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

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Ring theory, congruence modulo n      689 690
Ring theory, definition      673 674
Ring theory, field      677 678 681 682
Ring theory, group of units      747
Ring theory, homomorphism      697—700 706
Ring theory, ideal      684 700 706
Ring theory, idempotent element      697
Ring theory, integers modulo n      686—696
Ring theory, integral domain      677 678 681 682
Ring theory, isomorphic rings      698 699 704
Ring theory, isomorphism      698
Ring theory, kernel of a homomorphism      704
Ring theory, matrix rings      674 705
Ring theory, multiplicative identity      675
Ring theory, multiplicative inverse      677
Ring theory, proper divisors of zero      675
Ring theory, ring of matrices      674 705
Ring theory, ring of polynomials      799 801
Ring theory, ring properties      679—684
Ring theory, ring with unity      675
Ring theory, subring      682—684
Ring theory, subtraction      680
Ring theory, unit      677
Ring theory, unity      675
Ring with unity      675 801
Ringel, Gerhard      573 576
Rings of Saturn      42
Rinnooy Kan, A.H.G.      562 575 576
Riordan, John      412 444 445
Rise/fall permutation      495 496
Rivest, Ronald L.      504 507 624 625 638 643 654 668 759
Roberts, Fred S.      42 574 576
Robertson, N.      575 576
Robinson, J.A.      86
Roman, Steven      769 796 797 831 832
Rook      404 407
Rook polynomial      404—406 408 410 412 416 510 659
Root extraction      794
Root of a binary ordered tree      488
Root of a polynomial      802 804—806
Root of a tree      587—590
Root of multiplicity      2 805
Rooted binary tree      488 594
Rooted Fibonacci tree      626
Rooted ordered binary tree      488 489 506 596
Rooted tree      587—596 600 601
Rorres, Chris      A-21
Rosen, Kenneth H.      42 244 704 708
Ross, Kenneth A.      119 120
Rota, Gian Carlo      412 444 445
Rotating drum      536
Rotations      10 749 781 782 788 791 792
Rothman, Tony      831 832
Rothschild, Bruce L.      305
Roulette      163 164
Round-robin tournament      559
Rouvray, Dennis H.      574 576
Row major implementation      254
Row matrix      A-11
Row number      716
Row vector      A-11
Royal flush      152
RSA cryptosystem      759—761 795
Ruin problems      506
Rule for Proof by Cases      78
Rule of Complement      159 172
Rule of Conditional Proof      78
Rule of Conjunction      75 78
Rule of Conjunctive Simplification      78 94 137
Rule of Contradiction      76 78
Rule of Detachment      70 71 78 108
Rule of Disjunctive Amplification      78 137
Rule of Disjunctive Syllogism      75 78
Rule of Existential Generalization      117
Rule of Existential Specification      117
Rule of product      4—7 11 14—19 28 29 34 125 142 197 239 248 255 256 261 274 339 341 342 403 567
Rule of sum      3—5 16 19 34 125 132 148 262 264 274
Rule of the Constructive Dilemma      78
Rule of the Destructive Dilemma      78
Rule of Universal Generalization      110—114 126
Rule of Universal Specification      106—113 126
Rules for negating quantified statements      96
Rules of Inference      70—78 83 84 86 107—109 112 113 117 119
Rules of Inference, Law of the syllogism      72 73 78
Rules of Inference, Modus ponens      70 73 75 78
Rules of Inference, Modus tollens      73 76 78
Rules of Inference, Proof by (the method of) contradiction      76 80 84
Rules of Inference, Reductio ad Absurdum      76
Rules of Inference, Rule for proof by cases      78
Rules of Inference, Rule of conditional proof      78
Rules of Inference, Rule of conjunction      75 78
Rules of Inference, Rule of conjunctive simplification      78
Rules of Inference, Rule of detachment      70 78
Rules of Inference, Rule of disjunctive amplification      78
Rules of Inference, Rule of disjunctive syllogism      75 78
Rules of Inference, Rule of the constructive dilemma      78
Rules of Inference, Rule of the destructive dilemma      78
Rules of Inference, Rule of universal generalization      110—114 126
Rules of Inference, Rule of universal specification      106—113 126
Rules of Inference, Table of rules of inference      78
Run      33 34 192 482
Running time      452
Russell, Lord Bertrand Arthur William      119 135 187
Russell’s paradox      135 186 187
Rydell High School      16
Ryser, Herbert John      42 412 668 669 831 832
R[X]      799
S(m, n)      263
s(m,n)      267
S(x,k)      161
Saaty, Thomas L.      668
Sahni, Sartaj      641 642 668 669
Same cardinality (for sets)      A-23
Same likelihood      150 158
Same size (for sets)      A-23
Sample space      150—155 157—159 161—164 166—172 175—181 183 262 296 402 409 428
Samuel, Pierre      707 708 831 832
Sanders, D.P.      575 576
Sandler, R.      831
Saturated edge      645 649 650
Saturated hydrocarbons      573 581 584
Saturn      42
Scalar product      A-12—A-14
Scattering function      694 708
Schedule      815 825
Scholtz, Robert A.      796
Schroeder numbers      495
Schroeder, Ernst      119 377
Schwenk, Allen J.      628
Scientific American      575
Searching (algorithm)      501
Searching process      295 501
Second level of reachability      338
Second-order homogeneous recurrence relations      456—468
Security      693
Seed      689
Sefer Yetzirah (The Book of Creation)      41
Selection      14—16 19—22 26 see
Selection structure      51
Selection with repetition      26—29 32 415 423 485
Self-complementary graph      529 576
Self-dual      735
Self-dual Boolean function      744
Self-orthogonal Latin square      820
Semicircles      40
Semipath      650—653
Sentences      47 48 310
Separation      645
Separation property      646
SEQUENCE      255
Sequence of pseudorandom numbers      689 690
Sequence recognizer      326 327 332
Sequential circuit      309 see
Serial binary adder      323 324
Series network      65
Seshu, S.      574 576
Set braces      123 124
Set equality      125 126 252 314
Set of all possible outcomes      150
Set of indices      145
Set theory      87 119 123—129 133—155 211 247 303 304 309 311 313
Set theory of strings      309
Set theory, cardinality      124 186 A-23
Set theory, complement of a set      138
Set theory, countable set      164 303 A-24—A-32
Set theory, denumerable set      303 A-24
Set theory, disjoint sets      137 148
Set theory, element      123
Set theory, element argument      126 137 140 144
Set theory, empty set ($\emptyset$)      127
Set theory, equality of sets      125 126
Set theory, finite set      124 125 186 A-23 A-24
Set theory, generalized intersection of sets      146
Set theory, generalized union of sets      146
Set theory, infinite set      124 186 189 A-23—A-26 A-28 A-30
Set theory, intersection of sets      136 138
Set theory, intuitive definition of a set      123
Set theory, laws of set theory      139 144
Set theory, member      123
Set theory, membership      126
Set theory, membership table      143 144 146
Set theory, mutually disjoint sets      137 148
Set theory, null set ($\emptyset$)      127
Set theory, power set      128
Set theory, Principle of Duality      141
Set theory, proper subset      124—126
Set theory, relative complement      138
Set theory, set braces      123 124
Set theory, set of indices      145
Set theory, singleton subset      128
Set theory, size of a set      124 A-23
Set theory, subset      124—128 130—132 138 140 141 149
Set theory, superset      138
Set theory, symmetric difference      136
Set theory, uncountable set      303 A-28
Set theory, union of sets      136 138
Set theory, universe      123—128
Set theory, universe of discourse      123—128
Set theory, Venn diagram      141—144 146 148 155
Set theory, well-ordered set      194
Seven Bridges of Koenigsberg      378 513 518 533—535 573
Seyffarth, Karen      412
Seymour, P.D.      575 576
Shamir, Adi      759
Shannon, Claude Elwood      741—743 761 795 797
Sherbert, Donald R.      506 508
Shi-kie, Chu      188
Shier, Douglas R.      623 625 668 669
Shift      690
Shift cipher      691
Shimura, Goro      706
Shmoys, D.B.      562 575 576
Shortest — Path algorithm      667
Shrikhande, S.S.      819 831
Shushu jiuzhang      707
Siblings      588 593 612
Sichuan      707
Sieve method      411
Sigma notation      17 239
Signals      438 439 761
Signed numbers      681 705
Silvestri, Richard      795 797
Simple group      795
Simultaneous solution of a system of congruences      702
Singleton subset      128
Sink in a finite state machine      331
Sink in a transport network      631
Sink state      331
Size of a set      124 A-23
Sloane, Neil James Alexander      195 191
Smallest element      194
Smith, Henry John Stephen      243
Snowflake curve      475
Software development      203
Soifer, Alexander      304 305
Solow, Daniel      119 120
Solution of polynomial equations      830
Solvable group      830
Sorting      506 581 605 606 608
Sorting technique      450
Source in a network      631
Source of a directed edge      349 514
Source program      253 302
Space (blank)      310
Space complexity function      290
Spanning forest      582
Spanning subgraph      521 582 640
Spanning tree      582 596 597 599 631 638 640
Specification statement      369
Spencer, Joel H.      305
Sphere S(x, k)      161 see
Spine (of a caterpillar)      627 628
Split input (for a gating network)      720
Spokes (in the wheel graph)      519 520
Square matrix      A-11
Square of a graph      626
Stabilizer      785
STACK      490—492 507 605
Staircase paths      9 130 132
Stanat, Donald F.      333 334 378 507 508
Standard deviation      180 182 183
Standard form of a Latin square      816 817
Stanley, Richard Peter      444 507 508
Star of David      475
Starting state      320 324 329
State diagram      321 324 327
State table      321 322 324 331 372—375
State transition      320 321
Statement      47—121 127 140 311
Statement, compound statement      48 49
Statement, contradiction      53 58
Statement, contrapositive      62 63 92—94
Statement, converse      62 63 82 99
Statement, definitions      52 87 98 103—105 113
Statement, dual (of a) statement      59 62
Statement, if-then decision structure      51
Statement, if-then-else decision structure      51
Statement, inverse      62 63 82 92—94 99
Statement, logical equivalence      56—61 83 95
Statement, logical implication      69—73 75 89 91 95
Statement, logically equivalent statements      56 58 61—64 74 91 97 98
Statement, logically implies      69 92
Statement, negation      48
Statement, negation of quantified statements      92 96 97
Statement, open statement      86 87 89—92 105 106 109 123 126 194 195
Statement, primitive statement      48
Statement, quantified statement      87
Statement, tautology      53 58 59 69
Statement, theorem      105 106 110 112 119
Statement, truth tables      49
Statistics      3 33 175 188 815
Stein, Clifford      504 507 624 625 638 643 654 668
Steiner triple system      829
Steinhaus, Hugo Dynoizy      506 508
Stern, R.G.      562 575 576
Stifel, Michel      42
Stillwell, John      794 797 831 832
Stinson, Douglas R.      831
Stirling numbers of the first kind      267
Stirling numbers of the second kind      29 260 263—265 303 304 370 508 587
1 2 3 4 5 6 7 8 9 10 11 12 13
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