Borwein J., Bailey D. — Mathematics by Experiment: Plausible Reasoning in the 21st Century :: Электронная библиотека попечительского совета мехмата МГУ

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Borwein J., Bailey D. — Mathematics by Experiment: Plausible Reasoning in the 21st Century

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Название: Mathematics by Experiment: Plausible Reasoning in the 21st Century

Авторы: Borwein J., Bailey D.

Аннотация:

Primarily dealing with examples from analysis, but bringing in examples from other areas of mathematics, this book details subjects in modern mathematics in which intelligent computing plays a role. The authors first present the rationale and historical context of the experimental methodology, before turning in the main body of the work to examples that illustrate the power of the field.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 290

Добавлена в каталог: 11.06.2008

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Предметный указатель

Joint Photographic Experts Group (JPEG)      240
Joint Photographic Experts Group (JPEG), quantized images      241 $\dag$
Joyce, David      30 32
Joyce, Jeff      ix
JPEG      see Joint Photographies Experts Group
Julia sets      viii 32 238
Julia sets, 16,000 Poles of B(v)      238 $\ddag$
Kakeya's hypocycloid      82 $\ddag$
Kakeya's problem      81
Kamata, Yoshikiyo      113
Kanada, Yasumasa      7—8 30 62 110—112 114 115
Kanada, Yasumasa, frequency of digits of $\pi$       144
Kantian experiment      255
Kelly, L.M.      18
Kelly, L.M., proof illustration      19 $\dag$
Kepler, Johanes      35
Keynes, John Maynard      38 $\dag$ 43 101
Khintchine's constant      144 235
Klein, Ester      78
Klein, Felix      16 17
Knots      92
Knuth, Donald      30 121
Kuhn, Thomas      12 $\dag$
Lakatos, Imre      40 41 251
Lam, Clement      4
Lambert, Johann Heinrich      107
Land, Edwin      44
Landen, John      210
Laplace transform      196
Law and Order      117
Legendre's relation      117 200
Legendre, Adrien-Marie      107 200
Lehmann, W.      113
Lehmer's polynomial      8
Lehrer, Tom      37 $\dag$
Leibniz, Gottfried Wilhelm      104 241
Lenstra — Lenstra — Lovasz algorithm      see LLL
Lenstra, Hendrik      29 37
Levy, Silvio      viii $\dag$ 246 247
Lewin, Leonard      89 210 211
Lewis, Adrian      ix
Li, Xiaoye      x
Life of Pi      116 142
Liljedahl, Peter      41
Lindemann, Ferdinand von      107
Liouville, Joseph, Liouville numbers      165
Liouville, Joseph, Liouville's theorem      171 177
Lisonek, Petr      ix
Littlewood, John Edensor      6 65 80—81 81 96
Liu Hui      113
LLL      52 230
Log sine integral      88
Logistic iteration      50 50—53
Logistic iteration, Bifurcation plot      51 $\ddag$
Lucas numbers      239
Luke, Russell      ix
Lykken, David      43
Machin formula      105 135
Machin, John      105 113
Macklem, Mason      x
Madelung's constant      144
Madhava of Sanganiagramma      107 113
Mandelbrot set      32
Mandelbrot, Benoit      46 144
Mann iteration      78
Mathematics, humanist philosophy of      40
Mathematics, standards of rigor in      40
Matrix Reloaded      116
Matsunaga, Yoshisuke      113
Mattel, Yann      see Life of Pi
Mayer, Ernst      7
Mean iteration      203
Mean iteration, Archimedian iteration      204
Mean iteration, Gaussian iteration      203
Mean iteration, logarithmic mean      203
Medawar, P.B.      255 255 256
Merit factor problem      6
Mersenne primes      4
Meterology      42
Millennium Prize      4 38
Milnor, John      11 $\dag$
Minovitch, Michael      37
Monte Carlo simulation      141
Montgomery, Hugh, Riemann zeta function      69—72
Montgomery, Hugh, zero spacing plot      71 $\dag$
Moody, Robert      85 $\dag$
Moore's law      vii 2 4
Moore, Gordon      3
Morin, Mathew      ix
Mueller, Julia      69
Multivalued function      182
Mumford, David      ix 86
Napier, John      71
Nemeth, Tomas      86
Newcomb. Simon      148
Newton, Isaac      42—44 103 104 113
Newton, Isaac, calculation of $\pi$       106 $\ddag$ 105—106
Newton, Isaac, Newton's method      176 226—229
Niven, Ivan      139
Normal number      143 143—163 260
Normal number, absolutely normal      143
Normal number, addition      166
Normal number, graphical statistics      263 $\ddag$
Normal number, multiplication      165
Normal number, topological properties      165
North, Joseph Hoy      48
O'Donnell, James      97 $\dag$
Odlyzko, Andrew      ix x 70
Otho, Valentius      113
P versus NP problem      4—5
Papadopoulos. Jason      7
Parallel computer plat forms      4
Paris — Harrington Theorem      34
Parseval's equation      56
Pascal, Blaise, Pascal's triangle      45—47
Pascal, Blaise, Pascal's triangle, binomial coefficients      45—46
Pascal, Blaise, triangles mod 2      47 $\ddag$
Penrose. Roger. Ill perceptual dipper effect      240
Percival, Colin      7 124 127
Perelman, Grigori      38
Periodic attractor      160 162
Peters, Klaus      x 98
Physics      2
Pi (movie)      116
Pick's theorem      17—18
Planck, Max      12 $\dag$
Platonism      211
Plouffe, Simon      49 119 120
Poincare conjecture      38 97
Poincare, Henri      211 $\dag$
Pollak. Henry      62
Polya, George      vii $\dag$
Polya, George, change illustration      21 $\dag$
Polya, George, pictorial representations      21—22
Polygamma function      see Psi function
Polylogarithms, Euler sums      58

Pomerance, Carl      64 156
Pope John-Paul II      97
Primality checking      6
Prime counting function $\pi(x)$       64 69
Prime number theorem      13 63—64
Primitive prime factor      132
Principal-valued function      182
probability      42
Projective plane      4
Proper power      132
Pseudorandom generators      141 154
Psi function      207
PSLQ      52 53 123 127 130 230—232
PSLQ, calculation of $\pi$       122
PSLQ, Feynman diagrams      58 59
PSLQ, multipair      232—234
PSLQ, statement of algorithm      230
Psychology      2
Ptolemy      113
Q-linear Machin-type BBP arctangent formula      132
Quantum computing      5 6 41
Quantum physics      2 12 42 72
Qubit      41
Quinn, Frank      257 257
Rademacher, Hans      97
Ramanujan, Srinivasa      42 108 115 172
Ramanujan, Srinivasa, 75th birthday stamp      109 $\ddag$
Ramanujan, Srinivasa, calculation of $\pi$       108—109
Ramanujan, Srinivasa, Catalan's constant      238
Ramanujan, Srinivasa, lost notebook      213
Ramsey's theorem      33—34
Record, Robert      12 $\dag$
Reese, George      31
Riemann zeta function      56
Riemann zeta function, Euler sums      58
Riemann zeta function, Feynman diagrams      59
Riemann zeta function, Hurwicz zeta function      236
Riemann zeta function, modulus      95
Riemann zeta function, Modulus plot      96 $\ddag$
Riemann zeta function, normal numbers      167
Riemann zeta function, normality of      144
Riemann zeta function, prime numbers      68—69
Riemann zeta function, zero spacing plot      70 $\ddag$
Riemann, Georg Bernhard      10 98
Riemann, Georg Bernhard, manuscript      2 67
Riemann, Georg Bernhard, Prime Number Theorem      65—68
Riemann, Georg Bernhard, Riemann Hypothesis      6 68 70 72 95 97 117 253 254
Robinson, John, Firmament sculpture      84 $\ddag$
Romanus, Adrianus      113
Roth's theorem      153
Rudolph, Daniel      ix
Russell, Bertrand      10 32 84 84 241
Rutherford, W.      113
Salamin, Eugene      109 136 227
Santayana, George      101 $\dag$
Sarnak, Peter      39 $\dag$
Scharein, Rob      x 17
Schwalbe, Dan      86
Schwarz inequality      184 185
Sebah, Pascal      30
Seki Kowa      113
Sendov, Hristo      ix
Serrano, Luis      ix
Shanks, Daniel      110 114
Shanks, William      105 107 113
Sharp, Abraham      113
Shor, Peter      5 41
Siddhanta      113
Siegel, Carl Ludwig      68
Sierpinski, Waclaw      164
Sierpinski, Waclaw, paper triangle      94 $\ddag$
Sierpinski, Waclaw, random triangle      48 $\ddag$
Sierpinski, Waclaw, Sierpinski cube      31 31
Sierpinski, Waclaw, Sierpinski triangle      46—48 94
Sierpinski, Waclaw, Sierpinski's number      169
Simple connectedness      38
Simpson's paradox      256
Singular value      117
Skewes number      65
Sloane, Neil      ix 29 49
Sociology      2
Square Root Bug      180
Star Trek      116
Stephanos      19
Stirling's formula      197 197—198
STIRLING, JAMES      13
Stoicheff, Boris      95
Stoneham, R.G.      155
Stormer, F.C.W.      111
Strong Law of Large Numbers      164
Supernovas, Sylvester, James      18—19
Supernovas, Sylvester, James, Sylvester's theorem      17—18
Szekeies, George      78
Takano, K.      111
Takebe, Katahiro      113
Tangent numbers      49—50
Tartaglia, Niccolo Fontana      182
The Joy of Pi      116
The Simpsons      116
Thurston, Bill      98 $\dag$
Topology, experimental      92
Torus and 2-sphere      39 $\ddag$
Trapezoidal formula      198
Trefethen, Nick      x 22 30
Trilogarithm      210
Tsu Chung-Chih      104 107 113
Tukey, J.W.      215 $\dag$
Turing, Alan      1 241 242
Turing, Alan, Turing machines, halting problem for Turing machines      170
Ulam, Stanislaw      141
Uncertainty principle      183—188
Van Ceulen, Ludolph      113
Vertesi, Janet      x
Vierling. Angela      16 31
Viete. Francois      113
Viete. Francois, Viete's product      212
von Neumann, John      1 42 241 242
von Neumann, John, calculation of $\pi$       108
Von Vega, Georg F.      113
Wagon, Stan      86 141
Wang Fau      113
Weeks, Jeff      31 92
Weeks, Jeff, 2-bridge discovery      93 $\ddag$
Weisstein, Eric      28
Wiles, Andrew      9
Wilf — Zeilberger algorithm      245 250
Will Roger's phenomenon      256
Witten, Edward      97
Wolfram, Stephen      47
Wrench, John W.      114
Wright, Tim      30
Wriss, Asia      ix x 86
Z-linear Machin-type BBP arctangent formula      132
Zagier, Don      64 $\dag$
Zeilberger, Doron      245 251 252 252—254
Zucker, John      ix

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