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Scheinerman E.A. — Mathematics: A Discrete Introduction
Scheinerman E.A. — Mathematics: A Discrete Introduction

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Название: Mathematics: A Discrete Introduction

Автор: Scheinerman E.A.

Аннотация:

This book has two primary objectives: It teaches students fundamental concepts in discrete mathematics (from counting to basic cryptography to graph theory), and it teaches students proof-writing skills. With a wealth of learning aids and a clear presentation, the book teaches students not only how to write proofs, but how to think clearly and present cases logically beyond this course. Overall, this book is an introduction to mathematics. In particular, it is an introduction to discrete mathematics. All of the material is directly applicable to computer science and engineering, but it is presented from a mathematician's perspective. While algorithms and analysis appear throughout, the emphasis is on mathematics. Students will learn that discrete mathematics is very useful, especially those whose interests lie in computer science and engineering, as well as those who plan to study probability, statistics, operations research, and other areas of applied mathematics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Указатель в процессе заполнения

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 2005

Количество страниц: 592

Добавлена в каталог: 23.08.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C_{n}$      413
$K_{n, m}$      431
$K_{n}$      397
$\Delta$      68 181
$\Delta(G)$, $\delta(G)$      396
$\exists$      59
$\forall$      60
$\mathbb{C}$      544 553
$\mathbb{N}$      6 549 552
$\omega$      239
A      544
Abelian      341 544
Above      452
Acyclic      413 544
Addition, modular      310
Addition, Principle      68 142
Additive group      341
Adjacency matrix      395
Adjacent      393 544
Aleph null      210 461
Algebra      337
Algebra, boolean      27 544
Algorithm      299 328 544
Algorithm, Euclid's      300 301 546
Algorithm, Euler trail/tour      425
Algorithm, recursive      299
Algorithm, sorting      465
Algorithm, spanning tree      421
Alternating group      342
Anagram      100
AND      12 28 544
angle brackets      117
Antichain      453 544
antisymmetric      86 394 408 449 544
arbitrary      60 544
Argument      16 544
ASCII      371
Associative      31 65 213 234 310 339 340 481 544 552
Average      271
Average weighted      272
Axiom      149
Axiom of Choice      467
Basis step      146—147 158 163 544
Below      452
Bernoulli trial      262 544
Bijection      201 544
Bijective proof      56 106 121
Binomial coefficient      104 108 544
Binomial coefficient, formula      112
Binomial random variable      268 544
Binomial theorem      108 191 544
Bipartite graph      430 544
Bipartite graph, complete      431 545
Bipartition      430
Birthday problem      253 544
Bit string      43
Blackjack      290
Block      98
Boolean algebra      27 544
Cantor's theorem      209
Cardinality      544
Cardinality, multiset      117
Cardinality, set      50
Cardinality, transfinite      210 461
Carmichael number      370 544
Cartesian product      73 544
CEILING      241 544
Chain      453 544
Characterization theorem      415 419 431 544
Chebyshev's inequality      289
Chi ($\chi$)      428
Chinese remainder theorem      323 377 544
Choice      38
choose      104
Chromatic number      428 544
Claim      14 91 545
CLIQUE      402 545
Clique, number      402 545
Closed      338 340
Closed walk      406 407
Closure      310 319 338 552
Colorable      428 545
Coloring      428 545 550
Combinatorial proof      66 76—80 110 119 396 545
Combinatorics      104
Common divisor      298 545
Common divisor, greatest      299 547
Common multiple      332
Common multiple, least      332
Commutative      31 65 213 234 310 338 341 481 544 545 552
Comparable      453 545
Complement event      252
Complement graph      403 545
Complement set      75 106 545
Complete bipartite graph      431 545
Complete graph      397 545
Complex number      178 545 553
Component      410 545
Component, trivial      422
Composite      5 545
composition      211 234 545
Concatenation      407 545
Concatenation, lists      41
Conclusion      10 545
Conditional probability      258 545
Congruent, mod H      356
Congruent, mod n      90 545
Conjecture      8 545
Conjecture, factoring is hard      371
Conjecture, Goldbach      16
Connected      408 410 545
Contradiction      33 137 545
Contrapositive      15 32 135 545
CONVERSE      15 33 142 545
Corollary      14 545
Coset      361
Counterexample      25 545
Counterexample, smallest      142
Critical pair      469
Crossing-free embedding      436
Cryptography      370 545
cryptography, public-key      371 550
Cryptosystem, Rabin's      373
Cryptosystem, RSA      380
cube      435 545
Curve      436
Curve, simple      436
Curve, simple closed      436
Cut, edge      410 415 419 421 545
Cut, vertex      410 545
CYCLE      413 545
Cycle, Hamiltonian      421 547
Cycle, notation      218 545
Cyclic group      350 545
Cyclic shift      363
Data record      465
Declarative statement      8
Definition      2 545
Definition, recursive      169 301
Definition, unraveling      17
Degree, face      438 545
Degree, polynomial      181 298 546
Degree, up      456
Degree, vertex      395 546
Degree, vertex, maximum and minimum      396
Deletion, edge      400
Deletion, vertex      400
DeMorgan's law      31 73
Dependent events      260
Derangement      129 546
Diagram, Hasse      450 547
Diagram, Venn      64 257 551
Dice      246
Dice, nontransitive      255
Dice, tetrahedral      248
Difference      68 546
Difference, operator      181
Difference, symmetric      68 343 551
Dihedral group      342
DIMENSION      472 546
Direct proof      19 545
Disjoint      68 546
Disjoint, pairwise      68 549
Distance      235 546
DISTINCT      141 546
Distributive      31 65 311 482 553
div      296 546
divides      3 334 546
Divisible      3
Division, modular      315
Division, theorem      293
Divisor      3
Divisor, common      298 545
Divisor, greatest common      299 547
Domain      195 546
Dominance      474
Domino ring      426
Dual (poset)      454
Dummy variable      47 50 59 96
E(G)      396
EDGE      392
Edge deletion      400
Edge, cut      410 415 419 421 545
Edge, parallel      394
Edgeless      397 546
Element      50 546
Embedding      436
Embedding, crossing-free      436
Embedding, poset in n-dimensional space      474
Empty graph      397
Empty list      37 46
Empty product      46—48 325 525
Empty set      50 546
End point      393
End vertex      416
Enough      11
equal      553
Equal functions      213
Equal lists      37
Equal rational numbers      552
Equal sets      51
Equivalence, class      93 410 546
Equivalence, class, number of      102
Equivalence, logical      30 548
Equivalence, relation      89 409 546
Equivalent statements      12 259 546
Erasothenes, sieve of      334
Erdos — Szekeres Theorem      207
Euclid's Algorithm      300 301 546
Euler's formula      437 546
Euler's theorem      368 546
Euler's totient      332—333 345 367 381 551
Eulerian trail/tour/graph      422 546
Even      2 546
Even permutation      226 546
Event      250 546
Event, complement      252
Event, dependent      260
Event, implicit      268
Event, independent      260 547
Event, mutually exclusive      253
exactly      546
Examination scheduling      390
Exclusive OR      33 546
Existential quantifier      59 546
Expectation      272
Expectation, linearity of      278 548
Expected value      272 546
Expected value, linearity of      278
Extension, linear      462
Face      437
Face, degree      438
Fact      14 546
Factor      3 334
Factorial      45 546
Factorial of $\frac{1}{2}$      49
Factorial of negative integers      49
Factorial of zero      46
Factorial, falling      43
Factory, number      46
Factory, symmetry      232
Falling factorial      43
FALSE      9
Fence      476
Fermat's little theorem      362 546
Fibonacci number      152 165 169 171 178 336 546
Fifteen puzzle      230
Finer-than relation      451
finite      50
First-order recurrence relation      172
Five color theorem      443
Fixed point      279
FLOOR      241 546
flush      116 256
Forest      413 546
Formula, binomial coefficient      112
Formula, Euler's      437
Formula, midpoint      206
Formula, Stirling's      48 466 550
Four children      251
Four color map problem      390
Four color theorem      442 547
Four of a kind      116 251
Full house      116 256
Function      194 547
Function, composition      211
Function, distance preserving      235
Function, equal      213
Function, graph of      196
Function, identity      214 547
Function, inverse      198
Function, machine      193 211
Function, notation      194
Function, one-to-one      199 549
Function, onto      200 549
Function, order preserving      459
Fundamental Theorem of Arithmetic      326 547
Garbage collection      392
Gas/water/electricity problem      391 398 441
GCD      299 547
Generator      350
Glb      478 547
Goldbach's conjecture      16
Graph      389 392 547
Graph of a function      196
Graph, bipartite      430 544
Graph, bipartite, complete      431 545
Graph, coloring      428 550
Graph, complement      403 545
Graph, complete      397 545
Graph, component      410
Graph, connected      410
Graph, edgeless      397
Graph, empty      397
Graph, Eulerian      422 546
Graph, Hamiltonian      547
Graph, isomorphic      398 548
Graph, order      396
Graph, Petersen's      445
Graph, planar      437 549
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