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Odifreddi P., Sangalli A., Dyson F. Ч The Mathematical Century: The 30 Greatest Problems of the Last 100 Years
Odifreddi P., Sangalli A., Dyson F. Ч The Mathematical Century: The 30 Greatest Problems of the Last 100 Years

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Ќазвание: The Mathematical Century: The 30 Greatest Problems of the Last 100 Years

јвторы: Odifreddi P., Sangalli A., Dyson F.


The twentieth century was a time of unprecedented development in mathematics, as well as in all sciences: more theorems were proved and results found in a hundred years than in all of previous history. In The Mathematical Century , Piergiorgio Odifreddi distills this unwieldy mass of knowledge into a fascinating and authoritative overview of the subject. He concentrates on thirty highlights of pure and applied mathematics. Each tells the story of an exciting problem, from its historical origins to its modern solution, in lively prose free of technical details.

Odifreddi opens by discussing the four main philosophical foundations of mathematics of the nineteenth century and ends by describing the four most important open mathematical problems of the twenty-first century. In presenting the thirty problems at the heart of the book he devotes equal attention to pure and applied mathematics, with applications ranging from physics and computer science to biology and economics. Special attention is dedicated to the famous ''23 problems'' outlined by David Hilbert in his address to the International Congress of Mathematicians in 1900 as a research program for the new century, and to the work of the winners of the Fields Medal, the equivalent of a Nobel prize in mathematics.

This eminently readable book will be treasured not only by students and their teachers but also by all those who seek to make sense of the elusive macrocosm of twentieth-century mathematics.

язык: en

–убрика: ћатематика/

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

ed2k: ed2k stats

√од издани€: 2004

 оличество страниц: 223

ƒобавлена в каталог: 08.10.2014

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ѕредметный указатель
Curves: theory of distributions and      54Ч55
Cusano, Nicola      59
Cyclic groups      76
Cycloids      48
cylinders      105
da Vinci, Leonardo      49
Dantzig, George      121Ч123
Dartmouth College      149
Darwin, Charles      xi
Davis, Martin      148
de Caritat, Marie Jean Antoine Nicolas      95
de Fermat, Pierre      181
de Fermat, Pierre, analytic geometry and      45
de Fermat, Pierre, derivatives and      68Ч69
de Fermat, Pierre, infinitesimals and      59Ч62
de Fermat, Pierre, perfect numbers and      166Ч168
de Fermat, Pierre, prime numbers and      139Ч140
de Fermat, Pierre, probability theory and      116
de Giorgi, Ennio      50 184
de Laplace, Pierre Simon      xi 19 130
de Malves, Jean Paul de Gua      68
de Maupertuis, Pierre Louis      49
de Morgan, Augustus      34 155
de Saussure, Ferdinand      125Ч126
Debreu, Gerard      124 185
Decision problem      145Ч148
Dedekind, Richard      34Ч35 46
Deep Blue      151
Deep Thought      151
Dehn, Max      31 134 165
Deligne, Pierre      171 183
Deoxyribonucleic acid (DNA)      97 137Ч138 185
Derivatives, general equilibrium theory and      122Ч125
Derivatives, singularity theory and      68Ч71
Descartes, Rene      52
Descartes, Rene, analysis and      9 45
Descartes, Rene, methodology of      xiЧxvi
Descartes, Rene, real numbers and      34
Diamond, Fred      87
Diffeomorphisms      69
Differential topology      56Ч59
Dimensional space, Banach spaces and      114Ч116
Dimensional space, catastrophes and      69Ч71
Dimensional space, classification and      78Ч82
Dimensional space, crystallography and      xiv-xv 88 98Ч104 182
Dimensional space, Euler characteristic and      172Ч173
Dimensional space, exotic spaces and      57Ч59 136Ч137
Dimensional space, fixed-point theorem and      37Ч39
Dimensional space, fractals and      144Ч145 159Ч164
Dimensional space, functional analysis and      112Ч116
Dimensional space, Hilbert space and      113Ч116
Dimensional space, hyperbolic geometry and      43Ч47
Dimensional space, Kepler's problem and      88Ч91
Dimensional space, knot theory and      132Ч138
Dimensional space, lattice configurations and      87Ч91
Dimensional space, Lebesgue measure and      29Ч33
Dimensional space, Lie groups and      73Ч75
Dimensional space, manifolds and      56Ч59
Dimensional space, Poincare conjecture and      28 174Ч176
Dimensional space, polyhedra and      27Ч28
Dimensional space, topology and      37Ч39 56Ч59 see
Diophantine equations      147Ч148 179 182
Diophantus      26 82 84
Dirac, Paul      54
Dirichlet, Peter Lejeune      52Ч53 83
Discours sur l'origine de l'inegalite parmi les hommes (Rousseau)      109
Dissipative structures      71
Donaldson, Simon      57Ч58 136Ч137 184
Douady, Adrien      163
Douglas, Jessie      50 183
Dynamical systems theory      128Ч132 185
Dynamical systems theory, chaos theory and      71 143Ч144 151Ч154
Dynamical systems theory, computers and      143
Dynamical systems theory, instability and      152
Dyson, Freeman      xiЧxvi
e      41Ч42
Earth      129 152
Economics      37 96 121 185
Economics, general equilibrium theory and      122Ч125
Edmonds, Jack      176
Egyptians      92 98
Eilenberg, Samuel      18 184
Einstein, Albert      93Ч94 107
Electoral systems      95Ч96
Electromagnetism      107Ч108
Electronic Numerical Integrator and Calculator (Eniac)      142
Electroweak theory      58 75 185
Elementary proofs      172
Elements (Euclid)      169
Elements of Mathematics (Bourbaki group)      15
Ellipsoid method      177
Elliptic curves      85 137 182
Elliptic curves, singularity theory and      66Ч71
Elliptic operators      55
Elo points      150
Enriques Ч Kodaira theorem      82
Enriques, Federigo      81
Entscheiduugsproblem (decision problem)      145Ч148
Enzymes      97
Equations: abstract groups      73
Equations: action      49
Equations: arc of ellipse      66
Equations: associative property and      73
Equations: Diophantine      147Ч148 179 182
Equations: Dirichlet function      53
Equations: Euler's      42
Equations: Fermat's last theorem and      83 85Ч87
Equations: formulas and      71Ч72
Equations: fractal dimension      161
Equations: functional analysis      113
Equations: general theory of integral      112
Equations: grammatical productions      126
Equations: greatest common divisor      147
Equations: higher-degree      72
Equations: infinitesimals and      60Ч61
Equations: knot theory and      135
Equations: limit and      61
Equations: Maxwell's      107
Equations: Mertens      159
Equations: parabola      60
Equations: second-degree      71
Equations: Yang Ч Mills      75
Equilibrium theory      122Ч125 185
Erdos, Paul      172 184
Escher, Maurits      102Ч103
Etruscan Venus (Cox and Francis)      144
Euclid      9 15 168Ч169 181 see
Eudoxus      31
Euler's constant      43
Euler, Leonhard, analysis and      52
Euler, Leonhard, calculus of variation and      48
Euler, Leonhard, prime numbers and      139Ч140 169
Euler, Leonhard, principle of minimal action and      49
Euler, Leonhard, surface characteristics and      172Ч173
Euler, Leonhard, theory of congruences and      167Ч168
Euler, Leonhard, three-body problem and      129Ч130
Euler, Leonhard, transcendental numbers and      41Ч42
Exotic structures      57Ч59 136Ч137
Expected value      116Ч117
Expert Systems      149
Exponential time      180
Extensionality principle      10 22
Factorization      178Ч180
Faltings, Gerd      171 184
Faraday, Michael      xi
Farey, John      64
Fatou, Pierre      161Ч162
Fedorov, E.S.      98Ч99
Feit, Walter      77
Fermat's last theorem      26Ч27 43
Fermat's Last Theorem, elementary proof and      172
Fermat's Last Theorem, Hilbert's tenth problem and      147Ч148
Fermat's Last Theorem, progress on      82Ч87
Fermat's Last Theorem, Wiles and      87 171
Ferrari, Ludovico      72
Feynman integrals      137
Fields      33Ч36
Fields medal      xiii xvi
Fields Medal, Atiyah and      55 183
Fields Medal, Baker and      43 147 183
Fields Medal, Bombieri and      50 104 183
Fields Medal, Borcherds and      137 184
Fields Medal, Bourgain and      115 184
Fields Medal, Cohen and      65 183
Fields Medal, Connes and      115 184
Fields Medal, Deligne and      171 183
Fields Medal, Donaldson and      57 184
Fields Medal, Douglas and      50 183
Fields Medal, Faltings and      184
Fields Medal, Freedman and      81 184
Fields Medal, Gowers and      115 184
Fields Medal, Grothendieck and      115 171 183
Fields Medal, Hironaka and      82 183
Fields Medal, Hoermander and      55 183
Fields Medal, Jones and      115 135 184
Fields Medal, Kodaira and      81 183
Fields Medal, Kontsevich and      135 184
Fields Medal, McCullen and      163 184
Fields Medal, Milnor and      57 183
Fields Medal, Mori and      82 184
Fields Medal, Novikov and      57 104 176 183
Fields Medal, Roth and      41 183
Fields Medal, Schwartz and      55 115 183
Fields Medal, Selberg and      172 183
Fields Medal, Serre and      175 183
Fields Medal, significance of      4Ч6
Fields Medal, Smale and      124 174Ч175 183
Fields Medal, Thom and      176 183
Fields Medal, Thompson and      77 183Ч184
Fields Medal, Thurston and      80 184
Fields Medal, Wiles and      87
Fields Medal, Witten and      56 136 184
Fields Medal, Yau and      82 184
Fields Medal, Yoccoz and      132 163 184
Fields Medal, Zelmanov and      77 184
Fields, John Charles      5
Finite additivity      29
Finite automata      127
Finite fields      35
Finiteness theorem      175
Fischer Ч Griess Monster      136Ч137
Fischer, Ernst      114
Fixed-points      23 37Ч39 124
Fluxions      60Ч61
Fontana, Niccolo      72
Ford, Gerald      95
formulas      52
Foundations of Geometry (Hilbert)      30 46
Four-color theorem      142 154Ч159 181
Fourier sum      131
Fourier transform      xv
Fourier, Joseph      52
Fracnkel, Abraham      13Ч14
Fractals attractors and      162Ч163
Fractals attractors and, complex numbers and      162
Fractals attractors and, computers and      144Ч145 159Ч164
Fractals attractors and, self-similarity and      160Ч161
Fractions      41
Francis, George      144
Frechet, Maurice      113
Freedman, Michael      57Ч58 81 175 184
Frege, Gottlob      10Ч11 140Ч141
Frey, Gerhard      86Ч87
Functions      xiii
Functions, analysis and      112Ч116
Functions, calculus of variations      47Ч51
Functions, categories and      17Ч21
Functions, complexity theory and      176Ч180
Functions, comprehension principle and      22
Functions, continuous      39
Functions, delta      53Ч54
Functions, Dirichlet's definition of      52Ч53
Functions, elliptic      85 137
Functions, extensionality principle and      22
Functions, fixed point and      23 37Ч39
Functions, formulas and      52
Functions, general equilibrium theory and      122Ч125
Functions, Hamiltonian      49
Functions, Heaviside      53Ч54
Functions, Hilbert space and      113Ч114
Functions, index theorem and      55Ч56
Functions, lambda calculus and      21 23Ч24
Functions, Lebesgue measure and      29Ч33
Functions, modular      86Ч87
Functions, Moebius      182
Functions, monotonic      29 39
Functions, naive theory of      21Ч22
Functions, polynomial time and      176Ч180
Functions, principle of minimal action      49
Functions, quantum axioms and      112Ч116
Functions, Riemann integral and      31Ч32
Functions, Riemann Zeta      170Ч172
Functions, Russell's paradox and      22Ч23
Functions, semicontinuous      39
Functions, theory of distributions and      52Ч56
Fundamental groups      173Ч174
Galileo      48
Galois fields      36
Galois, Evariste      35 72Ч73 76
Game theory      93 185
Game theory, Borel and      110
Game theory, gambling and      116Ч119
Game theory, general equilibrium theory and      123Ч124
Game theory, Hobbes and      108Ч109
Game theory, minimax theorem and      110Ч112
Game theory, Nash equilibrium and      111
Game theory, perfect information and      110
Game theory, prisoner's dilemma and      111
Game theory, purpose of      108
Game theory, Rousseau and      109
Game theory, Zermelo and      109Ч110
Game theory, zero-sum games and      110Ч111
Gauss, Carl Friedrich      44
Gauss, Carl Friedrich, complex numbers and      34Ч35
Gauss, Carl Friedrich, curves and      105Ч106
Gauss, Carl Friedrich, lattice configurations and      88 90
Gauss, Carl Friedrich, probability theory and      118
Gauss, Carl Friedrich, quadratic reciprocity and      147
Gelfand, Alexandr      43
Gell-Mann, Murray      75 185
General equilibrium theory      93 122Ч125 185
General theory of integral equations      112
Gentzen, Gerhard      47
Geodesics      105
Geography      45
Geometry      9 11
Geometry, algebra and      45Ч46 171Ч172
Geometry, analytic      45Ч47
Geometry, ancient Greeks and      27Ч28
Geometry, classification and      78Ч82
Geometry, curvature and      104Ч108
Geometry, discrete      87Ч91
Geometry, four-color problem and      142 154Ч159 181
Geometry, fractals and      144Ч145 159Ч164
Geometry, functional analysis and      112Ч116
Geometry, hyperbolic      43Ч47 80Ч82
Geometry, infinitesimals and      59Ч63
Geometry, Kepler's problem and      87Ч91
Geometry, lattice configurations and      87Ч91
Geometry, Lebesgue measure and      29Ч33
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