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Derbyshire J. Ч Prime Obsession: Bernhard Riemann and the greatest unsolved problem in mathematics
Derbyshire J. Ч Prime Obsession: Bernhard Riemann and the greatest unsolved problem in mathematics

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Ќазвание: Prime Obsession: Bernhard Riemann and the greatest unsolved problem in mathematics

јвтор: Derbyshire J.

јннотаци€:

Bernhard Riemann would make any list of the greatest mathematicians ever. In 1859, he proposed a formula to count prime numbers that has defied all attempts to prove it true. This new book tackles the Riemann hypothesis. Partly a biography of Riemann, Derbyshire's work presents more technical details about the hypothesis and will probably attract math recreationists. It requires, however, only a college-prep level of knowledge because of its crystalline explanations. Derbyshire treats the hypothesis historically, tracking increments of progress with sketches of well-known people, such as David Hilbert and Alan Turing, who have been stymied by it. Carrying a million-dollar bounty, the hypothesis is the most famous unsolved problem in math today, and interest in it will be both sated and stoked by these able authors.


язык: en

–убрика: ћатематика/ѕопул€рные издани€/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2003

 оличество страниц: 446

ƒобавлена в каталог: 28.04.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
"Clariton"      356
"Derbyshire function"      242Ч243
"Elementary" methods      124Ч125 198
"Foundations"      18 185 225
"Sweet Betsy from Pike" (tune)      394 395
"Taiye"      82Ч83 pl.
"Villikens and his Dinah" (song)      395
$\mu(n)$      see "Moebius mu function"
$\mu(\sigma)$      see "Lindeloef mu function"
$\pi$      185
$\pi(N)$      see "Prime counting function"
$\varepsilon$      74 371
Abelian function      31 366
Abramowitz, Milton      373
Absolute error      234Ч235
Academies/societies, universities distinguished from      30 57
Adele      320Ч321
Adelic quantum mechanics      320
Airy, George      225
Alan Turing: The Enigma      262
Alexander I, Emperor of Russia      121Ч122
Alexanderson, Gerald      352Ч353
Algebra      119 194 209 225
Algebra, contrasted with geometry      385
Algebra, defined      17Ч18 86Ч87
Algebra, game theory      18
Algebraic field theory      269Ч271
Algebraic invariants, theory of      184 225
Algebraic number theory      87 184 185 194 318Ч321
Algebraic numbers      173Ч174 269
American Institute of Mathematics      xi 351Ч352
American Mathematical Society      290
Amplitude of a complex number      180Ч182 333Ч334
Analysis      119 130
Analysis in complex plane      182Ч183
Analysis, arithmetic and      18 86Ч87 89Ч90 91 96
Analysis, calculus in      87Ч88
Analysis, classic texts      15 226
Analysis, continuity concept      90Ч91
Analysis, defined      15 16 17 18 87
Analysis, functional      195
Analysis, invention      87Ч88
Analysis, limit concept      16 17 88 90Ч91
Analytic number theory      18 86Ч87 96 97Ч98 153 156 198 231Ч232 238Ч239 322
Anna, Empress of Russia      59
Anti-Semitism      163 254Ч255
Apery's number      371 399
Apery, Roger      371
Apostol, Tom      393Ч394
Argand, Jean-Robert      92
Argument of a function      36
Argument plane      210Ч216 218 219 221
Arithmetic      119
Arithmetic and analysis      18 86Ч87 89Ч90 91 96
Arithmetic of congruences      97
Arithmetic of matrices      272 273
Arithmetic, "arithmetic" vs. "number theory"      371Ч372
Arithmetic, clock      97 267
Arithmetic, defined      17 86
Artin, Emil      197 270 325 pl.
Association for Computing Machinery      261
AT&T Bell Labs      291 357
Atiyah, Sir Michael      385
Babbage, Charles      225
Bachmann, Paul      231 238 381
Backlund, Ralf Josef      258 263 384
Barnes, E.W.      223 379
Basel problem      59 62 63Ч65 75Ч76 214 332 370 399
Basel series      63Ч64
Basel University      58
Battle of Auerstaedt      49Ч50
Battle of Valmy      20 49
Bays Ч Hudson number      126 348
Bays, Carter      126 236 380
Bell, Eric Temple      55 59
Berkeley, George      88
Berlin Academy of Science      30 31 60 133 135 185
Berlin Society of Sciences      60
Berlin University      29 383
Bernoulli, Daniel      58 59
Bernoulli, Jakob      10 63 322 370
Bernoulli, Johann      10 58 63
Bernoulli, Nicholas      58
Bernstein, Felix      255 383
Berry, Sir Michael      291 312 316Ч317 342 356 386Ч387 390 pl.
Bertrand's postulate      124
Bertrand, Joseph      124
Bieberbach conjecture      383
Bierberbach, Ludwig      383
Big oh      237 238Ч245 383 396
Biron, Ernst Johann      59
Bohr Ч Landau theorem      394 396
Bohr, Harald      228 325 394
Bohr, Niels      228
Bollobas, Bela      229Ч230 378
Bolyai prize      377
Bolyai, Farkas      92
Bolzano, Bernard      92
Bombieri, Enrico      xiv
Book of Numbers, The (Conway and Guy)      369
Boole, George      18 225
Borchardt      135
Borel, Emile      92
Breaking the Code (Whitemore)      262
Brent, Richard P.      258
British mathematics and mathematicians      224Ч226
Brothers Grimm      26
Brouwer, Luitzen      170
Brunswick Polytechnic      193
Brunswick, Dukes of      49Ч50 pl.
Buckley, William F., Jr.      85
Bump, Daniel      352 391
Bump-Ng Theorem      352
Burkill, J.C.      376
Calcul des Residus (Lindeloef)      379
Calculus      119
Calculus and PNT      107Ч113
Calculus in analysis      87Ч88
Calculus, invention      87Ч88 313
Calculus, limit concept      16 175
Cambridge spy ring      226 380
Canonical form      40Ч41
Cantor, Georg      18 92 179
Caratheodory, Constantin      92 372
Card trick exercise      3Ч8
Carl Wilhelm Ferdinand, Duke of Brunswick      49Ч50 pl.
Caroline of Brunswick      368
Carroll, Lewis      395
Casti, John L.      377
Catherine the Great, Empress of Russia      60Ч61 121
Catherine, Empress of Russia (wife of Peter the Great)      58
Cauchy Ч Riemann equations      121
Cauchy, Augustin-Louis      92 119
Cayley, Arthur      225 226 277
Chaos theory      312Ч317 387Ч388
Characteristic of a field      268 395 402
Characteristic polynomial of a matrix      272Ч273 274 276
Charles of Sweden      56Ч57
Chebyshev bias      125Ч126 380
Chebyshev limits      154
Chebyshev, Pafnuty Lvovich      122Ч124 125 154 pl.
Chiliads      54
Chinese culture and language      82Ч84
Chowla, Sarvadaman      288 386
Chrystal, George      364
Church, Alonzo      195
Class number problem      386
Clay Mathematics Institute      xi 353Ч354
Clay, Landon T.      xi 353Ч354
Clebsch, Alfred      364
Clock arithmetic      97 267
Closed forms      63 64Ч65 75 171 176 314
College de France      159 317 354
Columbia University      164
Complete number system      173 320
Complex function theory      30Ч31 121 124 159 198 206Ч208 379
complex numbers      169Ч170 171 172 173 175Ч177 180 190
Complex Numbers and Functions (Estermann)      206
Complex numbers, amplitude      180Ч182 215
Complex numbers, conjugate      181 191 274 336
Complex numbers, functions of      201Ч204 206Ч208 216Ч217
Complex numbers, modulus      180Ч182
Complex numbers, to complex powers      204Ч205
Complex plane      180Ч181
Complex plane, analysis in      182Ч183
Complex plane, non-trivial zeros on      190Ч192
Complex plane, squaring function on      209Ч210
Congress of Vienna      20Ч21 61 92
Congruences, arithmetic of      97
Conjugate of a complex number      181
Connes, Alain      317Ч321 384 388 pl.
Conrey, Brian      353
Continuity      88 90Ч91 119
Continuum Hypothesis      170 188Ч189
Contour integration      402
Convergence and completeness of a number system      173
Convergence as illustrated by rulers      10Ч15 173
Convergence in Riemann's formula for J(x)      338Ч339 342
Convergence of a complex series      182Ч183
Convergence of a sequence for $sqrt{2}$      16 67 179
Convergence of a series for e      202Ч203
Convergence of Basel series      64
Convergence of sequences for $\pi$ and e      16 173
Convergence of series for 1/(1-x)      138
Convergence of series via sequences      16Ч17
Convergence of the eta series      145
Convergence of the zeta series for complex arguments      205
Convergence of the zeta series for real arguments      79
Convergence, absolute      150
Convergence, conditional      149Ч150 339
Conway, John      369
Counting logic vs. measuring logic      82Ч86
Courant Institute conference      245 351Ч352 355 359
Courant, Richard      187 255
Cours d'Analyse (Jordan)      226
Course of Pure Mathematics, A, (Hardy)      226
Coxeter, H.S.M. "Donald"      196 378
Cramer model      323Ч324
Cramer, Harald      323 388 394 pl.
Creasy, Sir Edward      20
Critical line      191 192 198Ч199 217 221Ч222 337 346Ч347
Critical line, height up      258Ч260
Critical line, number of zeros on      258 259 289Ч290
Critical strip      191 216 306Ч309
Critique of Pure Reason (Kant)      130
d'Oresme, Nicole      9 88
Data vs. datum      85Ч86
Davenport, Harold      372 383
Davis, Martin      187
Davis, Philip J.      122 123
de Bourienne, Louis      60
de Branges, Louis      383
de Fermat, Pierre      371
de la Vallee Poussin, Charles      x 153 155Ч156 161 189 223 232 237 352 356 376 pl.
de Maupertuis, Pierre      370
de Morgan, Augustus      226
de Tocqueville, Alexis      118
Decembrists      122
Dedekind, Richard      19 25 27 30 92 120 131 132 133 134 193 362Ч363 366 pl.
Deleglise, Marc      380
Deligne, Pierre      270 325 355 384 pl.
Denjoy's probabilistic interpretation      325 388
Density hypothesis      xiv
Derbyshire, John      pl. 8
derivatives      109 110
Desargue's Theorem      196
Descartes, Rene      18 164
Diamond, Harold      287 386
Differential geometry      128
Differentiation      41Ч42 109Ч110
Dirichlet, Lejuene      91 93 94Ч95 96Ч97 119 126Ч127 133 134 194 232 372 374 pl.
Disquisitiones Arithmeticae (Gauss)      93 97
Divergence and convergence compared      11Ч15
Divergence of harmonic series      9Ч10 18 63Ч64 338 399
Divergence of series for 1/(1-x)      139
Divergence of series of reciprocals of primes      154
Divergence of the zeta series for arguments less than one      80Ч81
Doxiadis, Apostolos      90
Dreyfus Affair      162Ч163 164 165
Dreyfus, Alfred      162Ч163
Dreyfus, Mathieu      162
DuBois-Reymond, Emil      253
Dukas, Paul      156
Dynamical systems      281 315
Dyson, Freeman      282 287 288 290Ч291 pl.
e      40Ч41 55 69 185 202Ч203 365Ч366
Ebell, Charlotte (mother of Bernhard Riemann)      22
Edwards, Harold      153 217 263 298 375 377 384
Eigenfunction      318
Eigenvalues      273 274 276 283 284 285 295
Einstein, Albert      128 165 313 386
Eisenstein, Gotthold      119 129
Elizabeth, Empress of Russia (daughter of Peter the Great)      58
Encke, Johann Franz      53Ч54
Entire functions      332Ч333
Eratosthenes of Cyrene      100Ч101 372
Erdos, Paul      125 378
Ernest Augustus, King of Hanover      26 366
Error term      190 234Ч235 236Ч237 241 243Ч244 326 327Ч349
Erwin Schroedinger Institute      352
Esterhazy, Major Count Ferdinand Walsin-      162
Estermann, Theodor      206 226 379
Eta function      145Ч146
Euclid of Alexandria      18 34 232
Euler product formula      105Ч106 373
Euler Ч Maclaurin summation      263
Euler Ч Mascheroni number      55 369Ч370
Euler, Catherine (nee Gsell)      59 62
Euler, Leonhard      9 15 40 55Ч56 58 59 60 61Ч62 65 75Ч76 87 88 95 97 98 100 106 121 146Ч147 374 pl.
Euler, Salome (nee Gsell)      62
Evelyn, John      56
Exiguus, Dionysus      84
Existence proofs      184Ч185
Exponential function for complex numbers      202
Exponential function, canonical form      40Ч41
Exponential function, defined      39Ч40
Exponential function, inverse of      43Ч44
exponentiation      68Ч69
Extended Riemann hypothesis      xiv
Extrapolation, card trick exercise      7Ч8
Extrapolation, defined      7
Factor, defined      32
Factor, proper      32
Factor, trivial      32 36
Factorial function      124 147
Faure, Felix      162 163
Fejer, Lipot      378
Fermat's last theorem      x xi 90 161 197 271 354 371
Fermi, Enrico      280
Feynman, Richard      291
Field theory      197 265Ч271
Field, characteristic of      268
Field, defined      266
Field, finite      267
Field, infinite      266
Fields medal      261 270 384 385
Finite fields      267 321Ч322
Form factor      287 288Ч289
Four-color theorem      x xi 197
Fourier, Joseph      92 93 119
1 2 3 4
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