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Ross Sh.M. Ч Topics in Finite and Discrete Mathematics
Ross Sh.M. Ч Topics in Finite and Discrete Mathematics



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Ќазвание: Topics in Finite and Discrete Mathematics

јвтор: Ross Sh.M.

јннотаци€:

Written for students in mathematics, computer science, operations research, statistics, and engineering, this text presents a concise lively survey of several fascinating non-calculus topics in modern applied mathematics. Sheldon Ross, noted textbook author and scientist, covers probability, mathematical finance, graphs, linear programming, statistics, computer science algorithms, and groups. He offers an abundance of interesting examples not normally found in standard finite mathematics courses: options pricing and arbitrage, tournaments, and counting formulas. The chapters assume a level of mathematical sophistication at the beginning calculus level, that is, a course in pre-calculus.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

»здание: 1st edition

√од издани€: 2000

 оличество страниц: 178

ƒобавлена в каталог: 04.07.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Abelian group      240
Addition theorem of probability      73Ч74
Alternating subgroup      255Ч256
Arbitrage      107Ч111
Arbitrage theorem      111Ч116 191Ч194
Arcs      see УEdges of a graphФ
Assignment problem      160Ч163 176Ч177
Associative property of groups      237
Augmentation algorithm      154Ч157
Ballot problem      58Ч60
Bar graph      220
Basic principle of counting      34
Basic principle of counting, generalized      35
BayesТ formula      84
Bernoulli random variable      89 92Ч93
BernoulliТs inequality      29
Best prize problem      82Ч84
Binary rooted tree      216
Binary search      213Ч214
Binomial coefficient      43
Binomial random variable      86 93
Binomial theorem      43Ч45
Birthday problem      75Ч76
Black Ч Scholes option formula      120
Bubble sort      203Ч206
Cardinality of a set      47
Cauchy Ч Schwarz inequality      232
CayleyТs group isomorphic theorem      246Ч247
CayleyТs Theorem      129Ч131
Characteristic function      31
ChebyshevТs inequality      227Ч228
Chromatic number      147 148
CLIQUE      134Ч135 139Ч140
Combinations      40
Communicate      124
Complement graph      136
Complement of a set      2
Complete graph      127
Component of a graph      124
Composition of permutations      237Ч238
Compound interest      97Ч100
Compound interest, continuously      99
Conditional probability      77Ч78 80Ч85
Connected graph      126
Coset      250
Coupon collecting identity      52
Coupon collecting problem      51Ч52
Cut      152
CYCLE      124
Cycle permutation      244
Cyclic subgroup      247 261
DeMorganТs laws      28
Diameter of graph      147
Digraph      see УDirected graphФ
Dijkstra algorithm      171Ч175
Directed graph      150
Domain of a function      17
Doubling rule      121
Dual linear program      188Ч190
Duality theorem of Linear Programming      190
Edges of a graph      124
Equipment selection problem      167Ч170
EuclidТs algorithm      25
EuclidТs division lemma      23
Euler cycle      141
Euler graph      142Ч144
Even permutation      254Ч258
Event      71
Expected value of a random variable      87Ч88 90Ч92
Fair      see УUnbiasedФ
Fermat numbers      252Ч254
FermatТs combinatorial identity      66
FermatТs Little Theorem      40 252
Finite set      1
Forwards contracts      109Ч110
Frequency table      220
Function      17Ч23
Function, concave      20Ч22
Function, convex      20Ч23
Function, decreasing      17
Function, increasing      17
Function, polynomial      19
Fundamental Theorem of Arithmetic      25Ч27
Futures contracts      110
GaloisТs theorem      259
Game theory      194Ч199
Geometric Brownian motion      120
Graph      125
Greatest common divisor      24
Greedy algorithm      131Ч134
Group      238
HallТs theorem      162
Hamiltonian permutation      141Ч142
HardyТs lemma      14
histogram      220
Identity element of a group      238
Inclusion-exclusion identity      48Ч49
Independence number      137
Independent events      80 95
Independent random variables      92
Independent set      137
Infinite set      1
Interest rate      97
Interest rate, effective      98
Interest rate, nominal      98
Interest rate, simple      97
Intersection graph      145
Intersection of sets      2Ч4
Inverse element      238 259
Isomorphic groups      246 261
LagrangeТs Theorem      251Ч253
Leaf      127
Line graph      220
Linear data fit      186Ч188
Linear function      183
Linear program      178
M-ary rooted tree      215
Mathematical induction      8Ч17
Mathematical induction, strong version of      16
Max-flow min-cut theorem      154
Maximum flow problem      150Ч160
Mean      see УExpected value of a random variableФ
MengerТs theorem      159
Merge sort      209Ч210
Minimax theorem of game theory      197Ч199
Minimum spanning tree problem      131Ч134
Multiplication theorem of probability      79
Negatively correlated data pairs      231
Node      see УVertex of a graphФ
Normal subgroups      254 261 262
Odd permutation      254 256
Odds      113
options      104Ч109
Order of a group      247 248Ч249
Partition of a set      54Ч55
Path      124 150
Permutation      36Ч38
Permutation graph      243
Permutation group      238Ч240
Permutation, as a function      237Ч238
Permutation, derangement      50Ч51 55Ч56
Permutation, inversion of      69 205 257Ч258
Permutation, parity sign of      255
Pigeonhole Principle      61Ч63 136
Positively correlated data pairs      231
Present value      100
Primal linear program      188
Prime factorization theorem      see УFundamental theorem of arithmeticФ
Prime number      25
PrimТs algorithm      146Ч147
Probabilistic method      138 140Ч142
probability      71Ч72
Put-call option parity formula      108Ч109
Quicksort algorithm      206Ч209
Random variables      85
Recursion equations      52Ч61
Root of tree      214
Rooted tree      214Ч216
Round-robin tournament      13 33 140Ч142
Saddlepoint      195
Sample correlation coefficient      231Ч232
Sample mean      223Ч224 234
Sample median      224
Sample mode      224
Sample percentile      234Ч235
Sample space      71
Sample standard deviation      227
Sample variance      225Ч226 234
Scatter diagram      230
Selection sort      203
Sequential search      210Ч212
Set      1
Shortest path      170Ч175
Sorting      203
Standard deviation      93
Standard linear programming problem      183Ч188
Standard normal distribution function      120
Statistical hypothesis tests      232Ч233
Statistics      220 223
Stem-and-leaf plot      221Ч222
Subgroup      244Ч245 260 261
Subset      2
Summation      4Ч8
Symmetric group      240
Tournament      178
Tournament win problem      163Ч165
Transposition      244
Transshipment problem      166Ч167
TREE      127Ч131
triangle      134Ч135
TuranТs Theorem      140
Unbiased      71
Union of sets      2Ч4
Universal set      2
Utility      89Ч90
Variance      92Ч93
Venn diagram      2Ч3
Vertex of a graph      124
Vertex of a graph, degree of      127
Well-ordering property of positive integers      14
Zero-sum game      194
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