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Scheinerman E.A. — Mathematics: A Discrete Introduction
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Название: Mathematics: A Discrete IntroductionАвтор: 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: Рубрика: Математика /Статус предметного указателя: Указатель в процессе заполнения ed2k: ed2k stats Издание: 2-nd editionГод издания: 2005Количество страниц: 592Добавлена в каталог: 23.08.2014Операции: Положить на полку |
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413 431 397 68 181 396 59 60 544 553 6 549 552 239 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 ( 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 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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