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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
"Computing Machines and Intelligence" (Turing)      149
"Foundations of Mathematics for the Working Mathematician" (Bourbaki group)      15
"Invisible hand"      122Ч123
"Publish or perish"      2
$\delta$ function      53Ч54
$\gamma$ (Euler's constant)      43
Abel, Niels      72
Abelian groups      73
Abstraction      1 72Ч73
Abstraction, categories and      18
Abstraction, fields and      33Ч36
Abstraction, functions and      21Ч24
Abstraction, Lebesgue measure and      29Ч33
Abstraction, set theory and      10Ч24
Abstraction, topology and      37Ч39
Adian, S.I.      77
Aeneid      47
Airplanes      48
Alexander the Great      132Ч133
Alexander, James      134Ч135 138
Algebra automorphisms      137
Algebra automorphisms, Boolean      140Ч142 182
Algebra automorphisms, fields and      33Ч36
Algebra automorphisms, finite groups and      71Ч77
Algebra automorphisms, fundamental theorem of      34Ч35
Algebra automorphisms, geometry and      45Ч46 171Ч172
Algebra automorphisms, grammatical productions and      128
Algebra automorphisms, invariants and      134Ч138
Algebra automorphisms, knot theory and      137
Algebra automorphisms, natural numbers      33Ч34
Algebra automorphisms, singularity theory and      66Ч71
Algebra automorphisms, structures and      16Ч17
Algebra automorphisms, transcendental numbers      39Ч43
Algebra automorphisms, von Neumann operators      115
Algebraic closure      36
Algebraic extension      35
Algebraic manifolds      81Ч82
Algorithms' complexity theory and      176Ч180
Algorithms' complexity theory and, computers and      145Ч148
Algorithms' complexity theory and, decision problem and      145Ч148
Algorithms' complexity theory and, exponential time and      180
Algorithms' complexity theory and, factorization and      178Ч180
Algorithms' complexity theory and, polynomial time and      176Ч180
Algorithms' complexity theory and, simplex method and      177
Algorithms' complexity theory and, Turing's definition of      176
Alhambra      98
Alternating groups      76
Analysis      9 11 182
Analysis, dynamical systems theory and      128Ч132
Analysis, fixed-point theorem and      37Ч39
Analysis, game theory and      108Ч112
Analysis, infinitesimals and      59Ч63
Analysis, knot theory and      132Ч138
Analysis, Lebesgue measure and      29Ч33
Analysis, nonstandard      62Ч63
Analysis, quantum axioms and      112Ч116
Analysis, Riemann hypothesis and      168Ч172
Analysis, set theory and      10Ч14
Analysis, social choice and      108Ч112
Analysis, theory of distributions and      52Ч56
Analytic geometry      45Ч47
Appel, Kenneth      142 157Ч158
Arabs      34 98
Archimedes      31 59
Area      29Ч33
Aristotelian logic      20
Arithmetic      9 11
Arithmetic (Diophantus)      26
Arithmetic, modular      35 179 182
Arnol'd, Vladimir      131Ч132
Arrow, Kenneth      96 124 185
Ars Conjectandi (Bernoulli)      117
artificial intelligence      141 185
Artificial intelligence, chess and      149Ч151
Artificial intelligence, exaggerations of      148Ч149
Artificial intelligence, expert systems and      149
Artificial intelligence, Shannon and      150
Artificial intelligence, Turing test and      149Ч151
Artin, Emil      171
Aspect, Alain      95
Associative property      73
Astronomy      45
Astronomy, orbital motion and      128Ч132 151Ч154
Astronomy, three-body problem and      129Ч131
Atiyah, Michael      55 176 183
Atomic bomb      142
atoms      xii 1
Atoms, complex numbers and      xiiiЧxiv
Atoms, Lie groups and      74Ч77
Attractors      152 162Ч163
Augustine      167
Austrians      109
Automata      127
Automatic Computing Engine (ACE)      142
Automorphisms      137
Axioms      107
Axioms, categories and      19Ч20
Axioms, computers and      142
Axioms, decision problem and      145Ч148
Axioms, hyperbolic geometry and      43Ч47
Axioms, incompleteness theorem and      13Ч14
Axioms, probability theorem and      116Ч119
Axioms, quantum mechanics and      112Ч116
Axioms, set theory and      65Ч66
Babbage, Charles      150
Babylonians      71 83 92
Bacon, Francis      xiЧxvi
Baire, Rene      53
Baker, Alan      43 147Ч148 183
Banach spaces      114Ч116
Banach, Stefan      33 39 114
Barycenter      130
Bayes's law      118
Bayes, Thomas      118
Bell, John      94Ч95
BELLE program      150Ч151
Beltrami, Eugenio      44
Berger, Robert      102
Berkeley, Bishop      60
Bernoulli, Daniel      117
Bernoulli, Jacques      117
Bernoulli, Jean      48
Bernstein, Serge      55
Bible, the      98
Bieberbach, Ludwig      102
Bifurcations      69Ч71
Bohr, Niels      93
Bolyai, Janos      30Ч31 44
Bolzano, Bernhard      63
Bombelli, Raffaele      34
Bombieri, Enrico      50 104 183
Boolean algebra      140Ч142 182
Boone, William      128
Borcherds, Richard      137 184
Borel, Emile      110
Botvinnik, Mikhail      150
Bourbaki group      xiiЧxiii
Bourbaki group, categories and      18Ч19
Bourbaki group, philosophy of      15Ч17
Bourbaki group, structure and      15Ч17
Bourgain, Jean      115 184
Brachistochrone      48
Bravais, Auguste      99
Breuil, Christophe      87
Brouwer, Luitzen      20
Brouwer, Luitzen, fixed-point theorem and      37Ч39 124
Brownawell, Dale      180
Burnside conjectures      77 182
Butterfly effect      143Ч144
Calabi Ч Yau manifolds      82 137
Calculus      182
Calculus, dynamical systems theory and      128Ч132
Calculus, functional analysis and      112Ч116
Calculus, infinitesimal      28 59Ч63
Calculus, lambda      21 23Ч24 185
Calculus, maxima/minima and      47Ч51
Calculus, Steiner problem and      179Ч180
Calculus, tensor      104Ч108
Calculus, Turing and      141
Calculus, variations and      47Ч51
Cantor, Georg      181
Cantor, Georg, decision problem and      146Ч147
Cantor, Georg, dimension and      37
Cantor, Georg, infinity and      63Ч66
Cantor, Georg, number theory and      46
Cantor, Georg, set theory and      10Ч15
Cantor, Georg, transcendental numbers and      41
Capitalism      120 125
Cardano, Gerolamo      34 72 116
Cartan, Elie      74
Carter, Jimmy      95
Cartesian thought      xiЧxvi
Castelnuovo, Guido      81
Catastrophe theory      69Ч71
Categories      17Ч21
Categories for the Working Mathematician (MacLane)      20
Cauchy, Augustin      61
Cavalieri, Bonaventura      60
Cayley, Arthur      72
Celestial Mechanics (Laplace)      130
Chaos theory      71
Chaos theory, attractors and      152 162Ч163
Chaos theory, butterfly effect and      143Ч144
Chaos theory, computers and      143Ч144 151Ч154
Chaos theory, instability and      152
Characteristics      36 40
Chess      149Ч151
Chevalley, Claude      76
Chomsky, Noam      126Ч127
Chromodynamics      58
Church, Alonzo      21 23Ч24 128 145Ч147
circles      27Ч28 31
Circles, fixed-point theorem and      38
Circles, hyperbolic geometry and      44
Circles, infinitesimals and      59
Circles, Kepler's problem and      87Ч91
Circles, lattice onfigurations and      87Ч91
Circles, Lebesgue measure and      33
Circles, Queen Dido and      47
Circles, tensor calculus and      104Ч108
City of God, The (Augustine)      167
Classes      11Ч12
Classes, catastrophes and      69Ч71
Classes, categories and      17Ч21
Classes, dimensional space and      78Ч82
Classes, elliptic curves and      66Ч71
Classes, finite groups and      71Ч77
Classes, P = NP problem and      176Ч180
Cobham, A.      176
Cobordism theory      55 176
Codimension      70
Cohen, Paul      65Ч66 183
Communism      120
Compactness      38
Complete metric spaces      39
Complete partial orders      39
complex numbers      xiiiЧxiv
Complex numbers, fractals and      162
Complex numbers, introduction of      34Ч35
Complex numbers, transcendental numbers and      42
Complexity theory      176Ч180 185
Comprehension principle      10Ч12 22
Computers ACE      142
Computers ACE, algorithms and      145Ч148
Computers ACE, artificial intelligence and      141 148Ч151 185
Computers ACE, atomic bomb and      142
Computers ACE, Babbage and      150
Computers ACE, beginnings of      140Ч141
Computers ACE, Boole and      140Ч141
Computers ACE, calculating power of      142Ч143
Computers ACE, chaos theory and      43Ч44 151Ч154
Computers ACE, CRAY      159
Computers ACE, cryptography and      178Ч180
Computers ACE, dynamic systems and      143
Computers ACE, ENIAC      142
Computers ACE, exaggeration of      139Ч140
Computers ACE, expert systems and      149
Computers ACE, four-color theorem and      142 154Ч159
Computers ACE, fractals and      144Ч145 159Ч164
Computers ACE, functions and      21Ч24
Computers ACE, graphics and      144Ч145 152Ч153 156Ч164
Computers ACE, languages and      127Ч128 146
Computers ACE, mindless use of      139Ч140
Computers ACE, polynomial time and      176Ч177
Computers ACE, prime number searches and      139
Computers ACE, proofs and      142 154Ч159
Computers ACE, topology and      39
Computers ACE, Turing and      141Ч142 149Ч151 185
Condorcet, Marquis of      95
Conic sections      46 52
Conic sections, algebraic curves and      66
Conic sections, elliptic curves and      66Ч71
Connectives      145
Connes, Alain      115 184
Conrad, Brian      87
Constructible numbers      40Ч41 65
Context-free language      127Ч128
Context-sensitive language      127
Continuous groups      xiv 73
Continuum Hypothesis      65Ч66 181Ч182
Contractable compact complexes      39
Convergence      123
Convexity      38
Conway, John      63 91 137 182
Cook, Stephen      177 180 182 185
Coordinate systems      45 108
Coordinate systems, functional analysis and      112Ч116
Coordinate systems, Lie groups and      72Ч77
Corank      70
Countable additivity      119
Cournot, Antoine-Augustin      122
Cours de linguistique generate (Saussure)      125
Cox, Donna      144
CRAY supercomputer      159
Creation of the World, The (Judaeus)      167
Crick, Francis      97 185
Cryptography      178Ч180
Crystallography      xivЧxv 88 182
Crystallography, symmetry groups and      98Ч104
Cubics      66
Curbastro, Gregorio Ricci      107
Curie, Marie      xii
Curves: algebraic      66Ч71
Curves: attractors and      152Ч153
Curves: boundary problems and      142 154Ч159
Curves: calculus ofvariations and      47Ч51
Curves: catastrophe theory and      69Ч71
Curves: chaos theory and      151Ч154
Curves: classification and      81
Curves: corank and      70
Curves: derivatives and      68Ч71
Curves: elliptic      66Ч71 85 137 182
Curves: Fermat's last theorem and      82Ч87
Curves: fixed-point theorem and      37Ч39
Curves: fractals and      144Ч145 159Ч164
Curves: Gauss and      105Ч106
Curves: minimal surfaces and      47Ч51
Curves: Newton's definition and      105
Curves: probability theory and      118Ч119
Curves: tensor calculus and      104Ч108
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