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| Mott J., Kandel A., Baker T. — Discrete mathematics for computer scientists and mathematicians |
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| Предметный указатель |
Searching algorithms, DFS 482 485
Searching sequences 415
selections see "Combinations" "Permutations"
Self-dual 2—valued Boolean functions 135
Self-dual plane graph 526—527
Self-loop 437
Semilattice 368 371
Sentence parsing 505
Sequences, "probe" 358
Sequences, binary search 415—418
Sequences, de Bruijn 539—541
Sequences, Fibonacci 111 270—273 278
Sequences, generating functions for, table 289
Sequences, graphic 444
Sequences, head of 282
Sequences, Lucas 278
Sequences, merging sorted sequences 423—424
Sequences, searching 415
Sequences, sorted 415
Sequences, tail of 282
Sequential counting 128—132
Series, arithmetic 110 115
Series, formal power 239 247—251
Series, geometric 110 116 249—251
SES see ""Soft" expert systems"
Sets, "extraordinary" 9
Sets, "ordinary" 9
Sets, absolute complement 4
Sets, antisymmetric relation 11
Sets, associative binary operations 16
Sets, associative property 5
Sets, binary operations 16
Sets, binary relation on 10
Sets, Boolean sum 5
Sets, Cantor's paradox 7
Sets, cartesian product 8 10
Sets, chain 363
Sets, characteristic function 2
Sets, closure property 383—384
Sets, commutative binary operations 16
Sets, commutative property 5
Sets, comparable elements 363
Sets, composition of relation 14—15
Sets, congruence class 12
Sets, congruence modulo n 12
Sets, containment 3—4
Sets, correspondence 13
Sets, countable 367
Sets, definition 1
Sets, DeMorgan's Laws 6 40—41 49 50 61 86
Sets, description 2—3
Sets, disjoint 5 211
Sets, distributive laws 5
Sets, domain of relation 10—11
Sets, elements 1
Sets, empty 4
Sets, enumerations 367—368
Sets, equality 4
Sets, equivalence relation 11
Sets, function, defined 13
Sets, glb 364
Sets, greatest element 364
Sets, idempotent property 5
Sets, images 13
Sets, incomparable elements 363
Sets, intersection 5
Sets, into function 14
Sets, inverse function 14
Sets, join of elements 368
Sets, least element 364
Sets, lower bound 364
Sets, lub 364
Sets, many-to-one function 14
Sets, mapping 13
Sets, meet of elements 368
Sets, members 1
Sets, null 4
Sets, one-to-one correspondence 14
Sets, one-to-one function 13
Sets, onto function 14
Sets, operator 13
Sets, ordered pair 9
Sets, P-closure 384
Sets, partially ordered see "Posets"
Sets, partition 350—351
Sets, power 7
Sets, preimages 13
Sets, proper subset 3—4
Sets, range of relation 10—11
Sets, reflexive relation 11
Sets, relation on 10
Sets, relative complement 4
Sets, Russell's paradox 7 9
Sets, single-valued function 13
Sets, singleton 4 442
Sets, subset 3—4
Sets, symmetric relation 11
Sets, symmetrical difference 5
Sets, system of distinct representatives 657 686
Sets, totally ordered 363
Sets, transformation 13
Sets, transitive relation 11
Sets, uncountable 367
Sets, union 4—5
Sets, universal 2—3
Sets, upper bound 364
Sets, Venn diagrams 6 212 214
Sets, well-defined function 13
Sets, well-ordered 366—367
Seven-segment display (SSD) 596—600 609 610
Sheffer stroke function 593
Shell sort algorithm 419
Shift registers 539—541
Shifting properties of generating functions 285—290
Sieve method see "Inclusion-exclusion principle
Similarity relations 713 726
Simple circuit 388 442
Simple digraph 333
Simple graph 437 438
Simple path 388 442
Simplification rule of inference 49
Single-valued function for sets 13
singleton set 4 442
Sink vertex 633 638 640
Size of a graph 437
Slack of an edge 639
Small scale integration (SSI) 600
Sorted lists, merging 282—284
Sorted sequences 415
Sorting algorithms, binary search 415—418
Sorting Algorithms, bubble sort 297 419 423
Sorting algorithms, interchange sort 418—423
Sorting Algorithms, merge sort 282—284 425—426
Sorting algorithms, run times 347
Sorting algorithms, Shell sort 419
Sorting algorithms, successive minima 419
Sorting algorithms, topological sort 428—432
Source vertex 633 638 640
Spanning subgraph 452
Spanning trees, BFS 482—485
Spanning trees, Cayley's formula 497
Spanning trees, defined 480
Spanning trees, DFS 482 485
Spanning trees, directed 480
Spanning trees, Kruskal's algorithm 486—489
Spanning trees, maximal 493
Spanning trees, minimal 485—489
Spanning trees, Prim's algorithm 494
Spanning trees, properties of 480—482
Spanning trees, Pruefer code 495—497
| Spanning trees, terminology associated with 482
Specialization 22
SSD see "Seven-segment display"
SSI see "Small scale integration"
Stanford Research Institute 722
Stanford University 722
Star graph 457—458
State diagrams, shift register 540
Stirling number of the second kind 209—210
Strategies for problem solving see "Reasoning"
strings 373—375
Strong inductive hypothesis 111 see
Strong mathematical induction 111—115 see
Strongly connected vertices 391—392
Subalgebra, Boolean 584
Subgraphs 334 452
Subgraphs, complement of 455—456
Subgraphs, connected components 391—392
Subject-predicate analysis 80—81
Subnormal fuzzy set 700
Subroutine, recursive 108
Subset of a fuzzy set 700
Subset of a set 3—4
Substitution solutions for recurrence relations 281—285
Subtree 482 507
Successive minima algorithm 419
Sum bit 614
Sum of generating functions 240
Sum rule 22 126—132 see principle
Sum-of-products form 591 605
Support of a fuzzy set 700
Switching mechanisms see also "Arithmetic logic unit" "Boolean minimization
Switching mechanisms, AND function 601 603
Switching mechanisms, equivalent 596
Switching mechanisms, EXCLUSIVE-OR function 602 603
Switching mechanisms, gate 596
Switching mechanisms, gate minimization 600—601
Switching mechanisms, Gray-code (to binary-code converter) 604
Switching mechanisms, INCLUSIVE-OR function 601 603
Switching mechanisms, INVERTER function 602 603
Switching mechanisms, NAND function 602 603
Switching mechanisms, NOR function 602 603
Switching mechanisms, seven-segment display 596—600 609 610
Syllogism, disjunctive 49
Syllogism, hypothetical 48 49
Symmetric closure of a relation 383
Symmetric directed graph 438
Symmetric relation on a set 11
Symmetrical difference of fuzzy sets 732
Symmetrical difference of sets 5
Symmetry of a binary relation 339 340
Symmetry of a fuzzy binary relation 713
Symmetry of a similarity relation 726
Symmetry of binomial coefficients 191
System of Distinct Representatives Problem 657 686 691
t-level set 708
t-part partition of a set 178
Tail of a sequence 282
Tautology 38
Terminal vertex 442
Termination of an algorithm 404
Terms in formal power series 239
Tetrahedron, edge graph of 458
The Assignment Problem 686
The Binomial theorem 201—205 see
The Chinese Remainder Theorem 360
The Chromatic Number Problem 406
The Coconut Problem 361
The Committee Problem 686 691
The Division Algorithm 64
The Extension Principle 714
The Four-Color Problem 569—571
The Fundamental Theorem of Arithmetic 118
The Hamiltonian Cycle Problem 406
The Knight's Tour Puzzle 555
The Koenigsberg Bridges 535—538
The Lancaster Equations of Combat 275
The Marriage Problem 687 689—691
The Multinomial theorem 205—207 see
The Planar Subgraph Problem 406
The Scheduling Problem 558—560
The Sieve of Eratosthenes 224—225
The Subgraph Isomorphism Problem 406
The Towers of Hanoi 282
Thin directed tree 506
Topological sorting 428—432
Torus 607
Total order relation 363
Transformation see "Functions"
Transitive (reflexive) closure of a fuzzy binary relation 713
Transitive (reflexive) closure of a relation 383
Transitive (reflexive) closure, Warshall's algorithm 407—412 539
Transitive relation on a set 11
Transitive rule 48 49
Transitivity in expert systems 724
Transitivity of a binary relation 339—340
Transitivity, improvement 727
transport networks see "Networks"
Traversable multigraph 537
Traversal algorithms 514—515 518
Traverse (path) 389
Trees, B-tree 503—504
Trees, binary search 512—514
Trees, child in 482
Trees, combinatorial relationships 501—503
Trees, complete binary 509—510
Trees, defined 468
Trees, descendant in 482
Trees, economy 486
Trees, edges 483
Trees, full 506
Trees, height of 501
Trees, height-balanced 510—512
Trees, internal vertex 482
Trees, leaf of 482
Trees, minimal spanning 494
Trees, nondirected 469
Trees, nontrivial 469
Trees, operator prefix and postfix notation 471—472
Trees, ordered 517
Trees, parent in 482
Trees, properties of 473—476
Trees, Pruefer code 495—497
Trees, root of 469
Trees, rooted 468
Trees, subtree 482
Trees, traversal algorithms 514—515 518
Trees, trivial 469
Trinomial 205
Tripartite graph 467
Triple primes 76
Trivial path 442
Trivial proof 61
Trivial tree 469
Truth set of a proposition 84
Truth tables 35 37—41 46
Truth tables for logic networks, AND function 601
Truth tables for logic networks, EXCLUSIVE-OR function 602
Truth tables for logic networks, full-adder 616
Truth tables for logic networks, Gray-code to binary-code converter 604
Truth tables for logic networks, half-adder 615
Truth tables for logic networks, INCLUSIVE-OR function 601
Truth tables for logic networks, INVERTER function 602
Truth tables for logic networks, multiplexers 623 625
Truth tables for logic networks, NAND function 602
Truth tables for logic networks, NOR function 602
Truth tables for logic networks, seven-segment display 597
Twin primes 76
Uncountable sets 367
Undetermined coefficients, method of, defined 311
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