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Kolman B., Busby R.C., Ross S. — Discrete Mathematical Structures
Kolman B., Busby R.C., Ross S. — Discrete Mathematical Structures

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Название: Discrete Mathematical Structures

Авторы: 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: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 3-rd edition

Год издания: 1996

Количество страниц: 544

Добавлена в каталог: 23.01.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
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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