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Rockmore D. Ч Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers
Rockmore D. Ч Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers



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Ќазвание: Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers

јвтор: Rockmore D.

јннотаци€:

For 150 years the Riemann hypothesis has been the holy grail of mathematics. Now, at a moment when mathematicians are finally moving in on a proof, Dartmouth professor Dan Rockmore tells the riveting history of the hunt for a solution.
In 1859 German professor Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the occurrence of the prime numbers. Rockmore takes us all the way from Euclid to the mysteries of quantum chaos to show how the Riemann hypothesis lies at the very heart of some of the most cutting-edge research going on today in physics and mathematics.


язык: en

–убрика: ћатематика/

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

ed2k: ed2k stats

√од издани€: 2005

 оличество страниц: 304

ƒобавлена в каталог: 10.06.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Euler Ч Galerkin methods      47
Euler's identity      79
Euler, Jacob      47
Euler, Leonhard      97 122 251
Euler, Leonhard, described      47Ч49
Euler, Leonhard, infinity of primes and      59Ч62 142
Euler, Leonhard, nicknames of      47 49
Euler, Leonhard, prime distribution analyzer of      77 81
Euler, Leonhard, Riemann      45 66 73 76Ч77
Euler, Leonhard, series of reciprocals of primes and      51Ч56 143
Evolution      63
Existence proof      151
Explicit formula (for counting the primes)      85Ч87
EXPONENT      33
Exponent, complex      78Ч81
Exponential growth      32Ч35
Extended Riemann hypothesis      219
Extrasensory perception      225
Factorials      251
Factors      229
Fast Fourier transform (FFT)      39
Feller, William      223Ч224
Fermat's last theorem      95 114Ч115 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      145Ч146
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 81Ч85 160 215
Fourier series      83Ч84
Fourier transform      83 178 184Ч185
Fourier, Jean-Baptiste-Joseph      81Ч85
Fourier, Jean-Baptiste-Joseph, described      82
Fractals      126
French Academy of Sciences      95
French Academy of Sciences, Grand Prize competition of      99 105Ч106
Frequency content      110
Frequency of waves      83Ч87
Frobenius transformation      220
Frobenius, Georg      220
Function      80
Function fields      143 145Ч147 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      30Ч31
Gauss, Carl Friedrich, discovery of fast Fourier transform (FFT)      39
Gauss, Carl Friedrich, discovery of non-Euclidean geometry      203Ч204
Gauss, Carl Friedrich, Encke and      40Ч41
Gauss, Carl Friedrich, integers and      110Ч115
Gauss, Carl Friedrich, Legendre and      38Ч44 93
Gauss, Carl Friedrich, nickname of      38
Gauss, Carl Friedrich, prime numbers and      39Ч44 69 106 119 120 126 132Ч133 141 185
Gauss, Carl Friedrich, relative error and      126Ч127
Gauss, Carl Friedrich, Riemann and      65Ч69
Gaussian integers      110Ч115
Gaussian primes      112Ч113
Gell-Mann, Murray      49Ч50
Geodesies      203Ч207
Geometria situs      48
Geometry      10Ч11 48
Geometry, algebraic      see algebraic geometry
Geometry, differential      39
Geometry, elliptic      204Ч205
Geometry, Euclidean      13 68 203Ч204
Geometry, hyperbolic      200Ч202 205Ч212
Geometry, non-Euclidean      39 66Ч67 200Ч209
Geometry, noncommutative      230
Geometry, Riemannian      66Ч69
Geometry, spectral      216Ч217
Georgia Institute of Technology      195
Giannoni, Marie-Joya      198 222
Gledhill, Joseph      242
Global triangle      204
GOE spacing distribution      198
Goedel, Kurt      135Ч136 142 154
Good Will Hunting      50
Gram, J.      128Ч129
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      236Ч237
Great circles      204Ч205
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      105Ч110 200 208 237 265
Hadamard, Jacques, described      105Ч106 140Ч141
Hadamard, Jacques, Prime Number Theorem and      106Ч107 129
Hadamard, Jacques, Riemann's zeta function and      107Ч110 119
Hamilton, William Rowan      170
Hamiltonians      170Ч177
Hamiltonians, atomic nucleus and      171Ч175
Hamiltonians, eigenvalues and eigenvectors      175Ч177
Hamiltonians, Hermitian symmetry of      175Ч177 198Ч200
Hamiltonians, proof of Riemann hypothesis and      227Ч228
Hardy, G.H.      65 162 163
Hardy, G.H., described      129Ч130
Hardy, G.H., infinite number of zeta zeros and      130Ч134 143
Harish Ч Chandra      163
Harmonic analysis      215 216
harmonic oscillator      228
Harmonic series      53Ч61 87
Harvard University      211 224 233
Hawking, Stephen      68
Hawkins prime      151Ч152
Hawkins, David      151Ч152 153
Heat      81Ч82
Heat equation      82
Heat, flow of      82Ч84 160
Height (of a zeta zero)      90Ч91
Heisenberg, Werner      135 179 187
Hejhal, Dennis      211 224 263
Heller, Eric      194n
Hermite, Charles      96 98Ч99 105Ч106 175
Hermitian symmetry      175Ч177 183 198Ч200
Hexagonal numbers      11
Hilbert (Reid)      179 260n
Hilbert space      171Ч172 179 218
Hilbert, David      121Ч125 172 177
Hilbert, David, described      121Ч122
Hilbert, David, invariant theory of      122Ч123
Hilbert, David, Polya Ч Hilbert approach      179Ч180 185 198Ч199 227 232
How to Solve It (Polya)      177Ч178 185
Hyperbolic geometry      200Ч202 205Ч212
Hyperbolic triangles      208
Hypothesis testing      226
i      73 78Ч79
IBM      198
Ideal number      115Ч116
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 52Ч53
Infinite series, harmonic      53Ч61 87
infinity      18Ч29
Infinity as a highly textured and nuanced notion      21Ч29
Infinity of primes      18Ч20 21 51 59Ч62
Infinity, defined      18
Infinity, Greeks and      51 53 70
Infinity, transfinite number      22Ч23
Institute for Advanced Study      136 154Ч164
Institute for Advanced Study, described      154Ч156
Institute for Advanced Study, faculty at      140 142 147 154Ч155 162
Institute for Advanced Study, visiting members at      155Ч156 249
Integers      9 110Ч111
Integers, gaussian      110Ч115
Integrable systems      190Ч193 198
Integrable systems, Deift and      243
Integral form (of Riemann's zeta function)      80Ч81 129
Integration      42
International Congress of Mathematics (ICM)      121Ч125
International Congress of Mathematics (ICM), Fields Medal and      142
Internet      16 265Ч266
Internet, credit card transactions on      16Ч18
Internet, graphs and      49
Introduction to Infinitesimal Analysis (Euler)      66
Introduction to Probability and Its Applications, An (Feller)      223Ч224
Invariant theory      122Ч123
Irrational numbers      70
Ising model      238Ч239
Ising, Ernst      238Ч239
Jaffe, Arthur      233
Jimbo, M.      237 239Ч240
Johansson, Kurt      233 245
Johansson, Kurt, mathematics of permutations and      245 255Ч260
Journal of the Indian mathematical society      209Ч210
Julliard School      221
Jung, Carl      225
Kaplansky, Irving      234
Karz, Nick      219Ч221 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      30Ч32
Legendre, Adrien-Marie, Gauss and      38Ч44 93
Legendre, Adrien-Marie, Prime Number Theories and      35Ч38 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      203Ч207
Linear transformation      169
Littlewood, J.E.      131Ч132 141 143
Logan, B.      255
Logarithm      32
Logarithm, natural      34Ч35
Logarithm, reciprocals of      41Ч42
Logarithmic growth      32Ч35
Logarithmic growth, decibel system and      34
Logarithmic growth, Richter scale and      33Ч34
Logarithmic integral      42
Long Term Capital Management      102
Los Alamos      249 265
MacArthur, "Genius" Fellowship      224
magic      221Ч225
Maginot Line      238
Malkiel, Burton      102
Maor, Eli      34n
Mathematical chaos      189Ч190
Mathematics      8
Mathematics, "unreasonable effectiveness of"      174
Mathematics, brevity of proof and      50Ч51
Mathematics, collaboration in      218
Mathematics, combinatorics      223
Mathematics, discrete      223
Mathematics, either-or nature of      134Ч136
Mathematics, infinity and      21
Mathematics, magic and      223
Mathematics, mathematicians      217
Mathematics, Pythagoras and      10
Mathematics, shoulders of giants and      46Ч62
Mathematics, theorems and      49Ч51
Matrices      164Ч185
Matrices, diagonal      167
Matrices, eigenvalues and eigenvectors      175Ч177
Matrices, examples of      165
Matrices, Hamiltonian      see Hamiltonians
Matrices, Hermitian      175Ч177 183
Matrices, multiplication and      169n
Matrices, orthogonal      219
Matrices, random      see random matrices
Matrices, symmetric      168
Matrices, symplectic      219
Matrices, transformative effects of      165Ч170
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      3Ч6 261Ч263
Millennium Prize Problems      6
Miller, Arthur      134Ч135
Milton, John      48
MIT      211 242
Mittag-Leffler, Gosta      141
Miwa.T      237 239Ч240
Moebius band (Mobius strip)      97
Moebius inversion formula      97Ч105 177 181 259
Moebius, A.E      97
Monge, Gaspard      83
Monte Carlo technique      250 253
Montgomery, Hugh      219 263
Montgomery, Hugh, described      156Ч157
Montgomery, Hugh, Dyson and      154 162 164 180
Montgomery, Hugh, Dyson Ч Montgomery Ч Odlyzko Law      180Ч185
Montgomery, Hugh, pair correlation and      157Ч160
Montgomery, Hugh, sine function and      161Ч162
Mori, Y.      237 239Ч240
Moser, Juergen      243
1 2 3 4
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