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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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30 Abelian group 339 Absorption properties of a lattice 212 222 Absurdity 54 Acceptance state 37 Acyclic symmetric relation 264 Addition principle 9 Addition principle for disjoint sets 10 Adjacent vertices 125 264 281 Algonthm(s) 22 425 Algonthm(s), branch of 426 Algonthm(s), Euclidean 24 Algonthm(s), Fleury's 290—291 Algonthm(s), greedy 273 Algonthm(s), Kruskal's 274 Algonthm(s), labeling 299 Algonthm(s), Prim's 268—269 273 Algonthm(s), running time of 179 445 Algonthm(s), structured 427 Algonthm(s), subroutine of 425 Algonthm(s), Warshall's 153 Alphabet 17 Alternating group on n letters 345 AND gate 227 Antecedent statement 52 Antisymmetric relation 122 Argument of a function 161 Array of dimension two 32 Array, linear 15 Array, m by n 32 Associative operation 39 322 Associative properties of a Boolean algebra 222 Associative properties of a lattice 212 Associative properties of logical operations 55 Associative properties of set operations 9 Associative property 39 Asymmetric relation 122 Automaton, pushdown 452 AVL tree 263 Axioms for probability space 89 B-tree of degree k 450 Backtracking 96 Backus — Naur notation 366 Base 2 exponential function 171 Basis step of induction 64 Biconditional statement 53 Bijection 165 Binary operation 39 319 Binary operation, associative 39 322 Binary operation, commutative 39 321 Binary operation, idempotent property of 322 Binary operation, identity of 40 Binary operation, on a set 319 Binary tree 247 Binary tree, complete 247 Binary tree, positional 251 Block of a partition 105 Block, maximal compatibility 443 BNF notation 366 Boolean algebra 219 Boolean algebra, De Morgan's laws for 221 Boolean algebra, involution property of 221 Boolean algebra, properties of 222 Boolean algebra, substitution rule for 221 Boolean expression 226 Boolean function 172 Boolean matrices, join of 34 Boolean matrices, meet of 34 Boolean matrices, mod-2 product of 408 Boolean matrices, mod-2 sum of 407 Boolean matrices, product of 35 Boolean matrix 34 Boolean matrix, complement of 142 Boolean polynomial 226 Boolean product 35 Boolean product, mod-2 408 Boolean sum (mod 2) of matrices 407 Bound, greatest lower 204 Bound, least upper 204 Bound, lower 204 Bound, upper 204 Bounded lattice 213 Branch of an algorithm 426 Bridge 290 Call statement 425 433 Cancellation property, left 340 Cancellation property, right 340 Capacity of a cut 304 Capacity of a flow 297 Cardinality of a set 3 Cartesian product 103 104 Catalan numbers 101 174—175 Catenation of strings 18 Ceiling function 171 Cell of a partition 105 Cell, storage 133 Central operator 250 Certain event 88 Chain 192 Chain, Markov 447 Characteristic equation 97 Characteristic function of a set 15 170 Chosen at random 91 Chromatic number 311 Chromatic polynomial 313 Circuit 282 Circuit, Euler 284 Circuit, Hamiltonian 293 Circuit, simple 282 Circular relation 132 Class, lower, of functions 177 CLIQUE 453 Closed with respect to an operation 39 319 Closure of a relation 145 Closure of an operation 39 Closure, reflexive 145 Closure, symmetric 145 Closure, transitive 145 151 Code word 402 Code, group 406 Code, parity check 403 Collision 173 Coloring of a graph 311 Coloring of a graph, proper 311 Column of a matrix 30 Combination of n objects taken r at a time 79 Combination of n objects taken r at a time, number of 79 Combination of n objects taken r at a time, number of, with repeats 80 Common divisor 23 Common divisor, greatest 23 Common multiple 26 Common multiple, least 26 Commutative operation 39 321 Commutative properties of a lattice 212 222 Commutative properties of logical operations 55 Commutative properties of set operations 8 Comparable elements of a poset 192 Compatibility, maximal block 443 Compatibility, relation 443 Compatible matching 307 Compatible strings 393 Complement of a Boolean matrix 142 Complement of a set 7 Complement of a set B with respect to A 7 Complement of an element of a lattice 214 Complement, properties of 9 Complementary relation 140 Complemented lattice 215 Complete binary tree 247 Complete graph 283 Complete matching 307 Complete n-tree 247 Component of a graph 282 Composition of paths 119 Composition of permutations 182 Composition of relations 146 compound statement 47 Computer representation of a digraph 134—135 Computer representation of a positional binary tree 251—252 Computer representation of a relation 134—135 Computer representation of a set 16 Computer representation of a tree 260 Conclusion 58 Conclusion of an implication 52 Conditional statement 52 Conditions for a recurrence relation 95 Congruence, machine 378 Congruence, mod a 129 Congruence, relation 332 350 Congruent to r mod a 129 Conjunction of statements (propositions) 47 Connected graph 282 Connected symmetric relation 125 Connected vertices 309 Connective 47 Connectivity relation 116 Consequent Statement 52 Conservation of flow 297 Constructive proof 83 Context-free grammars 363 Context-sensitive grammars 363 Contingency 54 Contradiction 54 Contradiction, proof by 60 Contrapositive of an implication 53 Converse of an implication 53 Corrects k or fewer errors 413 Correspondence, one to one between A and B 145 Correspondence, principle 198 corresponding to a string 382 Coset, leader 416 Coset, left, of a subgroup 351 Coset, right, of a subgroup 351 Countable set 17 Counterexample 62 Counting, multiplication principle of 73 Covering of a set 443 Cut 303 Cut, capacity of 304 Cycle(s) 116 Cycle(s) as a permutation 182 Cycle(s), disjoint 183 Cycle(s), simple 264 Cyclic, group 451 Cyclic, permutation 182 De Morgan's laws for Boolean algebras 221 De Morgan's laws for mathematical structures 40 De Morgan's laws for sets 9 De Morgan's laws for statements 55 Decoding function 413 Decoding function, maximum likelihood 414 Decoding table 417 Degree of a vertex 281 Derivation of a sentence 359 Derivation tree 360 Descendants of a vertex 248 Detect k or fewer errors 403 Deterministic 86 Diagonal, main, of a matrix 30 Diagonal, matrix 30 Diagram, Hasse 196 Diagram, logic 227 Diagram, master 372 Diagram, syntax 368 Diagram, Venn 3 Digraph 112 Digraph of a finite-state machine 377 Digraph of a relation 112 Digraph, cycle in 116 Digraph, edge of 112 Digraph, labeled 163 Digraph, path m 115 Digraph, vertex of 112 Direct derivability 359 Directed graph see “Digraph” Disconnected graph 282 Disconnected vertices 309 Discrete graph 282 Disjoint, cycles 183 Disjoint, events 88 Disjoint, sets 6 Disjunction of statements (propositions) 48 Distance between vertices 272 Distance, function 404 Distance, Hamming 404 Distance, minimum, of an encoding function 405 Distributive lattice 214 Distributive properties of a lattice 214 222 Distributive properties of logical operations 55 Distributive properties of set operations 9 Distributive property 40 divides 21 Divisor, common 23 Divisor, greatest common 23 Domain of a relation 109 doubly linked list 251 Dual partial order 192 Dual poset 192 EDGE 112 280 Edge, capacity of 297 Edge, end points of 280 Edge, undirected 125 264 Edge, weight of 271 295 Element, complement of 214 Element, greatest, of a poset 203 Element, idempotent 331 Element, identity 325 Element, inverse of 338 Element, least, of a poset 203 Element, maximal, of a poset 202 Element, minimal, of a poset 202 Element, of a matrix 30 Element, of a set 1 Element, order of 451 Element, syndrome of 419 Element, unit, of a poset 204 Element, zero, of a poset 204 Elementary event 90 Elementary probability 90 Empty relation 122 Empty sequence 17 Empty set 2 Empty set, properties of 9 Empty string 17 Encoding function 402 end points 280 Entry of a matrix 30 Equality of matrices 31 Equality of relation 121 Equality of sets 2 Equally likely outcomes 91 EQUIVALENCE 53 Equivalence classes of an equivalence relation 131 Equivalence relation 128 Equivalence relation, determined by a partition 129 Equivalent machines 393 Equivalent statements 54 Errors, corrects k or fewer 413 Errors, detects k or fewer 403 Errors, k or fewer 402
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