Proof, existence 83 Proof, indirect method 60 Proof, steps in 61 Proper coloring of a graph 311 Property of the distance function 404 Property of the empty set 9 Property, absorption 212 Property, associative 9 39 55 212 322 Property, cancellation 340 Property, closure 39 Property, commutative 8 39 55 212 321 Property, distributive 9 40 55 214 Property, idempotent 9 55 212 322 Proposition(s) 46 Proposition(s), conjunction of 47 Proposition(s), disjunction of 48 Proposition(s), equivalent 54 Proposition(s), logically equivalent 54 Proposition(s), negation of 47 Propositional function 49 Propositional variable 47 Prove a theorem 58 Pseudocode 27 428 429—430 Pushdown automaton 452 Quantification, existential 50 Quantification, universal 49 Quantifiers 49—50 Quasiorder 201 Quotient of an equivalence relation 131 Quotient, finite-state machine 378 Quotient, graph 284 Quotient, group 250 Quotient, Moore machine 379 Quotient, semigroup 333 Quotient, set 105 131 R-relative set of A 110 R-relative set of x 110 random selection 91 Range of a relation 109 Reachability relation 119 Recognition machine see “Moore machine” Recurrence relation 95 Recurrence relation, characteristic equation of 97 Recurrence relation, linear homogeneous of degree k 97 Recursive formula 14 (see also “Recurrence relation”) Recursive production 363 Reflexive closure of a relation 145 Reflexive relation 121 Regular expression 18 371 Regular expression, over A 18 Regular grammar 363 371 Regular graph 283 Regular Markov chain 448 Regular set 19 371 Regular subset 19 Relation(s) 107 Relation(s) from A to B 107 Relation(s) on A 107 Relation(s) on a set 107 Relation(s), acyclic symmetric 264 Relation(s), antisymmetric 122 Relation(s), asymmetric 122 Relation(s), circular 132 Relation(s), closure of 145 Relation(s), compatibility 443 Relation(s), complementary 140 Relation(s), composition of 146 Relation(s), computer representation of 134—135 Relation(s), congruence 332 350 Relation(s), connected symmetric 125 Relation(s), connectivity 116 Relation(s), digraph of 112 Relation(s), domain of 109 Relation(s), empty 122 Relation(s), equality 121 Relation(s), equivalence 128 Relation(s), equivalence, classes of 131 Relation(s), equivalence, determined by partition 129 Relation(s), graph of symmetric 124 Relation(s), inequality 122 Relation(s), input-output 162 Relation(s), inverse 140 Relation(s), irreflexive 121 Relation(s), less than 122 Relation(s), linear homogeneous, of degree it 97 Relation(s), matrix of 111 Relation(s), partial order 191 Relation(s), path in 115 Relation(s), production 358 Relation(s), quasiorder 201 Relation(s), range of 109 Relation(s), reachability 119 Relation(s), recurrence 95 Relation(s), reflexive 121 Relation(s), reflexive closure of 145 Relation(s), restriction of 113 Relation(s), symmetric 122
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