|
|
 |
| Àâòîðèçàöèÿ |
|
|
|
| Ïîèñê ïî óêàçàòåëÿì |
|
|
|
|
|
|
|
 |
|
|
|
| Rockmore D. — Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers |
|
|
|
| Ïðåäìåòíûé óêàçàòåëü |
Euler — Galerkin methods 47
Euler's identity 79
Euler, Jacob 47
Euler, Leonhard 97 122 251
Euler, Leonhard, described 47—49
Euler, Leonhard, infinity of primes and 59—62 142
Euler, Leonhard, nicknames of 47 49
Euler, Leonhard, prime distribution analyzer of 77 81
Euler, Leonhard, Riemann 45 66 73 76—77
Euler, Leonhard, series of reciprocals of primes and 51—56 143
Evolution 63
Existence proof 151
Explicit formula (for counting the primes) 85—87
EXPONENT 33
Exponent, complex 78—81
Exponential growth 32—35
Extended Riemann hypothesis 219
Extrasensory perception 225
Factorials 251
Factors 229
Fast Fourier transform (FFT) 39
Feller, William 223—224
Fermat's last theorem 95 114—115 125 148 262
Feynman diagrams 163
Feynman, Richard 163 171 237 249
Fields medal 155 202 209 215 220 229
Fields Medal, described 141 142
Fields, J.C 141
Figurate numbers 11
Finite fields 145—146
Fisher, Sir R.A. 226
Floyd's game 253
Floyd, Robert 253
Forcing 215
Foundations of Geometry (Hilbert) 123
Four scalar potential 228
Fourier analysis 69 81—85 160 215
Fourier series 83—84
Fourier transform 83 178 184—185
Fourier, Jean-Baptiste-Joseph 81—85
Fourier, Jean-Baptiste-Joseph, described 82
Fractals 126
French Academy of Sciences 95
French Academy of Sciences, Grand Prize competition of 99 105—106
Frequency content 110
Frequency of waves 83—87
Frobenius transformation 220
Frobenius, Georg 220
Function 80
Function fields 143 145—147 220
Fundamental Theorem of Arithmetic 14
Gambier, B. 238
Gardner, Martin 221 224
Gaudin distribution 183 198 199
Gaudin, Michel 175 183 234
Gauss, Carl Friedrich 29 47 59 115 122 209
Gauss, Carl Friedrich, described 30—31
Gauss, Carl Friedrich, discovery of fast Fourier transform (FFT) 39
Gauss, Carl Friedrich, discovery of non-Euclidean geometry 203—204
Gauss, Carl Friedrich, Encke and 40—41
Gauss, Carl Friedrich, integers and 110—115
Gauss, Carl Friedrich, Legendre and 38—44 93
Gauss, Carl Friedrich, nickname of 38
Gauss, Carl Friedrich, prime numbers and 39—44 69 106 119 120 126 132—133 141 185
Gauss, Carl Friedrich, relative error and 126—127
Gauss, Carl Friedrich, Riemann and 65—69
Gaussian integers 110—115
Gaussian primes 112—113
Gell-Mann, Murray 49—50
Geodesies 203—207
Geometria situs 48
Geometry 10—11 48
Geometry, algebraic see algebraic geometry
Geometry, differential 39
Geometry, elliptic 204—205
Geometry, Euclidean 13 68 203—204
Geometry, hyperbolic 200—202 205—212
Geometry, non-Euclidean 39 66—67 200—209
Geometry, noncommutative 230
Geometry, Riemannian 66—69
Geometry, spectral 216—217
Georgia Institute of Technology 195
Giannoni, Marie-Joya 198 222
Gledhill, Joseph 242
Global triangle 204
GOE spacing distribution 198
Goedel, Kurt 135—136 142 154
Good Will Hunting 50
Gram, J. 128—129
Grand unified theory 231 233
Grand Unitary Ensemble (GUE) 219
Grand Unitary Ensemble (GUE), spacing distribution 183 198 199 220
Graph 49
Graph theory 49
Gravity 46 48
Gravity and 237
Gravity, quantum 236—237
Great circles 204—205
Green, Ben 265
Group representation theory 220
Group theory 223
Gutzwiller, Martin 198 200 209
Guy, R. 134
Haas, H. 211 212 213
Hadamard, Jacques 105—110 200 208 237 265
Hadamard, Jacques, described 105—106 140—141
Hadamard, Jacques, Prime Number Theorem and 106—107 129
Hadamard, Jacques, Riemann's zeta function and 107—110 119
Hamilton, William Rowan 170
Hamiltonians 170—177
Hamiltonians, atomic nucleus and 171—175
Hamiltonians, eigenvalues and eigenvectors 175—177
Hamiltonians, Hermitian symmetry of 175—177 198—200
Hamiltonians, proof of Riemann hypothesis and 227—228
Hardy, G.H. 65 162 163
Hardy, G.H., described 129—130
Hardy, G.H., infinite number of zeta zeros and 130—134 143
Harish — Chandra 163
Harmonic analysis 215 216
harmonic oscillator 228
Harmonic series 53—61 87
Harvard University 211 224 233
Hawking, Stephen 68
Hawkins prime 151—152
Hawkins, David 151—152 153
Heat 81—82
Heat equation 82
Heat, flow of 82—84 160
Height (of a zeta zero) 90—91
Heisenberg, Werner 135 179 187
Hejhal, Dennis 211 224 263
Heller, Eric 194n
Hermite, Charles 96 98—99 105—106 175
Hermitian symmetry 175—177 183 198—200
Hexagonal numbers 11
Hilbert (Reid) 179 260n
Hilbert space 171—172 179 218
Hilbert, David 121—125 172 177
Hilbert, David, described 121—122
Hilbert, David, invariant theory of 122—123
Hilbert, David, Polya — Hilbert approach 179—180 185 198—199 227 232
How to Solve It (Polya) 177—178 185
Hyperbolic geometry 200—202 205—212
Hyperbolic triangles 208
Hypothesis testing 226
i 73 78—79
IBM 198
Ideal number 115—116
Ignominious 125 134
Imaginary axis 74
| imaginary numbers 72
Imaginary numbers, purely 74
Imaginary part of complex numbers 73 74
Imaginary Tale, An (Nahin) 72
Indian Institute of Technology 264
Induction and Analogy in Mathematics (Polya) 177
Infinite prime 229
Infinite series 49 52—53
Infinite series, harmonic 53—61 87
infinity 18—29
Infinity as a highly textured and nuanced notion 21—29
Infinity of primes 18—20 21 51 59—62
Infinity, defined 18
Infinity, Greeks and 51 53 70
Infinity, transfinite number 22—23
Institute for Advanced Study 136 154—164
Institute for Advanced Study, described 154—156
Institute for Advanced Study, faculty at 140 142 147 154—155 162
Institute for Advanced Study, visiting members at 155—156 249
Integers 9 110—111
Integers, gaussian 110—115
Integrable systems 190—193 198
Integrable systems, Deift and 243
Integral form (of Riemann's zeta function) 80—81 129
Integration 42
International Congress of Mathematics (ICM) 121—125
International Congress of Mathematics (ICM), Fields Medal and 142
Internet 16 265—266
Internet, credit card transactions on 16—18
Internet, graphs and 49
Introduction to Infinitesimal Analysis (Euler) 66
Introduction to Probability and Its Applications, An (Feller) 223—224
Invariant theory 122—123
Irrational numbers 70
Ising model 238—239
Ising, Ernst 238—239
Jaffe, Arthur 233
Jimbo, M. 237 239—240
Johansson, Kurt 233 245
Johansson, Kurt, mathematics of permutations and 245 255—260
Journal of the Indian mathematical society 209—210
Julliard School 221
Jung, Carl 225
Kaplansky, Irving 234
Karz, Nick 219—221 262
Karz, Nick, described 220
Kayal, Neeraj 264
Keating, Jonathan 226 227 228 262
Kendall, M.G. 102
Kepler, Johannes 46 47
Kerov, S. 255
Knuth, Donald E. 257
Kostelec, E 181n 184n 192n 193n 195n 201n 205n 208n
Kronecker, Leopold 7 8 70 111 137 220
Kummer, Eduard 115
Kyoto Prize 257
Lacroix, Sylvestre 83
Lagrange, Joseph-Louis 83
Landau, Edmund 130 142
Laplace, Pierre-Simon 47 83
Lavoisier, Antoine-Laurent 49
Legendre functions 31
Legendre, Adrien-Marie 29 47 61 66
Legendre, Adrien-Marie, death of 38
Legendre, Adrien-Marie, described 30—32
Legendre, Adrien-Marie, Gauss and 38—44 93
Legendre, Adrien-Marie, Prime Number Theories and 35—38 69 106
Lehman, R.Sherman 151
Lenstra, Hendrik 264
Levinson, Norman 151
Levy, Silvio 206n
Lewitt, Sol 256
Ley, Jos 206n
Line 204n
Line, straight 203—207
Linear transformation 169
Littlewood, J.E. 131—132 141 143
Logan, B. 255
Logarithm 32
Logarithm, natural 34—35
Logarithm, reciprocals of 41—42
Logarithmic growth 32—35
Logarithmic growth, decibel system and 34
Logarithmic growth, Richter scale and 33—34
Logarithmic integral 42
Long Term Capital Management 102
Los Alamos 249 265
MacArthur, "Genius" Fellowship 224
magic 221—225
Maginot Line 238
Malkiel, Burton 102
Maor, Eli 34n
Mathematical chaos 189—190
Mathematics 8
Mathematics, "unreasonable effectiveness of" 174
Mathematics, brevity of proof and 50—51
Mathematics, collaboration in 218
Mathematics, combinatorics 223
Mathematics, discrete 223
Mathematics, either-or nature of 134—136
Mathematics, infinity and 21
Mathematics, magic and 223
Mathematics, mathematicians 217
Mathematics, Pythagoras and 10
Mathematics, shoulders of giants and 46—62
Mathematics, theorems and 49—51
Matrices 164—185
Matrices, diagonal 167
Matrices, eigenvalues and eigenvectors 175—177
Matrices, examples of 165
Matrices, Hamiltonian see Hamiltonians
Matrices, Hermitian 175—177 183
Matrices, multiplication and 169n
Matrices, orthogonal 219
Matrices, random see random matrices
Matrices, symmetric 168
Matrices, symplectic 219
Matrices, transformative effects of 165—170
Matrices, unitary 219
Matter and energy 21
Mehta, Madan Lai 175 218 234 239 244 245
Memorylcss process 158
Mendeleyev, Dmitry 108
Mendelssohn, Rebecca 59
Mertens conjecture 104 181
Mertens, F. 104
Merton, Robert 102
METAFONT 257
Method of least squares 31 38 39 40
Metropolis, Nicholas 249 250
Millennium meeting 3—6 261—263
Millennium Prize Problems 6
Miller, Arthur 134—135
Milton, John 48
MIT 211 242
Mittag-Leffler, Gosta 141
Miwa.T 237 239—240
Moebius band (Mobius strip) 97
Moebius inversion formula 97—105 177 181 259
Moebius, A.E 97
Monge, Gaspard 83
Monte Carlo technique 250 253
Montgomery, Hugh 219 263
Montgomery, Hugh, described 156—157
Montgomery, Hugh, Dyson and 154 162 164 180
Montgomery, Hugh, Dyson — Montgomery — Odlyzko Law 180—185
Montgomery, Hugh, pair correlation and 157—160
Montgomery, Hugh, sine function and 161—162
Mori, Y. 237 239—240
Moser, Juergen 243
|
|
|
| Ðåêëàìà |
|
|
|
|
|
Î ïðîåêòå