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



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

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

Àííîòàöèÿ:

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.



ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 2004

Êîëè÷åñòâî ñòðàíèö: 223

Äîáàâëåíà â êàòàëîã: 08.10.2014

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
"Computing Machines and Intelligence" (Turing)      149
"Foundations of Mathematics for the Working Mathematician" (Bourbaki group)      15
"Invisible hand"      122—123
"Publish or perish"      2
$\delta$ function      53—54
$\gamma$ (Euler's constant)      43
Abel, Niels      72
Abelian groups      73
Abstraction      1 72—73
Abstraction, categories and      18
Abstraction, fields and      33—36
Abstraction, functions and      21—24
Abstraction, Lebesgue measure and      29—33
Abstraction, set theory and      10—24
Abstraction, topology and      37—39
Adian, S.I.      77
Aeneid      47
Airplanes      48
Alexander the Great      132—133
Alexander, James      134—135 138
Algebra automorphisms      137
Algebra automorphisms, Boolean      140—142 182
Algebra automorphisms, fields and      33—36
Algebra automorphisms, finite groups and      71—77
Algebra automorphisms, fundamental theorem of      34—35
Algebra automorphisms, geometry and      45—46 171—172
Algebra automorphisms, grammatical productions and      128
Algebra automorphisms, invariants and      134—138
Algebra automorphisms, knot theory and      137
Algebra automorphisms, natural numbers      33—34
Algebra automorphisms, singularity theory and      66—71
Algebra automorphisms, structures and      16—17
Algebra automorphisms, transcendental numbers      39—43
Algebra automorphisms, von Neumann operators      115
Algebraic closure      36
Algebraic extension      35
Algebraic manifolds      81—82
Algorithms' complexity theory and      176—180
Algorithms' complexity theory and, computers and      145—148
Algorithms' complexity theory and, decision problem and      145—148
Algorithms' complexity theory and, exponential time and      180
Algorithms' complexity theory and, factorization and      178—180
Algorithms' complexity theory and, polynomial time and      176—180
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      128—132
Analysis, fixed-point theorem and      37—39
Analysis, game theory and      108—112
Analysis, infinitesimals and      59—63
Analysis, knot theory and      132—138
Analysis, Lebesgue measure and      29—33
Analysis, nonstandard      62—63
Analysis, quantum axioms and      112—116
Analysis, Riemann hypothesis and      168—172
Analysis, set theory and      10—14
Analysis, social choice and      108—112
Analysis, theory of distributions and      52—56
Analytic geometry      45—47
Appel, Kenneth      142 157—158
Arabs      34 98
Archimedes      31 59
Area      29—33
Aristotelian logic      20
Arithmetic      9 11
Arithmetic (Diophantus)      26
Arithmetic, modular      35 179 182
Arnol'd, Vladimir      131—132
Arrow, Kenneth      96 124 185
Ars Conjectandi (Bernoulli)      117
artificial intelligence      141 185
Artificial intelligence, chess and      149—151
Artificial intelligence, exaggerations of      148—149
Artificial intelligence, expert systems and      149
Artificial intelligence, Shannon and      150
Artificial intelligence, Turing test and      149—151
Artin, Emil      171
Aspect, Alain      95
Associative property      73
Astronomy      45
Astronomy, orbital motion and      128—132 151—154
Astronomy, three-body problem and      129—131
Atiyah, Michael      55 176 183
Atomic bomb      142
atoms      xii 1
Atoms, complex numbers and      xiii—xiv
Atoms, Lie groups and      74—77
Attractors      152 162—163
Augustine      167
Austrians      109
Automata      127
Automatic Computing Engine (ACE)      142
Automorphisms      137
Axioms      107
Axioms, categories and      19—20
Axioms, computers and      142
Axioms, decision problem and      145—148
Axioms, hyperbolic geometry and      43—47
Axioms, incompleteness theorem and      13—14
Axioms, probability theorem and      116—119
Axioms, quantum mechanics and      112—116
Axioms, set theory and      65—66
Babbage, Charles      150
Babylonians      71 83 92
Bacon, Francis      xi—xvi
Baire, Rene      53
Baker, Alan      43 147—148 183
Banach spaces      114—116
Banach, Stefan      33 39 114
Barycenter      130
Bayes's law      118
Bayes, Thomas      118
Bell, John      94—95
BELLE program      150—151
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      69—71
Bohr, Niels      93
Bolyai, Janos      30—31 44
Bolzano, Bernhard      63
Bombelli, Raffaele      34
Bombieri, Enrico      50 104 183
Boolean algebra      140—142 182
Boone, William      128
Borcherds, Richard      137 184
Borel, Emile      110
Botvinnik, Mikhail      150
Bourbaki group      xii—xiii
Bourbaki group, categories and      18—19
Bourbaki group, philosophy of      15—17
Bourbaki group, structure and      15—17
Bourgain, Jean      115 184
Brachistochrone      48
Bravais, Auguste      99
Breuil, Christophe      87
Brouwer, Luitzen      20
Brouwer, Luitzen, fixed-point theorem and      37—39 124
Brownawell, Dale      180
Burnside conjectures      77 182
Butterfly effect      143—144
Calabi — Yau manifolds      82 137
Calculus      182
Calculus, dynamical systems theory and      128—132
Calculus, functional analysis and      112—116
Calculus, infinitesimal      28 59—63
Calculus, lambda      21 23—24 185
Calculus, maxima/minima and      47—51
Calculus, Steiner problem and      179—180
Calculus, tensor      104—108
Calculus, Turing and      141
Calculus, variations and      47—51
Cantor, Georg      181
Cantor, Georg, decision problem and      146—147
Cantor, Georg, dimension and      37
Cantor, Georg, infinity and      63—66
Cantor, Georg, number theory and      46
Cantor, Georg, set theory and      10—15
Cantor, Georg, transcendental numbers and      41
Capitalism      120 125
Cardano, Gerolamo      34 72 116
Cartan, Elie      74
Carter, Jimmy      95
Cartesian thought      xi—xvi
Castelnuovo, Guido      81
Catastrophe theory      69—71
Categories      17—21
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      152 162—163
Chaos theory, butterfly effect and      143—144
Chaos theory, computers and      143—144 151—154
Chaos theory, instability and      152
Characteristics      36 40
Chess      149—151
Chevalley, Claude      76
Chomsky, Noam      126—127
Chromodynamics      58
Church, Alonzo      21 23—24 128 145—147
circles      27—28 31
Circles, fixed-point theorem and      38
Circles, hyperbolic geometry and      44
Circles, infinitesimals and      59
Circles, Kepler's problem and      87—91
Circles, lattice onfigurations and      87—91
Circles, Lebesgue measure and      33
Circles, Queen Dido and      47
Circles, tensor calculus and      104—108
City of God, The (Augustine)      167
Classes      11—12
Classes, catastrophes and      69—71
Classes, categories and      17—21
Classes, dimensional space and      78—82
Classes, elliptic curves and      66—71
Classes, finite groups and      71—77
Classes, P = NP problem and      176—180
Cobham, A.      176
Cobordism theory      55 176
Codimension      70
Cohen, Paul      65—66 183
Communism      120
Compactness      38
Complete metric spaces      39
Complete partial orders      39
complex numbers      xiii—xiv
Complex numbers, fractals and      162
Complex numbers, introduction of      34—35
Complex numbers, transcendental numbers and      42
Complexity theory      176—180 185
Comprehension principle      10—12 22
Computers ACE      142
Computers ACE, algorithms and      145—148
Computers ACE, artificial intelligence and      141 148—151 185
Computers ACE, atomic bomb and      142
Computers ACE, Babbage and      150
Computers ACE, beginnings of      140—141
Computers ACE, Boole and      140—141
Computers ACE, calculating power of      142—143
Computers ACE, chaos theory and      43—44 151—154
Computers ACE, CRAY      159
Computers ACE, cryptography and      178—180
Computers ACE, dynamic systems and      143
Computers ACE, ENIAC      142
Computers ACE, exaggeration of      139—140
Computers ACE, expert systems and      149
Computers ACE, four-color theorem and      142 154—159
Computers ACE, fractals and      144—145 159—164
Computers ACE, functions and      21—24
Computers ACE, graphics and      144—145 152—153 156—164
Computers ACE, languages and      127—128 146
Computers ACE, mindless use of      139—140
Computers ACE, polynomial time and      176—177
Computers ACE, prime number searches and      139
Computers ACE, proofs and      142 154—159
Computers ACE, topology and      39
Computers ACE, Turing and      141—142 149—151 185
Condorcet, Marquis of      95
Conic sections      46 52
Conic sections, algebraic curves and      66
Conic sections, elliptic curves and      66—71
Connectives      145
Connes, Alain      115 184
Conrad, Brian      87
Constructible numbers      40—41 65
Context-free language      127—128
Context-sensitive language      127
Continuous groups      xiv 73
Continuum Hypothesis      65—66 181—182
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      112—116
Coordinate systems, Lie groups and      72—77
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      178—180
Crystallography      xiv—xv 88 182
Crystallography, symmetry groups and      98—104
Cubics      66
Curbastro, Gregorio Ricci      107
Curie, Marie      xii
Curves: algebraic      66—71
Curves: attractors and      152—153
Curves: boundary problems and      142 154—159
Curves: calculus ofvariations and      47—51
Curves: catastrophe theory and      69—71
Curves: chaos theory and      151—154
Curves: classification and      81
Curves: corank and      70
Curves: derivatives and      68—71
Curves: elliptic      66—71 85 137 182
Curves: Fermat's last theorem and      82—87
Curves: fixed-point theorem and      37—39
Curves: fractals and      144—145 159—164
Curves: Gauss and      105—106
Curves: minimal surfaces and      47—51
Curves: Newton's definition and      105
Curves: probability theory and      118—119
Curves: tensor calculus and      104—108
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