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Hein J.L. — Discrete Mathematics
Hein J.L. — Discrete Mathematics

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Название: Discrete Mathematics

Автор: Hein J.L.

Аннотация:

Discrete Mathematics, is designed for an introductory course in discrete mathematics for the prospective computer scientist, applied mathematician, or engineer who wants to learn how the ideas apply to computer sciences. The choice of topics-and the breadth of coverage-reflects the desire to provide students with the foundations needed to successfully complete courses at the upper division level in undergraduate computer science courses.

This book differs in several ways from current books about discrete mathematics. It presents an elementary and unified introduction to a collection of topics that has not been available in a single source. A major feature of the book is the unification of the material so that it does not fragment into a collection of seemingly unrelated ideas.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 656

Добавлена в каталог: 19.03.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
AA      See Assignment axiom
AAA      See Array assignment axiom
Absorption laws, Boolean algebra      526
Absorption laws, logic      318
Absorption laws, sets      22 29
Abstract algebra      514
Abstract data type      536—549
Abstract data type, binary trees      547
Abstract data type, lists      541
Abstract data type, natural numbers      537
Abstract data type, priority queues      548
Abstract data type, queues      545
Abstract data type, stacks      543
Abstract data type, strings      542
Abstract syntax tree      148
Accumulating parameter      251
Ackermann's function      250
Ackermann, W.      345 640
action      554
Acyclic graph      47
Add      See Addition rule
Addition rule      334
Adjacency matrix      188
Adjacent vertices      43
Al-Khowarizmi      507
Algebra      507 510—576
Algebra of matrices      520
Algebra of polynomials      520
Algebra of power series      521
Algebra of vectors      520
Algebra, abstract      514
Algebra, abstract data type      536
Algebra, boolean      522—534
Algebra, carrier of      510
Algebra, concrete      514
Algebra, definition of      510
Algebra, expression      510
Algebra, field      519
Algebra, functional      556
Algebra, group      517
Algebra, groupiod      517
Algebra, high school      509
Algebra, moniod      517
Algebra, morphism      573
Algebra, process      554
Algebra, quotient of      568
Algebra, relational      551
Algebra, ring      519
Algebra, semigroup      517
Algebra, signature of      511
Algebra, subalgebra of      569
Algebraic expression      510
Algorithm      507
Alphabet      37
Ambiguous grammar      146
AND      See Conjunction
AND gate      528
Andrews, P.В.      639
Antecedent      313 332
antisymmetric      179
Appel, K.      44 639
Append operation      120
apply function      87
Applying a substitution      463
ApplyToAll function      86
Apt, K.R.      439 639
Arithmetic progression      238
Arity      63
Array assignment axiom      434
Artin, Emil      226
Ascending chain      217
Assignment axiom      422
Asymptotic behavior      299
atom      360 479
Atomic formula      360
Attributes      41
Average case optimal algorithm      275
Axiom      334
Backtracking      493
Backus — Naur form      148
Backus, J.      557 639
Backwards check      398
Bag      25
Bag combinations      269
Bag intersection      26
Bag permutations      263
Bag subbag      25
Bag sum      26
Bag union      26
Basic equality      178
Basis of mathematical induction      235
Bernstein, F.      104
Best operation      548
Better operation      549 551
BIFO property      548
Big oh      304
Big Omega      305
Big theta      300
Bijection      94
Bijective function      94
binary function      63
Binary relation      42 178—187
Binary relation, antisymmetric      179
Binary relation, basic equality      178
Binary relation, closure      183—187
Binary relation, composition      179
Binary relation, converse      184
Binary relation, equivalence      197—212
Binary relation, generator of      183
Binary relation, irreflexive      179
Binary relation, kernel      207
Binary relation, linear order      216
Binary relation, partial order      215—232
Binary relation, reflexive      178
Binary relation, reflexive closure      183
Binary relation, symmetric      178
Binary relation, symmetric closure      183
Binary relation, total order      216
Binary relation, transitive      178
Binary relation, transitive closure      183
Binary resolution      476
Binary search      258
Binary search tree      53 163
Binary tree      52—54 123—124 163—166 547
Binary tree, inorder traversal      166
Binary tree, left subtree      52
Binary tree, postorder traversal      166
Binary tree, preorder traversal      164
Binary tree, right subtree      52
Binding      363 462
Binomial coefficient      266
Binomial theorem      267
Birthday problem      272
BNF      See Backus — Naur form
Boole, George      523
Boolean algebra      522 523 534
Boolean algebra, absorption laws      526
Boolean algebra, axioms      523 534
Boolean algebra, complement      523 534
Boolean algebra, De Morgan's laws      527
Boolean algebra, digital circuits      528—532
Boolean algebra, duality principle      525
Boolean algebra, idempotent properties      525
Boolean algebra, involution      527
Boolean algebra, minimal CNF      533
Boolean algebra, minimal DNF      532
Boolean algebra, negation      523 534
Boolean algebra, properties      534
Boolean algebra, simplifying expressions      524
Bound variable      362
Boyle, J.      476 641
Branch      50
Brassard, G      639
Bratley, P.      639
Breadth-first search strategy      497
Breadth-first traversal      48
Burke, Edmund      177
Burton, David F.      507
Calculus      312
Cancellation technique      82 280
Cantor, Georg      26 100 104
Cardinality      22 94
Carrier      510
Carroll, Lewis      309 395
Case definition of function      65
Casting out by nines      576
cat      See Concatenation
CD      See Constructive dilemma
Ceiling function      67
Chain      217
Chang, G      474 639
Characteristic function      73
Children      50
Chinese remainder theorem      567
Chromatic number      44
Cichelli, R.J.      98 639
Clausal form      454
Clause      454
Closed      569
Closed form      282
Closure of binary relation      183—187
Closure, existential      368
Closure, inductive definition      112 246
Closure, language      133
Closure, positive      133
Closure, properties      133
Closure, reflexive      183
Closure, symmetric      183
Closure, transitive      183 498
Closure, universal      368
CNF      See Conjunctive normal form
Codomain      63
Collection      10
Collision      97
Coloring a graph      44
Combinations      265—269
Comparable      216
Comparison sorting      264
Complement, Boolean algebra      523 534
Complement, properties      22
Complement, set      21
Complete graph      44
Completeness      344
Component      31
Composition of binary relations      179
Composition of functions      79
Composition of statements      424
Composition of substitutions      463
Composition rule      424
Computable number problem      104
Computation tree      492
Concatenation of lists      159
Concatenation of strings      131 543
Conclusion      3 313 332
Concrete algebra      514
Conditional      313
Conditional proof      336—340
Conditional proof rule      336
Conditional statement      3
Congruence      563—567
Congruence relation      564
CONJ      See Conjunction rule
Conjunction      2 313
conjunction rule      334
Conjunctive normal form      325
Connected      47
Connective      313 314 360
Connective, complete set      328
Cons function      116
Consequence rule      423
Consequent      313 332
Consistent      335
ConsRight function      158
Constructive dilemma      351
constructor      113
Contingency      317
Continuum Hypothesis      107
Contradiction      8 317
Contrapositive      4
CONVERSE      4
Converse of binary relation      184
Converting decimal to binary      72
Conway's challenge sequence      173
Coppersmith, D.      256 639
Correct program      421
Countable      101
Countably infinite      101
Counterexample      6
Countermodel      366
Counting bag combinations      269
Counting bag permutations      263
Counting combinations      265—269
Counting difference rule      24
Counting finite sets      22—25
Counting inclusion exclusion principle      23
Counting infinite sets      100—107
Counting permutations      262—265
Counting product rule      54
Counting tuples      54—56
Counting union of countable sets      102
Counting union rule      22
cp      See Conditional proof rule
Cross product      33
CYCLE      46
Dag      See Directed acyclic graph
DD      See Destructive dilemma
De Morgan's laws, Boolean algebra      527
De Morgan's laws, logic      318
De Morgan's laws, sets      22
Decidable      369
Decision problem      369
Decision tree      258—260
Decoding      565
Degree      44
Delete function      502
Delong, H.      639
Depth      50
Depth-first search strategy      493
Depth-first traversal      49
Deque      550
Derangement      277 298
Derivation      136 138
Derivation tree      134
Descartes, Rene      33
Descending chain      217
Description problem      508
Destructive dilemma      351
Destructors      116
Diagonalization      106
dictionary order      226
Difference      20
Difference, counting rule      24
Digital circuit      528—532
Digital circuit, AND gate      528
Digital circuit, full adder      531
Digital circuit, gate      528
Digital circuit, half-adder      530
Digital circuit, logic gate      528
Digital circuit, NOT gate      528
Digital circuit, OR gate      528
1 2 3 4 5
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