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.

Язык:

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

$(v, b, r, k, \lambda)$ -design      825 826 831
      15 21 41 42 436
$(^{-n}_r), n > 0$       422
$(^{n}_{n_1,n_2,n_3,...,n_t})$       23
      279
$a \equiv b$ (mod n)      686
$A\sim B$       A-23
, , $A^{+}$ , A*      315
, the n-th Catalan number      38 490
$c(P, \overline{P})$       646
$Dfi(\upsilon)$       616 619—621
      402 403 410
, , E      371
      374
$f \in O(g)$       290 291
$f \in O(g)$ on S      5 498
$f \in \Omega(g)$       293
$f \in \Theta(g)$       294
$f(x)\equiv g(x)$ (mod s(x))      808
$f^{-1}$       283
$f^{-1}(B_1)$       285
(contradiction)      53
      719 734
$g \circ f$       280
      830
      813 818
      626
      549
(the nth harmonic number)      202
      348 A-16
      559
      540 543
      352 523
$K_{3,3}$       542 543
$K_{m,n}$       541
(the nth Lucas number)      216
$m \times n$ matrix      A-11
$M_2(\mathbb{C})$ , $M_2(\mathbb{Q})$ , $M_2(\mathbb{R})$ , $M_2(\mathbb{Z})$       674
$P(G, \lambda)$       566—568 570
      532 542 667
,       405 406
,       750
      787 789 794 830
(tautology)      53
(the nth triangular number)      198
      520 572
$\aleph_0$ (aleph null)      303 A-30 A-31
$\alpha$       457 458 469
$\beta [=(1-\sqrt{5})/2]$       457
$\beta$ (blank, space)      311
$\beta(G)$       564 666
$\chi(G)$       565 621
$\delta(G)$       664 665
$\ell_\infty$       827 828
$\emptyset$ (the null set)      127
$\exists x$       88
$\forall x$       88 124
$\gamma(G)$       577
$\kappa(G)$       517 549 615
$\lambda$ (for a design)      826
$\lambda$ (the empty string)      310 323
$\lambda^(n)$       567
$\lambda_{xy}$       825
$\lim_{n\rightarrow \infty} r_n = L$       103
$\lim_{x\rightarrow a} f(x) = L$       99 100
$\mathbb{N}$       133
$\mathbb{Q}$ , $\mathbb{Q}^+$ , $\mathbb{Q}^*$       133
$\mathbb{R}$ , $\mathbb{R}^+$ , $\mathbb{R}^*$       133 134
$\mathbb{Z}$ , $\mathbb{Z}^+$       133 134
$\mathbb{Z}_n$       134 686
$\mathbf{C}$ , $\mathbf{C}^{*}$       134
$\mathscr{R}^c$ (converse of relation $\mathscr{R}$ )      282
$\mu_X$       177
$\nu$       320
$\omega$ (output function)      320
$\omega(G)$       293
$\overline{A}$       138
$\phi(n)$ (Euler’s phi function)      394 395 689 692 747 759 760
$\Pi$ notation      239
$\Sigma$ notation      17
$\Sigma^+$ , $\Sigma^*$       310
$\Sigma^0$ , $\Sigma$ , $\Sigma^n$       309
$\sigma_X$ (standard deviation)      180 182 183
$\sigma_X^2$ (variance)      180
$\theta$       294
$\underline{f}:A\rightarrow B$       252
$\underline{g}$ dominates f on S      498
(0, 1)-matrix      345 347 348 352 378 see
(i,j)-entry of a matrix      A-1 1
(m + 1, m) parity-check code      764 765
(n, m) block code      764 see
1-equivalence      338
1-equivalent states ()      371
2-isomorphic graphs      555
2-methyl propane      584
a is congruent to b modulo n      686
a-z cut      645
Abel, Niels Henrik      705 745 794 830
Abelian group      161 745 746 799
Absolute value      219 224
Absorption Laws for a Boolean algebra      735
Absorption Laws for Boolean functions      713
Absorption Laws for Boolean variables      713
Absorption Laws for logic      59
Absorption Laws for set theory      139
Abstract algebra      394 624 742
Access function      254
Achilles      119
Ackermann, Wilhelm      259
Ackermann’s function      259
Acronym      155
Aczel, Amir D.      706 708
Addition      136 137
Addition of binary numbers      720
Addition of equivalence classes of integers (in $\mathbb{Z}_n$ )      687
Addition of equivalence classes of polynomials      809
Addition of matrices      A-12
Addition of polynomials      800
Additions      636 637
Additive identity for a ring      674
Additive identity for matrices      A-13
Additive identity for real numbers      103
Additive inverse for a ring element      674 679 680 701
Additive inverse for integers      278
Additive inverse for matrices      A-13
Additive inverse for real numbers      103
additive rule      162 168 172
Address in a universal address system      589
Address in computer memory      5 694
Address, class A address      12
Address, class B address      12
Address, class C address      12
Address, internet address      12
Address, local address      12
Adjacency list      379
Adjacency list representation      378 379
Adjacency matrix (for a graph)      352 539 600
Adjacency of a pair of vertices      352
Adjacent from      349 514
Adjacent mark ordering algorithm      453 506
Adjacent to      349 514
Adjacent vertices      349
Adleman, Leonard      759
Affine Cipher      691 692 759
Affine plane      820—822 826—828 831
Aggregate      123
Aho, Alfred V.      378 506 507 574 575 623 624 642 667 668 708
Ahuja, Ravendra K.      562 575 637 643 654 668
Al-jabr      242
Al-Khowarizmi, Abu Ja’far Mohammed ibn Musa      242

Albert, A. Adrian      831
Aleph      303
alfa      226
Algebra      123 242
Algebra of logic      742
Algebra of propositions      55 57 58 see
Algebra of switching circuits      742
Algebra of switching functions      711
Algebraic coding theory      18 761—779 795 796
Algebraic coding theory, (m + 1, m) parity-check code      764 765
Algebraic coding theory, (n, m) block code      764
Algebraic coding theory, binary representations      778 779
Algebraic coding theory, binary symmetric channel      762 763
Algebraic coding theory, block code      764
Algebraic coding theory, code word      763 769 771 772 774 776—778
Algebraic coding theory, coding schemes      763
Algebraic coding theory, coset leader      775—777
Algebraic coding theory, d(x, y)      766
Algebraic coding theory, decoding      763
Algebraic coding theory, decoding algorithm      772
Algebraic coding theory, decoding by coset leaders      776
Algebraic coding theory, decoding function      764 767
Algebraic coding theory, decoding scheme      769
Algebraic coding theory, decoding table      774 775
Algebraic coding theory, decoding table with syndromes      776
Algebraic coding theory, distance      766
Algebraic coding theory, distance function      766 767
Algebraic coding theory, dual code      773
Algebraic coding theory, efficiency of a coding scheme      764
Algebraic coding theory, encoding      763
Algebraic coding theory, encoding function      763 764 767 769 771 773
Algebraic coding theory, equivalent codes      778
Algebraic coding theory, error      762
Algebraic coding theory, error correction      767—769
Algebraic coding theory, error detection      767—769
Algebraic coding theory, error pattern      762 763 771 779
Algebraic coding theory, five-times repetition code      765 769
Algebraic coding theory, generator matrix      769 771 772 774 111
Algebraic coding theory, Gilbert bound      773
Algebraic coding theory, Golay, Marcel      761 795 796
Algebraic coding theory, group code      773 774 776 111
Algebraic coding theory, Hamming bound      773
Algebraic coding theory, Hamming code      778
Algebraic coding theory, Hamming matrix      778
Algebraic coding theory, Hamming metric      767
Algebraic coding theory, Hamming, Richard      761 766 795 796
Algebraic coding theory, independent events      762
Algebraic coding theory, majority rule      765
Algebraic coding theory, message      763 769 777 778
Algebraic coding theory, minimum distance between code words      767—769 771 773 774
Algebraic coding theory, minimum weight of nonzero code words      774
Algebraic coding theory, mixed strategy      768
Algebraic coding theory, multiple errors      763
Algebraic coding theory, nearest neighbor      771
Algebraic coding theory, noise      761
Algebraic coding theory, parity-check code      764 765
Algebraic coding theory, parity-check equations      770 111
Algebraic coding theory, parity-check matrix      772 774 776—779
Algebraic coding theory, probability      761—765
Algebraic coding theory, rate of a code      764 778
Algebraic coding theory, received word      762 763 111
Algebraic coding theory, retransmission      765 769
Algebraic coding theory, S(x,k)      161
Algebraic coding theory, Shannon, Claude Elwood      761 795 797
Algebraic coding theory, sphere (S(x,k))      767
Algebraic coding theory, syndrome      771 775—777 779
Algebraic coding theory, systematic form      778
Algebraic coding theory, transmission error      762 767
Algebraic coding theory, triangle inequality      767
Algebraic coding theory, triple repetition code      765 768 769
Algebraic coding theory, weight      766
Algebraic coding theory, wt(x)      766
Algebraic expression      590
Algebraic formulae      623
Algebraic structures      745 761
Algebraic substitution      449
Algorism      242
Algorithm      41 42 233 242—244 289 290 294 295 297 299—301 349 378 442 599 605 613 615 619—621 624 632 633 636—642 649 653
Algorithmic manner      631
Algorithms, adjacent mark ordering      458 506
Algorithms, articulation points      619 620
Algorithms, biconnected components      619 620
Algorithms, binary search      501—503
Algorithms, breadth-first search      598 599
Algorithms, bubble sort      450
Algorithms, decoding      772
Algorithms, depth-first search      597 598 617
Algorithms, Dijkstra’s shortest-path      633 634 667 668
Algorithms, divide-and-conquer      496—503
Algorithms, Edmonds — Karp algorithm      653—657 663
Algorithms, Euclidean algorithm for integers      232 233
Algorithms, Euclidean algorithm for polynomials      808
Algorithms, exponentiation      297—299
Algorithms, Fibonacci numbers      477 478
Algorithms, Ford — Fulkerson algorithm      654—657 663
Algorithms, generating permutations      453 506
Algorithms, greatest common divisor      232 233
Algorithms, greatest common divisor (recursive)      455
Algorithms, Huffman tree      613
Algorithms, Kruskal’s algorithm      639—641
Algorithms, linear search      296 302
Algorithms, maximum value      301
Algorithms, Merge Sort      496 608
Algorithms, merging two sorted lists      607
Algorithms, minimization process for a finite state machine      372—373
Algorithms, nonisomorphic trees on n labeled vertices      586 587
Algorithms, polynomial evaluation      301
Algorithms, Priifer code for a labeled tree      586 587
Algorithms, Prim’s algorithm      641—643 668
Algorithms, searching an array      295 296
Algorithms, topological sorting algorithm      360 361
Algorithms, universal address system      589
Alkane      584
Allowable choices      87
alpha testing      185
Alphabet      18 309—311 313 315 316 337 338 609 610
Alphabetical ordering      589
Alternating sequence      650
Alternating triple      135
Alternative form of the Principle of Mathematical Induction      206—208 217 238 298 458 503 582 583
American Journal of Mathematics      411
American National Standards Institute      125
An Investigation in the Laws of Thought on Which Are Founded the Mathematical Theories of Logic and Probability      119
An Investigation of the Laws of Thought      186 711 742
Analysis      444
Analysis of Algorithms      3 247 259 292 294—300 304 305 453 473 503 A-1 A-6
Analytic Theory of Probability      150 188
Analytical engine      242
Analytische Zahlentheorie      304
Ancestor      588 616—619
AND      48 50
AND gate      149 719 720
Annals of Mathematics      706
ANSI FORTRAN      125
Antichain      381
Antisymmetric property (of a relation)      340 341 347 348 353 357 358 376 377
Anton, Howard      A-21
AP(F)      822 824 826—828
Apianus, Petrus      188
Appel, Kenneth      565 573 575
Application Specific Integrated Circuit      149
Applied Boolean algebra      742
Approximately equal ( $\dot{=}$ )      7
Approximation theory      304
arbitrary      110
ARC      321 329 349 514
Argue by the converse      74 82 109 547
Argue by the inverse      75 82 110
Argument      47 53 67 72 74 75 107 108 112
Aristotle      117 118 238

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