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N. Vilenkin, George Yankovsky (translator) — Combinatorial mathematics for recreation
N. Vilenkin, George Yankovsky (translator) — Combinatorial mathematics for recreation

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Название: Combinatorial mathematics for recreation

Авторы: N. Vilenkin, George Yankovsky (translator)

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Revised

Год издания: 1972

Количество страниц: 207

Добавлена в каталог: 12.11.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absorbing barriers      83
Al-Kashi      72 112
Alexandria      20 26
Algebraic fractions      104
Alternating sums of combinations      37
Ambo      29
Amino acids      13
Anagrams      26
Application of the theory of recurrence relations to problems of transmitting information      103
Archimedes      26
Arithmetic hexagon      78
Arithmetic pentagon      78
Arithmetic square      70—72
Arithmetic triangle      72—74
Array(s) of dots      65
Array(s), dual      67
Array(s), normal      66
Array(s), self-dual      67
Barriers, absorbing      83
Base-m number system      75
Base-n system of numeration      11
Bernoulli, Jakob      7 55
Binomial coefficients      73
Binomial theorem      110
Boltzmann, L.      59
Bookshelf problem      40
Bose      59
Bose — Einstein statistics      59
Bouquet of flowers      55
Brownian motion      81
Building a stairway      39
Buying cakes      30
Buying candy      63
Cakes, buying      30
Candy, buying      63
Caravan in the desert      46
Cardano formula      72
Cardano, G.      72
Change, getting      64
Characteristic equation      101
Characteristic equation, equal roots of      102
Chebyshev, P.      55
Checker in the corner      77
Checkerboard problems      16
Chess      70ff
Chess king      74
Coefficients, binomial      73
Combinations      22 27
Combinations with repetitions      31
Combinations, alternating sums of      37
Combinations, new properties of      51
Combinations, properties of      33
Combinations, properties of, geometric proof of      79
Combinatorial mathematics      7
Combinatorial problems of information theory      61
Combinatorial problems with restrictions      39ff
Combinatorics      7
Combinatorics and chess      70ff
Combinatorics and series      104ff
Combinatorics of partitions, summary of      122
Combinatorics, general rules of      9ff 13ff
Composite numbers      20
Computer, "Strela"      12
Computer, electronic digital      12
Convergence of number series      105
Convergence, interval of      106
Crew of spaceship      15
Czar Dadon      82
Decomposition into partial fractions      116
Derangements      44
Derangements, general problem of      44
Diagonal, principal      71
Difficulties of a majordomo      94
Diffusion      82
Dirac      see "Fermi — Dirac" statistics"
Divergence of number series      105
Divergent series      105
Dividend      104
Dividing polynomials      104
Divisor      104
DNA      13
Domino problem      15
Dominoes      54
Dual arrays      67
e (the number)      106
Einstein, A.      59
Electronic digital computer      12
Entrance-exams problem      61
Equation, characteristic      101
Equation, equal roots of      102
Eratosthenes      20
Eratosthenes, sieve of      20
Euclid      20
Euler's formula      67
Euler's theorem      66 68
Euler, L.      7 55 67—68
Exclusion      see "Principle of" "Formula
Extended arithmetic triangle      73
Extracting square roots      114
Factorial      23
Factorization      56
Fermat, P.      7
Fermi — Dirac statistics      59
fibonacci      89
Fibonacci numbers      89 91 101
Figurate numbers      71 72
Figures, Zener      42
Flags on masts      58
Football championship      22
Football championship again      32
Formula, Cardano      72
Formula, Euler's      67
Formula, inclusion and exclusion      19 37
Fractions, algebraic      104
Fractions, partial, decomposition into      116
Functions, Gaussian      82
Functions, generating      109 116 119
gambling      7
games of chance      7
Gauss, K.      82
Gaussian function      82
General problem of postage stamps      61
General problem of the rooks      84
General rules of combinatorics      13ff
Generalized arithmetic triangle      74 75
Generating functions      109 116 119
Generating functions and partitions of integers      119
genetic code      13
Genoese lottery      29
Geometric proof of properties of combinations      79
Getting change      64
Greatest integer (in)      53
Henry III      27
Hexagon, arithmetic      78
Hipparchus      20
Hooke, R.      26
How many people don't know foreign languages      17
Hunting mushrooms      57
Huygens, Christian      27
inclusion      see "Principle of" "Formula
Infinite series      105
Infinite series, sum of      105
Information theory      33
Integers, partitioning      65
Integers, partitions of      59
Integers, partitions of, generating functions and      119
Interval of convergence      106
k-arrangements      9 22
King Arthur's Round Table      40
Knights, two      87
LANCELOT      40
Languages (How many people don't know foreign languages)      17
Leibniz, G.W.      7 27
Liber Abaci      89
Linear recurrence relations with constant coefficients      100
Linguistic problems      24
Lions and tigers      39
Lottery, Genoese      29
Lottery, number      29
Lotto      7
Lucky trolleybus tickets      96
Mailing packages      60
Mailing photographs      57
Majordomo problem, alternative solution of      98
Majordomo problem, third solution      103
Majordomo, difficulties of (first solution)      94
Mathematics, combinatorial      7
Maxwell — Boltzmann statistics      59
Maxwell, G.G.      59
Mere, Chevalier de      7
Merry-go-round      47
Money, paying      62
Morse code      11
Motion, Brownian      81
Multinomial theorem      111
Multiplying and dividing numbers      92
Mushrooms, hunting      57
New properties of combinations      51
Newton's Binomial Theorem      109
Newton's series      112
Newton, Sir Isaac      26 112
Nicomedes      71
Nonlinear recurrence relation      118
Number "one"      32
Number lottery      29
Number series      105
Number series, convergence of      105
Number series, divergence of      105
number systems      10
Number systems, base-m      75
Number(s), $C_{m}(k,n)$, properties of      75
Number(s), composite      20
Number(s), e      106
Number(s), Fibonacci      89 91 101
Number(s), figurate      71
Number(s), multiplying and dividing      92
Number(s), prime      20
Number(s), pyramidal      72
Number(s), triangular      71
Number-of-divisors problem      56
Numerical triangle      148
Olympiad, Moscow Mathematics      80
Omar Khayyam      72 112
One      32
Operations on power series      107
Order of recurrence relations      99
Partial fractions, decomposition into      116
Particle statistics      59
Partitioning integers      65
Partitions of integers      59 119
Partitions of integers, generating functions and      119
Partitions, combinatorics of (summary)      122
Partitions, process of successive      91
Pascal's triangle      72
Pascal, B.      7 55 72 112
Paying money      62
Pentagon, arithmetic      78
permutations      22
Permutations of n elements      23
Permutations with repetitions      9ff 22 25
Permutations without repetitions      22
Photographs, mailing      57
Picking apples      56
Placing objects into cells      55
Polygons, problems involving      93
Polynomials, dividing      104
Postage stamps, general problem of      61
Power series      107
Power series, operations on      107
Power series, sum of      107
Power series, use of to prove identities      108
Prime numbers      20
Principal diagonal      71
Principle of inclusion and exclusion      18 19 37
Principle of inclusion and exclusion, particular case of      37
Principle, teakettle      17
Problem des manages      96
Problem(s) of points      7
Problem(s) of the rooks      23 28
Problem(s) of the rooks, general      84
Problem(s) of the two ranks      51
Problem(s), bookshelf      40
Problem(s), checkerboard      16
Problem(s), combinatorial (of information theory)      61
Problem(s), combinatorial (with restrictions)      39ff
Problem(s), derangements (general)      44
Problem(s), des manages (problem des manages)      96
Problem(s), domino      15
Problem(s), entrance-exams      61
Problem(s), general (of the rooks)      84
Problem(s), involving polygons      93
Problem(s), linguistic      24
Problem(s), majordomo, alternative solution      98
Problem(s), majordomo, first solution      95
Problem(s), majordomo, third solution      103
Problem(s), number-of-divisors      56
Problem(s), postage stamps (general)      61
Problem(s), rabbit      89
Product of a series      107
Product, rule of      13 14
Properties of combinations      33
Properties of the numbers $C_{m}(k,n)$      75
Pyramidal numbers      72
Pythagoras      71
Quaterno      29
Queen of Shamakha      82
Queen's realm      82
Quinto      29
Quotient      104
Rabbit problem      89
Random walks      80
Random walks on an infinite plane      84
Recurrence relations      89ff 116
Recurrence relations, application to information transmission      103
Recurrence relations, linear (with constant coefficients)      100
Recurrence relations, nonlinear      118
Recurrence relations, order of      99
Recurrence relations, solution of      99 100
Recurrence relations, solution of, general      100
Recurrence tables      97
Relations, recurrence      89ff 116
Remainder      104
Riordan, John      8
Rooks, problem of      23 28
Roots, square, extracting      114
Round dance      25
Rule of product      13 14
Rule of sum      13
Saturn, ring of      27
Science club      22
Secret lock      11
Self-dual arrays      67
Semaphore      11
Series      104ff
Series, divergent      105
Series, infinite      105
Series, infinite, sum of      105
Series, Newton's      112
Series, number      105
Series, number, convergence of      105
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