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Rockmore D. Ч Stalking the Riemann Hypothesis
Rockmore D. Ч Stalking the Riemann Hypothesis

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Ќазвание: Stalking the Riemann Hypothesis

јвтор: Rockmore D.

јннотаци€:

In 1859 a German professor named Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the baffling occurrence of prime numbers; coming up with its proof has been the holy grail of mathematicians ever since. In 'Stalking the Riemann Hypothesis, Dan Rockmore, a prominent mathematician in his own right, takes us from Euclid's pondering of the infinitude of the primes through modern efforts to prove the Riemann hypothesis-efforts that astonishingly connect the primes to the statistics of solitaire, chaos theory, and even the mysteries of quantum mechanics. Along the way, he introduces us to the many brilliant and fascinating thinkers who have contributed to this work, from the most famous mathematician of all time, Carl Friedrich Gauss (Riemann's teacher), to the intellectual giants David Hilbert and Freeman Dyson.
A lively, comprehensive, and accessible examination of one of the most compelling unsolved problems in mathematics, 'Stalking the Riemann Hypothesis tells us the full story of the quest to find that elusive solution.


язык: en

–убрика: ћатематика/

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

ed2k: ed2k stats

√од издани€: 2006

 оличество страниц: 292

ƒобавлена в каталог: 11.03.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
"Black box"      174
"Cost of close"      225Ч227
"Hilbert problems"      123Ч125 134Ч136 215 243
"Mathematical Problems"      121Ч125
"Neutrino billiards"      228
"On Formally Undecidable Propositions of Principia Mathematica and Related Systems"      135Ч136
"On the Hypotheses That Lie at the Foundation of Geometry"      66Ч69
"On the Number of Primes Less Than a Given Magnitude"      63Ч64
"Round Table" of magicians      221
"von Koch snowflake"      126
Absolute error      126
Abundant number      12
Adeles      230Ч231
Agrawal, Manindra      264
Alcph zero      22
Alexander, James      155
Algebraic geometry      122Ч123 125
Algebraic geometry,"modern"      144 145
Algebraic number theory      115 123
Algebraic numbers      71Ч72
Algebraic topology      125
Algebraists      170
Algorithms      248Ч259
Algorithms, asymptotic analysis of      255
Algorithms, deterministic      264n
Algorithms, for checking primes      264
Algorithms, Monte Carlo      250
Algorithms, polynomial-time      264
Algorithms, probabilistic      264n
algorithms, sorting      250Ч259
Amicable number      12
Amplitude of waves      83Ч87
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 (Stappard)      50
Arenstorf, R.R      265
Argand, Jean      75n
Aristotle      49
Arithmetic progression      60Ч61 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 Machincn'      150
Astrophysics      21
Asymptotics      23Ч30
AT&T      248 258
Atomic nuclei      163Ч164 see
Atomic nuclei, eigenvalues and eigenvectors      175Ч177
Atomic nuclei, ensemble behavior of      174Ч175
Atomic nuclei, Hamiltonian matrix and      171Ч175
Atomic nuclei, radiation from      172Ч173
Atomic nuclei, statistical physics and      173Ч175
Atomic nuclei, strong and weak forces in      171 237
Atomic nuclei, wave function and      171Ч172 176Ч179
Auburn, David      50
Bachelier, Louis      102
Baik, Jinho      233 245
Baik, Jinho, mathematics of permutations and      255Ч260
Bamberger family      154
Barrow, John      47
Base      33
Basic conjecture of quantum chaos      197Ч200
Basor, Estcllc      234Ч235
Beautiful Mind, A      50
Bell Laboratories      181 255
Bell-shaped curve      235Ч236 240
Berlin Academy      64Ч65
Betry, described      187 188Ч189
Betry, Hamiltonian matrix and      227 228
Betry, Sir Michael      197Ч198 208 211 231 262
Bicbcrbach conjecture      262Ч263
big bang      21 31
Billiard tables for physicists      190Ч207 211Ч222
Billiard tables for physicists, "neutrino billiards"      228
Billiard tables for physicists, circular      191Ч192
Billiard tables for physicists, elliptical      192Ч193
Billiard tables for physicists, hyperbolic geometry and      200Ч202 205Ч212
Billiard tables for physicists, Poincarc disk and      200Ч209
Billiard tables for physicists, rectangular      191
Billiard tables for physicists, Russian      193Ч196
Billiard tables for physicists, specular reflection and      191
Binary expansion      17Ч18
Binary sequences      16
bits      16
Black Ч Scholcs equation      102
Black, Fischer      102
Bohigas, Oriol      198 211Ч222 222
Bohr, Harald      130 142
Bohr, Niels      49 130 187 190 227
Boltzmann, Ludvvig      173
Bolyai      203
Borderlands between classical and quantum mechanics      see УSemidassical limitФ
Bosons      239
Bourbaki, Charles      144Ч145
Bourbaki, Nicholas      144
Boxcar      160Ч161
Brahe, Tycho      46 47
Brcuer, 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      75Ч76
Calendars      46
California Polytechnic State University      234
Cambridge University      162 163
Cantor, Georg      22 125 135 215
Card shuffling      245 248Ч259
Card shuffling, perfect      249
Card shuffling, riffle      248
cardinal number      22
Cardinality      22Ч23
Cardona, Girolamo      73 215
Cauchy, Augustin Ч Louis      69
Cavley, Arthur      169Ч170 257
Celestial mechanics      48
Central limit theorem      100Ч104
Central limit theorem, first appearance of      236
CERES      39
Chaos      189
Chaos, quantum      see УQuantum chaosФ
Chaotic dynamical systems      189Ч190 193Ч195
Choquet, Gustave      231
City College of New York      224 234
Clay Institute of Mathematics      6
Clay Prize      262
Closed trajectory      191
Cohen, continuum hypothesis and      215
Cohen, described      214Ч226
Cohen, Paul J.      230Ч231
Coin-tossing, repeated      100Ч104 137Ч138 151Ч152
Coincidence      225Ч227
College de France      229
Colors      166Ч169
Columbia University      141 152
Combinations      246
Combinatorial enumeration      247
Combinatorial optimization      247
Combinatorics      223 245Ч247
Commutative multiplication      169n 230
Complex analysis      69 76
Complex conjugates      176Ч177
complex numbers      69 70Ч73
Complex numbers, geometric representation of      75
Complex plane      73Ч76 110
Complex power      78Ч81
Complexity theory      149
Composite numbers      12Ч13
Composite numbers, Cramer      137Ч139
Compounding continuously      35 78Ч79
Comptes Rendus      95
Computation, limits of      132Ч134
Computational complexity      149
Computers      123 128 149Ч151
Computers, algorithms and      249Ч250
Computers, asymptotic analysis and      255
Computers, permutations and      247Ч249
Computers, physics of      228
Computers, TeX and      257
Comrie, L.J.      140
Conlocal ellipse      193
Connes, Alain      228Ч231 262 265
Connes, described      229
Constant curvature      67Ч68
Constant of motion      193
Constructive numbers      70Ч71
Continuum Hypothesis      215
Convergent Series      53
Conway, J.      134
coordinates      68
Copernicus      50
Coram, Marc      226Ч227
Correlation      157Ч160
Correspondence      8Ч9
Correspondence principle      187 190 227
Countabiliry      22
Courant Institute of Mathematical Sciences      3Ч6 243 245 261Ч263
Cramer composites      137Ч139
Cramer primes      137Ч139 151
Cramer, Carl Harald      136Ч139 151 153
Cramer, described      136Ч137
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)      129Ч130
Critical line, percentage of zeta zeros on      131 151
Critical strip      89Ч92
Critical strip, de la Vallee Ч Poussin      119Ч120
Cryptography      17Ч18
Cubic polynomials      72Ч73
Curvature      67Ч68 207
CYCLE      251Ч253
Dalton, John      49
Dartmouth College      234 264
Darwin, Charles      63
Dcligne, Pierre      220
de Branges dc Bourcia, Louis      262Ч263 265
de la Vallee Ч Poussin      106Ч110 265
de la Vallee Ч Poussin, described      106Ч107
de la Vallee Ч Poussin, Prime Number Theorem and      106Ч107 129 139
de la Vallee Ч Poussin, Riemann's zeta function and      107Ч110 119Ч120
De Moivre, Abraham      236
Death of a Salesman (Miller)      134Ч135
Decibel system      34
Dedckind cuts      116
Dedckind zeta function      93 116 143
Dedckind, described      115
Dedckind, Richard      93 115Ч126
Deficient number      12
Deift, described      241Ч243
Deift, integrable systems and      243
Deift, mathematics of permutations and      255Ч260
Deift, Percy      233 255 262
Deift, Tracy Ч Widom distribution and      240Ч246
Denninger, Chrisroph      262
density      41
Denumcrability      22
Descartes, Rene (Cartesian philosophy), 32n      68 122
Description of Egypt (Fourier)      82
Diaconis, "cost of close" and      225Ч227
Diaconis, described      221
Diaconis, magic and      221Ч225
Diaconis, Persi      221Ч227 243Ч244 246 249
Differential equations      238
Differential geometry      39
Digger, x      166 195
Digital communication      16Ч18
Digital cryptography      17Ч18
DIMENSION      202n
Dimension of a space      229Ч230
Diophantine problems      144
Dirichlet L-scries      61 109Ч110 137 143 219
Dirichlet zeta function      116
Dirichlet, described      59
Dirichlet, Gustav      45 47 265
Dirichlet, infinity of primes and      59Ч62 108Ч110
Dirichlet, prime distribution analyzer of      77 80 81
Dirichlet, Riemann and      65Ч69 76Ч78 84
Discrete mathematics      223
Disquisitiones anthmeticae (Gauss)      38Ч39
Divergent series      53
Divisibility      12
Divisibility, for Gaussian integers      112
Doctrine of Chances, The (de Moivre)      236
Drevfus, Alfred      106
Duke University      243
Dynamical systems, chaotic      193Ч195
Dynamical systems, simplest      191Ч193
Dyson Ч Montgomery Ч Odlyzko Law      180Ч185 188
Dyson, described      162Ч164
Dyson, Freeman      263
Dyson, Hamiltonians and      170Ч177 180
Dyson, matrices and      165 233 234
Dyson, Mildred Atkcy      162
Dyson, Montgomery and      154 162 164 180
Dyson, Sir George      162 163
e      34 72
e, quantified      34Ч35 78Ч79
e: The Story of a Number (Maor)      34h
Edwards, H.      140
Eigenvalues      175Ч177
Eigenvalues, of a random matrix      258
Eigenvalues, on the edge      236Ч240
Eigenvalues, Tracy Ч Wisdom distributions and      234Ч241 245Ч246
Eigenvalues, zeta zeros and      175Ч185 199Ч200 210Ч221 220 225Ч229 232
Eigenvectors      175Ч176
Einstein, Albert      4 50 68 102 202 231 236
Einstein, Institute for Advanced Study and      136 142 154 155
Electromagnetic waves      84
Electrons      163 171
Elements (Euclid)      13 203
Elliptic geometry      204Ч205
Encke Gap      40
Encke, Johann      40Ч41
encrypted messages      17Ч18
Ensemble behavior      174Ч175
Enumeration      246Ч247
Eratosthenes      15
Eratosthenes,"sieve" of      15Ч16 24
Erdoes, Taul      141
Ergodic motion      194Ч195
Ergodicity      190
Error correction      17
Error term      119Ч120 126Ч127
Escher, M.C.      206
Essay on a Manner of Representation of Imaginary Quantities through Geometric Constructions (Argand)      75b
Euclid      13 122
Euclid, geometry of      13 68 203Ч204
Euclid, proof of the infinitude of primes      18Ч20 21 24 28 50 51 60
Euler equations      47
Euler factorization      55Ч57 61
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