Grimaldi R.P., Rothman D.J. — Discrete and Combinatorial Mathematics: An Applied Introduction :: Электронная библиотека попечительского совета мехмата МГУ

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Grimaldi R.P., Rothman D.J. — Discrete and Combinatorial Mathematics: An Applied Introduction

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Название: Discrete and Combinatorial Mathematics: An Applied Introduction

Авторы: Grimaldi R.P., Rothman D.J.

Аннотация:

Provides an introductory survey in both discrete & combinatorial mathematics. Intended for the beginning student designed to introduce a wide variety of applications & develop mathematical maturity of the student by studying an area that is so different form the traditional coverage in calculus & different equations. DLC: Mathematics. — This text refers to an out of print or unavailable edition of this title.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 5th edition

Год издания: 2004

Количество страниц: 833

Добавлена в каталог: 15.04.2008

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Предметный указатель

Finite state machine, internal states      320 321 327 371
Finite state machine, k-equivalent states      338 371
Finite state machine, k-unit delay machine      329
Finite state machine, Mealy machine      333
Finite state machine, minimization process      371—376 378
Finite state machine, next state      320
Finite state machine, next state function      320
Finite state machine, one-unit delay machine      329
Finite state machine, output      320—322 324 328 329
Finite state machine, output alphabet      320 321
Finite state machine, output function      320
Finite state machine, pigeonhole principle      327
Finite state machine, reachability      338
Finite state machine, reachable state      330
Finite state machine, redundant state      371 373
Finite state machine, reset      321
Finite state machine, second level of reachability      338
Finite state machine, sequence recognizer      326 327 332
Finite state machine, serial binary adder      323 324
Finite state machine, sink (state)      331
Finite state machine, starting state      320 329
Finite state machine, state diagram      321 324 327
Finite state machine, state table      321 322 324 331
Finite state machine, strongly connected machine      331
Finite state machine, submachine      331
Finite state machine, transfer sequence      331
Finite state machine, transient state      330
Finite state machine, transition sequence      331
Finite state machine, transition table      321
Finite state machine, two-unit delay machine      329
Finite strings      310
Finite three-dimensional geometry      831
Finizio, Norman      506 507
First level of infinity      303 A-30
First level of reachability      338
First-degree factor      805 806
First-in first-out structure      598
First-order linear recurrence relations      448 450
Fisher, R.A.      831
Fissionable material      486
Five-times repetition code      765 769 see
Fixed (invariant)      781 783 789
Fixed order      597
Fixed point (of a function)      403
Flach, Matthias      706
Floor function ( $\lfloor x \rfloor$ )      253 254 297 496 602
Flow in a transport network      644—654 656 662 663
Flow of current      536
flowchart      203 204 349
Folding method (for hashing)      694
Fontane, Johnny      186
For all x      88
For any x      88
For at least one x      88
For each x      88
For every x      88
For some x      87 88
Forbidden positions      406 408
Ford — Fulkerson algorithm      654—657
Ford, Lester Randolph, Jr.      649 653 654 668 669
Foreign Office at Bletchley Park      333
Forest      581 639 641 642
Formal Logic; or, the Calculus of Inference, Necessary and Probable      118
Formulario Mathematico      243
Forward edge      650 651 654 655
Foulds, L.R.      562 575 576
Foundations of mathematics      333
Foundations of the Theory of Probability      188
Founder of information theory      795
Four-color conjecture      573
Four-color problem      565 575
Fourier, Joseph Baptiste Joseph      303
Foxtrot      226
Fractals      506
Free variable      88
Frege, Gottlieb      119
Frequency of occurrence      611 692
Frey, Gerhard      706
Frobenius, Georg      796
Front (of a list)      598 599
Fulkerson, Delbert Ray      649 653 654 668 669
Full binary tree      611
Full house      152
Full m-ary tree      614
full-adder      721
Function      99 175 186 211 247 252—257 259—263 267—271 278—293 295 302 303 309 311 318 320 376 394 395 403 409 410 602 644 660 673 697—704 712 739
Function complexity      247
Function composition      see "Composite function"
Function dominance      292 294 341 498
Function inverse      see "Inverse of a function"
Function,       279
Function, $f^{-1}$       283
Function, access function      254
Function, Ackermann’s function      259
Function, associative binary operation      268
Function, Big-Oh notation      290
Function, bijective function      279 283
Function, binary operation      267—269
Function, Boolean function      712
Function, ceiling function      254
Function, characteristic function      307
Function, closed binary operation      267 268 270
Function, codomain      253 279 281 287
Function, commutative binary operation      268 270
Function, composite function      280 281
Function, composition of functions      278 280 282
Function, constant function      261
Function, decoding      767
Function, definition      252
Function, distance function      766 767
Function, domain      175 253 257 270 281 287
Function, dominance      292—294
Function, encoding      763 764 767 769 771 773
Function, equality      279
Function, Euler’s phi function      394 395 689
Function, exponential      402 A-1 A-5
Function, extension      257
Function, finite function      247 284 302
Function, finite sequence of n terms      A-25
Function, fixed point      403
Function, floor function      253 254 297
Function, function complexity      247
Function, function dominance      290—292 294 498
Function, greatest integer function      253 297
Function, hashing function      673 694 695 708
Function, identity function      279
Function, image of a set      256 257
Function, image of an element      253
Function, incompletely specified Boolean function      732
Function, infinite sequence      A-25
Function, injective function      255
Function, inverse function      278 283 285 A-9
Function, invertible function      282—285 287
Function, logarithmic      A-1 A-5
Function, mapping      252
Function, monary operation      267
Function, monotone increasing function      494 495 500 501 503 608 609
Function, next state function      320 682
Function, notation      253
Function, one-to-one correspondence      279 303
Function, one-to-one function      255—257 409 410
Function, onto function      260—263 265
Function, order (of a function)      290 292 293
Function, order-preserving function      366 509
Function, output function      320 682
Function, partial function      260
Function, phi function      394 395
Function, powers of a function      282
Function, pred (predecessor)      307
Function, preimage of a set      285—287

Function, preimage of an element      253
Function, projection      270 271
Function, range      253
Function, recursive function      453
Function, restriction      257
Function, scattering function      694 708
Function, self-dual Boolean function      744
Function, sequence      255
Function, space complexity function      290
Function, succ (successor)      307
Function, surjective function      260
Function, switching function      712
Function, symmetric Boolean function      744
Function, time complexity function      290 297—299
Function, trunc(ation)      254
Function, unary operation      267 268
Fundamental conjunction      715—718 721 723 724 732 738
Fundamental disjunction      717 718
Fundamental theorem of algebra      356
Fundamental Theorem of Arithmetic      193 237—240 244 254 265 275 314 342 394 703 704 A-29
F[x]      802
F[x]/(s(x))      810
G      523
g dominates f      290
G-e (e an edge)      522
G-v (v a vertex)      522
Galileo      303
Gallian, Joseph A.      707 708 795 796
Gallier, Jean H.      119 120
Galois field      813 818
Galois theory      707 795 831
Galois, Evariste      707 794 795 813 830 831
Gambler’s ruin      510
games of chance      188
Gardiner, Anthony      795 796
Gardner, Martin      39 42 507 795 796
Garland, Trudi Hammel      506 507
Garrett, Paul      693 708 795 796
Gate      720
Gating network      309 719—722 731
Gauss, Carl Friedrich      377 705 707
gcd (greatest common divisor) for integers      231—236 240 394 453 454 688 734 737
gcd (greatest common divisor) for polynomials      807 808
General solution of a homogeneous recurrence relation      468
General solution of a nonhomogeneous recurrence relation      471
General solution of a second-order linear homogeneous recurrence relation with constant coefficients      456
Generalizations of the principle of inclusion and exclusion      397—401
Generalized associative law for $\cup$       213
Generalized associative law for $\wedge$       212
Generalized associative law for a group      746
Generalized associative law of addition of real numbers      214—216
Generalized associative law of multiplication of real numbers      214 215
Generalized associative laws in a ring      674
Generalized Binomial Theorem      422
Generalized DeMorgan’s laws      146
Generalized distributive laws in a ring      674
Generalized intersection of sets      146
Generalized union of sets      146
Generated recursively      A-26
Generates      753
Generating function      303 415—445 452 482—487 489 505 783 790 791
Generating function in solving recurrence relations      482—487
Generating function, calculational techniques      418—431
Generating function, convolution of sequences      430 431 440
Generating function, definition      418
Generating function, distributions      415—417
Generating function, exponential generating functions      436—439 443
Generating function, geometric series      419
Generating function, moment generating function      443 444
Generating function, nonlinear recurrence relation      487—490
Generating function, ordinary generating function      436
Generating function, partitions of integers      432—435
Generating function, power series      417
Generating function, rook polynomial      416
Generating function, summation operator      440—442
Generating function, table of identities      424
Generator matrix      769 771 772 774 777 see
Generator of a cyclic group      755
GENERIC      110
Genesereth, Michael R.      119 120
Geometric progression      447
Geometric random variable      430 446
Geometric series      419 423 428 476
Geometrie die Lage      622
Geometry      123 222 242 506 794 795
Gerasa      707
Germain, Sophie      705
Gersting, Judith L.      333 334
GF      813
GF(n)      821 824 827 828
Gilbert bound      773 see
Gill, Arthur      333 334
Giornale di matematiche      820
glb (greatest lower bound)      363 709
Global result      632 639
Goedel, Kurt      187
Goedel’s Proof      188
Golay, Marcel J.E.      761 795 796
Goldberg, Samuel      506 507
Golden ratio      457 469 506
Golomb, Solomon W.      796
Gone With the Wind      47 48 52
Gopolan, K. Gopal      743
Gorenstein, Daniel      795 796
Graceful (labeling of a tree)      627 628
Graff, Michael      795
Graham, Ronald Lewis      304 305 506 507 642 667—669
Grandparent      593
Graph coloring      564—573 575
Graph isomorphism      523 526—528 699
Graph planarity      352 615
Graph theory      324 349—354 378 379 395 396 411 513—579 615—621 624 631 632 657 659—665 667 730 see "Transport "Trees"
Graph theory in degree (of a vertex)      535
Graph theory,       626
Graph theory,       549
Graph theory,       559
Graph theory,       540—543 547
Graph theory,       352 523
Graph theory, $K_{3,3}$       542 543 547
Graph theory, $K_{m,n}$       541
Graph theory, $P(G,\lambda)$       566—568 570
Graph theory,       532 542 667
Graph theory,       520 572
Graph theory, $\beta(G)$ , the independence number of G      564 666
Graph theory, $\chi(G)$ , the chromatic number of G      565 621
Graph theory, $\delta(G)$       664 665
Graph theory, $\gamma(G)$ , the domination number of G      577
Graph theory, $\kappa(G)$ , the number of components of G      517 549 615
Graph theory, $\omega(G)$ , the clique number of, G      578
Graph theory, $\overline{G}$       523
Graph theory, 2-isomorphic graphs      555
Graph theory, adjacency list      379
Graph theory, adjacency list representation      378 379
Graph theory, adjacency matrix      352 539 600
Graph theory, adjacent from      349 514
Graph theory, adjacent to      349 514
Graph theory, adjacent vertices      349
Graph theory, algorithm for articulation points      619 620
Graph theory, arc      349 514
Graph theory, articulation point      615—621 624
Graph theory, associated undirected graph      350 353 517
Graph theory, biconnected component      615 619—621 624
Graph theory, biconnected graph      615
Graph theory, binary tree      488 595 600
Graph theory, bipartite graph      541 542 558 659 660 662—665 668
Graph theory, bridge      550
Graph theory, chromatic number      413 565 615 621
Graph theory, chromatic polynomial      413 564—571 574
Graph theory, circuit      516 534 551
Graph theory, clique      578

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