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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 |
Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
Ïðåäìåòíûé óêàçàòåëü
"Black box" 174 "Cost of close" 225—227 "Hilbert problems" 123—125 134—136 215 243 "Mathematical Problems" 121—125 "Neutrino billiards" 228 "On Formally Undecidable Propositions of Principia Mathematica and Related Systems" 135—136 "On the Hypotheses That Lie at the Foundation of Geometry" 66—69 "On the Number of Primes Less Than a Given Magnitude" 63—64 "Round Table" of magicians 221 "von Koch snowflake" 126 Absolute error 126 Abundant number 12 Adeles 230—231 Agrawal, Manindra 264 Alcph zero 22 Alexander, James 155 Algebraic geometry 122—123 125 Algebraic geometry,"modern" 144 145 Algebraic number theory 115 123 Algebraic numbers 71—72 Algebraic topology 125 Algebraists 170 Algorithms 248—259 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 250—259 Amicable number 12 Amplitude of waves 83—87 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 60—61 108 265 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 23—30 AT&T 248 258 Atomic nuclei 163—164 see Atomic nuclei, eigenvalues and eigenvectors 175—177 Atomic nuclei, ensemble behavior of 174—175 Atomic nuclei, Hamiltonian matrix and 171—175 Atomic nuclei, radiation from 172—173 Atomic nuclei, statistical physics and 173—175 Atomic nuclei, strong and weak forces in 171 237 Atomic nuclei, wave function and 171—172 176—179 Auburn, David 50 Bachelier, Louis 102 Baik, Jinho 233 245 Baik, Jinho, mathematics of permutations and 255—260 Bamberger family 154 Barrow, John 47 Base 33 Basic conjecture of quantum chaos 197—200 Basor, Estcllc 234—235 Beautiful Mind, A 50 Bell Laboratories 181 255 Bell-shaped curve 235—236 240 Berlin Academy 64—65 Betry, described 187 188—189 Betry, Hamiltonian matrix and 227 228 Betry, Sir Michael 197—198 208 211 231 262 Bicbcrbach conjecture 262—263 big bang 21 31 Billiard tables for physicists 190—207 211—222 Billiard tables for physicists, "neutrino billiards" 228 Billiard tables for physicists, circular 191—192 Billiard tables for physicists, elliptical 192—193 Billiard tables for physicists, hyperbolic geometry and 200—202 205—212 Billiard tables for physicists, Poincarc disk and 200—209 Billiard tables for physicists, rectangular 191 Billiard tables for physicists, Russian 193—196 Billiard tables for physicists, specular reflection and 191 Binary expansion 17—18 Binary sequences 16 bits 16 Black — Scholcs equation 102 Black, Fischer 102 Bohigas, Oriol 198 211—222 222 Bohr, Harald 130 142 Bohr, Niels 49 130 187 190 227 Boltzmann, Ludvvig 173 Bolyai 203 Borderlands between classical and quantum mechanics see “Semidassical limit” Bosons 239 Bourbaki, Charles 144—145 Bourbaki, Nicholas 144 Boxcar 160—161 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 75—76 Calendars 46 California Polytechnic State University 234 Cambridge University 162 163 Cantor, Georg 22 125 135 215 Card shuffling 245 248—259 Card shuffling, perfect 249 Card shuffling, riffle 248 cardinal number 22 Cardinality 22—23 Cardona, Girolamo 73 215 Cauchy, Augustin — Louis 69 Cavley, Arthur 169—170 257 Celestial mechanics 48 Central limit theorem 100—104 Central limit theorem, first appearance of 236 CERES 39 Chaos 189 Chaos, quantum see “Quantum chaos” Chaotic dynamical systems 189—190 193—195 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 214—226 Cohen, Paul J. 230—231 Coin-tossing, repeated 100—104 137—138 151—152 Coincidence 225—227 College de France 229 Colors 166—169 Columbia University 141 152 Combinations 246 Combinatorial enumeration 247 Combinatorial optimization 247 Combinatorics 223 245—247 Commutative multiplication 169n 230 Complex analysis 69 76 Complex conjugates 176—177 complex numbers 69 70—73 Complex numbers, geometric representation of 75 Complex plane 73—76 110 Complex power 78—81 Complexity theory 149 Composite numbers 12—13 Composite numbers, Cramer 137—139 Compounding continuously 35 78—79 Comptes Rendus 95 Computation, limits of 132—134 Computational complexity 149 Computers 123 128 149—151 Computers, algorithms and 249—250 Computers, asymptotic analysis and 255 Computers, permutations and 247—249 Computers, physics of 228 Computers, TeX and 257 Comrie, L.J. 140 Conlocal ellipse 193 Connes, Alain 228—231 262 265 Connes, described 229 Constant curvature 67—68 Constant of motion 193 Constructive numbers 70—71 Continuum Hypothesis 215 Convergent Series 53 Conway, J. 134 coordinates 68 Copernicus 50 Coram, Marc 226—227 Correlation 157—160 Correspondence 8—9 Correspondence principle 187 190 227 Countabiliry 22 Courant Institute of Mathematical Sciences 3—6 243 245 261—263 Cramer composites 137—139 Cramer primes 137—139 151 Cramer, Carl Harald 136—139 151 153 Cramer, described 136—137 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) 129—130 Critical line, percentage of zeta zeros on 131 151 Critical strip 89—92 Critical strip, de la Vallee — Poussin 119—120 Cryptography 17—18 Cubic polynomials 72—73 Curvature 67—68 207 CYCLE 251—253 Dalton, John 49 Dartmouth College 234 264 Darwin, Charles 63 Dcligne, Pierre 220 de Branges dc Bourcia, Louis 262—263 265 de la Vallee — Poussin 106—110 265 de la Vallee — Poussin, described 106—107 de la Vallee — Poussin, Prime Number Theorem and 106—107 129 139 de la Vallee — Poussin, Riemann's zeta function and 107—110 119—120 De Moivre, Abraham 236 Death of a Salesman (Miller) 134—135 Decibel system 34 Dedckind cuts 116 Dedckind zeta function 93 116 143 Dedckind, described 115 Dedckind, Richard 93 115—126 Deficient number 12 Deift, described 241—243 Deift, integrable systems and 243 Deift, mathematics of permutations and 255—260 Deift, Percy 233 255 262 Deift, Tracy — Widom distribution and 240—246 Denninger, Chrisroph 262 density 41 Denumcrability 22 Descartes, Rene (Cartesian philosophy), 32n 68 122 Description of Egypt (Fourier) 82 Diaconis, "cost of close" and 225—227 Diaconis, described 221 Diaconis, magic and 221—225 Diaconis, Persi 221—227 243—244 246 249 Differential equations 238 Differential geometry 39 Digger, x 166 195 Digital communication 16—18 Digital cryptography 17—18 DIMENSION 202n Dimension of a space 229—230 Diophantine problems 144 Dirichlet L-scries 61 109—110 137 143 219 Dirichlet zeta function 116 Dirichlet, described 59 Dirichlet, Gustav 45 47 265 Dirichlet, infinity of primes and 59—62 108—110 Dirichlet, prime distribution analyzer of 77 80 81 Dirichlet, Riemann and 65—69 76—78 84 Discrete mathematics 223 Disquisitiones anthmeticae (Gauss) 38—39 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 193—195 Dynamical systems, simplest 191—193 Dyson — Montgomery — Odlyzko Law 180—185 188 Dyson, described 162—164 Dyson, Freeman 263 Dyson, Hamiltonians and 170—177 180 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 34—35 78—79 e: The Story of a Number (Maor) 34h Edwards, H. 140 Eigenvalues 175—177 Eigenvalues, of a random matrix 258 Eigenvalues, on the edge 236—240 Eigenvalues, Tracy — Wisdom distributions and 234—241 245—246 Eigenvalues, zeta zeros and 175—185 199—200 210—221 220 225—229 232 Eigenvectors 175—176 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 204—205 Encke Gap 40 Encke, Johann 40—41 encrypted messages 17—18 Ensemble behavior 174—175 Enumeration 246—247 Eratosthenes 15 Eratosthenes,"sieve" of 15—16 24 Erdoes, Taul 141 Ergodic motion 194—195 Ergodicity 190 Error correction 17 Error term 119—120 126—127 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 68 203—204 Euclid, proof of the infinitude of primes 18—20 21 24 28 50 51 60 Euler equations 47 Euler factorization 55—57 61
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