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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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Abelian group 349 Absorption properties of a lattice 252 Absurdity 54 Acceptance state 393 Acyclic symmetric relation 312 Addition principle 11 Addition principle for disjoint sets 11 Adjacent vertices 127 199 310 Algorithm(s) 23 444 Algorithm(s), branch of 446 Algorithm(s), Euclidean 25 Algorithm(s), Fleury's 209 Algorithm(s), greedy 323 Algorithm(s), Kruskal's 324—325 Algorithm(s), Prim's 317—318 322—323 Algorithm(s), running time of 194 466 Algorithm(s), structured 446 Algorithm(s), subroutine of 445 Algorithm(s), Warshall's 160 Alphabet 19 Alternating group on n letters 356 AND gate 268 Antecedent statement 52 Antisymmetric relation 124 Argument of a function 168 Array of dimension two 32 Array, linear 16 Array, m by n 33 Associative operation 40 332 Associative properties of a lattice 251 Associative properties of logical operations 56 Associative properties of set operations 10 Associative property 40 Asymmetric relation 124 Automaton, pushdown 474 Axioms for probability space 89 B-tree of degree k 471 Backtracking 95 Backus — Naur notation 378 Base 2 exponential function 178 Basis step of induction 64 Biconditional statement 53 Bijection 172 Binary operation 40 Binary operation on a set 330 Binary operation, associative 40 332 Binary operation, commutative 40 332 Binary operation, idempotent property of 332 Binary operation, identity of 41 Binary tree 290 Binary tree, complete 290 Binary tree, positional 294 Block of a partition 103 Block, maximal compatibility 464 BNF notation 378 Boolean algebra 261 Boolean algebra, De Morgan's laws for 263 Boolean algebra, involution property of 263 Boolean algebra, properties of 263 Boolean algebra, substitution rule for 262 Boolean expression 268 Boolean function 179 Boolean matrices, mod 2 product of 427 Boolean matrices, mod 2 sum of 426 Boolean matrices, product of 36 Boolean matrix 35 Boolean matrix, complement of 148 Boolean polynomial 267 Boolean product 36 Boolean product, mod 2 427 Boolean sum (mod 2) of matrices 426 Bound, greatest lower 242 Bound, least upper 242 Bound, lower 242 Bound, upper 242 Bounded lattice 253 Branch of an algorithm 446 Bridge 209 Call statement 445 453 Cancellation property, left 350 Cancellation property, right 350 Cardinality of a set 4 Cartesian product 102 103 Catenation of strings 19 Ceiling function 178 Cell of a partition 103 Cell, storage 137 Central operator 292 Certain event 87 Chain 227 Chain, Markov 468 Characteristic equation 97 Characteristic function of a set 17 177 Chosen at random 90 Chromatic number 218 Chromatic polynomial 220 Circuit 199 Circuit, Euler 204 Circuit, Hamiltonian 213 Circuit, simple 199 Circular relation 136 Class, lower, of functions 192 CLIQUE 476 Closed with respect to an operation 40 330 Closure of a relation 151 Closure of an operation 40 Closure, reflexive 151 Closure, symmetric 151 Closure, transitive 151 157 Code word 422 Code, group 425 Code, parity check 422 Collision 180 Coloring of a graph 218 Coloring of a graph, proper 218 Column of a matrix 30 Combination of n objects taken r at a time 78 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 79 Common divisor 24 Common divisor, greatest 24 Common multiple 26 Common multiple, least 26 Commutative operation 40 332 Commutative properties of a lattice 251 Commutative properties of logical operations 56 Commutative properties of set operations 10 Comparable elements of a poset 226 Compatibility block, maximal 464 Compatibility block, relation 464 Compatible strings 413 Complement of a Boolean matrix 148 Complement of a set 7 Complement of an element of a lattice 254 Complement of set B with respect to A 7 Complement, properties of 10 Complementary relation 146 Complemented lattice 255 Complete binary tree 289 Complete graph 200 Complete n-tree 289 Component of a graph 199 Composition of paths 121 Composition of permutations 182 Composition of relations 152 compound statement 47 Computer representation of a digraph 136—144 Computer representation of a positional binary tree 295—296 Computer representation of a relation 136—144 Computer representation of a set 17 Computer representation of a tree 306 Conclusion 59 Conclusion of an implication 52 Conditional statement 52 Conditions for a recurrence relation 95 Congruence, machine 393 Congruence, mod a 27 Congruence, relation 342 362 Congruent to r mod a 27 Conjunction of statements (propositions) 48 Connected graph 199 Connected symmetric relation 127 Connective 47 Connectivity relation 117 Consequent Statement 52 Constructive proof 82 Context-free grammars 376 Context-sensitive grammars 376 Contingency 54 Contradiction 54 Contradiction, proof by 61 Contrapositive of an implication 53 Converse of an implication 53 Corrects k or fewer errors 433 Correspondence, one to one between A and B 173 Coset, leader 436 Coset, left, of a subgroup 363 Coset, right, of a subgroup 363 Countable set 18 Counterexample 63 Counting, multiplication principle of 73 Covering of a set 464 Cycle(s) 117 Cycle(s) as a permutation 183 Cycle(s), disjoint 185 Cycle(s), simple 311 Cyclic group 473 Cyclic permutation 183 De Morgan's laws for Boolean algebras 263 De Morgan's laws for mathematical structures 41 De Morgan's laws for sets 10 De Morgan's laws for statements 56 Decoding function 432—433 Decoding function, maximum likelihood 434 Decoding table 437 Degree of a vertex 198 Derivation of a sentence 371 Derivation tree 373 Descendants of a vertex 290 Detect k or fewer errors 422 Deterministic 85 Diagonal main, of a matrix 30 Diagonal matrix 31 Diagram, Hasse 231 Diagram, logic 269 Diagram, master 387 Diagram, syntax 381 Diagram, Venn 3 Digraph 111 Digraph of a finite-state machine 393 Digraph of a relation 111 Digraph, cycle in 117 Digraph, edge of 111 Digraph, labeled 169 Digraph, path in 116 Digraph, vertex of 111 Direct derivability 370 Directed graph see "Digraph" Disconnected graph 199 Discrete graph 200 Disjoint, cycles 185 Disjoint, events 87 Disjoint, sets 6 Disjunction of statements (propositions) 48 Distance, between vertices 322 Distance, Hamming 424 Distance, minimum, of an encoding function 424 Distributive lattice 253 Distributive properties of a lattice 253 Distributive properties of logical operations 56 Distributive properties of set operations 10 Distributive property 40 divides 22 Divisor, common 24 Divisor, greatest common 24 Domain of a relation 109 doubly linked list 295 Dual partial order 226 Dual poset 226 EDGE 111 197 Edge, end points of 198 Edge, undirected 127 310 Edge, weight of 215 321 Element of a matrix 31 Element of a set 1 Element, complement of 254 Element, greatest, of a poset 240 Element, idempotent 341 Element, identity 335 Element, inverse of 349 Element, least, of a poset 240 Element, maximal, of a poset 239 Element, minimal, of a poset 239 Element, order of 472 Element, syndrome of 439 Element, unit, of a poset 241 Element, zero, of a poset 241 Elementary event 89 Elementary probability 89 Empty relation 124 Empty sequence 19 Empty set 2 Empty set, properties of 10 empty strings 19 Encoding function 422 end points 198 Entry of a matrix 31 Equality of matrices 31 Equality of relation 124 Equality of sets 3 Equally likely outcomes 90 EQUIVALENCE 53 Equivalence classes of an equivalence relation 134 Equivalence relation 131 Equivalence relation, determined by a partition 132 Equivalent machines 413 Equivalent statements 55 Errors, corrects k or fewer 433 Errors, detect k or fewer 422 Errors, k or fewer 422 Euclidean algorithm 25 Euler circuit 204 Euler path 204 Even permutation 186 Event(s) 86 Event(s), certain 87 Event(s), disjoint 87 Event(s), elementary 89 Event(s), frequency of occurrence 88 Event(s), impossible 87 Event(s), mutually exclusive 87 Event(s), probability of 87 Everywhere-defined function 171 Existence proof 82 Existential quantification 50 Explicit formula 15 Exponential function base 2 178 Expression, Boolean 268 Expression, over A 19 Expression, regular 19
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