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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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Euclidean algorithm 24 Euler circuit 286 Euler path 286 Even permutation 185 Event(s) 87 Event(s), certain 88 Event(s), disjoint 88 Event(s), elementary 90 Event(s), frequency of occurrence 88 Event(s), impossible 88 Event(s), mutually exclusive 88 Event(s), probability of 88 Everywhere-defined function 164 Existence proof 83 Existential quantification 50 Expected value 93 Explicit formula 14 Exponential function base 2 171 Expression, Boolean 226 Expression, over A 18 Expression, regular 18 Factor semigroup 333 Factorial n 76 Fibonacci sequence 95 99 Finite group 341 Finite sequence 13 Finite set 3 Finite-state machine 375 Finite-state machine, congruence on 378 Finite-state machine, digraph of 377 Finite-state machine, input set of 375 Finite-state machine, monoid of 383 Finite-state machine, quotient of 378 Finite-state machine, state of 375 Finite-state machine, state set of 375 Finite-state machine, state transition table of 376 Fleury's algorithm 290—291 Floor function 171 Flow 297 Flow chart 428 Flow, conservation of 297 Flow, value of 297 for statement 432—433 Formula, explicit 14 Formula, recursive 14 Free monoid 382 Free semigroup 325 Frequency of occurrence of E in n trials 88 Function 161 Function statement 434 Function, argument of 161 Function, base 2 exponential 171 Function, boolean 172 Function, ceiling 171 Function, characteristic, of a set 15 170 Function, decoding associated with e 413 Function, distance 404 Function, encoding 402 Function, everywhere defined 164 Function, floor 171 Function, hashing 172 Function, identity 163 Function, invertible 165 Function, log base 171 Function, matching 307 Function, maximum likelihood decoding 414 Function, mod n 27 170 Function, one to one 164 Function, onto 164 Function, permutation 180 Function, propositional 49 Function, propositional, Function, state transition 375 Function, value of 161 Fundamental Homomorphism Theorem 335 Gate, and 227 Gate, or 227 GO TO statement 427 435 Grammar 358 Grammar, context sensitive 363 Grammar, context-free 363 Grammar, phrase structure 358 grammar, regular 363 Grammar, Type n (n = 0, 1, 2, 3) 363 Graph 280 Graph of a symmetric relation 124 Graph, chromatic number of 311 Graph, coloring of 311 Graph, complete 283 Graph, components of 282 Graph, connected 282 Graph, disconnected 282 Graph, discrete 282 Graph, linear 283 Graph, path in 281 Graph, planar 312 Graph, quotient 284 Graph, regular 283 Graph, sub- 283 Graph, weighted 271 Greatest common divisor 23 Greatest element of a poset 203 Greatest lower bound 204 Greedy algorithm 273 Group code 406 Group(s) 338 Group(s) of symmetries of the triangle 344 Group(s), Abelian 339 Group(s), alternating on n letters 345 Group(s), code 406 Group(s), cyclic 451 Group(s), finite 341 Group(s), inverse in 338 Group(s), Klein 4 348 Group(s), normal subgroup of 351 Group(s), order of 341 Group(s), product of 349 Group(s), quotient 350 Group(s), subgroup of 344 Group(s), symmetric, on n letters 344 guard 49 Hall's Marriage Theorem 309 Hamiltonian circuit 293 Hamiltonian path 293 Hamming distance 404 Hashing function 172 Hasse diagram 196 Height of a tree 246 Homogeneous linear relation of degree k 97 Homomorphic image 329 Homomorphism of semigroups 329 Homomorphism, fundamental theorem 335 Homomorphism, kernel of 353 Homomorphism, natural 353 Hypotheses 58 Hypothesis 52 Idempotent element 331 Idempotent properties of a binary operation 322 Idempotent properties of a lattice 212 Idempotent properties of a set 9 Idempotent properties of logical operations 55 Identity element 325 Identity function 163 Identity matrix 33 Identity of a binary operation 40 IF THEN ELSE statement 427 430 Image of a 161 Image, homomorphic 329 Implication 52 Implication, contrapositive of 53 Implication, converse of 53 Impossible event 88 In-degree of a vertex 112 Inclusion-Exclusion Principle 10 Incomparable elements of aposet 199 Indirect method of proof 60 Induction step 64 Induction, principle of mathematical 64 Induction, strong form of 68 Inequality relation 122 Inference, rules of 58 Infinite sequence 13 Infinite set 3 Infix notation 259 Influence, two-stage 453 Initial conditions for a recurrence relation 95 Inorder search of a tree 258 Input of a machine 375 Input set of a machine 375 Input-output relation 162 Interior vertices of a path 153 Intersection of sets 5 Interval in a lattice 216 Invariant of a loop 67 Inverse of a binary operation 40 Inverse of an element 338 Inverse, relation 140 Inverter 227 Invertible function 165 Involution property m a Boolean algebra 221 Irreflexive relation 121 Isolated vertex 281 Isomorphic lattices 209 Isomorphic posets 198 Isomorphic semigroups 327 Isomorphism 198 327 Join of two elements in a lattice 207 Join of two matrices 34 k or fewer errors 402 413 Karnaugh map 232 Kernel 353 Key 172 Klein 4 group 348 Kruskal's algorithm 274 Labeled digraph 163 Labeled tree 250 Labeling algorithm 299 Language of a Moore machine 384 Language of a phrase structure grammar 360 Language, semantics of 358 Language, syntax of 358 Language, Type n (n = 0, 1, 2, 3) 363 Lattice(s) 207 Lattice(s), absorption properties of 212 Lattice(s), associative properties of 212 Lattice(s), bounded 213 Lattice(s), commutative properties of 212 Lattice(s), complemented 214 Lattice(s), distributive 214 Lattice(s), distributive properties of 214 Lattice(s), idempotent properties of 212 Lattice(s), isomorphic 210 Lattice(s), modular 217 Lattice(s), nondistributive 214 Lattice(s), sub- 209 Laws, De Morgan's 9 40 55 221 Least common multiple 26 Least element of a poset 203 Least upper bound 204 Leaves of a tree 247 Left cancellation property 340 Left coset of a subgroup 351 Left pointer 252 Left side of production 358 Left subtree 255 Lemma 130 Length of a path 115 Length of a string 363 384 Less than relation 122 Level in a tree 246 Level n vertices 246 Level, same 430 Lexicographic order 193 lg, log base 2 function 174 Likelihood, maximum decoding function 414 Likelihood, maximum technique 414 Linear array 15 Linear graph 283 Linear homogeneous relation of degree k 97 Linear order 192 Linearly ordered set 192 Linked-list representation of a relation 134—135 Linked-list representation of a sequence 133 Linked-list representation of a tree 260 LIST 15 List, doubly linked 251 List, linked 133 Local variable 434 Log base 2 function 171 174 Logic diagram 227 Logic gate 227 Logical connectives 47—49 Logically equivalent propositions (statements) 54 Logically follows 58 Loop 281 428 Loop invariant 67 Lower bound 204 Lower class 177 Lower order 177 Machine(s), acceptance state 377 Machine(s), congruence 378 Machine(s), digraph of 377 Machine(s), equivalent 393 Machine(s), finite-state 375 Machine(s), input set of 375 Machine(s), input(s) of 375 Machine(s), language of 384 Machine(s), monoid of 383 Machine(s), Moore 377 Machine(s), output of 375 Machine(s), quotient 378 Machine(s), quotient Moore 379 Machine(s), recognition 377 Machine(s), starting state of 377 Machine(s), state of 375 Machine(s), state set of 375 Machine(s), state transition function of 375 Machine(s), state transition table of 376 Main diagonal of a matrix 30 Map, Karnaugh 232 Mapping 161 Markov chain 447 Markov chain, state vector of 447 Master diagram of a regular grammar 372 Matching, compatible with a relation 307 Matching, complete 307 Matching, function 307 Matching, maximal 307 Matching, problem 307 Mathematical induction, principle of 64 Mathematical induction, strong form of 68 Mathematical structure 38 Mathematical system 38 Matrices, Boolean product of 35 Matrices, equal 31 Matrices, join of 35 Matrices, meet of 35 Matrices, mod-2 Boolean product of 408 Matrices, mod-2 sum of 407 Matrices, product of 32 Matrices, sum of 31
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