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Kolman B., Busby R.C., Ross S. — Discrete Mathematical Structures
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Название: Discrete Mathematical StructuresАвторы: Kolman B., Busby R.C., Ross S.Аннотация: Tying together discrete mathematical topics with a theme, this text stresses both basic theory and applications, offering students a firm foundation for more advanced courses. It limits the mathematics required (no calculus), and explains the small amount of linear algebra that is needed. The book uses algorithms and pseudocode to illustrate techniques, provides coding exercises and features sections on mathematical structures, the predicate calculus, recurrence relations, functions for computer science, growth of functions and minimal spanning trees.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 3-rd editionГод издания: 1996Количество страниц: 544Добавлена в каталог: 23.01.2014Операции: Положить на полку |
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Moore machine 393 Moore machine, acceptance state of 393 Moore machine, language of 402 Moore machine, quotient 396 Moore machine, starting state of 393 Multiple, common 26 Multiple, least common 26 Multiplication principle of counting 73 Multiplication table 351 Mutually exclusive event 87 N-tree 290 n-tree, complete 290 Natural homomorphism 345 Negation of a statement 47 Negation, properties of 56 Neighbor, nearest, of a set vertices 322 Neighbor, nearest, of a vertex 322 Noise 421 Nondistributive lattice 253 Nonterminal symbol 370 Normal production 379 Normal subgroup 363 Notation, Backus — Naur 378 Notation, infix 304 Notation, postfix 304 Notation, prefix 302 O (big oh) 191 Odd permutation 186 Offspring of a vertex in a tree 287 One-to-one correspondence between A and B 172 One-to-one function 171 Onto function 171 Operation 40 330 Operation, associative 40 332 Operation, binary 40 Operation, binary on a set 330 Operation, commutative 40 332 Operation, idempotent property of binary 332 Operation, table 331 Operation, unary 40 OR gate 268 Order of a group 352 Order of an element in a group 472 Order, lexicographic 228 Order, linear 227 Order, lower 191 Order, partial 225 Order, product partial 228 Order, same 191 Ordered pair 101 Ordered tree 289 Out-degree of a vertex 113 Outcome(s) 86 Outcome(s), equally likely 90 Output of a machine 391 Parent 287 Parity check code 422 Parity check matrix 429 Parse tree 376 Parsing a sentence 376 Partial order 225 Partial order, dual 226 Partial order, product 228 Partially ordered set 225 Partition 103 Partition, block of 103 Partition, cell of 103 Path(s) in a graph 199 Path(s) in relations 116 Path(s), composition of 121 Path(s), Euler 204 Path(s), Hamiltonian 213 Path(s), interior vertices of 159 Path(s), length of 116 Path(s), simple 199 311 Permutation(s) 75 Permutation(s) of n objects taken r at a time, number of 75 Permutation(s), cyclic 183 Permutation(s), even 186 Permutation(s), function 181 Permutation(s), odd 186 Permutation(s), product of 182 Phrase structure grammar 370 Phrase structure grammar, derivation in 371 Phrase structure grammar, language of 371 Phrase structure grammar, nonterminal symbol of 370 Phrase structure grammar, production of 370 Phrase structure grammar, production relation of 370 Phrase structure grammar, regular 376 Phrase structure grammar, terminal symbol of 370 Phrase structure grammar, type n, (n=0, 1, 2, 3) 376 Pigeonhole Principle 82 Pigeonhole principle, extended 84 Planar graph 219 POINTER 137 Pointer, left 295 Pointer, right 295 Polish form 302 Polish form, reverse 304 Polynomial, Boolean 267 Polynomial, chromatic 220 Poset(s) 225 Poset(s), dual 226 Poset(s), greatest element of 240 Poset(s), Hasse diagram of 231 Poset(s), isomorphic 234 Poset(s), join of 246 Poset(s), least element of 240 Poset(s), linearly ordered 227 Poset(s), maximal element of 239 Poset(s), minimal element of 239 Poset(s), unit element of 241 Poset(s), zero element of 241 Positional tree 294 Positional tree, binary 294 Postfix form 304 Postorder search 303 Power set of a set 4 Predicate 49 Prefix form 302 Premises 59 Preorder search of a tree 300 Prim's algorithm 317—318 322—323 Prime number 23 Prime, relatively 24 130 Principle addition 11 Principle extended pigeonhole 84 Principle multiplication, of counting 73 Principle of correspondence 235 Principle of Mathematical Induction 64 Principle pigeonhole 82 print statement 455 Probabilistic 85 Probability of an event 87 Probability, elementary 89 Probability, space, axioms for 89 Probability, transition 468 Product in a semigroup 334 Product of two groups 361 Product of two matrices 32 Product of two permutations 182 Product of two semigroups 342 Product, Boolean, of two matrices 36 Product, cartesian 102 103 Product, mod 2 Boolean 427 Product, partial order 228 Product, set 102 Production 370 Production relation 370 Production, left 370 Production, normal 379 Production, recursive 379 Production, right 370 Proof by contradiction 61 Proof, constructive 82 Proof, existence 82 Proof, indirect method 61 Proof, steps in 62 Proper coloring of a graph 218 Property of the distance function 424 Property of the empty set 10 Property, absorption 252 Property, associative 10 40 56 251 332 Property, cancellation 350 Property, commutative 10 40 56 251 332 Property, distributive 10 40 56 253 Property, idempotent 10 56 251 332 Proposition(s) 46 Proposition(s), conjunction of 48 Proposition(s), disjunction of 48 Proposition(s), equivalent 55 Proposition(s), logically equivalent 55 Proposition(s), negation of 47 Propositional function 49 Propositional variable 47 Prove a theorem 59 Pseudocode 28 447 449 Pushdown automaton 474 Quantification, existential 50 Quantification, universal 49 Quantifiers 49—50 Quasiorder 238 Quotient of an equivalence relation 134 Quotient, finite-state machine 394 Quotient, graph 202 Quotient, group 362 Quotient, Moore machine 396 Quotient, semigroup 344 Quotient, set 103 R-relative set of A 109 R-relative set of x 109 random selection 90 Range of a relation 109 Reachability relation 121 Recognition machine see "Moore machine" Recurrence relation 95 Recurrence relation, characteristic equation of 97 Recurrence relation, linear homogeneous of degree k 96 Recursive formula 15 see Recursive production 379 Reflexive closure of a relation 151 Reflexive relation 124 Regular expression 19 Regular expression, over A 19 Regular grammar 376 385 Regular graph 200 Regular Markov chain 469 Regular set 20 385 Regular subset 20 Relation(s) 106 Relation(s) from A to B 106 Relation(s) on A 106 Relation(s) on a set 106 Relation(s), acyclic symmetric 312 Relation(s), antisymmetric 124 Relation(s), asymmetric 124 Relation(s), circular 136 Relation(s), closure of 151 Relation(s), compatibility 464 Relation(s), complementary 146 Relation(s), composition of 152 Relation(s), computer representation of 138—139 Relation(s), congruence 342 362 Relation(s), connected symmetric 127 Relation(s), connectivity 117 Relation(s), digraph of 111 Relation(s), domain of 109 Relation(s), empty 124 Relation(s), equality 124 Relation(s), equivalence 131 Relation(s), equivalence, classes of 134 Relation(s), equivalence, determined by a partition 132 Relation(s), graph of symmetric 127 Relation(s), inequality 124 Relation(s), input-output 169 Relation(s), inverse 146 Relation(s), irreflexive 124 Relation(s), less than 125 Relation(s), linear homogeneous, of degree k 96 Relation(s), matrix of 111 Relation(s), partial order 225 Relation(s), path in 116 Relation(s), production 370 Relation(s), quasiorder 238 Relation(s), range of 109 Relation(s), reachability 121 Relation(s), recurrence 95 Relation(s), reflexive 124 Relation(s), reflexive closure of 151 Relation(s), restriction of 114 Relation(s), symmetric 124 Relation(s), symmetric closure of 151 Relation(s), transitive 128 Relation(s), transitive closure of 151 157 Relatively prime 24 130 Restriction of a relation 114 Return statement 445 452—453 Reverse Polish form 304 Right cancellation property 350 Right coset of a subgroup 363 Right pointer 295 Right side of a production 370 Right subtree 300 Root of a tree 287 Rooted tree 287 Row of a matrix 30 Rules of Inference 59 Running time of an algorithm 194 466 Same level 449 Same order 191 Sample space 86 Search, inorder 303 Search, postorder 303 Search, preorder 300 Search, tree 299 Searching a tree 299 Selection 447 Selection, random 90 Semantics of a language 369 Semigroup(s) 334 Semigroup(s), factor 344 Semigroup(s), free 335 Semigroup(s), homomorphism 339 Semigroup(s), isomorphic 337 Semigroup(s), isomorphism 337 Semigroup(s), product of 334 Semigroup(s), quotient 344 Semigroup(s), sub- 335 Sentence parsing 376 SEQUENCE 14 Sequence of values 16 Sequence, empty 19 Sequence, Fibonacci 95 Sequence, finite 14 Sequence, infinite 14 Sequence, initial conditions for 95 Sequence, set corresponding to 16 Set(s) 1 Set(s), alphabet 19 Set(s), binary operation on 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