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

$\pi$ , algorithms for calculating      103
$\pi$ , algorithms for calculating, BBP algorithm      119—125
$\pi$ , algorithms for calculating, Borwein quartic algorithm      110 117—118
$\pi$ , algorithms for calculating, early algorithms      104—107
$\pi$ , algorithms for calculating, Salamin — Brent algorithm      109 110 227
$\pi$ , algorithms for computing, spigot algorithm      140
$\pi$ , Biblical references      103 136
$\pi$ , calculations of      8
$\pi$ , continued fraction      108
$\pi$ , early estimates      103
$\pi$ , formulas for calculating      107 109 111 115 119 122 126 134 135
$\pi$ , frequency of digits      144
$\pi$ , irrationality      107 139
$\pi$ , popular media      116—117 142
$\pi$ , random walk      147 $\ddag$
$\pi$ , strings of digits      110
$\pi$ , transcendental      107
A Beautiful Mind      116
Abel, Niels Henrik      10
Achilles, Alf-Christian      28
Adaniohik, Victor      ix
Aeronautical engineering      2
AGM inequality      211
Ainazon.com      97
Al-Kashi      107 113
Al-Khowarizmi      113
Andrews, George      214 $/dag$

Apostol, Tom      72
Apostol, Tom, $\sqrt{2}$ proof      73 $\ddag$
Archimedes      42 113
Archimedes, calculation of $\pi$       103—104
Aristotelian experiment      255
Arithmetic-geometric mean (AGM)      13 201
Arithmetic-geometric mean (AGM), calculation of $\pi$       109—110
Arithmetic-geometric mean (AGM), high-precision arithmetic      228
Arndt, Joerg      143 $\dag$
Arrow, Kenneth      12 $\dag$
Aryahhata      113
Au-Young, Enrico      56 247
Baconian experiment      255
Bailey — Crandall hypothesis      150
Ballantine's series      135
Barnsley, Michael      48
Barwise, Jon      2
Bauschke, Heinz      ix
BBP-type formulas      120 127—131
BBP-type formulas, BBP sequence      150
BBP-type formulas, normal numbers      148 152
Bellard, Fabrice      124 127
Benford, Frank      148
Benford, Frank, Benford's principle      148
Berlinski, David      1 $\dag$
Berry, Michael      72 $\dag$
Bert, Paul      19
Bert, Paul, geometry text      68—69 20
Besicovitch, Abram S.      81
Bessel functions, Euler's constant      138
beta function      193
Beta function, normal numbers      167
Bianchii group      88
biology      2
Bohr, Harald      96 $\dag$
Bohr-Mollerup theorem      192 206
Bollobas, Bela      x 80 96
Bolzano, Bernhard      9
Borel, Emile, Borel — Cantelli lemma      152 164
Borel, Emile, Borel — Cantelli lemma, normal number theorem      164
Borrell, Lee      29
Borwein cubic/quartic iteration      see $\pi$ algorithms
Borwein, David      108 132
Borwein, Peter      ix 110 119
Bouyer, Martine      114 135
Bradley, David      ix
Brahmagupta      113
Brent MacMillan algorithm      138
Brent, Richard      109 136 227
Briggs, Henry      74 $\dag$
Broadhurst, David      8—9 54 58
Brouwer, Luitzen Egbertus Jan      111 241
Buffons needle      139
Cantor, Georg      211
Caratheodory, Constantin      182 $\dag$
Cardano, Girolaino      182
Catalan, Eugene, Catalan numbers      22
Catalan, Eugene, Catalan's constant      61 127 144 238 240
Cauchy, Augustin-Louis      10
Cauchy, Augustin-Louis, Cauchy — Goursat theorem      177
Cauchy, Augustin-Louis, Cauchy — Schwarz inequality      188 190 191
Cayley, Arthur, counting rooted trees      22
Cellular automata      17
Cesaro average      79
Chaitin's constant      144 164 170
Chaitin, Gregory      ix 29 252 254
Champernowne number      147 167
Chang Hong      113
Chang, Jon      x
Chang, Sun-Yung Alice      39 $\dag$
Chaos theory      see dynamical systems
Chretien, Joan      17 71
Chti Shih-Chieh      17
Chudnovsky, David and Gregory      ix x 114 144
Civilization      39 $\dag$
Clarke, Arthur C.      37 $\dag$
Clausen functions      89
Clausen, Thomas      113
Clay Mathematics Institute      38 56 72
Cohen, Joel      215
Computer algebra systems      2
Computer algebra systems, failures of      179—183
Computer algebra systems, proofs using      3
Constant recognition      60 63 229
Constant recognition, HJLS algorithm      230
Constant recognition, practical extensions      234
Constant recognition, PSLQ algorithm      230—232
Constant recognition, PSLQ, multipair      232—234
Constructivism      74
Contact      116
Continued fractions      235
Continued fractions, Euler's constant      240
Convolutions      216 218
Convolutions, cyclic convolution      216
Convolutions, devil's convolution      225 226
Convolutions, linear convolution      216
Copeland — Erdoes constant      171
Corless, Robert      ix 179 182
Cosmology      2
Costa, Celso, Costa surface      86 99
Coxeter, H.S.M.(Donald)      18 83 84
Coxeter, H.S.M.(Donald), 4-D polytope      85 $\ddag$
Coxeter, H.S.M.(Donald), kaleidoscope      83 $\ddag$
Cramer. Harald      08
Crandall, Richard      ix 7 28 64 77 83 149 167 184
Cryptography      33
Csicsery, George Paul      x
Darwin, Charles      111
Dase, Johan Zacharias      113
Dase, Johan Zacharias, calculation of $\pi$       106
Davis. Martin      241 242
De Doelder      57
De la Llave, Rafael      246 247
De La Vallee Poussin      13
De Lagny, Thomas      113
de Morgan, Augustus      16 $\dag$ 43
De Smit, Bart      29 37
Dedekind, Richard      9 32
Derangement      208
Desmic configuration      19
Devlin, Keith      2
Dickson, Stewart      29
Dilogarithm      210

Dirac, Paul      18
Dirichlet, Lejeune      195
Discrete cosine transform (DCT)      240
Discrete Fourier transform (DFT)      216—218
Duijvestijn's dissection      80 81
Dynamical systems      50 236—238
Dyson, Freeman      70—72
Economics      2 42
Edison, Thomas      44
Einstein's brain      85
Eisenstein integers      88
Elliptic integrals, complementary integrals      200
Elliptic integrals, complete      117 199
Elliptic integrals, decimal expansion      144
Embree, Mark      30
ENIAC      108 134
ENIAC, photo      134 $\dag$
Entanglement      41
Epstein, David      viii $\dag$ 97 246 247
Equidistributed sequence      150 160
Erdoes, Paul      6 18 33 69 78 171—173
Erdoes, Paul, Erdoes Number Project      173
Erdoes, Paul, photo      173 $\ddag$
Escher, Maurits C.      37 84
Euclid, Elements      19 32
Euclid, Euclidean algorithm      230
Euclid, prime numbers      63
Euler, Leonhard      42 105 138
Euler, Leonhard, Euler numbers      49—50
Euler, Leonhard, Euler sums      56—58
Euler, Leonhard, Euler sums, quantum field theory      58
Euler, Leonhard, Euler — Maclaurin summation      57 188
Euler, Leonhard, Euler — Zagier sums      see Euler sums
Euler, Leonhard, Euler's constant      138 144 240
Euler, Leonhard, gamma function      195
Euler, Leonhard, Riemann zeta function      99—100
Experimental mathematics      2 264
Experimental Mathematics (journal)      2 27 99 246 249
Factorization      5 41
False proofs      97
Faraday, Michael      37
Fast Fourier transform (FFT)      108 115 186—188 216—218
Fast Fourier transform (FFT), high-precision arithmetic      223—225
Fateman, Richard      ix 28 78
Fee, Greg      ix
Feigenbaum's constant      53 144
Feigenbaum, Mitchell      53
Fenchel, Werner, Fenchel — Legendre conjugate      191
Fenchel, Werner, Fenchel — Young inequality      190
Ferguson, Claire      53
Ferguson, D.F.      107 114
Ferguson, Helaman      ix x 30 36 52—56 86 230
Ferguson, Helaman, "Eight-Fold Way"      55 $\ddag$
Ferguson, Helaman, "Figure-Eight Knot Complement"      55 $\ddag$
Ferguson, Helaman, "Invisible Handshake"      87 $\ddag$
Ferguson, Helaman, sculptures      30 53—56 86—92
Ferguson, Samuel      36
Fermat's last theorem      9 97
Feynman diagrams      58
Feynman, Richard      43 44
Fibonacci, Leonardo      113
Finch, Steven      ix 30
Finite attractor      150 160 162
Fluid dynamics      2
Four color theorem      7 40 97
Fractal cards      94
Frege, Gottlob      10 241
Fundamental theorem of algebra      175—177
Galilean experiment      256
Galois, Evariste      172
Galway, William      x 132
Gamma function      192 192—195
Gamma function, formulas      194 206
Gamma function, Psi function      207
Gamma function, volumes of balls      195
Gauss, Carl Friedrich      12 $\dag$ 12—13 42 44 64 95 95 115
Gauss, Carl Friedrich, arithmetic-geometric mean (AGM)      13
Gauss, Carl Friedrich, experimental Gaussian      189 $\ddag$
Gauss, Carl Friedrich, Gauss — Kuz'min distribution      235 240
Gauss, Carl Friedrich, Gaussian distribution      185
Gauss, Carl Friedrich, on the AGM      15 $\ddag$
Gauss, Carl Friedrich, on the leminscate      14 $\ddag$
Gauss, Carl Friedrich, Prime Number Theorem      63—64
Gauss, Eugene      100
Gelfond — Sclmeider theorem      74 82
Generating functions      21
Gerrietts, Marty      115 $\ddag$
Girgensohn, Roland      x 173 247
Goedel, Kurt      1 $\dag$ 241
Goedel, Kurt, Goedel statements      34
Goedel, Kurt, Goedel's theorem      7 34 35
Golay, Marcel      6
Goldbach, Christian      57 99
Goldbach, Christian, Goldbach conjecture      252
Goldston, Daniel      69
Goodstein, Reuben, Goodstein sequences      34
Goodstein, Reuben, Goodstein's theorem      35
Gosper, William      108 111 114
Gourdon, Xavier      30
Grabiner, Judith      10
Graham, Ronald      ix 62
Granville, Andrew      ix 30
Gravitational boosting      37
Gray, Alfred      86
Gregory, James, Gregory — Leibniz formula      105 139 205
Gregory, James, Gregory's series      48 50 105
Griffeath, David      30 94
Grossman, Jerry      30 173
Guilloud, Jean      114 135
Hadamard, Jacques      10 $\dag$ 13
Hadamard, Jacques, prime number theorem      10
Haenel, Christoph      ix 143
Hales, Thomas      30 35
Hamming, Richard      45 $\dag$
Happy end problem      78
Hardy, G.H.      11 $\dag$ 32 42 96 241
Hayes, Brian      40 $\dag$
Hepting, Darrell      46
Hersh, Reuben      40
Herzberg, Gerhard      95
Heyting, Arend      111
Hida, Yozo      x
High-precision arithmetic      218—229
High-precision arithmetic, advanced operations      225—229
High-precision arithmetic, arbitrary precision      221—222
High-precision arithmetic, double-double      219—221
High-precision arithmetic, fast Fourier transform (FFT)      223—225
High-precision arithmetic, IEEE-754 standard      218
High-precision arithmetic, Karatsuba Multiplication      222—223
High-precision arithmetic, quad-double      219—221
Hilbert, David      35
Hitchhiker's Guide to the Galaxy      117
HJLS algorithm      see constant recognition
Hoelder's inequality      190 192 194
Hoffman, David      99
Hohmann transfer ellipses      37
Hot spot lemma      155 166
Hypergeometric function, calculation of $\pi$       122
Hypergeometric function, normal numbers      167
Hypocycloid      82
Indo-Arabic number system      104
Integer relation algorithm      51—52 61—62 230
Integer relation algorithm, calculation of $\pi$       123
Integer relation algorithm, LLL      52
Integer relation algorithm, polynomials      51
Integer relation algorithm, PSLQ      52
Intuitionism      74
Jaffe, Arthur      257 257
Jeffrey, Dave      179 182 183
Jeffrey, David      ix

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