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| Mott J.L., Kandel A., Baker T.P. — Discrete Mathematics For Computer Scientists And Mathematicians |
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| Ïðåäìåòíûé óêàçàòåëü |
Henkin, Leon 110
High-order languages (HOLs) 720
Homogeneous recurrence relations (HR) 266 306—311 see "Recurrence
Homomorphism for Boolean algebras 585
How to Solve It 18
HR see "Homogeneous recurrence relations"
Hyperedges 728—731
Hypergraphs 728—731
Hyperpaths 728—731
Hypothesis of a proposition 35 47
Hypothesis, formulation of 23
Hypothesis, inductive 103
Hypothesis, strong inductive 111
Hypothetical syllogism 48 49
IC see "Integrated circuit"
Icosahedron, edge graph of 458
Idempotent laws for Boolean algebras 580—581
Idempotent property of sets 5
IEC see "International Electrotechnical Commission"
IEEE Standard No.91 for logic symbols 601
IHR see "Inhomogeneous recurrence relations"
Images of set elements 13
Implication 35
Implication, law of 40
Implication, logical 45—46
Implication, proof of see "Proof methods
In-degree of a vertex 333 439
Incident from, on, to edge 333 439
Inclusion-exclusion, principle of, derangements 226—228
Inclusion-exclusion, principle of, Euler's 0—function 225—226
Inclusion-exclusion, principle of, for three sets 213—218
Inclusion-exclusion, principle of, for two sets 212—213
Inclusion-exclusion, principle of, formulation and statement of 218—219
Inclusion-exclusion, principle of, proofs 220—222
Inclusion-exclusion, principle of, Sieve of Eratosthenes 224—225
INCLUSIVE-OR function 601 603
Incubation stage of development 21—22
Independent postulates 579
Indirect counting 132—133
Indirect proof 61 65—66
Induction and Analogy in Mathematics 18
Induction, mathematical 103—108
Induction, strong mathematical 111—115
Inductive hypothesis 103 see
Inductive reasoning 22—24
Inductive step 103 111
Inefficient algorithms 406
Inference Engine 720 721 727—731
Inference, faulty 46
Inference, rules of see also "Reasoning" "Proof methods
Inference, rules of, addition 49
Inference, rules of, conjunction 49
Inference, rules of, constructive dilemma 49
Inference, rules of, contraposition 49 50
Inference, rules of, defined 45
Inference, rules of, DeMorgan's Laws 6 40—41 49 50 61 86
Inference, rules of, destructive dilemma 49
Inference, rules of, detachment 47—48 49
Inference, rules of, disjunctive syllogism 49
Inference, rules of, existential generalization 99
Inference, rules of, existential specification 98
Inference, rules of, hypothetical syllogism 48 49
Inference, rules of, modus ponens 47—48 49
Inference, rules of, modus tollens 49
Inference, rules of, simplification 49
Inference, rules of, transitive rule 48 49
Inference, rules of, universal generalization 98
Inference, rules of, universal specification 97—98
Inference, valid 46—47
Inhomogeneous recurrence relations (IHR) 266 see "Recurrence
Inhomogeneous recurrence relations (IHR), example solutions 306—311
Inhomogeneous recurrence relations (IHR), summary of particular solutions 318
Inhomogeneous recurrence relations (IHR), undetermined coefficients, method of 311—319
Initial condition 110 268
Initial term of a series 110
Initial vertex 442
Inner product of operators 397
Inorder traversal (LNR) 515 518
Integers, divisibility of 359—360
Integers, modulo m 354—358
Integers, prime see "Primes"
Integers, relatively prime 356
Integrality of Flows Theorem 672
Integrated circuit (IC) 600
Integration: small, medium, large,and very large scale 600
Interchange sort algorithm 418—423
Intermediate vertex 634
Internal vertex 482
International Electrotechnical Commission (IEC) Publication 117—15 for logic symbols 601
Intersection of fuzzy sets 705 731—732
Intersection of graphs 456—457
Intersection of relations 379
Intersection of sets 5
Into function for sets 14
Invariant assertion 426
Invariant of graphs 334
Inverse of a proposition 41
Inverse of a relation 381—382
Inverse of a set 14
Inverse, multiplicative 247—251
INVERTER function 602 603
Involution law for Boolean algebras 583
Irreducible form of a Boolean expression 605
Irredundant form of Boolean expression 605
Irreflexivity of a binary relation 339 340
Isolated vertex 439
Isomorphisms, Boolean 585
Isomorphisms, graph 334 406 449—457
Iteration 281—285
Join of elements 368
Join of relations 380
Join-semilattice 368
Karnaugh map 607—609 610—611
Karnaugh, M. 607
Karp 671
Kempe, A.B. 569 571
Kempe-chain argument 569—571
Kernel of a fuzzifier 710—711
Kirkman, Thomas P. 543
Knowledge-Based Consultant (Expert) Systems see "Expert systems"
Konig 689
Konig — Egervary theorem 695
Konig's theorem 695
Kruskal's algorithm 486—489
Kruskal, J.B.Jr. 486
Labeling, algorithm 674—675
Labeling, backward 675
Labeling, edge 632—633 636
Labeling, forward 675
Labeling, graph 444
Labeling, vertex 674—675
Lagrange's interpolation formula 88
Large scale integration (LSI) 600
Latin rectangle 693
Latin square 96—97 693
Lattice 368 578
Law of contradiction 34
Law of contrapositive 40 49 50
Law of Double Negation 40
Law of hypothetical syllogism 48 49
Law of implication 40
Law of the excluded middle 34
Leaf of a tree 482
Least element of a set 364
Least upper bound (lub) 364
Left child, edge, subtree 507
Length of a path 388 391
Leonardo of Pisa (Fibonacci) 269
Level of a vertex 469 501
Level-order index of binary tree vertex 509
| Lexicographic ordering of strings 373—375
Linear permutation 148—151
Linear recurrence relation 266
Linearity of generating functions 257
Linguistic approximations see "Fuzzy relations" "Fuzzy ""Soft"
Link (general fuzzy relation) 726—727
Literal for a Boolean variable 590
Literal variable 605
LNR see "Inorder traversal"
Logic gates, AND 601 603
Logic gates, EXCLUSIVE-OR 602 603
Logic gates, INCLUSIVE-OR 601 603
Logic gates, inverter 602 603
Logic gates, minimization of 600—601
Logic gates, NAND 602 603
Logic gates, NOR 602 603
Logic micro-operations in an ALU 619—621
Logic symbols 601—603
Logic, equivalences 85—86
Logic, existence proofs 87—88
Logic, existential quantifier 83—87 89—91
Logic, first order, defined 80
Logic, fundamentals of, abbreviated truth table 38—39
Logic, fundamentals of, five basic connectives 34—38
Logic, fundamentals of, propositional functions of two variables 39—42
Logic, fundamentals of, valid inferences and propositions 33—34
Logic, multiple quantifiers 89—91
Logic, open propositions 81—86
Logic, predicate, in expert systems 723—724
Logic, proof by counterexample 87 89
Logic, proof by example 87
Logic, proof by exhaustion 87 89
Logic, quantifiers, defined 82—83
Logic, subject-predicate analysis 80—81
Logic, universal quantifier 83—87 89—91
Logic, universe of discourse 81—82
Logical connectives 34—38
Logical implication 45—46
Logical inferences, fallacies see "Fallacies"
Logical inferences, faulty inference 46
Logical inferences, logical consequence 46
Logical inferences, logical implication 45—46
Logical inferences, rules of inference see "Inference rules
Logical inferences, valid inference 46—47
Logically equivalent propositional functions 38
Loop 333 437
Loop-free digraph 333
Loop-free graph 437
Lower bound of a set 364
LRN see "Postorder traversal"
LSI see "Large scale integration"
Lub see "Least upper bound"
Lucas sequence 278
Lukasiewicz, Jan 471
Magic square 96
Many-to-one function for sets 14
Mapping see "Functions"
Matching, complete 687 689—691
Matching, condition 689
Matching, maximal 687
Matching, network 688—689
Mathematical Discovery 18
Mathematical induction 103—108 see
Matrix, adjacency 396—402 450
Matrix, Boolean 396—402
Matrix, multiplicity 536—537
Maximal flows in networks 641 645—652
Maximal flows in networks, construction of 671—677
Maximal flows in networks, The Max Flow-Min Cut Theorem 659—660 667—669
Maximal matching 687
Maximal planar graph 534
Maximal spanning tree 493
Maximum-length shift register sequence 539—541
Maxterm Boolean expressions 590—592
Medical diagnosis expert system 722
Medium scale integration (MSI) 600
Meet of elements 368
Meet-semilattice 368
Members of a set 1
Membership function 699—704
Menger 689
Menger's Theorem 695
Merge sort algorithm 282—284 425—426
Merging sorted lists 282—284
Merging sorted sequences 423—424
Mersenne primes 120
Method of characteristic roots 300—304
Method of undetermined coefficients see "Undetermined coefficients method
Micro-operations in an ALU 619—621
Mineral deposit expert system 722
Minimal cuts in networks 645—652
Minimal spanning trees 494
Minimization of Boolean functions see "Boolean functions minimization
Minterm Boolean expressions 590—592
Modular arithmetic 354—358
Modular law for Boolean algebras 587
modus ponens 47—48 49 724
Modus Tollens 49
Monotone increasing functions 346
MSI see "Medium scale integration"
Multigraphs 333 437 438
Multigraphs of plane graphs 526—527
Multigraphs, directed 538
Multigraphs, Eulerian paths and circuits in 537—539
Multigraphs, nondirected 537—538
Multigraphs, The Konigsberg Bridges 535—538
Multigraphs, traversable 537
multinomial 205
Multinomial coefficients 205—207 see
Multiple edges 333
Multiple quantifiers 89—91
Multiplexers 621—626
Multiplication of generating function by a scalar 240
Multiplicative inverse, of formal power series 247—251
Multiplicities of graph edges 535—536
Multiplicity matrix of a graph 536—537
Mutually exclusive events 127
Mux see "Multiplexers"
MYCIN expert system 722
n-ary fuzzy relation 711—713
n-colorable graph 558
NAND function 602 603
Negation of a proposition 34
Neighbor vertices 439
Net flow across a cut 649
Net flow into, out of a vertex 638 640
Networks, capacity function 633
Networks, complete matching 687 689—691
Networks, cuts in see "Cuts"
Networks, defined 633
Networks, edge capacity 633—634
Networks, edge labeling 632—633 636
Networks, flows in see "Flows in networks"
Networks, intermediate vertex 634
Networks, matching 687 688—689
Networks, maximal matching 687
Networks, sink, source vertex 633 638 640
Newton's identity for binomial coefficients 191—192
NLR see "Preorder traversal"
Non sequitur fallacy 51
Noncomputable functions 377—378
Nonconstructive existence proof 87 88
Nondeterministic algorithms 419
Nondirected graphs 333
Nondirected multigraphs 333
Nondirected path 388
Nondirected trees 469
Nonisomorphic graphs 449—457
Nonlinear recurrence relations 321—322
Nonplanar graph 523 524—525
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