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

Method of undetermined coefficients      483
Methodus Differentialis      310
Metric      799
Metric space      799
Meyer, Paul L.      179
Miller, George Abraham      830
MIN      235
Minimal covering of a graph      603
Minimal distinguishing string      391—393
Minimal dominating set      603 757
Minimal element (of a poset)      376
Minimal product of sums      753 754 773
Minimal spanning tree      665—670 694 695
Minimal spanning tree algorithms      666 669
Minimal sum of products      747 748 756 758—760 773
Minimization process      349 388—393
Minimization process algorithm      389
Minor      A-22
Minterm      741
Mirsky, Leon      695 696
MiUbanke, Annabella      239
Mobius inversion formula      428
MOD      228 469
Mod n      717
Modulo n relation      350
modus ponens      80 84 88 126 127 323
Modus Tollens      83 84 86 88 126 127
Moment generating function      457 458
Monary operation      158 267 762
Monic polynomial      884
Monotone increasing function      516
Moon, John Wesley      650 652
Moore, Edward Forrest      343 345 396
Morash, Ronald P.      140
Moser, L.      508 524
Multigraph      363 534 542 657
Multinomial coefficient      28
Multinomial theorem      28 37 124
Multiple of a polynomial      839
Multiple of an integer      213
Multiple output network      746
Multiple root      842
Multiples of group elements      780
Multiplication of equivalence classes of integers (in $\mathbf Z_n$ )      718
Multiplication of equivalence classes of polynomials      846 847
Multiplication of polynomials      836
Multiplicative cancellation in $\mathbf Z$ )      213
Multiplicative identity for matrices      A-19
Multiplicative identity for real numbers      120
Multiplicative identity in a ring      703
Multiplicative inverse (of a nonzero real number)      120 280
Multiplicative inverse for a matrix      A-19
Multiplicative inverse in a ring      706
Multiplicity of a root      842
Multiplicity of an edge      534
Murty, U.S.R.      599 601 695
Mutually disjoint sets      158 171
n choose r      19
n factorial      7
n!      7 206 298
n!, Stirling’s approximation formula      310
n-Butane      610
n-cube      602
n-fold product      246
n-graph      534
n-tuple      246 272
Nand (connective)      75
NAND gate      754
Napier, John      A-7
Natural logarithm      A-8
Nearest neighbor      803
Necessary condition      52
Negation      52
Negation of quantified statements      109 110 113 114
Nemhauser, G.L.      585 600 601
Nested multiplication method      308
Network dual      572 573
Network electrical      572 573 607
Network feedback      774
Network gating      315 745 773
Network linear (resistance)      473
Network logic      745
Network multiple output      746
Network parallel      73
Network PERT      372 394
Network Program Evaluation and Review Technique      372 394
Network series      73
Network switching      72—74
Network transport      671
Neutrons      43 497 498
Newsom, Carroll V.      139 140 311 312
Newton, Sir Isaac      310
Next state      328
Next state function      329
Nievergelt, Jurg      523 524
Nine-times repetition code      805 (see also “Algebraic coding theory”)
Niven, Ivan      240 241 458 732
No degree      836
Node      363 530 “Vertices”)
Noether, Emmy      731
Noise (in a binary symmetric channel)      794
Non-Euclidean geometry      859
Nonempty universe      102
Nonhomogeneous recurrence relation      463 471 482—492
Nonlinear recurrence relations      499—504
Nonplanar graph      560—563
Nontrivial subgroup      780
Nor (connective)      75
NOR gate      754
Normal subgroup      831 872
Null child      622
Null graph      541
Null set $(\emptyset)$       148
Number theory      35 214 215 238—241 309 310 409 428 445 701 730
O(g) (order of g)      294
O(g) on      5 513
Object program      252 308
octahedron      568
Octal system (base 8)      218
Odd integer      131
Ohm’s Law      474
Ohm’s Law for electrical flow      598
On the Theory of Groups, as Depending on the Symbolic Equation $\theta=1$       830
One element of a Boolean algebra      762
One factor      692
One-terminal-pair-graph      572
One-to-one correspondence      280 309 442 448 505 684 A-27
One-to-one function      255 282 285 290 684
One-unit delay machine      339
One’s complement      220—223
Onto function      260 262—265 271 272 282 285 290 355 384 403 407 408 428 453 526
Open interval      153
Open statement      99 122 123 143 147 184 185
Open switch      72
Open walk      531
operands      157
Operation      157 158
Operations research      600 657 694
Optics      522
Optimal spanning tree      665 666 669 670
Optimal tree      641 642
Optimization      44 248 333 607
Or (connective)      52
Or (exclusive)      434
OR gate      745
Order for the vertices of a tree      620 621
Order g (or Order of g), O(g)      294
Order in a tree      616 617
Order of a group      778
Order of a group element      787 788

Order of a linear recurrence relation      471
Ordered binary tree      500
Ordered pair      246 250 251
Ordered rooted tree      616
Ordered set      A-30
Ordinary generating function      449 (see also “Generating function”)
Ore, Oystein      583 695 696
Organic compounds      827 828
Origin (of an edge)      363 530
Orthogonal Latin squares      854—858 872
Out degree of a vertex      554
Outgoing degree of a vertex      554
Output (for a finite state machine)      328
Output (from a gate)      745 746
Output (from an algorithm)      227 293
Output alphabet      328
Output function      252 329
Overcounting      23 25 428
Overflow error      222
O’Bryant, Kevin      651 652
p is sufficient for q      52
p(m, n), the number of partitions of m into exactly n positive summands      457 458
p(n), the number of partitions of n      445 456
P(n, r)      8 44
Page, E. S.      523 524
Pair of orthogonal Latin squares      854—858
Pairwise disjoint subboards      422
Pairwise incidence matrix      866 867
Palindrome      16 327
Palmer, Edgar M.      600 602
Papadimitriou, Christos H.      343 345
Parallel classes      862—864
Parallel network      73
Parent      615
Parity-check code      797 (see also “Algebraic coding theory”)
Parity-check equations      802 (see also “Algebraic coding theory”)
Parity-check matrix      804 806 807 811
Parker, Ernest Tilden      858 872
Partial fraction decomposition      441 495 496
Partial order      349 353—356 372—379 394 395
Partial order for a Boolean algebra      765—767
Partial ordering relation      353 372 “Poset”)
Partially ordered set      372 (see also «Poset”)
Particular solution      483 484 489 490
Partition      382—386 388 395 717 791
Partitions of integers      36 37 445—448 456—458 523
Pascal program for Euler’s phi function      410
Pascal program for the binary search      518
Pascal program for the bubble sort      464
Pascal program for the calculation of Fibonacci numbers      299
Pascal program for the calculation of Fibonacci numbers (recursive)      489
Pascal program for the Euclidean algorithm      229
Pascal program for the Euclidean algorithm (recursive)      469
Pascal programming language      14 44 55 60 61 104 253 287 301 314 385 468
Pascal, Blaise      45 179 240
Pascal’s triangle      152 153 155 178
Patashnik, Oren      311 312 522 524
Path (in a graph)      365 532 533
Path (staircase)      10 149 151 152
Pattern inventory      817 824—828
Pawlak, Zdzislaw      651
PDP      11 5
Peacock, George      176
Peano, Giuseppe      240 395
Peano’s postulates      240
Peirce, Charles Sanders      138
Pendant vertex      550 569 609
Perfect integer      238
Perfect matching      692
Perfect, H.      695 696
Permutation      6—9 19 20 44 45 408 409 428 449 467 502—504 523
Permutation group      783 815
Permutation matrix      697
PERT network      372 394
Petersen graph      563 590 600
Petersen, Gerald R.      773
Petersen, Julius Peter Christian      600
photons      43
Pi mesons      43
Pi notation      235
Pigeonhole Principle      275—278 290 309 311 338 831
Planar graph      560 599
Planar-one-terminal-pair-graph      572
Planarity of graphs      366 (see also “Planar graph”)
Planck’s constant      43
Platonic solids      567 568
Pless, Vera      831 832
Points at infinity      869
Polaris submarine      372
Polish notation      619
Polya, George      651 652 777 832
Polya’s Method of Enumeration      600 651 812 824—828 832
Polya’s theory in graphical enumeration      600
Polyhedra      598
Polynomial equation      829
Polynomial in the indeterminate x      835
Polynomial ring      837 871
Polynomial time complexity      296
pop      502
POSET      372—379 382 394 397 399 400
Poset antichain      400
Poset chain      399
Poset embedding      397
Poset gib (greatest lower bound)      378 379
Poset greatest element      377
Poset greatest lower bound (glb)      378
Poset Hasse diagram      373—376 394
Poset lattice      379
Poset least element      377
Poset least upper bound (lub)      378
Poset length of a chain      399
Poset lower bound      378
Poset lub (least upper bound)      378 379
Poset maximal chain      399
Poset maximal element      376
Poset minimal element      376
Poset topological sorting algorithm      375—377 394
Poset total order      374—376 394
Poset upper bound      378
Poset well-ordered poset      382
Positive closure of a language      322
Postorder (traversal)      620 651
Power series      435 436 445 457 496
Power set      148
Powers of $\Sigma$       316
Powers of a function      284
Powers of a group element      780
Powers of a language      322
Powers of a real number      A-1
Powers of a relation      358 359
Powers of an alphabet      316
Powers of strings      318
Precedence graph      364
Precedes      361
Pred (predecessor) function      314
Prefix      319 350 640
Prefix codes      333 640 641 643 651
Prefix notation      619
Pregel River      551
Preimage (of a set)      287—290
Preimage (of an element)      251
Premise      58 77 80 124 129
Preorder (traversal)      620 624 651
Prepositional calculus      763
Prim, Robert Clay      665 694 696
Primary key      275
Prime integer (or number)      134 183 214 719
Prime polynomial      844
Primitive statement      52
Prim’s algorithm      669 670 695

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