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Rockmore D. — Stalking the Riemann Hypothesis
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Íàçâàíèå: Stalking the Riemann HypothesisÀâòîð: Rockmore D. Àííîòàöèÿ: 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.
ßçûê: Ðóáðèêà: Ìàòåìàòèêà /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 2006Êîëè÷åñòâî ñòðàíèö: 292Äîáàâëåíà â êàòàëîã: 11.03.2008Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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Ïðåäìåòíûé óêàçàòåëü
Moses 93 Mosteller, Fred 224 225 Mount Holyoke 244—245 Multivalued function 147—148 Nachlass (Riemann) 140 Nahin, Paul 72 Napoleon 81—82 Nash, John, Jr. 152—153 Natal University 211 Natural logarithm 34—35 Natural numbers 7—20 Natural numbers, as "God given" 7 70 111 137 Natural numbers, composites 12—13 Natural numbers, defined 7 Natural numbers, primes see “Prime numbers” Ncudcckcr, Werner 152 negative numbers 71 Nevanlinna, R. 145 New York Times 148 149 New York University 3—6 241 243 261—263 Newlands, John 108 Newman, Charlie 262 263 Newton, described 46—47 Newton, Isaac 38 48 50 52 82 236 Nobel prize 102 150 152 155 163 171 174 257 Nobel Prize, mathematics and 141—142 Nobel, Alfred 141—142 Non-Euclidean geometry 39 123 201 203—205 Noncommutative geometry 230 Noncommutative multiplication 169n 230 Nonlinear differential equations 238 Nonobstructive proof 265 Nonoricntable surface 97 Nontrivial zeta zeros 89—92 Nonzero 11 An Nuclear weapons 249—250 255 NUMBER 259 Number theorists 10 Number theory 10 53 265 Numerical methods 250 Numerosity, pattern of 8—10 Occam's razor 221 Odlyzko, Andrew 179n 198 199 218 258 263 Odlyzko, described 180—181 Odlyzko, Dyson — Moncgomery — Odlyzko Law 180—185 On the Propagation of Heat in Solid Bodies (Fourier) 81 Operator 177 Operator theory 234 Operator, integral 178—179 Operator, zeta zeros and 180 220 Origin of Species, The (Darwin) 63 orthogonal matrices 219 Overfitting data 38 40 p-adic numbers 229—230 Pacific Institute of Mathematical Sciences 265 Painlcve equations 237 238 Painleve transcendants 237—240 256 Painleve, described 238—239 Painleve, Paul 237—240 246 Pair correlations 157—160 164 Parallel postulate 203—204 Partial differential equation 82 Patience sorting 253—254 Patterns 8—14 Patterns, figurate numbers and 10—11 Patterns, numerosity 8—10 Patterns, patterns within 11—14 Pavlovskii, V.V 228 Peer review 148 Perfect number 12 Perfect shuffles 249 Periodic functions 83 Periodic orbit 191 192 permutations 245—259 Permutations, computer science and 247—249 Petain, Marshal 238 Philosophy 10 Physics 171 Physics, bridge between quantum mechanics and see “Scmidassical limit” Physics, physicists 217 Physics, statistical 233 Pi 58 70—71 72 Planar domains 196 Planck's constant 187—188 Planck, Max 187 Plato 13 63 Poe, Edgar Allan 24 236 Poincare conjecture 202 Poincare disk 200—209 Poincare disk, chaos in 207—209 Poincare, described 202 Poincare, Henri 102 Point 204n Poisson process 158—160 Poisson, Simeon — Denis 158 Polya Prize 260 Polya — Hilbert approach 179—180 185 198—199 227 232 Polya, described 177—178 Polya, George 177—180 259—260 Polya, integral operators and 178—179 Polynomial 72 Polytechnical School of Delft 95—96 Pomerance, Carl 264 Pons, Jean — Louis 40 Population density 41 Poussin, Nicholas 107 119 120 Preprocessing 248 Primal curve 28—29 32 Primal waves 86—87 Primality tests 15—16 264 Prime distribution analyzer (PDA) 76—77 Prime distribution analyzer (PDA), Dirichlet's 77 81 Prime distribution analyzer (PDA), Eulcr's 77 81 Prime distribution analyzer (PDA), Riemannian 77—81 Prime factorization 14 20 Prime number theorem 63 91—94 95 Prime Number Theorem, Cramer primes and 138—139 Prime Number Theorem, Gauss and 42—44 69 106 119 120 126 132—133 137 141 185 Prime Number Theorem, Lcgendre and 35—38 69 Prime Number Theorem, mathematically written 36n Prime Number Theorem, proof of 105 106—107 116 118 119 129 139 Prime Number Theorem, statement of 35 Prime numbers, algorithms for checking 264 Prime numbers, as the integral atoms 14—15 Prime numbers, asymptotic study of 23—30 51 118—129 Prime numbers, cardinality of 22—23 Prime numbers, composites and 12—13 Prime numbers, Cramer 137—139 151 Prime numbers, defined 4 Prime numbers, digital cryptography and 17—18 Prime numbers, error correction and 16—17 Prime numbers, Euclid s proof of the infinitude of 18—20 21 24 28 50 51 Prime numbers, first cartographers of 30—45 Prime numbers, Gauss and see “Gauss Carl Prime numbers, Gaussian 112—123 Prime numbers, graphs of occurrence of 25—29 Prime numbers, harmonic series and 55—61 Prime numbers, Hawkins 151—152 Prime numbers, infinity of 18—20 21 51 59—62 Prime numbers, irregular appearance of 23—29 Prime numbers, Lcgendre and see “Legendre Adrien 23—29 Marie” Prime numbers, music of 81—85 Prime numbers, pattern within the pattern 11—14 Prime numbers, periodic tables for 59—61 107—110 Prime numbers, Riemann hypothesis and see “Riemann hypothesis” Prime numbers, search for 14—16 Prime numbers, series of reciprocals of 51—59 Prime numbers, shape of 21—29 Prime numbers, slowing occurrence of 41—42 Prime numbers, speaking in 16—18 Prime numbers, twin 23—24 Prime numbers, zeta zeros and see “Zeta zeros” Princeton University 154 155 174 195 214 218 219 242—243 262 Probabilistic number theory 137 Probability theory 223 Proof (Auburn) 50 Proof of Riemann hyporhesis, code breaking and 149—152 Proof of Riemann hyporhesis, Cramer and 136—139 Proof of Riemann hyporhesis, de la Vallee — Poussin and 107—110 Proof of Riemann hyporhesis, early twentieth century pursuit of 120—127 Proof of Riemann hyporhesis, eigenvalues and see “Eigenvalues” Proof of Riemann hyporhesis, epilogue 263—266 Proof of Riemann hyporhesis, first steps in 128—153 Proof of Riemann hyporhesis, Hadamardand 107—110 Proof of Riemann hyporhesis, Hamiltonian matrix and 227—228 Proof of Riemann hyporhesis, limits of computation 132—134 Proof of Riemann hyporhesis, Millennium meeting and 3—6 261—263 Proof of Riemann hyporhesis, Nash and 152—153 Proof of Riemann hyporhesis, rwo-pronged assault 129 Proof of Riemann hyporhesis, search for 131 Proof of Riemann hyporhesis, Sicgel and 139—140 Proof of Riemann hyporhesis, Stieltjes and 95—99 104—105 Proof of Riemann hyporhesis, true, false, or neither 134—136 Pseudosphere 207 Ptolemy I. 13 50 Purdue University 262 265 Putnam Exam 234 Pythagoras (Pythagoreans) 10—13 54 Pythagoras (Pythagoreans), theorem of 113n 114 115 Quadratic formula 72 Quantization 196—200 Quantum chaos 187—190 Quantum chaos, basic conjecture of 197—200 Quantum chaos, Berry and 187 188—189 197—198 Quantum chaos, billiard tabic analogy see “Billiard tables for physicists” Quantum chaos, comparison of distributions 222 Quantum chaos, making order out of 213—231 Quantum chaos, Sarnak and 217—221 Quantum chaos, zeta zeros and 199 Quantum chromodynamics (QCD) 237 Quantum electrodynamics (QED) 163 171 237 Quantum gravity 236—237 quantum mechanics 115 136—137 see Quantum mechanics, classical physics and 171 Quantum mechanics, Planck's constant and 187—188 Quantum mechanics, spectral lines and 172—173 Quantum mechanics, uncertainty principle and 135 187—188 Quantum mechanics, wave function and 171—172 176—179 Rademachcr, Hans 147—149 RAF Bomber Command 162—163 Rains, Eric 258 Random matrices 173—175 177—180 218 Random Matrices (Mchta) 218 239 244 245 Random matrices, Deift and 244—246 Random matrices, RSK and 258—259 Random matrices, Tracy — Widom distributions and 234—241 Random walk 100—104 177 178 Random Walk Down Wall Street, A (Malkiel) 102 Randomness 157—160 Randomness, understanding through 173—175 Rational integers 114 Rational numbers 70 116 Real axis 74 Real numbers 116 Real part of complex numbers 73 74 Reciprocals, of logarithms 41—42 Reciprocals, of Riemann's zeta function 96—99 Reeds, Jim 248 Reid, Constance 179 260n Relative (percentage) error 126—127 Relativity theory, general 136 236—237 Relativity theory, special 202 Repulsion 160 Reseating data 158—160 Rhind papyrus 246—247 Rhind, Henry 246 Rhodes University 242 Richter scale 33 Riemann hypothesis 88—94 125 Riemann hypothesis, as "very likely" 91—94 Riemann hypothesis, as possibly undecidable 134—136 Riemann hypothesis, attempts to prove see “Proof of Riemann hypothesis search for” Riemann hypothesis, claimed proofs (dc Branges) 262—263 265—266 Riemann hypothesis, complex numbers and 70—73 Riemann hypothesis, complex plane and 73—76 Riemann hypothesis, defined 4—5 47 88—91 Riemann hypothesis, equivalence to eigenvalue properties of matrix 179 185 Riemann hypothesis, extended 219 Riemann hypothesis, for function fields 145—147 Riemann hypothesis, for L-series 110 Riemann hypothesis, generalized 120—121 Riemann hypothesis, incorrect refutation (Rademache) 147—149 Riemann hypothesis, Polya — Hilbert approach 179—180 Riemann hypothesis, publication of 63—64 Riemann hypothesis, quest to settle 4—6 Riemann hypothesis, raw material for 53 Riemann hypothesis, road to 64—69 Riemann hypothesis, web of connections to 259—260 Riemann hypothesis, zeta function and see “Riemanns zeta function” Riemann hypothesis, zeta zeros and 4 5 88—91 Riemann surfaces 147 Riemann — Hilbert problems 243—244 Riemann — Siegel formula 139—140 150—151 Riemann's zeta function 5 see search Riemann's zeta function, "zoo" of zeta functions and 142—143 218 Riemann's zeta function, creation of 76—81 Riemann's zeta function, Fourier analysis and 81—85 Riemann's zeta function, integral form of 80—81 129 Riemann's zeta function, logarithm of 81 Riemann's zeta function, music of the prime powers and 81—85 Riemann's zeta function, reciprocal of 96—99 Riemann's zeta function, Riemann hypothesis and 88—94 Riemann's zeta function, zeros of 85—92 119 125—126 Riemann, academic mentors of 45 59 61—62 65—69 76—78 Riemann, Bemhard 4—6 63—94 Riemann, death of 65 92—93 Riemann, early life 65—66 Riemann, formulation of zeta function 80 Riemann, notes of 64—65 Riemann, reinvention of space 66—69 Riemann, statement of Riemann hypothesis 88—91 Riemannian geometry 66—69 Riemannian manifold 68 Riemannian prime distribution analyzer 77—81 Riemanns Zeta Function (Edwards) 140 Riffle shuffling 248 Rising sequence 252—259 Robinson — Schensted — Knuth (RSK) construction 257—259 Robinson, Gilbert de Beauregard 257 Rosser, John Barkery 151 Royal Danish Academy 75 Royal Society 150 Rubinstein, Michael 219 Rudnick, Zeev 218—229 Rutgers University 233 Saddle point 207 Samak, Cohen and 214—226 Samak, described 214 263 Samak, Katz and 219—221 Samak, Peter 143 185 227 231 244 260 262 Samak, quantum chaos and 217—221 Samak, Rudnick and 218—229 Sato, M. 237 239—240 Saxena, Nitin 264 Scattering theory 242—243 Schcnsted, Craige 257 Schmit, Charles 198 Schoenfeld, Lowell 151 Scholcs, Myron 102 Schrodinger, Erwin 179
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