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| Mott J., Kandel A., Baker T. — Discrete mathematics for computer scientists and mathematicians |
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| Ïðåäìåòíûé óêàçàòåëü |
Nontrivial tree 469
NOR function 602 603
Normal form, conjunctive and disjunctive 591—592
Normal fuzzy set 700
Normal probability density function 732
NP-complete problems 406—407
Null graph 457
Null set 4
Null string 373
O( ) see "Big O notation"
Octahedron, edge graph of 458
One-to-one correspondence 13 14 133—134
Onto function for sets 14
Open path 442
Open proposition 81—86
Operations on fuzzy sets see "Fuzzy set operations"
Operations on integers modulo m 355—358
Operations on relations see "Relations"
Operations on sets see "Sets"
Operator on operators 397
Operator postfix, prefix notation 471—472
operators, boolean 398—400
operators, set see "Sets"
Opposite of a proposition 41—42
OR function, EXCLUSIVE and INCLUSIVE 601 602 603
OR, OR.AND Boolean operators 398—400
OR-VERTEX 729—731
Order of a graph 437
Ordered pair 9
Ordered partition of a set 177—181 182—184
Ordered selection of objects 143
Ordered tree 517
Ordering relations on strings see "Strings"
Ordering relations, enumeration see "Enumeration"
Ordering relations, lexicographic 373—375
Ordering relations, partial 340—341 362—363 580
Ordering relations, topological 428—432
Ordering relations, total 363
Ordinary generating functions see "Generating functions"
Organic molecules as graphs 446—447
Out-degree of a vertex 333 439
P-closure of a set 384
Palindrome 138
Paradox, Cantor's 7
Paradox, Russell's 7 9
Parent of a vertex 482
Parent vertex in binary tree 507
Parsing a sentence 505
Partial correctness of an algorithm 404
Partial fraction decomposition 252—257
Partial ordering relations 340—341 362—363 580
Partially ordered sets see "Posets"
Partition of a set 126 350—351
Partition, ordered 177—181 182—184
Partition, unordered 181—184
Parts of a set 178
Pascal's identity 192—194 265
Pascal's triangle 193—194
Pascal's triangle and Fibonacci numbers 273
Pascal's triangle as a recurrence relation 265
Path graph 457
Paths in graphs, circuit 388 442
Paths in graphs, closed 442
Paths in graphs, cycle 388 442
Paths in graphs, directed 388
Paths in graphs, edge-disjoint 442
Paths in graphs, endpoints 388
Paths in graphs, Eulerian 537—539
Paths in graphs, flow-augmenting 666
Paths in graphs, Hamiltonian 543—548
Paths in graphs, hyperpaths 728—731
Paths in graphs, length of 388
Paths in graphs, maximal length 391
Paths in graphs, nontrivial 388—389
Paths in graphs, open 442
Paths in graphs, simple 388 442
Paths in graphs, traverse a vertex 389
Paths in graphs, trivial 442
Paths in graphs, vertex-disjoint 442
Patterns in Plausible Inference 18
Perfect integer 75
permutations see also "Combinations" "Inclusion-exclusion principle
Permutations with constrained repetitions 172—177
Permutations with unlimited repetitions 162—164
Permutations, circular 150—151
Permutations, defined 143
Permutations, linear 148—151
Permutations, ordered partitions 177—181 182—184
Permutations, repetition numbers 144 146
Permutations, summary of use 182—184
Permutations, unordered partitions 181—184
Permutations, without repetitions 148—151
Petersen graph 463 464
Pigeonhole Principle 67—71
Planar graphs, 5-Color Theorem 569—571
Planar graphs, chromatic numbers for 569—571
Planar graphs, critical 529
Planar graphs, crossovers 523
Planar graphs, cycles 524
Planar graphs, defined 523
Planar graphs, dual of 526—527
Planar graphs, Euler's formula 530—532
Planar graphs, exterior region 525
Planar graphs, faces 525
Planar graphs, Kempe-chain argument 569—571
Planar graphs, maximal planar 534
Planar graphs, multigraphs 526—527
Planar graphs, polyhedral 531 532
Planar graphs, properties of 530—532
Planar graphs, regions of 525 569
Planar graphs, self-dual 527
Planar graphs, The Four-Color Problem 569—571
Platonic solids, edge graphs of 458
Polyhedral plane graph 531 532
Polynomial, characteristic see "Characteristic polynomial"
Polynomial-bounded algorithms 406
Poset diagrams 364 365
Posets 362 364—368 370
Possibility assignment equation 716—717
Possibility distribution 715—720
Possibility Postulate 716
Possibility theory 715—720
Possibility, related to probability 718—720
Possibility/probability consistency principle 719
Post hoc ergo propter hoc fallacy 30
Postorder traversal (LRN) 515 518
Postulates, consistent and independent 579
Powell, M.B. 565
Power series, formal 239
Power series, formal, division of 247—251
Power series, formal, multiplicative inverse 247—251
Power set 7 9
Predicate 81—82
Predicate logic in expert systems 723—724
Preimages of set elements 13
Premise 35 47
Preorder traversal (NLR) 514 515 518
Prim's algorithm 494
Primes, adjacent 76
Primes, Euclidean 118
Primes, Fermat 120
Primes, Mersenne 120
Primes, quadruple 76
Primes, triple 76
Primes, twin 76
Primitive triple 77
Principle of duality 580
Principle of Mathematical Induction 103—108
Probability density functions 732—733
Probability, related to possibility 718—720
| Probability-based methods in expert systems 723—724
Problem-solving strategies see "Reasoning"
Problems, houses and utilities 523—525
Problems, NP-complete 406—407
Problems, System of Distinct Representatives Problem 657 686 691
Problems, The Assignment Problem 686
Problems, The Chromatic Number Problem 406
Problems, The Coconut Problem 361
Problems, The Committee Problem 686 691
Problems, The Four-Color Problem 569—571
Problems, The Hamiltonian Cycle Problem 406
Problems, The Knight's Tour Puzzle 555
Problems, The Koenigsberg Bridges 535—538
Problems, The Marriage Problem 687 689—691
Problems, The Planar Subgraph Problem 406
Problems, The Scheduling Problem 558—560
Problems, The Subgraph Isomorphism Problem 406
Problems, The Towers of Hanoi 282
Product of fuzzy sets 705—706
Product of generating functions 240—241
Product rule 128—132
Product-of-sums form 591 612
Progression, arithmetic 110 115
Progression, geometric 110 116 249—251
Projection of a relation 379—380
Proof, methods of see also "Inference rules "Reasoning"
Proof, methods of, conditional proof 62—63 72
Proof, methods of, diagonal argument 377—378
Proof, methods of, direct proof 61 63—64
Proof, methods of, existence proofs 87—88
Proof, methods of, indirect proof (proof by contrapositive) 61 65—66
Proof, methods of, pigeonhole principle 67—71
Proof, methods of, proof by cases 61—62 71
Proof, methods of, proof by contradiction 61 66—67
Proof, methods of, proof by contrapositive 61 65—66
Proof, methods of, proof by counterexample 87 89
Proof, methods of, proof by elimination of cases 62 71
Proof, methods of, proof by equivalence 63 64—65
Proof, methods of, proof by example 87
Proof, methods of, proof by exhaustion 87 89
Proof, methods of, proof by mathematical induction 103—108 111—115
Proof, methods of, trivial proof 61
Proof, methods of, vacuous proof 61
Proper divisor 75
Proper subgraph 334
Proper subset 3—4
Propositional function 37—42
Propositions 33 see fundamentals
Propositions, conjunction and disjunction of 34
Propositions, equivalent 38
Propositions, negation of 34
Propositions, open 81—86
Propositions, quantified 97—100
PROSPECTOR expert system 722
Proximity relations 713 726
Pruefer code of a tree 495—497
Pythagorean triple 77
Quadruple primes 76
Quantified propositions 97—100
Quantifiers, existential 83—87 89—91
Quantifiers, multiple 89—91
Quantifiers, universal 83—87 89—91
Quasi-strongly connected vertices 498—500
Query language 725
Quotient 64
Range of relation on a set 10—11
Rational roots theorem 89
Reasoning see also "Inference rules "Proof methods
Reasoning, "analysis-synthesis" 24—26
Reasoning, approach 17—19
Reasoning, aspects of discovery 21—22
Reasoning, circular 29—30
Reasoning, elements of an argument 19—20
Reasoning, fallacies see "Fallacies"
Reasoning, inductive 22—24
Reasoning, working backward 26—27
Reasoning, working forward 20—21
Recurrence relations 110 see
Recurrence relations, boundary conditions 268
Recurrence relations, characteristic roots solutions 300—304
Recurrence relations, compound interest as 274
Recurrence relations, defined 266
Recurrence relations, derangements as 274
Recurrence relations, divide-and-conquer relations 285 321—322
Recurrence relations, Fibonacci relation 269—273
Recurrence relations, generating function solutions 290—296
Recurrence relations, homogeneous 266 306—311
Recurrence relations, initial conditions 268
Recurrence relations, linear 266
Recurrence relations, merge sort algorithm 282—284 425—426
Recurrence relations, models 274—275
Recurrence relations, nonlinear 321—322
Recurrence relations, shifting properties of generating functions 285—290
Recurrence relations, solution, defined 267
Recurrence relations, substitution solutions 281—285
Recurrence relations, systems of 319—322
Recurrence relations, The Lancaster Equations of Combat 275
Recurrence relations, The Towers of Hanoi 282
Recursion 108—109
Recursion theorem 109—111
Recursive formula to describe a set 3
Recursive subroutine 108
Reflexive fuzzy binary relation 713
Reflexive general fuzzy relation 726
Reflexive relation on a set 11
Reflexivity of a binary relation 339 340
Reflexivity of a similarity relation 726
Regions of a planar graph 569
Regions of a plane 525
Regular directed tree 505
Relations, closure property 383—384
Relations, complement 379
Relations, composition 382—383
Relations, difference 379
Relations, general fuzzy 726—727
Relations, intersection 379
Relations, inverse 381—382
Relations, join 380
Relations, meet 368
Relations, P-closure of a set 384
Relations, projection 379—380
Relations, proximity 713 726
Relations, set see "Sets"
Relations, similarity 713 726
Relations, symmetric closure 383
Relations, total ordering 363
Relations, transitive (reflexive) closure 383
Relations, union 379
Relations, well-ordering 105 366—367
Relative complement of a set 4
Relatively prime integers 356
Remainder 64
Repetition numbers 144 146
Resolution identity 708—710
Revelation stage of development 22
Reverse edge 666
Right child, edge, subtree 507
Root of a tree 469 482
Rooted tree 468
Roots, characteristic 300—304
Rule of Detachment 47—48 49
Rule, product 128—132
Rule, sum 22 126—132
Rules of Inference see "Inference rules
Russell's paradox for sets 7 9
Russell, Bertrand 9
S-D cut 647—651
Saturated edge 639
Searching algorithms, BFS 482—485
Searching algorithms, binary 415—418
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