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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
Euler's 0-function      225—226
Euler's formula      530—532
Euler, Leonhard      535
Eulerian circuit, multigraph, path      537—539
Exclusive-or function      602 603
Existence proofs      87—88
Existential generalization      99
Existential quantifier      83—87 89—91
Existential specification      98
Experimentation stage of development      21
Expert systems (ES)      720 722 723—724 see
Expert systems (ES), diagram      721
Explanatory knowledge base (EKB)      725—727
Exterior region of a plane graph      525
Faces of a plane      525
Factorials, binomial coefficients as      191
Factorials, defined      136
Fallacies, "vicious circle"      29
Fallacies, affirming the consequent      50
Fallacies, ambiguity      28
Fallacies, amphiboly      28
Fallacies, begging the question      29—30
Fallacies, circular reasoning      29—30
Fallacies, denying the antecedent      50—51
Fallacies, equivocation      28
Fallacies, false cause      30
Fallacies, faulty inference      29—30 46
Fallacies, hasty generalization      30
Fallacies, non sequitur      51
Fallacies, post hoc ergo propter hoc      30
Fallacies, unwarranted assumptions      29—30
False cause, fallacy of      30
Faulty inference, fallacy of      29—30 46
Fermat primes      120
Fibonacci (Leonardo of Pisa)      269
Fibonacci numbers      111 113—114 116
Fibonacci numbers and Pascal's triangle      273
Fibonacci numbers for large n      273
Fibonacci numbers for vertices in height balanced binary tree      511—512
Fibonacci numbers, general solution for      271—273
Fibonacci numbers, sums of      270—271
Fibonacci Quarterly      270
Fibonacci relation      269—270
Fibonacci relation, general solution of      271—273
Fibonacci sequence      111 270—273 278
Finite Boolean algebra      588
Finite graph      437
First order logic      see "Logic first
Flow-augmenting path      666
Flow-augmenting path algorithm      676
Flows in networks      671
Flows in networks, "greedy" method for increasing      663
Flows in networks, across a cut      649
Flows in networks, capacity constraint      638
Flows in networks, conversation equation      638
Flows in networks, defined      638
Flows in networks, flow into, out of a vertex      638 640
Flows in networks, flow-augmenting path algorithm      676
Flows in networks, Integrality of Flows Theorem      672
Flows in networks, maximal      641 645—652
Flows in networks, maximal, construction of      671—677
Flows in networks, minimal cuts      645—652
Flows in networks, net      638 640 668
Flows in networks, net flow into, out of a vertex      638 640
Flows in networks, S-D cuts      647—651
Flows in networks, saturated edge      639
Flows in networks, slack of an edge      639
Flows in networks, The Max Flow-Min Cut Theorem      659—660 667—669
Flows in networks, unsaturated edge      639
Flows in networks, value of      640
Flows in networks, vertex labeling algorithm      674—675
Forcing functions and particular solutions to IHR      318
Forcing functions, defined      306
Ford, L.R.Jr.      659 671
Forest      478 500—501
Formal power series      239
Formal power series, division of      247—251
Formal power series, multiplicative inverse      247—251
Forward chaining in expert systems      724
Forward edge      666
Forward labeling      675
Frame of reference for an argument      19—20
Free Boolean algebra      590
FRKB      see "Fuzzy Relational Knowledge Base"
Fulkerson, D.R.      659 671
Full directed tree      506
full-adder      614 615—621
Functionally complete operations on Boolean algebras      592—593
Functions on integers modulo m      355—358
Functions, forcing      306 318
Functions, isomorphisms      449—457
Functions, monotone increasing      346
Functions, noncomputable      377—378
Functions, propositional      37—40
Functions, set      see "Sets"
Fuzzification, fuzzifier      710—711
Fuzzy binary relation      713
Fuzzy Relational Knowledge Base (FRKB)      724—727
Fuzzy relations, @-transitive      713
Fuzzy relations, anti-symmetrical      713
Fuzzy relations, composition of      713
Fuzzy relations, fuzzy binary relation      713
Fuzzy relations, general fuzzy relation      726—727
Fuzzy relations, link      726—727
Fuzzy relations, n-ary fuzzy relation      711—713
Fuzzy relations, proximity relations      713 726
Fuzzy relations, reflexive      713
Fuzzy relations, similarity relations      713 726
Fuzzy relations, symmetrical      713
Fuzzy relations, transitive closure      713
Fuzzy restriction      718
Fuzzy set operations, "hard" and "soft" AND      705
Fuzzy set operations, Cartesian product      707
Fuzzy set operations, complement      705
Fuzzy set operations, concentration      706
Fuzzy set operations, convex combination      707—708
Fuzzy set operations, dilation      706
Fuzzy set operations, fuzzification, fuzzifier      710—711
Fuzzy set operations, intersection      705 731—732
Fuzzy set operations, kernel of a fuzzifier      710—711
Fuzzy set operations, max (#) symbol      704—705
Fuzzy set operations, min (&) symbol      704—705
Fuzzy set operations, product      705—706
Fuzzy set operations, resolution identity      708—710
Fuzzy set operations, t-level set      708
Fuzzy set operations, The Extension Principle      714
Fuzzy set operations, union      705 731
Fuzzy sets      see also ""Soft" expert systems"
Fuzzy sets, cardinality of      714
Fuzzy sets, containment      700
Fuzzy sets, contrasted with conventional sets      2
Fuzzy sets, convex      732
Fuzzy sets, crossover point      701
Fuzzy sets, defined      699—700
Fuzzy sets, examples of      701—704
Fuzzy sets, grade of membership      699—704
Fuzzy sets, height      700
Fuzzy sets, membership function      699—704
Fuzzy sets, normal      700
Fuzzy sets, operations on      see "Fuzzy set operations"
Fuzzy sets, subnormal      700
Fuzzy sets, subset      700
Fuzzy sets, support      700
Fuzzy sets, symmetrical difference      732
Fuzzy sets, The Extension Principle      714
Gambler's ruin      277
Gamma probability density function      733
Gates      596 see "Boolean minimization
Gates, minimization of      600—601
GCD      see "Greatest common denominator" "Greatest
General fuzzy relation (link)      726—727
Generalization      22
Generalized Petersen graph      464
Generating functions      see also "Recurrence relations"
Generating functions, calculating coefficients      247—251
Generating functions, defined      239
Generating functions, division of power series      247—251
Generating functions, equality of      240
Generating functions, equivalent expressions for      290
Generating functions, linearity of      257
Generating functions, models      241—244
Generating functions, multiplication by a scalar      240
Generating functions, partial fraction decomposition      252—257
Generating functions, product of      240—241
Generating functions, shifting properties of      285—290
Generating functions, solutions to recurrence relations      290—296
Generating functions, sum of      240
Generating functions, table of      289
Generating rule      110
Geometric series      110 116 249—251
Girth of a graph      465
Glb      see "Greatest lower bound"
Goals of an argument      19
Goldbach conjecture      119
Good's diagrams      540
Grade of membership      699—704
Graph Theory With Applications      551
Graphic sequences      444
Graphs of platonic solids      458
Graphs, "bridge" edge      541
Graphs, "The First Theorem of Graph Theory"      440—441
Graphs, "The Sum of Degrees Theorem"      440—441
Graphs, (connected) components      391—392 472
Graphs, adjacency matrix      396—402 450
Graphs, AND/OR graphs      728—731
Graphs, bipartite      457 547—548
Graphs, chromatic numbers      see "Chromatic numbers"
Graphs, circuit      388 442
Graphs, circuit rank      481
Graphs, circumference      465—466
Graphs, closed path      442
Graphs, coloring      see "Chromatic numbers"
Graphs, complement of subgraph      455—456
Graphs, complete      452—453 531
Graphs, complete bipartite      457 531—532
Graphs, complete fc-partite      467
Graphs, critical planar      529
Graphs, crossing number      534
Graphs, cube      458
Graphs, cubic      439 464—465
Graphs, cycle      388 442 457 524
Graphs, defined      437
Graphs, degree sequence      439
Graphs, diameter      465
Graphs, dodecahedron      458
Graphs, dual      569
Graphs, edges      see "Edges of graphs"
Graphs, endpoints      388
Graphs, Eulerian      537—539
Graphs, finite      437
Graphs, forest      478
Graphs, generalized Petersen      464
Graphs, girth      465
Graphs, graphic sequence      444
Graphs, Gray-code (to binary-code converter)      604
Graphs, Havel-Hakimi result      447
Graphs, hypergraphs      728—731
Graphs, icosahedron      458
Graphs, intersection      456—457
Graphs, invariant      334
Graphs, isomorphic      334 449—457
Graphs, k-chromatic      559 561
Graphs, k-critical      561
Graphs, k-partite      467
Graphs, k-regular      439
Graphs, labelings      444
Graphs, loop-free      437
Graphs, multigraphs      333 437 438
Graphs, multiplicities of edges      535—536
Graphs, multiplicity matrix      536—537
Graphs, n-colorable      558
Graphs, nondirected graphs      333
Graphs, nondirected path      388
Graphs, nonisomorphic      449—457
Graphs, nonplanar      523 524—525
Graphs, nonsimple      438
Graphs, nontrivial path      388—389
Graphs, null      457
Graphs, octahedron      458
Graphs, open path      442
Graphs, order of      437
Graphs, organic molecules as      446—447
Graphs, path graph      457
Graphs, paths      see "Paths in graphs"
Graphs, Petersen      463 464
Graphs, polyhedral      531 532
Graphs, proper subgraph      334—335
Graphs, quasi-strongly connected      498—500
Graphs, self-dual      527
Graphs, simple      437 438
Graphs, simple path      388 442
Graphs, size of      437
Graphs, spanning subgraph      452
Graphs, star      457—458
Graphs, subgraph      334 452
Graphs, symmetric directed      339 340 438
Graphs, tetrahedron      458
Graphs, trees      see "Trees"
Graphs, tripartite      467
Graphs, union      457
Graphs, vertices      see "Vertices of graphs"
Graphs, viewed as directed graphs      438—439
Graphs, Warshairs algorithm      407—412 539
Graphs, wheel      457 562—563
Greatest common denominator (GCD)      78
greatest common divisor (GCD)      356
Greatest element of a set      364
Greatest lower bound (glb)      364
Greedy algorithm      486—487 567
Grinberg's Theorem      548—551
Grounds for an argument      19
Haken, W.      569
half-adder      614—615
Hall's Marriage Theorem      689—691
Hall, P.      689
Hamilton's dodecahedron game      543
Hamilton, Sir William Rowan      543
Hamiltonian graphs, defined      543
Hamiltonian graphs, Dirac's theorem      551
Hamiltonian graphs, Grinberg's theorem      548—551
Hamiltonian graphs, Hamiltonian circuit, cycle      543—551
Hamiltonian graphs, Hamiltonian path      543—548
hashing algorithms      357—358
Hasse diagrams      see "Poset diagrams"
Hasty generalization, fallacy of      30
Havel — Hakimi result      447
Head of a sequence      282
Heawood, P.J.      569
Height balanced binary tree      510—512
Height of a fuzzy set      700
Height of a tree      501
Height of a vertex      500—501
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
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