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