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

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Название: Topics in Finite and Discrete Mathematics

Автор: Ross Sh.M.

Аннотация:

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.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 2000

Количество страниц: 178

Добавлена в каталог: 04.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Abelian group      240
Addition theorem of probability      73—74
Alternating subgroup      255—256
Arbitrage      107—111
Arbitrage theorem      111—116 191—194
Arcs      see “Edges of a graph”
Assignment problem      160—163 176—177
Associative property of groups      237
Augmentation algorithm      154—157
Ballot problem      58—60
Bar graph      220
Basic principle of counting      34
Basic principle of counting, generalized      35
Bayes’ formula      84
Bernoulli random variable      89 92—93
Bernoulli’s inequality      29
Best prize problem      82—84
Binary rooted tree      216
Binary search      213—214
Binomial coefficient      43
Binomial random variable      86 93
Binomial theorem      43—45
Birthday problem      75—76
Black — Scholes option formula      120
Bubble sort      203—206
Cardinality of a set      47
Cauchy — Schwarz inequality      232
Cayley’s group isomorphic theorem      246—247
Cayley’s Theorem      129—131
Characteristic function      31
Chebyshev’s inequality      227—228
Chromatic number      147 148
CLIQUE      134—135 139—140
Combinations      40
Communicate      124
Complement graph      136
Complement of a set      2
Complete graph      127
Component of a graph      124
Composition of permutations      237—238
Compound interest      97—100
Compound interest, continuously      99
Conditional probability      77—78 80—85
Connected graph      126
Coset      250
Coupon collecting identity      52
Coupon collecting problem      51—52
Cut      152
CYCLE      124
Cycle permutation      244
Cyclic subgroup      247 261
DeMorgan’s laws      28
Diameter of graph      147
Digraph      see “Directed graph”
Dijkstra algorithm      171—175
Directed graph      150
Domain of a function      17
Doubling rule      121
Dual linear program      188—190
Duality theorem of Linear Programming      190
Edges of a graph      124
Equipment selection problem      167—170
Euclid’s algorithm      25
Euclid’s division lemma      23
Euler cycle      141
Euler graph      142—144
Even permutation      254—258
Event      71
Expected value of a random variable      87—88 90—92
Fair      see “Unbiased”
Fermat numbers      252—254
Fermat’s combinatorial identity      66
Fermat’s Little Theorem      40 252
Finite set      1
Forwards contracts      109—110
Frequency table      220
Function      17—23
Function, concave      20—22
Function, convex      20—23
Function, decreasing      17
Function, increasing      17
Function, polynomial      19
Fundamental Theorem of Arithmetic      25—27
Futures contracts      110
Galois’s theorem      259
Game theory      194—199
Geometric Brownian motion      120
Graph      125
Greatest common divisor      24
Greedy algorithm      131—134
Group      238
Hall’s theorem      162
Hamiltonian permutation      141—142
Hardy’s lemma      14
histogram      220
Identity element of a group      238
Inclusion-exclusion identity      48—49
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      2—4
Inverse element      238 259
Isomorphic groups      246 261
Lagrange’s Theorem      251—253
Leaf      127
Line graph      220
Linear data fit      186—188
Linear function      183
Linear program      178
M-ary rooted tree      215
Mathematical induction      8—17
Mathematical induction, strong version of      16
Max-flow min-cut theorem      154
Maximum flow problem      150—160
Mean      see “Expected value of a random variable”
Menger’s theorem      159
Merge sort      209—210
Minimax theorem of game theory      197—199
Minimum spanning tree problem      131—134
Multiplication theorem of probability      79
Negatively correlated data pairs      231
Node      see “Vertex of a graph”
Normal subgroups      254 261 262
Odd permutation      254 256
Odds      113
options      104—109
Order of a group      247 248—249
Partition of a set      54—55
Path      124 150
Permutation      36—38
Permutation graph      243
Permutation group      238—240
Permutation, as a function      237—238
Permutation, derangement      50—51 55—56
Permutation, inversion of      69 205 257—258
Permutation, parity sign of      255
Pigeonhole Principle      61—63 136
Positively correlated data pairs      231
Present value      100
Primal linear program      188
Prime factorization theorem      see “Fundamental theorem of arithmetic”
Prime number      25
Prim’s algorithm      146—147
Probabilistic method      138 140—142
probability      71—72
Put-call option parity formula      108—109
Quicksort algorithm      206—209
Random variables      85
Recursion equations      52—61
Root of tree      214
Rooted tree      214—216
Round-robin tournament      13 33 140—142
Saddlepoint      195
Sample correlation coefficient      231—232
Sample mean      223—224 234
Sample median      224
Sample mode      224
Sample percentile      234—235
Sample space      71
Sample standard deviation      227
Sample variance      225—226 234
Scatter diagram      230
Selection sort      203
Sequential search      210—212
Set      1
Shortest path      170—175
Sorting      203
Standard deviation      93
Standard linear programming problem      183—188
Standard normal distribution function      120
Statistical hypothesis tests      232—233
Statistics      220 223
Stem-and-leaf plot      221—222
Subgroup      244—245 260 261
Subset      2
Summation      4—8
Symmetric group      240
Tournament      178
Tournament win problem      163—165
Transposition      244
Transshipment problem      166—167
TREE      127—131
triangle      134—135
Turan’s Theorem      140
Unbiased      71
Union of sets      2—4
Universal set      2
Utility      89—90
Variance      92—93
Venn diagram      2—3
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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