Grimaldi R.P. — Discrete and combinatorial mathematics. An introduction :: Электронная библиотека попечительского совета мехмата МГУ

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Grimaldi R.P. — Discrete and combinatorial mathematics. An introduction

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Название: Discrete and combinatorial mathematics. An introduction

Автор: Grimaldi R.P.

Аннотация:

This is an excellent book for self study. However, there are parts in this book that must be rearranged or deleted. For example, I think Catalan numbers should be deleted. This might be useful for the matrix chaining problem, but that's in the realms of algorithm design (specifically in dynamic programming). Also, I do not understand why Grimaldi sandwiched in a chapter on Finite State Machines between two chapters on Functions and Relations. Maybe he should make a section on languages for FSMs, but I recommend Sipser's Introduction to the Theory of Computation if you want to learn about FSMs.

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Рубрика: Computer science/Дискретная математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 3rd edition

Год издания: 1994

Количество страниц: 1024

Добавлена в каталог: 17.11.2005

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Предметный указатель

Finite state machine, output      328
Finite state machine, output alphabet      328 329
Finite state machine, output function      329
Finite state machine, pigeonhole principle      338
Finite state machine, reachability      350
Finite state machine, reachable state      340
Finite state machine, redundant state      388
Finite state machine, reset      330
Finite state machine, second level of reachability      350
Finite state machine, sequence recognizer      335 343
Finite state machine, serial binary adder      332
Finite state machine, sink (state)      341
Finite state machine, starting state      329
Finite state machine, state diagram      329 330
Finite state machine, state table      329
Finite state machine, strongly connected machine      341
Finite state machine, submachine      341
Finite state machine, transfer sequence      341
Finite state machine, transient state      340 341
Finite state machine, transition sequence      341
Finite state machine, transition table      329
Finite state machine, two-unit delay machine      339 340
Finite strings      317
Finizio, Norman      522 523
First level of infinity      A-35
First level of reachability      350
First-in first-out structure      626
First-order linear recurrence relations      461—467
Fisher, R.A.      872
Fissionable material      498
Five-times repetition code      798 (see also “Algebraic coding theory”)
Fixed (invariant)      817
Fixed point (of a function)      419
Floor function ([x])      252 253 629
Flow in a transport network      672 679
flowchart      194 195 363
Folding method (for hashing)      721
Ford, Lester Randolph, Jr.      679 695 696
Forest      607
Formal Logic; or, the Calculus of Inference, Necessary and Probable      138
Formulario Mathematico      240
FORTRAN      145 384 385
FORTRAN compiler      252
Foulds, L.R.      585 600 601
Foundations of mathematics      139 343
Four-byte address      5
Four-color problem      589 598—600
Fourier, Joseph Baptiste Joseph      309
Free variable      100 123
Frege, Gottlieb      138
Friedman, Arthur D.      773
Fulkerson, D.R.      599 601 679 695 696
Full binary tree      640
Full m-ary tree      644
full-adder      746 747
Function      113 202 245 251—257 259—265 267—269 271 272 280—290 294—296 304 308 309 315 317 409—411 418 419 516 701 720—722 732 735—743 745 754 758 772 795 796 799 801 804 A-1 A-4—A-6 A-8 A-10 A-30
Function       280
Function associative binary operation      268
Function codomain      252
Function complexity      245
Function composition      see “Composite function”
Function decoding      796 804
Function domain      252
Function dominance      294—296 353 513
Function INT      253
Function inverse      see “Inverse of a function”
Function logarithmic      A-1 A-8
Function mapping      251
Function notation      251 252
Function one-to-one correspondence      280 309 505 684
Function order (of a function)      294
Function output function      329
Function pred (predecessor)      314
Function preimage of a set      287—290
Function preimage of an element      251
Function projection      271—273
Function range      252
Function restriction      257
Function sequence      254
Function succ (successor)      314
Function trunc(ation)      253
Function unary operation      267
Function, $f^{-1}$       285
Function, access function      253 259
Function, Ackermann’s function      259 260
Function, Big-Oh notation      294—296
Function, bijective function      280
Function, binary operation      267
Function, Boolean function      736—743 745—754
Function, ceiling function      253 254
Function, characteristic function      313
Function, closed binary operation      267 269—271
Function, commutative binary operation      268
Function, composite function      281
Function, composition of functions      281—285 287 A-10
Function, constant function      261
Function, delta function      606
Function, distance function      799
Function, dominance      294
Function, encoding      795 801 804
Function, equality      281
Function, Euler’s phi function      409—411
Function, exponential      418 A-1 A-4—A-6
Function, extension      257
Function, finite function      245 254 255 262 290 308
Function, finite sequence of n terms      A-30
Function, fixed point      419
Function, floor function      252 253
Function, function complexity      245
Function, function dominance      294—296
Function, greatest integer function      252 253
Function, hashing function      701 720 721 732
Function, identity function      280
Function, image of a set      256
Function, image of an element      251
Function, incompletely specified Boolean function      758
Function, increasing function      313
Function, infinite sequence      A-30
Function, injective function      255
Function, inverse function      285 A-10
Function, invertible function      284—286 290
Function, monary operation      267
Function, monotone increasing function      516
Function, next state function      329
Function, one-to-one function      255 282 285 290 684
Function, onto function      260 262—265 271 272 282 285 290 355 384 403 407 408 428 453 526
Function, phi function      409—411
Function, powers of a function      284
Function, recursive function      469
Function, scattering function      720 732
Function, self-dual Boolean function      774
Function, space complexity function      294
Function, surjective function      260
Function, switching function      735—743 745 772
Function, symmetric Boolean function      774
Function, time complexity function      294 304
Fundamental conjunction      740
Fundamental disjunction      741
Fundamental theorem of algebra      371
Fundamental Theorem of Arithmetic      183 232—234 236 241 254 265 276 321 354 355 409 728 A-33
G - e (e an edge)      540
g dominates f      294
g dominates f on S      513
Gaffian, Joseph A.      731 732 831 832
Galileo      309
Galois field      851 872
Galois theory      731 831
Galois, Evariste      731 830 831 851 871 872
Gambler’s ruin      525
Gardiner, Anthony      831 832

Gardner, Martin      523 831 832
Garland, Trudi Hammel      522 524
Gating network      315 745 773
Gauss, Carl Friedrich      395 730 732
gcd (greatest common divisor), for integers      226 235
gcd (greatest common divisor), for polynomials      845
General solution (of a recurrence relation)      462
Generalizations of the principle of inclusion and exclusion      413—417
Generalized associative law for $\cup$       204
Generalized associative law for $\wedge$       203
Generalized associative law for a group      778
Generalized associative law of addition of real numbers      206
Generalized associative laws in a ring      702
Generalized Binomial Theorem      439
Generalized DeMorgan’s laws      167
Generalized distributive laws (for set theory)      169
Generalized distributive laws in a ring      702
Generalized intersection of sets      166
Generalized union of sets      166
Generating function      310 433—443 446—450 454—458 466 493—499 501 522 817 820 821 824 825
Generating function, calculational techniques      436—443
Generating function, convolution of sequences      443
Generating function, exponential generating function      449—453
Generating function, in solving recurrence relations      493—499
Generating function, moment generating function      457 458
Generating function, nonlinear recurrence relation      501 502
Generating function, ordinary generating function      449
Generating function, partitions of integers      445—448
Generating function, summation operator      454 455
Generating function, table of identities      440
Generator matrix      801 806 807
Generator of a cyclic group      787
GENERIC      128
Geometric progression      461 462
Geometric series      437 440 487
Geometrie die Lage      650
Geometry      831
Germain, Sophie      730
Gersting, Judith L.      343 344
gib (greatest lower bound)      378 379
Gilbert bound      806 (see also “Algebraic coding theory”)
Gill, Arthur      343 344
Giomale di Matematiche      859
Godel’s proof      178
Goel, Kurt      177
Golay, Marcel J.E.      793 831 832
Goldberg, Samuel      523 524
Golden ratio      481
Gorenstein, Daniel      831 832
Graceful (labeling of a tree)      654
Graham, Ronald Lewis      311 312 522 524 670 694 696
Graph coloring      588—595
Graph isomorphism      540 544—546 723 724
Graph planarity      366 645
Graph theor, labeled directed graph      333
Graph theory      207 248 330 333 362—368 372—376 394—397 411 412 428 529—535 537—546 549—556 558—573 576—595 598—607 613 645—647 653—655 657 658 683 684 689 692 694 757 832 “Transport “Trees”)
Graph theory $deg(\upsilon)$       550
Graph theory $G-\upsilon$ ( $\upsilon$ a vertex)      540
Graph theory $id(\upsilon)$       554
Graph theory       366 540
Graph theory $K_{3,3}$       561 562
Graph theory $K_{m, n}$       561
Graph theory $P(G, \lambda)$       590
Graph theory       537
Graph theory $\beta(G)$ , the independence number of G      587
Graph theory $\chi(G)$ , the chromatic number of G      588—591
Graph theory $\gamma(G)$ , the domination number of G      603
Graph theory $\omega(G)$ , the clique number of G      605
Graph theory $\overline G$       541
Graph theory $\sigma(G)$       689
Graph theory adjacency list      397
Graph theory adjacency list representation      395 397
Graph theory adjacency matrix      367 559
Graph theory adjacent vertices      363 530
Graph theory algorithm for articulation points      647 651
Graph theory arc      330 363
Graph theory articulation point      577 645—647 651
Graph theory associated undirected graph      364 533
Graph theory biconnected component      645—647 651
Graph theory biconnected graph      645
Graph theory binary tree      499 500
Graph theory bipartite graph      561 580 683 684 689
Graph theory bridge      570
Graph theory chromatic number      588—591
Graph theory chromatic polynomial      589—595 600
Graph theory circuit      532 571
Graph theory clique      604
Graph theory clique number      605
Graph theory closed path      365
Graph theory closed walk      531 566 569
Graph theory cocycle      586
Graph theory color-critical graph      598 650
Graph theory comb graph      604 605
Graph theory complement of a graph      540 541
Graph theory complement of a subgraph in a graph      613
Graph theory complete bipartite graph      561
Graph theory complete directed graph      581
Graph theory complete graph      366 368 540 580 581
Graph theory complete n-partite graph      606
Graph theory components      366 368 533
Graph theory connected graph      364 533
Graph theory covering number      603
Graph theory covering of a graph      603
Graph theory cut-set      569 571—573
Graph theory cut-vertex      577
Graph theory cycle      365 532 571—573 578
Graph theory d(a, b)      658
Graph theory Decomposition Theorem for Chromatic Polynomials      592
Graph theory deficiency      689
Graph theory deficiency of a graph      689
Graph theory deg(R)      566
Graph theory degree of a region      566
Graph theory degree of a vertex      550
Graph theory Dijkstra’s Shortest-Path Algorithm      657 665
Graph theory directed cycle      365 373 532
Graph theory directed edge      330 363
Graph theory directed Euler circuit      554 555
Graph theory directed graph      363 364 372 373 394 395 530
Graph theory directed path      532
Graph theory directed walk      532
Graph theory distance      535 653
Graph theory dominating set      603 757
Graph theory domination number      603
Graph theory dual graph      568 569 571
Graph theory edges      363 530
Graph theory electrical networks      598 600
Graph theory elementary subdivision      562
Graph theory embedding      560
Graph theory Euler circuit      552 578 579
Graph theory Euler trail      552 553 578 579
Graph theory Euler, Leonard      396
Graph theory Euler’s Theorem for Connected Planar Graphs      564 598
Graph theory Four-color problem      589 598—600
Graph theory G - e (e an edge)      540
Graph theory graceful labeling of a tree      654
Graph theory graph coloring      588—595
Graph theory graph isomorphism      540 544—546
Graph theory Hamilton cycle      578 599 600
Graph theory Hamilton path      578 599
Graph theory Hasse diagram      373—376
Graph theory Herschel graph      587 590
Graph theory historical development      600
Graph theory homeomorphic graphs      562
Graph theory in degree (of a vertex)      554
Graph theory incidence matrix      559
Graph theory incident      530
Graph theory incoming degree (of a vertex)      554
Graph theory independence number      587
Graph theory independent set of vertices      587 655
Graph theory index list      397

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