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| Ïîèñê ïî óêàçàòåëÿì |
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| Rockmore D. — Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers |
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| Ïðåäìåòíûé óêàçàòåëü |
"Black box" 174
"Cost of close" 225—227
"Hilbert problems" 123—125 134—136 215 243
"Mathematical Problems" 121—125
"Neutrino billiards" 228
"On Formally Undecidable Propositions of Principia Mathematica and Related Systems" 135—136
"On the Hypotheses That Lie at the Foundation of Geometry" 66—69
"On the Number of Primes Less Than a Given Magnitude" 63—64
"Round Table" of magicians 221
"von Koch snowflake" 126
Absolute error 126
Abundant number 12
Adeles 230—231
Agrawal, Manindra 264
Aleph zero 22
Alexander, James 155
Algebraic geometry 122—123 125
Algebraic geometry, "modern" 144 145
Algebraic number theory 115 123
Algebraic numbers 71—72
Algebraic topology 125
Algebraists 170
Algorithms 248—259
Algorithms for checking primes 264
Algorithms, asymptotic analysis of 255
Algorithms, deterministic 264n
Algorithms, Monte Carlo 250
Algorithms, polynomial-time 264
Algorithms, probabilistic 264n
algorithms, sorting 250—259
Amicable number 12
Amplitude of waves 83—87
Analog computers 150
analog-to-digital converters 255
Analysis 51
Analysis of the Infinite (Euler) 49 59
Analytic continuation 80n
Analytic number theory 115
Applied linear algebra 129
Arcadia (Stoppard) 50
Arenstorf, R.R 265
Argand, Jean 75n
Aristotle 49
Arithmetic progression 60—61 108 265
Arithmetic, "odometer" 146
Arithmetic, fundamental theorem of 14
Arithmetic, transfinite numbers and 215
Art of Computer Programming, The (Knuth) 257
Association for Computing Machinery 150
Astrophysics 21
Asymptotics 23—30
AT&T 248 258
Atomic nuclei 163—164
Atomic nuclei, eigenvalues and eigenvectors 175—177
Atomic nuclei, ensemble behavior of 174—175
Atomic nuclei, Hamiltonian matrix and 171—175
Atomic nuclei, radiation from 172—173
Atomic nuclei, statistical physics and 173—175
Atomic nuclei, strong and weak forces in 171 237
Atomic nuclei, wave function and 171—172 176—179 see
Auburn, David 50
Bachelier, Louis 102
Baik, Jinho 233 245
Baik, Jinho, mathematics of permutations and 255—260
Bamberger family 154
Barrow, John 47
Base 33
Basic conjecture of quantum chaos 197—200
Basor, Estelle 234—235
Beautiful Mind, A 50
Bell Laboratories 181 255
Bell-shaped curve 235—236 240
Berlin Academy 64—65
Berry, Sir Michael 197—198 208 211 231 262
Berry, Sir Michael, described 187 188—189
Berry, Sir Michael, Hamiltonian matrix and 227 228
Bieberbach conjecture 262—263
big bang 21 31
Billiard tables for physicists 190—207 211—212
Billiard tables for physicists, "neutrino billiards" 228
Billiard tables for physicists, circular 191—192
Billiard tables for physicists, elliptical 192—193
Billiard tables for physicists, hyperbolic geometry and 200—202 205—212
Billiard tables for physicists, Poincare disk and 200—209
Billiard tables for physicists, rectangular 191
Billiard tables for physicists, Russian 193—196
Billiard tables for physicists, specular reflection and 191
Binary expansion 17—18
Binary sequences 16
bits 16
Black — Scholes equation 102
Black, Fischer 102
Bohigas, Oriol 198 211—212 222
Bohr, Harald 130 142
Bohr, Niels 49 130 187 190 227
Boltzmann, Ludwig 173
Bolyai 203
Borderlands between classical and quantum mechanics see semiclassical limit
Bosons 239
Bourbaki, Charles 144—145
Bourbaki, Nicholas 144
Boxcar 160—161
Brahe, Tycho 46 47
Breuer, Marcel 156
Bristol University 189
Brown, Robert 102
Brownian motion 102
Bulk spectrum 232
Bunimovich's stadium 194 195 200
Bunimovich, Leonid 195
Calculus 10 46 47 49 52 57 236
Calculus, extending, to the complex world 75—76
Calendars 46
California Polytechnic State University 234
Cambridge University 162 163
Cantor, Georg 22 125 135 215
Card shuffling 245 248—259
Card shuffling, perfect 249
Card shuffling, riffle 248
cardinal number 22
Cardinality 22—23
Cardona, Girolamo 73 215
Cauchy, Augustin-Louis 69
Cayley, Arthur 169—170 257
Celestial mechanics 48
Central limit theorem 100—104
Central limit theorem, first appearance of 236
CERES 39
Chaos 189
Chaos, quantum see quantum chaos
Chaotic dynamical systems 189—190 193—195
Choquet, Gustave 231
City College of New York 224 234
Clay Institute of Mathematics 6
Clay Prize 262
Closed trajectory 191
Cohen, Paul J. 230—231
Cohen, Paul J., continuum hypothesis and 215
Cohen, Paul J., described 214—216
Coin-tossing, repeated 100—104 137—138 151—152
Coincidence 225—227
College de France 229
Colors 166—169
Columbia University 141 152
Combinations 246
Combinatorial enumeration 247
Combinatorial optimization 247
Combinatorics 223 245—247
Commutative multiplication 169n 230
Complex analysis 69 76
| Complex conjugates 176—177
complex numbers 69 70—73
Complex numbers, geometric representation of 75
Complex plane 73—76 110
Complex power 78—81
Complexity theory 149
Composite numbers 12—13
Compounding continuously 35 78—79
Comptes Rendus 95
Computation, limits of 132—134
Computational complexity 149
Computers 123 128 149—151
Computers, algorithms and 249—250
Computers, asymptotic analysis and 255
Computers, permutations and 247—249
Computers, physics of 228
Computers, TeX and 257
Comrie, L.J. 140
Confocal ellipse 193
Connes, Alain 228—231 262 265
Connes, Alain, described 229
Constant curvature 67—68
Constant of motion 193
Constructibte numbers 70—71
Continuum Hypothesis 215
Convergent Series 53
Conway, J. 134
coordinates 68
Copernicus 50
Coram, Marc 226—227
Correlation 157—160
Correspondence 8—9
Correspondence principle 187 190 227
Countability 22
Courant Institute of Mathematical Sciences 3—6 243 245 261—263
Crame'r, Carl Harald 136—139 151 153
Crame'r, Carl Harald, described 136—137
Cramer 137—139
Cramer composites 137—139
Cramer primes 137—139 151
Critical line 92 125
Critical line, connection to Riemann hypothesis 92
Critical line, connection to Riemann hypothesis for L-series 110
Critical line, infinity of zeta zeros on (Hardy) 129—130
Critical line, percentage of zeta zeros on 131 151
Critical strip 89—92
Critical strip, de la Vallee — Poussin 119—120
Cryptography 17—18
Cubic polynomials 72—73
Curvature 67—68 207
CYCLE 251—253
Dalton, John 49
Dartmouth College 234 264
Darwin, Charles 63
Dcdekind cuts 116
Dcdekind, Richard 93 115—116
de Branges de Bourcia, Louis 262—263 265
de la Vallee-Poussin 106—110 265
de la Vallee-Poussin, described 106—107
de la Vallee-Poussin, Prime Number Theorem and 106—107 129 139
de la Vallee-Poussin, Riemann's zeta function and 107—110 119—120
De Moivre, Abraham 236
Death of a Salesman (Miller) 134—135
Decibel system 34
Dedekind zeta function 93 116 143
Deficient number 12
Deift, Percy 233 255 262
Deift, Percy, described 241—243
Deift, Percy, integrable systems and 243
Deift, Percy, mathematics of permutations and 255—260
Deift, Percy, Tracy — Widom distribution and 240—246
Deligne, Pierre 220
Denninger, Christoph 262
density 41
Denumcrability 22
Descartes, Rene (Cartesian philosophy) 32n 68 122
described 115
Described, Hamiltonians and 170—177 180
Described, matrices and 165 233 234
Described, Montgomery and 154 162 164 180
Description of Egypt (Fourier) 82
Diaconis, Persi 221—227 243—244 246 249
Diaconis, Persi, "cost of close" and 225—227
Diaconis, Persi, described 221
Diaconis, Persi, magic and 221—225
Differential equations 238
Differential geometry 39
Digger x 166 195
Digital communication 16—18
Digital cryptography 17—18
DIMENSION 202n
Dimension of a space 229—230
Diophantine problems 144
Dirichlet L-series 61 109—110 137 143 219
Dirichlet zeta function 116
Dirichlet, Gustav 45 47 265
Dirichlet, Gustav, described 59
Dirichlet, Gustav, infinity of primes and 59—62 108—110
Dirichlet, Gustav, prime distribution analyzer of 77 80 81
Dirichlet, Gustav, Riemann and 65—69 76—78 84
Discrete mathematics 223
Disquisitiones arithmetical (Gauss) 38—39
Divergent series 53
Divisibility 12
Divisibility for Gaussian integers 112
Doctrine of Chances, The (de Moivre) 236
Dreyfus, Alfred 106
Duke University 243
Dynamical systems, chaotic 193—195
Dynamical systems, simplest 191—193
Dyson — Montgomery — Odlyzko Law 180—185 188
Dyson, Freeman 263
Dyson, Freeman, described 162—164
Dyson, Mildred Atkey 162
Dyson, Sir George 162 163
e 34 72
e, quantified 34—35 78—79
e: The Story of a Number (Maor) 34n
Edwards, H. 140
Eigenvalues 175—177
Eigenvalues of a random matrix 258
Eigenvalues on the edge 236—240
Eigenvalues, Tracy — Wisdom distributions and 234—241 245—246
Eigenvalues, zeta zeros and 175—185 199—200 210—211 220 225—229 232
Eigenvectors 175—176
Einstein, Albert 4 50 68 102 202 231 236
Einstein, Albert, Institute for Advanced Study and 136 142 154 155
Electromagnetic waves 84
Electrons 163 171
Elements (Euclid) 13 203
Elliptic geometry 204—205
Encke Gap 40
Encke, Johann 40—41
encrypted messages 17—18
Ensemble behavior 174—175
Enumeration 246—247
Eratosthenes 15
Eratosthenes, "sieve" of 15—16 24
Erdoes, Paul 141
Ergodic motion 194—195
Ergodicity 190
Error correction 17
Error term 119—120 126—127
Escher, M.C. 206
Essay on a Manner of Representation of Imaginary Quantities through Geometric Constructions (Argand) 75n
Euclid 13 122
Euclid, geometry of 13 68 203—204
Euclid, proof of the infinitude of primes 18—20 21 24 28 50 51 60
Euler equations 47
Euler factorization 55—57 61
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