The Princeton companion to mathematics:
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| Sprache: | English |
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[2008]
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| Online-Zugang: | Table of contents only Inhaltsverzeichnis |
| Beschreibung: | XX, 1034 Seiten Illustrationen, Diagramme |
| ISBN: | 9780691118802 0691118809 |
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| 245 | 1 | 0 | |a The Princeton companion to mathematics |c editor: Timothy Gowers ; associate editors: June Barrow-Green, The Open University, Imre Leader, University of Cambridge |
| 246 | 1 | 3 | |a Companion to mathematics |
| 246 | 1 | 3 | |a Mathematics |
| 264 | 1 | |a Princeton |b Princeton University Press |c [2008] | |
| 300 | |a XX, 1034 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematics -- Study and teaching (Higher) | |
| 650 | 0 | 7 | |a Mathematiker |0 (DE-588)4037945-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Mathematik |0 (DE-588)4037944-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Mathematik |0 (DE-588)4037944-9 |D s |
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| 689 | 2 | 0 | |a Mathematiker |0 (DE-588)4037945-0 |D s |
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| 700 | 1 | |a Gowers, Timothy |0 (DE-588)123782716 |4 edt | |
| 700 | 1 | |a Barrow-Green, June |d 1953- |0 (DE-588)173057047 |4 edt | |
| 700 | 1 | |a Leader, Imre |d ca. 20./21. jh. |0 (DE-588)1270110667 |4 edt | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4008-3039-8 |w (DE-604)BV042522493 |
| 856 | 4 | 2 | |q text/html |u http://www.loc.gov/catdir/toc/ecip0818/2008020450.html |3 Table of contents only |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016254327&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
Datensatz im Suchindex
| _version_ | 1805082893867810816 |
|---|---|
| adam_text |
Contents
Preface
ix
Ш.15
Contributors
xvii
Ш.16
Ш.17
Ш.18
Part
I Introduction
Ш.19
Ш.20
I.I
What Is Mathematics About?
1
Ш.21
1.2
The Language and Grammar of Mathematics
8
Ш.22
1.3
Some Fundamental Mathematical Definitions
16
1.4
The General Goals of Mathematical Research
48
Ш.23
Ш.24
TTT
9Ç
ill.
¿J
Ш.26
Part
Π
The Origins of Modern
Ш.27
Mathematics
Ш.28
Ш.29
П.1
From Numbers to Number Systems
77
Ш.30
П.2
Geometry
83
Ш.31
П.З
The Development of Abstract Algebra
95
Ш.32
П.4
Algorithms
106
Ш.ЗЗ
П.5
The Development of Rigor in
Ш.34
Mathematical Analysis
117
Ш.35
П.6
The Development of the Idea of Proof
129
Ш.36
II.
7
The Crisis in the Foundations of Mathematics
142
Ш.37
Ш.38
Ш.39
Part
Ш
Mathematical Concepts
Ш.40
Ш.41
Ш.1
The Axiom of Choice
157
Ш.42
Ш.2
The Axiom of Determinacy
159
Ш.43
Ш.З
Bayesian Analysis
159
Ш.44
Ш.4
Braid Groups
160
Ш.45
Ш.5
Buildings
161
Ш.46
Ш.6
Calabi-Yau Manifolds
163
Ш.47
Ш.7
Cardinals
165
Ш.48
Ш.8
Categories
165
Ш.49
Ш.9
Compactness and Compactiflcation
167
Ш.50
ШЛО
Computational Complexity Classes
169
Ш.51
Ш.11
Countable and Uncountable Sets
170
Ш.52
Ш.12
C* -Algebras
172
Ш.53
Ш.13
Curvature
172
Ш.54
Ш.14
Designs
172
Ш.55
Determinants
174
Differential Forms and Integration
175
Dimension
180
Distributions
184
Duality
187
Dynamical Systems and Chaos
190
Elliptic Curves
190
The Euclidean Algorithm and
Continued Fractions
191
The
Euler
and NavLer-Stokes Equations
193
Expanders
196
The Exponential and Logarithmic Functions
199
The Fast Fourier Transform
202
The Fourier Transform
204
Fuchsian Groups
208
Function Spaces
210
Galois Groups
213
The Gamma Function
213
Generating Functions
214
Genus
215
Graphs
215
Hamiltonians
215
The Heat Equation
216
Hubert Spaces
219
Homology and Cohomology
221
Homo
topy
Groups
221
The Ideal Class Group
221
Irrational and Transcendental Numbers
222
The Ising Model
223
Jordan Normal Form
223
Knot Polynomials
225
K-Theory
227
The Leech Lattice
227
L-Functions
228
lie Theory
229
Linear and Nonlinear Waves and
Solitons 234
Linear Operators and Their Properties
239
Local and Global in Number Theory
241
The Mandelbrot Set
244
Manifolds
244
Matroids
244
Measures
246
VI
Contents
III.
5 6
Metric
Spaces
247
ΙΠ.57
Models of Set Theory
248
Ш.Ѕ8
Modular Arithmetic
249
Ш.59
Modular Forms
250
ΠΙ.60
Moduli Spaces
252
Ш.61
The Monster Group
252
Ш.62
Normed Spaces and Banach Spaces
252
Ш.63
Number Fields
254
Ш.64
Optimization and
Lagrange
Multipliers
255
Ш.65
Orbifolds
257
Ш.66
Ordinals
258
Ш.67
The Peano Axioms
258
Ш.68
Permutation Groups
259
Ш.69
Phase Transitions
261
Ш.70
TT
261
Ш.71
Probability Distributions
263
Ш.72
Projective
Space
267
Ш.73
Quadratic Forms
267
ΙΠ.74
Quantum Computation
269
Ш.75
Quantum Groups
272
Ш.76
Quaternions, Octonions, and Normed
Division Algebras
275
Ш.77
Representations
279
Ш.78
Ricci
Flow
279
Ш.79
Riemann Surfaces
282
Ш.80
The Riemann
Zeta
Function
283
Ш.81
Rings, Ideals, and Modules
284
Ш.82
Schemes
285
Ш.83
The
Schrödinger
Equation
285
Ш.84
The Simplex Algorithm
288
Ш.85
Special Functions
290
Ш.86
The Spectrum
294
Ш.87
Spherical Harmonics
295
Ш.88
Symplectic Manifolds
297
Ш.89
Tensor Products
301
Ш.90
Topological Spaces
301
Ш.91
Transforms
303
Ш.92
Trigonometric Functions
307
Ш.93
Universal Covers
309
Ш.94
Variational Methods
310
Ш.95
Varieties
313
Ш.96
Vector Bundles
313
Ш.97
Von
Neumann Algebras
313
Ш.98
Wavelets
313
Ш.99
The Zermelo-Fraenkel Axioms
314
Part TV Branches of Mathematics
ГУЛ
Algebraic Numbers
315
rv.2 Analytic Number Theory
332
rv.3 Computational Number Theory
348
rv.4 Algebraic Geometry
363
IV.
5
Arithmetic Geometry
372
IV.6 Algebraic Topology
383
IV.7 Differential Topology
396
IV.8 Moduli Spaces
408
IV.9 Representation Theory
419
rv.10 Geometric and Combinatorial Group Theory
431
ГУЛІ
Harmonic Analysis
448
IV.12 Partial Differential Equations
455
IV.13 General Relativity and the Einstein Equations
483
rv.14 Dynamics
493
IV.15 Operator Algebras
510
IV.16 Mirror Symmetry
523
IV.17 Vertex Operator Algebras
539
IV.18 Enumerative and Algebraic Combinatorics
550
IV.19 Extremal and Probabilistic Combinatorics
562
rv.20 Computational Complexity
575
IV.21 Numerical Analysis
604
IV.22 Set Theory
615
IV.23 Logic and Model Theory
635
IV.24 Stochastic Processes
647
IV.25 Probabilistic Models of Critical Phenomena
657
IV.26 High-Dimensional Geometry and Its
Probabilistic Analogues
670
Part V Theorems and Problems
v.i
V.2
V.3
V.4
V.5
V.6
V.7
V.8
V.9
V.10
V.ll
V.12
V.13
V.14
V.I
5
V.16
V.17
V.18
V.19
V.20
V.21
V.22
V.23
V.24
V.25
The ABC Conjecture
681
The Atiyah-Singer Index Theorem
681
The Banach-Tarski Paradox
684
The Birch-Swinnerton-Dyer Conjecture
685
Carleson's Theorem
686
The Central Limit Theorem
687
The Classification of Finite Simple Groups
687
Dirichlet's Theorem
689
Ergodic Theorems
689
Fermat's Last Theorem
691
Fixed Point Theorems
693
The Four-Color Theorem
696
The Fundamental Theorem of Algebra
698
The Fundamental Theorem of Arithmetic
699
Gödel's
Theorem
700
Gromov's Polynomial-Growth Theorem
702
Hubert's
Nullstellensatz
703
The Independence of the
Continuum Hypothesis
703
Inequalities
703
The Insolubility of the Halting Problem
706
The Insolubility of the Quintic
708
Iiouvffle's Theorem and Roth's Theorem
710
Mostow's Strong Rigidity Theorem
711
The
Τ
versus NT Problem
713
The
Poincaré
Conjecture
714
Contents
vu
V.26
The Prime Number Theorem and the
Riemann Hypothesis
V.27 Problems and Results in
Additive Number Theory
V.28 From Quadratic Reciprocity to
Class Field Theory
V.29 Rational Points on Curves and
the Mordell Conjecture
V.30 The Resolution of Singularities
V.31 The Riemann-Roch Theorem
V.32 The Robertson-Seymour Theorem
V.33 The Three-Body Problem
V.34 The Uniformization Theorem
V.
3 5
The Weil Conjectures
Part VI Mathematicians
VI.
1
Pythagoras (ca.
569
B.c.E.-ca.
494
b.C.e.)
VL2 Euclid (ca.
325
B.c.E.-ca.
265
B.C.E.)
VI.3 Archimedes (ca.
287
B.C.E.-212 B.c.E.)
VI.4
Apollonius
(ca. 262
в.с.Е.-са.
190
в.С.Е.)
VI.
5 Abu Ja'f
ar
Muhammad ibn
Musa al-Khwãrizmí
(800-847)
VI.6 Leonardo
of
Pisa
(known as Fibonacci)
(ca. 1170^8.1250)
VI.
7
Girolamo Cardano
(1501-1576)
VI.8
Rafael Bombelli (1526-after
1572)
VI.9
François
Viète
(1540-1603)
VI.10
Simon
Stevin
(1548-1620)
VI.
11
René Descartes
(1596-1650)
VI.12 Pierre
Fermat
(1607-1665)
VI.13
Blaise
Pascal
(1623-1662)
VI.14 Isaac Newton
(1642-1727)
VI.15
Gottfried
Wilhelm
Leibniz
(1646-1716)
VI.16
Brook
Taylor
(1685-1731)
VI.17
Christian
Goldbach (1690-1764)
VI.
18
The Bernoullis
(fl.
1
8th century)
VI.19 Leonhard
Euler
(1707-1783)
VI.20
Jean Le Rond d'Alembert
(1717-1783)
VI.21 Edward Waring
(ca. 1735-1798)
VI.22 Joseph Louis
Lagrange (1736-1813)
VI.23 Pierre-Simon Laplace
(1749-1827)
VI.24
Adrien-Marie Legendre
(1752-1833)
VI.25 Jean-Baptiste Joseph Fourier
(1768-1830)
VI.26 Carl
Friedrich
Gauss
(1777-1855)
VI.27
Siméon-Denis Poisson
(1781-1840)
VI.28 Bernard Bolzano
(1781-1848)
VI.29
Augustin-Louis
Cauchy
(1789-1857)
VI.30 August Ferdinand
Möbius
(1790-1868)
VI.31
Nicolai
Ivanovich Lobachevskii
(1792-1856)
VI.32 George Green
(1793-1841)
VI.33 Niels
Henrik Abel (1802-1829)
VI.34
714
VI.35
VI.36
715
VI.37
VI.38
718
VI.39
VI.40
720
VI.41
722
VI.4
2
723
VI.43
725
VI.44
726
VI.4
5
728
V1.46
729
VI.4
7
VI.48
VI.49
VI.50
733
VI.51
734
VI.52
734
VI.53
735
VI.54
VI.55
736
VI.56
VI.57
737
VI.
58
737
VI.59
737
VI.60
737
VI.61
738
VI.62
739
VI.63
740
VI.64
741
VI.65
742
VI.66
743
VI.67
745
VI.68
745
VI.69
745
VI.
70
747
VI.71
749
VI.
72
750
VI.73
751
VI.74
752
VI.75
754
VI.76
755
VI.77
755
VI.78
757
VI.79
757
VI.80
758
VI.81
759
VI.82
759
VI.83
760
VI.84
760
VI.85
János Bolyai
(1802-1860) 762
Carl Gustav Jacob Jacobi (1804-1851) 762
Peter Gustav Lejeune Dirichlet (1805-1859) 764
William
Rowan Hamilton
(1805-1865) 765
Augustus
De Morgan (1806-1871) 765
Joseph Liouville (1809-1882) 766
Eduard Kummer (1810-1893) 767
Évariste
Galois
(1811-1832) 767
James Joseph Sylvester (1814-1897) 768
George
Boole
( 1815 -1864) 769
Karl
Weierstrass
(1815-1897) 770
Pafnuty Chebyshev (1821-1894) 771
Arthur Cayley (1821-1895) 772
Charles Hermite (1822-1901) 773
Leopold Kronecker (1823-1891) 773
Georg Friedrich Bernhard Riemann
(1826-1866) 774
Julius Wilhelm Richard Dedekind (1831-1916) 776
Emile
Leonard
Mathieu
(1835-1890) 776
Camille
Jordan (1838-1922) 777
Sophus Ue
(1842-1899) 777
Georg
Cantor
(1845-1918) 778
William Kingdon
Clifford
(1845-1879) 780
Gottlob
Frege (
1848-192 5) 780
Christian Felix Klein (1849-1925) 782
Ferdinand Georg Frobenius (1849-1917) 783
Sofya (Sonya) Kovalevskaya (1850-1891) 784
William Burnside (1852-1927) 785
Jules Henri
Poincaré
(1854-1912) 785
Giuseppe Peano (1858-1932) 787
David Hubert (1862-1943) 788
Hermann Minkowski (1864-1909) 789
Jacques Hadamard
(1865-1963) 790
Ivar Fredholm
(1866-1927) 791
Charles-Jean de la Vallèe
Poussin
( 1866-1962) 792
Felix Hausdorff (1868-1942) 792
Elie Joseph Cartan
(1869-1951) 794
Emile
Borei
(1871-1956) 795
Bertrand
Arthur William
Russell (1872-1970) 795
Henri Lebesgue (1875-1941) 796
Godfrey
Harold Hardy
(1877-1947) 797
Frigyes
(Frédéric) Riesz
( 1880-19 56) 798
Luitzen Egbertus
Jan Brouwer
(1881-1966) 799
Emmy Noether
(1882-1935) 800
Wacław Sierpiński
(1882-1969) 801
George
Birkhoff
(1884-1944) 802
John Edensor Littlewood
(1885-1977) 803
Hermann Weyl
(1885-1955) 805
Thoralf Skolem
(1887-1963) 806
Srinivasa Ramanujan
(1887-1920) 807
Richard
Courant
(1888-1972) 808
Stefan Banach
( 1892-194 5) 809
Norbert
Wiener
(1894-1964) 811
VIU
Contents
VI.86
Emil Artin (1898-1962) 812
VI.87
Alfred Tarski (1901-1983) 813
VI.88 Andrei Nikolaevich Kolmogorov (1903-1987) 814
VI.89
Alonzo
Church
(1903-1995) 816
VI.90 William Vallance Douglas Hodge (1903-1975) 816
VI.91 John von Neumann (1903-1957) 817
VI.92 Kurt
Godei
(1906-1978) 819
VI.93
André
Weil (1906-1998) 819
VI.94 Alan
Turing (1912-19S4)
821
VI.95 Abraham Robinson (1918-1974) 822
VI.96 Nicolas Bourbaki (1935-) 823
Part vn The Influence of Mathematics
VILI
Mathematics and Chemistry
827
νπ.2
Mathematical Biology
837
vn.3 Wavelets and Applications
848
vn.4 The Mathematics of Traffic in Networks
862
Vn.5 The Mathematics of Algorithm Design
871
Vn.6 Reliable Transmission of Information
878
vn.7 Mathematics and Cryptography
887
VII.8 Mathematics and Economic Reasoning
895
VH.9 The Mathematics of Money
910
vn.10 Mathematical Statistics
916
VILII
Mathematics and Medical Statistics
921
VII.
12
Analysis, Mathematical and Philosophical
928
Vn.13 Mathematics and Music
935
Vn.14 Mathematics and Art
944
PartVin Final Perspectives
VIII. 1
The Art of Problem Solving
955
Vni.2 "Why Mathematics?" You Might Ask
966
Vin.3 The Ubiquity of Mathematics
977
Vin.4 Numeracy
983
Vin.5 Mathematics: An Experimental Science
991
vni.6 Advice to a Young Mathematician
1000
VIII.7
A Chronology of Mathematical Events
1010
Index
1015 |
| adam_txt |
Contents
Preface
ix
Ш.15
Contributors
xvii
Ш.16
Ш.17
Ш.18
Part
I Introduction
Ш.19
Ш.20
I.I
What Is Mathematics About?
1
Ш.21
1.2
The Language and Grammar of Mathematics
8
Ш.22
1.3
Some Fundamental Mathematical Definitions
16
1.4
The General Goals of Mathematical Research
48
Ш.23
Ш.24
TTT
9Ç
ill.
¿J
Ш.26
Part
Π
The Origins of Modern
Ш.27
Mathematics
Ш.28
Ш.29
П.1
From Numbers to Number Systems
77
Ш.30
П.2
Geometry
83
Ш.31
П.З
The Development of Abstract Algebra
95
Ш.32
П.4
Algorithms
106
Ш.ЗЗ
П.5
The Development of Rigor in
Ш.34
Mathematical Analysis
117
Ш.35
П.6
The Development of the Idea of Proof
129
Ш.36
II.
7
The Crisis in the Foundations of Mathematics
142
Ш.37
Ш.38
Ш.39
Part
Ш
Mathematical Concepts
Ш.40
Ш.41
Ш.1
The Axiom of Choice
157
Ш.42
Ш.2
The Axiom of Determinacy
159
Ш.43
Ш.З
Bayesian Analysis
159
Ш.44
Ш.4
Braid Groups
160
Ш.45
Ш.5
Buildings
161
Ш.46
Ш.6
Calabi-Yau Manifolds
163
Ш.47
Ш.7
Cardinals
165
Ш.48
Ш.8
Categories
165
Ш.49
Ш.9
Compactness and Compactiflcation
167
Ш.50
ШЛО
Computational Complexity Classes
169
Ш.51
Ш.11
Countable and Uncountable Sets
170
Ш.52
Ш.12
C* -Algebras
172
Ш.53
Ш.13
Curvature
172
Ш.54
Ш.14
Designs
172
Ш.55
Determinants
174
Differential Forms and Integration
175
Dimension
180
Distributions
184
Duality
187
Dynamical Systems and Chaos
190
Elliptic Curves
190
The Euclidean Algorithm and
Continued Fractions
191
The
Euler
and NavLer-Stokes Equations
193
Expanders
196
The Exponential and Logarithmic Functions
199
The Fast Fourier Transform
202
The Fourier Transform
204
Fuchsian Groups
208
Function Spaces
210
Galois Groups
213
The Gamma Function
213
Generating Functions
214
Genus
215
Graphs
215
Hamiltonians
215
The Heat Equation
216
Hubert Spaces
219
Homology and Cohomology
221
Homo
topy
Groups
221
The Ideal Class Group
221
Irrational and Transcendental Numbers
222
The Ising Model
223
Jordan Normal Form
223
Knot Polynomials
225
K-Theory
227
The Leech Lattice
227
L-Functions
228
lie Theory
229
Linear and Nonlinear Waves and
Solitons 234
Linear Operators and Their Properties
239
Local and Global in Number Theory
241
The Mandelbrot Set
244
Manifolds
244
Matroids
244
Measures
246
VI
Contents
III.
5 6
Metric
Spaces
247
ΙΠ.57
Models of Set Theory
248
Ш.Ѕ8
Modular Arithmetic
249
Ш.59
Modular Forms
250
ΠΙ.60
Moduli Spaces
252
Ш.61
The Monster Group
252
Ш.62
Normed Spaces and Banach Spaces
252
Ш.63
Number Fields
254
Ш.64
Optimization and
Lagrange
Multipliers
255
Ш.65
Orbifolds
257
Ш.66
Ordinals
258
Ш.67
The Peano Axioms
258
Ш.68
Permutation Groups
259
Ш.69
Phase Transitions
261
Ш.70
TT
261
Ш.71
Probability Distributions
263
Ш.72
Projective
Space
267
Ш.73
Quadratic Forms
267
ΙΠ.74
Quantum Computation
269
Ш.75
Quantum Groups
272
Ш.76
Quaternions, Octonions, and Normed
Division Algebras
275
Ш.77
Representations
279
Ш.78
Ricci
Flow
279
Ш.79
Riemann Surfaces
282
Ш.80
The Riemann
Zeta
Function
283
Ш.81
Rings, Ideals, and Modules
284
Ш.82
Schemes
285
Ш.83
The
Schrödinger
Equation
285
Ш.84
The Simplex Algorithm
288
Ш.85
Special Functions
290
Ш.86
The Spectrum
294
Ш.87
Spherical Harmonics
295
Ш.88
Symplectic Manifolds
297
Ш.89
Tensor Products
301
Ш.90
Topological Spaces
301
Ш.91
Transforms
303
Ш.92
Trigonometric Functions
307
Ш.93
Universal Covers
309
Ш.94
Variational Methods
310
Ш.95
Varieties
313
Ш.96
Vector Bundles
313
Ш.97
Von
Neumann Algebras
313
Ш.98
Wavelets
313
Ш.99
The Zermelo-Fraenkel Axioms
314
Part TV Branches of Mathematics
ГУЛ
Algebraic Numbers
315
rv.2 Analytic Number Theory
332
rv.3 Computational Number Theory
348
rv.4 Algebraic Geometry
363
IV.
5
Arithmetic Geometry
372
IV.6 Algebraic Topology
383
IV.7 Differential Topology
396
IV.8 Moduli Spaces
408
IV.9 Representation Theory
419
rv.10 Geometric and Combinatorial Group Theory
431
ГУЛІ
Harmonic Analysis
448
IV.12 Partial Differential Equations
455
IV.13 General Relativity and the Einstein Equations
483
rv.14 Dynamics
493
IV.15 Operator Algebras
510
IV.16 Mirror Symmetry
523
IV.17 Vertex Operator Algebras
539
IV.18 Enumerative and Algebraic Combinatorics
550
IV.19 Extremal and Probabilistic Combinatorics
562
rv.20 Computational Complexity
575
IV.21 Numerical Analysis
604
IV.22 Set Theory
615
IV.23 Logic and Model Theory
635
IV.24 Stochastic Processes
647
IV.25 Probabilistic Models of Critical Phenomena
657
IV.26 High-Dimensional Geometry and Its
Probabilistic Analogues
670
Part V Theorems and Problems
v.i
V.2
V.3
V.4
V.5
V.6
V.7
V.8
V.9
V.10
V.ll
V.12
V.13
V.14
V.I
5
V.16
V.17
V.18
V.19
V.20
V.21
V.22
V.23
V.24
V.25
The ABC Conjecture
681
The Atiyah-Singer Index Theorem
681
The Banach-Tarski Paradox
684
The Birch-Swinnerton-Dyer Conjecture
685
Carleson's Theorem
686
The Central Limit Theorem
687
The Classification of Finite Simple Groups
687
Dirichlet's Theorem
689
Ergodic Theorems
689
Fermat's Last Theorem
691
Fixed Point Theorems
693
The Four-Color Theorem
696
The Fundamental Theorem of Algebra
698
The Fundamental Theorem of Arithmetic
699
Gödel's
Theorem
700
Gromov's Polynomial-Growth Theorem
702
Hubert's
Nullstellensatz
703
The Independence of the
Continuum Hypothesis
703
Inequalities
703
The Insolubility of the Halting Problem
706
The Insolubility of the Quintic
708
Iiouvffle's Theorem and Roth's Theorem
710
Mostow's Strong Rigidity Theorem
711
The
Τ
versus NT Problem
713
The
Poincaré
Conjecture
714
Contents
vu
V.26
The Prime Number Theorem and the
Riemann Hypothesis
V.27 Problems and Results in
Additive Number Theory
V.28 From Quadratic Reciprocity to
Class Field Theory
V.29 Rational Points on Curves and
the Mordell Conjecture
V.30 The Resolution of Singularities
V.31 The Riemann-Roch Theorem
V.32 The Robertson-Seymour Theorem
V.33 The Three-Body Problem
V.34 The Uniformization Theorem
V.
3 5
The Weil Conjectures
Part VI Mathematicians
VI.
1
Pythagoras (ca.
569
B.c.E.-ca.
494
b.C.e.)
VL2 Euclid (ca.
325
B.c.E.-ca.
265
B.C.E.)
VI.3 Archimedes (ca.
287
B.C.E.-212 B.c.E.)
VI.4
Apollonius
(ca. 262
в.с.Е.-са.
190
в.С.Е.)
VI.
5 Abu Ja'f
ar
Muhammad ibn
Musa al-Khwãrizmí
(800-847)
VI.6 Leonardo
of
Pisa
(known as Fibonacci)
(ca. 1170^8.1250)
VI.
7
Girolamo Cardano
(1501-1576)
VI.8
Rafael Bombelli (1526-after
1572)
VI.9
François
Viète
(1540-1603)
VI.10
Simon
Stevin
(1548-1620)
VI.
11
René Descartes
(1596-1650)
VI.12 Pierre
Fermat
(1607-1665)
VI.13
Blaise
Pascal
(1623-1662)
VI.14 Isaac Newton
(1642-1727)
VI.15
Gottfried
Wilhelm
Leibniz
(1646-1716)
VI.16
Brook
Taylor
(1685-1731)
VI.17
Christian
Goldbach (1690-1764)
VI.
18
The Bernoullis
(fl.
1
8th century)
VI.19 Leonhard
Euler
(1707-1783)
VI.20
Jean Le Rond d'Alembert
(1717-1783)
VI.21 Edward Waring
(ca. 1735-1798)
VI.22 Joseph Louis
Lagrange (1736-1813)
VI.23 Pierre-Simon Laplace
(1749-1827)
VI.24
Adrien-Marie Legendre
(1752-1833)
VI.25 Jean-Baptiste Joseph Fourier
(1768-1830)
VI.26 Carl
Friedrich
Gauss
(1777-1855)
VI.27
Siméon-Denis Poisson
(1781-1840)
VI.28 Bernard Bolzano
(1781-1848)
VI.29
Augustin-Louis
Cauchy
(1789-1857)
VI.30 August Ferdinand
Möbius
(1790-1868)
VI.31
Nicolai
Ivanovich Lobachevskii
(1792-1856)
VI.32 George Green
(1793-1841)
VI.33 Niels
Henrik Abel (1802-1829)
VI.34
714
VI.35
VI.36
715
VI.37
VI.38
718
VI.39
VI.40
720
VI.41
722
VI.4
2
723
VI.43
725
VI.44
726
VI.4
5
728
V1.46
729
VI.4
7
VI.48
VI.49
VI.50
733
VI.51
734
VI.52
734
VI.53
735
VI.54
VI.55
736
VI.56
VI.57
737
VI.
58
737
VI.59
737
VI.60
737
VI.61
738
VI.62
739
VI.63
740
VI.64
741
VI.65
742
VI.66
743
VI.67
745
VI.68
745
VI.69
745
VI.
70
747
VI.71
749
VI.
72
750
VI.73
751
VI.74
752
VI.75
754
VI.76
755
VI.77
755
VI.78
757
VI.79
757
VI.80
758
VI.81
759
VI.82
759
VI.83
760
VI.84
760
VI.85
János Bolyai
(1802-1860) 762
Carl Gustav Jacob Jacobi (1804-1851) 762
Peter Gustav Lejeune Dirichlet (1805-1859) 764
William
Rowan Hamilton
(1805-1865) 765
Augustus
De Morgan (1806-1871) 765
Joseph Liouville (1809-1882) 766
Eduard Kummer (1810-1893) 767
Évariste
Galois
(1811-1832) 767
James Joseph Sylvester (1814-1897) 768
George
Boole
( 1815 -1864) 769
Karl
Weierstrass
(1815-1897) 770
Pafnuty Chebyshev (1821-1894) 771
Arthur Cayley (1821-1895) 772
Charles Hermite (1822-1901) 773
Leopold Kronecker (1823-1891) 773
Georg Friedrich Bernhard Riemann
(1826-1866) 774
Julius Wilhelm Richard Dedekind (1831-1916) 776
Emile
Leonard
Mathieu
(1835-1890) 776
Camille
Jordan (1838-1922) 777
Sophus Ue
(1842-1899) 777
Georg
Cantor
(1845-1918) 778
William Kingdon
Clifford
(1845-1879) 780
Gottlob
Frege (
1848-192 5) 780
Christian Felix Klein (1849-1925) 782
Ferdinand Georg Frobenius (1849-1917) 783
Sofya (Sonya) Kovalevskaya (1850-1891) 784
William Burnside (1852-1927) 785
Jules Henri
Poincaré
(1854-1912) 785
Giuseppe Peano (1858-1932) 787
David Hubert (1862-1943) 788
Hermann Minkowski (1864-1909) 789
Jacques Hadamard
(1865-1963) 790
Ivar Fredholm
(1866-1927) 791
Charles-Jean de la Vallèe
Poussin
( 1866-1962) 792
Felix Hausdorff (1868-1942) 792
Elie Joseph Cartan
(1869-1951) 794
Emile
Borei
(1871-1956) 795
Bertrand
Arthur William
Russell (1872-1970) 795
Henri Lebesgue (1875-1941) 796
Godfrey
Harold Hardy
(1877-1947) 797
Frigyes
(Frédéric) Riesz
( 1880-19 56) 798
Luitzen Egbertus
Jan Brouwer
(1881-1966) 799
Emmy Noether
(1882-1935) 800
Wacław Sierpiński
(1882-1969) 801
George
Birkhoff
(1884-1944) 802
John Edensor Littlewood
(1885-1977) 803
Hermann Weyl
(1885-1955) 805
Thoralf Skolem
(1887-1963) 806
Srinivasa Ramanujan
(1887-1920) 807
Richard
Courant
(1888-1972) 808
Stefan Banach
( 1892-194 5) 809
Norbert
Wiener
(1894-1964) 811
VIU
Contents
VI.86
Emil Artin (1898-1962) 812
VI.87
Alfred Tarski (1901-1983) 813
VI.88 Andrei Nikolaevich Kolmogorov (1903-1987) 814
VI.89
Alonzo
Church
(1903-1995) 816
VI.90 William Vallance Douglas Hodge (1903-1975) 816
VI.91 John von Neumann (1903-1957) 817
VI.92 Kurt
Godei
(1906-1978) 819
VI.93
André
Weil (1906-1998) 819
VI.94 Alan
Turing (1912-19S4)
821
VI.95 Abraham Robinson (1918-1974) 822
VI.96 Nicolas Bourbaki (1935-) 823
Part vn The Influence of Mathematics
VILI
Mathematics and Chemistry
827
νπ.2
Mathematical Biology
837
vn.3 Wavelets and Applications
848
vn.4 The Mathematics of Traffic in Networks
862
Vn.5 The Mathematics of Algorithm Design
871
Vn.6 Reliable Transmission of Information
878
vn.7 Mathematics and Cryptography
887
VII.8 Mathematics and Economic Reasoning
895
VH.9 The Mathematics of Money
910
vn.10 Mathematical Statistics
916
VILII
Mathematics and Medical Statistics
921
VII.
12
Analysis, Mathematical and Philosophical
928
Vn.13 Mathematics and Music
935
Vn.14 Mathematics and Art
944
PartVin Final Perspectives
VIII. 1
The Art of Problem Solving
955
Vni.2 "Why Mathematics?" You Might Ask
966
Vin.3 The Ubiquity of Mathematics
977
Vin.4 Numeracy
983
Vin.5 Mathematics: An Experimental Science
991
vni.6 Advice to a Young Mathematician
1000
VIII.7
A Chronology of Mathematical Events
1010
Index
1015 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author2 | Gowers, Timothy Barrow-Green, June 1953- Leader, Imre ca. 20./21. jh |
| author2_role | edt edt edt |
| author2_variant | t g tg j b g jbg i l il |
| author_GND | (DE-588)123782716 (DE-588)173057047 (DE-588)1270110667 |
| author_facet | Gowers, Timothy Barrow-Green, June 1953- Leader, Imre ca. 20./21. jh |
| building | Verbundindex |
| bvnumber | BV023050945 |
| callnumber-first | Q - Science |
| callnumber-label | QA11 |
| callnumber-raw | QA11.2 .P745 2008 |
| callnumber-search | QA11.2 .P745 2008 |
| callnumber-sort | QA 211.2 P745 42008 |
| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)884238663 (DE-599)BSZ287810704 |
| dewey-full | 510 51022 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 510 22 |
| dewey-search | 510 510 22 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Philosophie Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV023050945 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:24:38Z |
| indexdate | 2024-07-20T07:39:54Z |
| institution | BVB |
| isbn | 9780691118802 0691118809 |
| language | English |
| lccn | 2008020450 |
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| physical | XX, 1034 Seiten Illustrationen, Diagramme |
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| publisher | Princeton University Press |
| record_format | marc |
| spelling | The Princeton companion to mathematics editor: Timothy Gowers ; associate editors: June Barrow-Green, The Open University, Imre Leader, University of Cambridge Companion to mathematics Mathematics Princeton Princeton University Press [2008] XX, 1034 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Mathematik Mathematics -- Study and teaching (Higher) Mathematiker (DE-588)4037945-0 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematik (DE-588)4037944-9 s DE-604 DE-188 Mathematiker (DE-588)4037945-0 s Gowers, Timothy (DE-588)123782716 edt Barrow-Green, June 1953- (DE-588)173057047 edt Leader, Imre ca. 20./21. jh. (DE-588)1270110667 edt Erscheint auch als Online-Ausgabe 978-1-4008-3039-8 (DE-604)BV042522493 text/html http://www.loc.gov/catdir/toc/ecip0818/2008020450.html Table of contents only Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016254327&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | The Princeton companion to mathematics Mathematik Mathematics -- Study and teaching (Higher) Mathematiker (DE-588)4037945-0 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4037945-0 (DE-588)4037944-9 |
| title | The Princeton companion to mathematics |
| title_alt | Companion to mathematics Mathematics |
| title_auth | The Princeton companion to mathematics |
| title_exact_search | The Princeton companion to mathematics |
| title_exact_search_txtP | The Princeton companion to mathematics |
| title_full | The Princeton companion to mathematics editor: Timothy Gowers ; associate editors: June Barrow-Green, The Open University, Imre Leader, University of Cambridge |
| title_fullStr | The Princeton companion to mathematics editor: Timothy Gowers ; associate editors: June Barrow-Green, The Open University, Imre Leader, University of Cambridge |
| title_full_unstemmed | The Princeton companion to mathematics editor: Timothy Gowers ; associate editors: June Barrow-Green, The Open University, Imre Leader, University of Cambridge |
| title_short | The Princeton companion to mathematics |
| title_sort | the princeton companion to mathematics |
| topic | Mathematik Mathematics -- Study and teaching (Higher) Mathematiker (DE-588)4037945-0 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Mathematik Mathematics -- Study and teaching (Higher) Mathematiker |
| url | http://www.loc.gov/catdir/toc/ecip0818/2008020450.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016254327&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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