|
|
 |
| Àâòîðèçàöèÿ |
|
|
|
| Ïîèñê ïî óêàçàòåëÿì |
|
|
|
|
|
|
|
 |
|
|
|
| Derbyshire J. — Prime Obsession: Bernhard Riemann and the greatest unsolved problem in mathematics |
|
|
|
| Ïðåäìåòíûé óêàçàòåëü |
Fractions 174—175 177—178
Fractions, improper 171
Fractions, mixed 171
Fractions, powers 66—67
Fractions, proper 171
Fractions, vulgar 171
France, anti-Semitism in 163
France, Dreyfus Affair 162—163 164 165
France, nineteenth century culture and politics 157—158 159
Franklin, James 325 326 389
Frederick the Great, King of Prussia 59—60 61 92
Frege, Gottlob 360
French Academie des Sciences 154
French Revolution 19
Freudenthal, Hans 127 131
Friedrich Wilhelm IV, King of Prussia 30
Friedrich Wilhelm, Duke of Brunswick 51
Fry, John xi 352—353
Function theory 121 133 209—210 221 225
Functions see also "Prime counting function" "Other
Functions of complex numbers 201—204 206—208 216—217
Functions, area under 113
Functions, argument of 36 207—208
Functions, constant 67
functions, defined 35—36 129
Functions, domain of 36—37 70 138—142 201 331—332
Functions, entire 332—333
Functions, gradient of 111
Functions, graphing 37
Functions, limit on size of 239
functions, mapping 36
Functions, value of 36 67 207—208 212 214 216
Functions, zero of 139 148 154 385
Functions, zeta 37
Galois, Evariste 369
Game theory 18 372
Gardner, Martin 367
Gathorne-Hardy, Jonathan 25
Gaudin, Michel 387
Gauss, Carl Friedrich 27 29 31 48—49 50—54 87 90 92 93 96 120—121 126 128 131 132—133 134 135 159 193 194 201 235 369 374 375 pl.
Gaussian orthogonal ensemble (GOE) 316
Gaussian Unitary Ensemble (CUE) 286—287 291 294 315 387
Gaussian-normal random number 283
Gel'fond, Alexander 354
Generalized Riemann hypothesis xiv
Geometric number theory 87
Geometry 119
Geometry, defined 17 86
Geometry, differential 128
Geometry, Euclidean 18
Geometry, foundations of 185
Geometry, non-Euclidean 122 130—131
Geometry, topology 18
George II, King of England 26
George III, King of England and Hanover 26 60
George IV, King of England and Hanover 21 368
George V, King of Hanover 48 368
Germain, Sophie 92
Germany, Berlin mob 30
Germany, educational system 24—25 29 30 93 120
Germany, mathematics and mathematicians in 91—93 185 254—256
Germany, Nazi control of 254—256 264
Germany, structure 21 24
Germany, unification of 160 366 368
Ghosh, Amit xiv
Gleick, James 387
Goedel, Kurt 195 391
Goettingen Seven 26—27 119 120
Goettingen University 26—27 29 30—31 51 93 94 119 120 130 133 134 166 185 230 252 254—256 257 264 363—364
Goettingen, city of 255—256 383
Goffman, Erving 52 257
Gogol, Nikolai 122
Goldbach conjecture 90 197 371 379
Goldbach, Christian 90
Golden Key, The 55 59 72 97 135 222
Golden Key, The and Moebius function 245—246
Golden Key, The, calculus version 309—311
Golden Key, The, expression 105 138 303—304
Golden Key, The, proof of 102—104 107
Golden Key, The, sieve of Eratosthenes and 100—101
Golden Key, The, turning 303—311
Gonek, Steve xiv
Gordan's problem 184
Gordan, Paul Albert 185
Gradient 108—109 110 111 114
Gram, Jorgen Pedersen 154 198—199 257 258 263 pl.
Grand Riemann hypothesis xiv
Gray, Jeremy J. 377
Griffiths, Phillip A. x
Gruenbaum, Branko 378
Gsell, Catherine 59 62
Gsell, Salome 62
Gutzwiller, Martin 316 321
Guy, Richard 369
Habilitation 119—120
Hadamard's three circles theorem 159 376
Hadamard, Jacques x 92 153 154—156 158—159 160—161 163—166 189 194 223 230 232 352 356 359 361 376 pl.
Hadamard, Lucie 163
Hadamard, Mathieu-Georges 164
Hadamard, Pierre 158—159
Hamiltonian operator 224 318
Handbook of Mathematical Functions (Abramowitz and Stegun) 373
Handbuch der Lehre von der Verteilung der Primzahlen (Landau) 231—232 238—239
Hanoverian kings 21 368
Hardy, G.H. 52—53 92 224 226 227—229 232 287 359—360 361 376 pl.
Harmonic series 9 58
Harmonic series, convergence of 11—15
Harmonic series, divergence of 9—10 12 63 64 76 88 399
Harmonic series, infinity in 15—16
Harvard University xi 166 353
Haselgrove, Brian 259
Hasse, Helmut 270
Hebrew University of Jerusalem 164—165 230
Heilbronn, Hans 232
Hejhal, Dennis 322
Heliotrope 128
Hensel, Fanny (nee Mendelssohn) 388
Hensel, Kurt 319 388
Herglotz, Gustav 255 256
Hermite, Charles 159—160 174 194 275
Hermitian matrix 275—276 277 282 283 284—285 286 288—289 295
Hilbert — Polya conjecture 277—278 279
Hilbert, David x 92 159 166 170 184—190 196—197 252 253—254 256 276 277 279 353 354 377 391 pl.
Hilbert, Franz 186
Hirst, Thomas 94—95
Hitler, Adolph 254
Hodges, Andrew 262 377 384
Hollond, H.A. 375
Hudson, Richard 126 236 380
Hungarians 377—378
Hutchinson, J.I. 258 263
Huxley, Martin 357
Huygens, Christiaan 58
i 176
Ignorabimus principle 253
Imaginary axis 180
imaginary numbers 169—170 175—178 180
Improper fraction 171
Incomplete number system 173
Industrial Revolution 118
Infinite field 266
Infinite product 373
Infinite series 59 63 75 138 145 149—150 304—305
infinity 15
Infinity of irrational numbers 179
Infinity of prime numbers 34 95—97 105
Infinity of rational numbers 179
Infinity, point at 214
Ingham, Albert 125
Institute for Advanced Study (Princeton) x 125 264 287 291
| Integers 171 172 173 174
Integrable problems 314
Integrals 88 110—112 127 160 305 306
Integration 42 110 111 113 149 335
Integration, contour 394
International Congress of Philosophy 225
International Congresses of Mathematicians x 165—166 184 188 225
Introduction to the Theory of the Riemann Zeta-Function, An (Patterson) 217 385
Inverse function 41—42 43 44 221
Irrational numbers 40 69 76 170 171 172 173 174 175 179 266 367
Irrational powers 67
Iwaniec, Henryk xiv
J(X) 299—302 305—307 328—330
Jacobi, Carl 119
Jacoby, Johanna 230
Johns Hopkins University 154
Johnson, Dr. 53
Johnson, Paul 61
Jordan's Theorem 226
Jordan, Camille 226
Kanigel, Robert 221 228—229
Kant, Immanuel 130 252
Katz, Nicholas 245 368 387
Keating, Jonathan 316 350—351 390
Kepler's laws 314
King's College, Cambridge 261 380
Klein, Felix 92 159
Koch, Elise 31 362 363—364
Koenig, Samuel 370
Kronecker, Leopold 135 170 185 188 376—377
Kulik, Yakov 153
Kummer, Eduard 135 372
Kummer, Ottilie (nee Mendelssohn) 372
Lagrange, Joseph-Louis 92
Landau, Edmund 38 224 230—232 238—239 255—256 276 278 325 394 pl.
Laplace, Pierre-Simon 92 93
Lead diagonal of a matrix 272
League for Human Rights 164
League of Nations 164
Least squares method 53 54
Lebesgue, Henri 33 88 92
Legendre, Adrien-Marie 53 54—55 92 93 232 369
Lehman's Theorem 236
Lehman, R. Sherman 236 258 259
Lehmer, Derrick 258
Lehrer, Tom 374
Leibnitz, Gottfried 22 88 112 370
Lermontov, Mikhail 122
Letters to a German Princess (Euler) 62
lh see "Lindeloef Hypothesis"
Li(x) 113—117 328 333 335—336 373 394 396—397
Liddell, Alice 395
Limit and continuity 91
Limit as a fundamental concept in calculus 88
Limit of a sequence 16 175
Limit of a series 17
Limit, analysis as the study of 16—18 87—88 90—91
Limit, harmonic series has no 9
Limit, irrational powers defined via 67
Lindeloef Hypothesis, diagram 401
Lindeloef Hypothesis, interesting mainly in critical strip 216
Lindeloef Hypothesis, Lindeloef and 379
Lindeloef Hypothesis, RH and 393 401—402
Lindeloef Hypothesis, stated 399 401—402
Lindeloef mu function 394 400—402
Lindeloef, Ernst 223 379 384 395 pl.
Listing, Johann 374 381
Littlewood violation 235—236 326 345 348 356 380
Littlewood, Ann 229—230
Littlewood, J.E. 193 223—224 225 227 229 230 231 233 235 349 357 375 394 pl.
ln 75
Lobachevsky, Nikolai 122 130
LOG function 43—44 69 70—75 107—109 110 111 149 203—204 244 328
Log integral function 113—117 332 333 335—336 337 340 356—357
Log, "taking a" 71—72
Log, defined 69
Log, natural (base e) 69 75
Lorenz, Edward 314—315
Lower bound 380
M(k) see "Mertens's function"
Maclaurin, Colin 263
Maier, Helmut 324
Mallory, George 90
Man Who Knew Infinity, The (Kanigel) 227
Many-body problem 281
Many-valued function 43 203
Massachusetts Institute of Technology 314—315
Mathematica software package 284—285 373 389—390
Mathematical thinking, development of 69 152 170—174 194—196
Mathematicians Apology, A (Hardy) 227 359
Matrices, arithmetic of 272 273
Matrices, characteristic polynomial of 272—273 274 276 282
Matrices, defined 195
Matrices, eigenvalues of 273 274 276 283 284 285 295
Matrices, inventor of 225 277
Matrices, lead diagonal 272
Matrices, trace of 273 274 283
Maugham, Somerset 29
Maxwell, James Clerk 226
Measure theory 88
Measuring logic vs. counting logic 82—86 90—91
Median 387
Mehta, Madan Lal 288 386
Meissel, Ernst 153—154
Meller, N.A. 258
Mendelssohn, Felix 94 95
Mendelssohn, Ottilie 372
Mendelssohn, Rebecca 94 95 133
Mendes-France, Michel 389
Mengoli, Pietro 10 370
Mertens's function 250—251 322
Mertens, Franz 154
Mittag-Leffler, Goesta 92 372
MOD see "Modulo" "Modulus
Modified Generalized Riemann Hypothesis xiv
Modified Grand Riemann Hypothesis xiv
MODULO 97 395 403
Modulus of a complex number 180—182 333—334 396—399
Moebius inversion 302—303
Moebius mu function 245—251 302—303 322 343—344 345 362
Moebius strip 381—382
Moebius, August Ferdinand 249 381 382
Moments of zeta function xiv
Monge, Gaspard 92
Montgomery — Odlyzko law 292—294 312 352 355 387
Montgomery, Hugh 193 231—232 287—288 290—291 352 356 pl.
Moon and Sixpence, The (Maugham) 28
Nachlass 257 383
Napoleon 49—50
Napoleonic Wars 19—20 24 49—50 61 92 118
National Science Foundation 353
Natural numbers 170 171 172 173 174
negative numbers 65 70 80—81 176
Neuenschwander, Erwin 24 365
Newman, James R. 128
Newson, Mary Winston 189
Newton, Sir Isaac 88 149 225 304 313
Ng, E.K.-SW. 391
Nicholas I, Emperor of Russia 122
Noether, Emmy 186 231
Non-deductive logic 325—326
Number theory 18 86—87 96 97—98 114 151 153 156 225 231 313 371—372
Numbers, bogus history of 174—175
Numbers, counting vs. measuring 83—86
Numbers, historical knowledge of 174—175 195
o see "Big oh"
Odlyzko, Andrew 161 218 257 259—261 263—264 278 291 292 294 326 352 356 357—358 361 pl.
Oklahoma State University 353
Olbers, Heinrich 90
On the Concept of Number (Kronecker) 185
|
|
|
| Ðåêëàìà |
|
|
|
|
|
Î ïðîåêòå