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.

Язык:

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

$(n_1, n_2, n_3, \dots, n_t)$       28
$(\upsilon,b,r,k,\lambda)$ -design      865—867 872 874
      280
$a\equiv b$ (mod n)      717
      322
$c(P, \bar P)$       674
      418—420
      388
$f(x)\equiv g(x) (mod s(x))$       846
$f:A\to B$       251
$f\in O(g)$       294
$f\in O(g)$ on S      513
$f^{-1}$       285
$f^{-1}B_1$       287
(contradiction)      58 86
$G-\upsilon$ ( $\upsilon$ vertex)      540
      851 857 871
$g\circ f$       281
$id(\upsilon)$       554
      361
      366 491 540
$K_{3,3}$       561 562
$K_{m, n}$       561
$L_{\infty}$       869
$M_2(C), M_2(Q), M_2(\mathbf R), M_2(\mathbf Z)$       702
(aleph null)      A-35 A-36
$od(\upsilon)$       554
$P(G,\lambda)$       590
      153
      421
      783
      783 830
(tautology)      58
      537
$x^{(n)}$       606
      153
      153 717
$\beta(G)$       587
$\binom{-n}r n \underset {n}{>} 0$       438
$\binom{n}r$       19 44 45 438
$\chi(G)$       588—591
$\emptyset$ (the null set)      100
$\exists ! x$       120
$\exists x$       100
$\forall x$       100 145
$\gamma(G)$       603
$\lambda$ (the empty string)      316
$\lambda^{(n)}$       591
$\lim\limits_{n\to\infty} r_n = L$       121
$\lim\limits_{x\to\alpha} f(x) = L$       113 114
$\mathbf N$       153
$\mathfrak R^c$ (converse of relation $\mathfrak R$ )      284
$\omega (G)$       605
$\overline G$       541
$\phi(n)$ (Euler’s phi function)      409—411 720 779
$\Pi$ notation      235
$\Sigma$ notation      22
$\sigma(G)$       689
$\Sigma^+,\Sigma^*$       317
$\Sigma^0,\Sigma,\Sigma^n$       316
$\textbf R,\textbf R^+,\textbf R^*$       153
(0, l)-matrix      359 395
(i, j)-entry of a matrix      A-13
(n, m) block code      796 (see also “Algebraic coding theory”)
1-equivalence      350
1-equivalent states       388
2-isomorphic graphs      576
2-methyl propane      610
a - z cut      673
a is congruent to b modulo n      717
Abel, Niels Henrik      730 777 830 872
Abelian group      173 777
abs      216
Absorption Laws, for a Boolean algebra      764
Absorption Laws, for Boolean functions      737
Absorption Laws, for Boolean variables      737
Absorption Laws, for logic      65
Absorption Laws, for set theory      160
Access function      253 259
Access permissions      17
Achilles      139
Ackermann, Wilhelm      260
Ackermann’s function      259 260
Addition of binary numbers      746
Addition of equivalence classes of integers (in $\mathbf Z_n$ )      718
Addition of equivalence classes of polynomials      846
Addition of matrices      A14
Addition of polynomials      836
Additive identity for matrices      A 15
Additive identity for real numbers      120
Additive inverse of a matrix      A 15
Additive inverse of a real number      120
Additive inverse of an integer      280
Address in a universal address system      616
Address in computer memory      5 720
Adjacency list      397
Adjacency list representation      395 397
Adjacency matrix for a graph      367 559
Adjacent from      363 530
Adjacent mark ordering algorithm      523
Adjacent to      363 530
Adjacent vertices      363 530
Affine plane      859—864 866—868
Aho, Alfred V.      395 396 523 600 601 651 652 670 694 695
Al-jabr      288
Al-Khowarizmi, Abu Ja’far Mohammed ibn Musa      238 239
Albert, A. Adrian      872 873
Aleph      310
Algebra of propositions      61 63 64
Algebra of switching circuits      772
Algebra of switching functions      735
Algebraic coding theory      23 173 777 793—811 831
Algebraic coding theory, (n, m) block code      796
Algebraic coding theory, binary symmetric channel      794
Algebraic coding theory, block code      796
Algebraic coding theory, code word      795
Algebraic coding theory, coding schemes      795—797
Algebraic coding theory, coset leader      808
Algebraic coding theory, d(x, y)      798
Algebraic coding theory, decoding      796 804
Algebraic coding theory, decoding algorithm      804
Algebraic coding theory, decoding by coset leaders      809
Algebraic coding theory, decoding table      807 808
Algebraic coding theory, decoding table with syndromes      809
Algebraic coding theory, distance      798
Algebraic coding theory, distance function      799
Algebraic coding theory, dual code      805
Algebraic coding theory, efficiency of a coding scheme      796
Algebraic coding theory, encoding      795 801 804
Algebraic coding theory, equivalent codes      811
Algebraic coding theory, error correction      800
Algebraic coding theory, error detection      800
Algebraic coding theory, error pattern      794
Algebraic coding theory, five-times repetition code      798
Algebraic coding theory, generator matrix      801 806 807
Algebraic coding theory, Gilbert bound      806
Algebraic coding theory, Golay, Marcel      793
Algebraic coding theory, group code      806
Algebraic coding theory, Hamming bound      806
Algebraic coding theory, Hamming code      811
Algebraic coding theory, Hamming matrix      811
Algebraic coding theory, Hamming metric      799
Algebraic coding theory, Hamming, Richard      793 794 798
Algebraic coding theory, independent events      794
Algebraic coding theory, majority rule      797 798
Algebraic coding theory, message      794 795
Algebraic coding theory, metric      799
Algebraic coding theory, metric space      799
Algebraic coding theory, nearest neighbor      803
Algebraic coding theory, nine-times repetition code      805

Algebraic coding theory, noise      794
Algebraic coding theory, parity-check code      797
Algebraic coding theory, parity-check equations      802
Algebraic coding theory, parity-check matrix      804 806 807 811
Algebraic coding theory, probability      794—797
Algebraic coding theory, rate of a code      796 811
Algebraic coding theory, received word      795
Algebraic coding theory, S(x, k)      799
Algebraic coding theory, Shannon, Claude Elwood      793
Algebraic coding theory, sphere (S(x, k))      799
Algebraic coding theory, syndrome      803
Algebraic coding theory, systematic form      811
Algebraic coding theory, triangle inequality      799
Algebraic coding theory, triple repetition code      797
Algebraic coding theory, weight of x      798
Algebraic coding theory, wt(x)      798
Algebraic structures      794
Algorism      238
Algorithm      44 45 227 238 239 293 294 297—305 511 512
Algorithms, adjacent mark ordering      467 468 523
Algorithms, binary search      517—519
Algorithms, breadth-first search      626
Algorithms, constructing a Huffman tree      642 643
Algorithms, counting nonisomorphic labeled trees      613 614
Algorithms, decoding      804
Algorithms, depth-first search      624
Algorithms, determining articulation points      647 651
Algorithms, Dijkstra’s shortest-path algorithm      660
Algorithms, divide-and-conquer algorithms      511—520 523 634
Algorithms, division algorithm for integers      215—218 225 226 231 253 276 278 293 717 788 789
Algorithms, division algorithm for polynomials      839—841 845—847
Algorithms, Euclidean algorithm for integers      226—229 293 468 469 522 719
Algorithms, Euclidean algorithm for polynomials      845
Algorithms, exponentiation      302
Algorithms, generating permutations      467 468
Algorithms, greatest common divisor      229
Algorithms, greatest common divisor (recursive)      469
Algorithms, Kruskal’s algorithm      666
Algorithms, labeling procedure      676 677
Algorithms, Merge Sort      637 638
Algorithms, merging two sorted lists      635
Algorithms, minimization process (finite state machine)      389
Algorithms, Prim’s algorithm      669
Algorithms, searching an unsorted array      300 301
Algorithms, topological sorting algorithm      375 376
Algorithms, universal address system      616
Alkane      610
Allowable choices      99
Alphabet      23 316
Alternative form of mathematical induction      see “Mathematical induction” “Alternative
American Journal of Mathematics      428
An Investigation in the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probability      138
An Investigation of the Laws of Thought      176 735 772
Analysis of Algorithms      3 245 260 296—305 311 485 486 A-8
Analytic Theory of Probability      173
Analytical engine      239
Analytische Zahlentheorie      310
Ancestor      615
AND      52
AND gate      171 745
ANSI FORTRAN      145 384
Antichain      400
Antisymmetric property (of a relation)      352 353 367 373 394
Anton, Howard      A 24
AP(F)      860
Apianus, Petrus      178
Appel, Kenneth      589 599—601
ARC      330 363
Argue by the converse      85 127
Argue by the inverse      85 128
Argument      51 58 77 80 124
Aristotle      137 138 233
Arithmetica      239
Arithmetica Integra      45
Arrangement      6—12 19—23 33 35 44 316 418 428 449 450
Arrangement (circular)      11 12
Arrangements with forbidden positions      424—426
Ars Conjectandi      44
Articulation point      577 645—647 651
Articulation point algorithm      647 651
Aschbacher, Michael      831
Assignment problem      683 695
Associated homogeneous relation      483 484 489 490
Associated undirected graph      364 533
Associative binary operation      268
Associative law of addition for integers      132
Associative law of addition for real numbers      111
Associative law of multiplication for matrices      A-18
Associative laws for a Boolean algebra      764
Associative laws for a ring      701 702
Associative laws for Boolean functions      737
Associative laws for Boolean variables      737
Associative laws for logic      64 108
Associative laws for set theory      160
Associative property for composition of relations      358
Associative property for function composition      283
Associative property in a group      777 830
Atkins, Joel E.      651 652
Atom of a Boolean algebra      767 773
Augarten, Stan      239 241
Auluck, F. C      476 523
Automata theory      343
Auxiliary variables      474
Average-case complexity      300 301
Baase, Sara      311 651 652 668 670 694 695
Babbage, Charles      239
Bachmann, Paul Gustav Heinrich      310
Back edge (of a tree)      646
Backtrack(ing)      621 624
Balanced (rooted) tree      629
Balanced complete binary tree      634
Balanced incomplete block design      865 866 869
Ballot problem      50
Barnette, David      600 601
Barnier, William J.      343 344
Barwise, Jon      139 140
Base      A-1 2 8 16 218—220
Base (for a number system)      218
Base (for a recursive definition)      202
Base-changing formula      A-8
BASIC      6 55 60 253 618 726
Basic connectives      52—54 75 100 101
Basic connectives and (conjunction)      52
Basic connectives but      54
Basic connectives exclusive or      52
Basic connectives if and only if (biconditional)      53
Basic connectives if... then (implication)      52
Basic connectives inclusive or (disjunction)      52
Basic connectives nand      75
Basic connectives negation (not)      52
Basic connectives nor      75
Basic connectives not (negation)      52
Basic connectives or (disjunction)      52
Basic connectives quantifiers      100
BASIC program for complex number arithmetic      727
Basis step      185 186 188 189 196
Beckenbach, Edwin F.      832
Behzad, Mehdi      599 601
Bell numbers      524
Bell, Eric Temple      524
Bellman, R.      585 600 601
Bellmore, M.      585 600 601
Berge, Claude      599 695
Berger, Thomas R.      732 872 873
Bernays, Paul      139
Bernoulli trial      173
Bernoulli, Jakob      44
Bernoulli, Johann      308
Bertrand, Joseph Louis Frangois      50
Best case complexity      300 301

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