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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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Relation(s), symmetric closure of 145 Relation(s), transitive 125 Relation(s), transitive closure of 145 151 Relatively prime 24 127 Restriction of a relation 113 Return statement 434 Reverse Polish form 259 Right cancellation property 340 Right coset of a subgroup 351 Right pointer 252 Right side of a production 358 Right subtree 255 Root of a tree 245 Rooted tree 245 Row of a matrix 30 Rules of Inference 58 Running time of an algorithm 179 445 Same level 430 Same order 176 Sample space 86 Search, inorder 258 Search, postorder 258 Search, preorder 255 Search, tree 255 Searching a tree 255 Selection 428 Selection, random 91 Semantics of a language 358 Semigroup(s) 324 Semigroup(s), factor 333 Semigroup(s), free 325 Semigroup(s), homomorphism 329 Semigroup(s), isomorphic 327 Semigroup(s), isomorphism 327 Semigroup(s), product of 331 Semigroup(s), quotient 333 Semigroup(s), sub- 326 Sentence parsing 363 SEQUENCE 13 Sequence, empty 17 Sequence, Fibonacci 95 99 Sequence, finite 13 Sequence, infinite 13 Sequence, initial conditions for 95 Sequence, of values 15 Sequence, set corresponding to 14 Set(s) 1 Set(s), alphabet 17 Set(s), binary operation on 319 Set(s), cardinality of 3 Set(s), characteristic function of 15 Set(s), closed 319 Set(s), combination of, taken r at a time 79 Set(s), complement of 7 Set(s), complement of B with respect to A 7 Set(s), contained in 3 Set(s), corresponding to a sequence 14 Set(s), countable 17 Set(s), disjoint 6 Set(s), element of 1 Set(s), empty 2 Set(s), equal 2 Set(s), finite 3 Set(s), infinite 3 Set(s), input, of a machine 375 Set(s), intersection of 5 Set(s), linearly ordered 192 Set(s), member of 1 Set(s), mutually exclusive 88 Set(s), operations, properties of 8—9 Set(s), partially ordered 191 Set(s), partition of 105 Set(s), permutation of 75 Set(s), power set of 3 Set(s), product 103 Set(s), quotient 105 131 Set(s), R-relative 110 Set(s), regular 19 Set(s), regular expression over 18 371 Set(s), state, of a machine 375 Set(s), strings from 17 Set(s), subset of 3 Set(s), symmetric difference of 7 Set(s), uncountable 17 Set(s), union of 5 Set(s), universal 3 Set(s), Venn diagram of 3 Sibling of a vertex 246 Simple circuit 282 Simple cycle 264 Simple path 264 282 Sink 297 Sorting, topological 197 Source 297 Space, axioms for 89 Space, probability 89 Space, sample 86 Spanning tree 266 Spanning tree, minimal 272 Spanning tree, undirected 266 Square matrix 30 Starting state 377 State(s) 375 447 State(s) of a finite-state machine 375 State(s), acceptance 377 State(s), set of a machine 375 State(s), starting 377 State(s), transition function 375 382 State(s), transition table 376 State(s), vector, of a Markov chain 447 Statement(s) 46 Statement(s), CALL 425 433 Statement(s), compound 47 Statement(s), conditional 52 Statement(s), conjunction of 47 Statement(s), contradiction of 54 Statement(s), contrapositive of 53 Statement(s), converse of 53 Statement(s), disjunction of 48 Statement(s), equivalent 54 Statement(s), FOR 432—433 Statement(s), GOTO 427 435 Statement(s), IF THEN ELSE 427 430 Statement(s), logically equivalent 54 Statement(s), logically following from 58 Statement(s), negation of 47 Statement(s), PRINT 435 Statement(s), RETURN 434 Statement(s), UNTIL 432 Statement(s), WHILE 428 431 Steady-state vector 448 Steps in proof 61 Storage cell 133 String(s) 14 17 String(s), catenation of 18 String(s), compatible 393 String(s), empty 17 String(s), length 363 384 Structure, mathematical 38 Structured algorithm 427 Subgraph 283 Subgroup 344 Subgroup, coset of 351 Subgroup, normal 351 Subgroup, trivial 345 Sublattice 209 Submonoid 326 SUBROUTINE 425 433 SUBROUTINE statement 426 433 Subsemigroup 326 Subset 3 Subset, regular 19 Substitution rule for Boolean algebras 221 Subtree of a tree 248 Subtree, corresponding to a vertex 248 Subtree, left 255 Subtree, right 255 Sum of matrices 31 Sum, mod-2 407 Supersink 306 Supersource 306 Symmetric closure of a relation 145 Symmetric difference, of two sets 7 Symmetric group on n letters 344 Symmetric matrix 34 Symmetric relation 122 Symmetric relation, acyclic 264 Symmetric relation, graph of 124 Symmetry of a figure 342 Syndrome of an element 419 Syntax of a language 358 Syntax, diagram 368 System, mathematical 38 T flip-flop 376 Table, binary operation 321 Table, decoding 417 Table, multiplication 341 Table, state transition 376 Table, truth 47 225 Tautology 54 Terminal symbol 359 Theta class 177 Time, running, of an algorithm 179 445 Topological sorting 197 Towers of Hanoi 442 Transformation 163 Transition function, state 375 382 Transition function, state corresponding to a string 382 Transition, matrix 447 Transition, probability 447 Transitive closure of a relation 145 151 Transitive relation 125 Transport network 297 Transpose of a matrix 34 Transposition 184 Traveling salesperson problem 295 Traversing a tree 255 Tree(s) 245 Tree(s), AVL 263 Tree(s), B-tree of degree k 450 Tree(s), binary 247 Tree(s), complete binary 247 Tree(s), complete n-tree 247 Tree(s), computer representation of positional binary 251—252 Tree(s), derivation 360 Tree(s), height of 246 Tree(s), inorder search of 258 Tree(s), labeled 250 Tree(s), leaves of 247 Tree(s), linked list representation of 260 Tree(s), M-tree 247 Tree(s), minimal spanning 272 Tree(s), ordered 247 Tree(s), parse 363 Tree(s), positional 251 Tree(s), positional binary 251 Tree(s), postorder search of 258 Tree(s), preorder search of 255 Tree(s), rooted 245 Tree(s), search 255 Tree(s), searching 255 Tree(s), spanning 266 Tree(s), subtree of 248 255 Tree(s), traversing 255 Tree(s), Tree(s), root of 245 Tree(s), undirected 264 Tree(s), undirected, edge in 264 Tree(s), undirected, spanning 266 Tree(s), vertex of 245 Tree(s), walking 255 Truth table 47 225 Two-stage influence 453 Type n (n = 0, 1, 2, 3), language 363 Type n (n = 0, 1, 2, 3), phrase structure grammar 363 Unary operation 39 Uncountable set 17 Undirected edge 125 264 Undirected spanning tree 266 Undirected tree 264 Union of sets 5 Unit element of a poset 204 Universal quantification 49 Universal set 3 Universal set, properties of 9 until statement 432 Upper bound 204 Value of a function 161 Value of the flow 297 Variable, local 434 Vector, state 447 Vector, steady-state 448 Venn diagram 3 Venn, John 3 Vertex 112 280 Vertex in a tree T 248 Vertex, degree of 281 Vertex, descendants of 248 Vertex, in-degree of 112 Vertex, isolated 281 Vertex, level n 246 Vertex, nearest neighbor of 272 Vertex, offspring of 246 Vertex, out-degree of 113 Vertex, subtree beginning with 248 Vertex, visiting 254 Vertices, adjacent 125 264 281 Vertices, connected 309 Vertices, disconnected 309 Vertices, distance between 272 Vertices, interior, of a path 153 Vertices, nearest neighbor of 272 Walking a tree 255 Warshall's algorithm 153 Weight of a word 403 Weight of an edge 271 295 Weighted graph 271 while statement 428 432 Word 17 401 Word, code 402 Word, weight of 403 Zero, element of a poset 204 Zero, matrix 31
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