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Mott J., Kandel A., Baker T. — Discrete mathematics for computer scientists and mathematicians
Mott J., Kandel A., Baker T. — Discrete mathematics for computer scientists and mathematicians



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Íàçâàíèå: Discrete mathematics for computer scientists and mathematicians

Àâòîðû: Mott J., Kandel A., Baker T.

Àííîòàöèÿ:

An awesome book on Discrete Math. A must read for an undergrad CS student


ßçûê: en

Ðóáðèêà: Computer science/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Èçäàíèå: 2nd

Ãîä èçäàíèÿ: 1986

Êîëè÷åñòâî ñòðàíèö: 763

Äîáàâëåíà â êàòàëîã: 07.05.2014

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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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
1 2 3 4 5 6 7
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