Development of mathematics: 1900 - 1950:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English French |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
1994
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 729 S. Ill., graph. Darst. |
| ISBN: | 3764328215 9783034899130 0817628215 9783034891141 |
Internformat
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| 245 | 1 | 0 | |a Development of mathematics: 1900 - 1950 |c ed. by Jean-Paul Pier |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 1994 | |
| 300 | |a XVII, 729 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 648 | 4 | |a Geschichte 1900-2000 | |
| 648 | 7 | |a Geschichte 1900-1990 |2 gnd |9 rswk-swf | |
| 648 | 7 | |a Geschichte 1900-1950 |2 gnd |9 rswk-swf | |
| 650 | 4 | |a Mathématiques - Histoire - 20e siècle | |
| 650 | 7 | |a Wiskunde |2 gtt | |
| 650 | 4 | |a Geschichte | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematics |x History |y 20th century | |
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| 655 | 7 | |0 (DE-588)1071861417 |a Konferenzschrift |y 1992 |z Bourglinster |2 gnd-content | |
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Datensatz im Suchindex
| _version_ | 1804123960563990529 |
|---|---|
| adam_text | Table of Contents
Introduction xii
List of Participants xv
Titles of Lectures xix
Guidelines 1900 1950 1
Jean Dieudonne
Une breve histoire de la topologie 35
Introduction 35
1 L apport de Riemann 36
2 Les notions topologiques dans les espaces W 38
3 Espaces metriques et espaces topologiques 39
4 Homeomorphismes et dimension 41
5 Levolution de la Topologie generale 42
6 La prehistoire de la Topologie algebrique, de Riemann a Poincare ... 43
7 Les idees de Poincare et l intervention de l algebre 45
8 Les debuts de l homologie 52
9 Les premieres applications de l homologie 60
10 La formation de l armature algebrique 65
11 Les diverses theories homologiques 75
12 Produits et coproduits 89
13 Constructions topologiques 96
14 L aspect algebrique de l homotopie 99
15 Premieres relations entre homotopie et homologie 108
16 Fibrations 113
17 Applications des fibrations 124
18 L homologie et la cohomologie generalisees 131
19 La topologie geometrique des varietes lisses 135
20 La theorie generale des varietes 140
21 Les varietes de dimension infinie 144
22 Les varietes de petite dimension 146
Index 150
viii Table of Contents
Joseph L. Doob
The Development of Rigor in Mathematical
Probability, (1900 1950) 157
1 Introduction 157
2 What is the real world (nonmathematical) problem? 158
3 The law of large numbers 158
4 What is probability? 160
5 Mathematical probability before the era of precise definitions 161
6 The development of measure theory 161
7 Early applications of explicit measure theory to probability 162
8 Kolmogorov s 1933 monograph 165
9 Expansion backwards of the Kolmogorov basis 167
10 Uncountable index sets 167
11 Reluctance to accept measure theory by probabilists 167
12 New relations between functions made possible by the
mathematization of probability 168
13 What is the place of probability theory in measure theory, and more
generally in analysis? 168
Gaetano Fichera
Vito Volterra and the birth of functional analysis 171
Bibliography 183
Marcel Guillaume
La Logique Mathematique en sa jeunesse 185
Avant Propos 185
Table des Matieres 187
Introduction 192
Les premiers fruits du dix neuvieme siecle 197
Les temps optimistes 214
Les premieres maturations de l ere de la connaissance limitee 241
Du developpement de la theorie de la demonstration, apres 1930 248
De la theorie des ensembles, de 1930 a la veille de la fin
de la premiere moitie du vingtieme siecle 253
De la notion de modele, jusqu aux temps de la semantique 258
De la formation de la province de la recursivite, jusqu en 1950 269
Des progres et controverses, posterieurs a 1930, touchant
mathematiques et logique intuitionnistes 290
Table of Contents ix
Des avances, apres 1930, au carrefour entre logique propositionnelle,
algebre et topologie 293
Des theoremes et methodes generaux issus des debuts de la
theorie des modeles 303
Sur les modeles de la theorie des types simple et de la theorie des
ensembles, durant les quinze dernieres annees avant 1950 304
Des premieres applications mathematiques et des premieres notions
theoriques de la theorie des modeles 317
Postface, sur Fetat de la logique vers 1950 321
Bibliographic 322
Walter K. Hayman
Function Theory 1900 1950 369
1 Introduction 369
2 Entire functions 369
3 Meromorphic functions and Nevanlinna Theory 374
4 Functions in the unit disk 377
Bibliography 380
Christian Houzel
La prehistoire des conjectures de Weil 385
H. Kornblum 385
E. Artin 387
F.K. Schmidt 395
H. Hasse 398
A. Weil 401
Bibliographic 411
Jean Pierre Kahane
Des series de Taylor au mouvement brownien,
avec un apercu sur le retour 415
Les travaux de Borel de 1896 1897 sur les series de Taylor,
tels que Borel les analyse en 1912 415
Que veut dire «en general»? 417
Le point de vue de Steinhaus 418
A la rencontre du mouvement brownien 421
Le nouveau role moteur des probabilites 425
References 427
x Table of Contents
Andre Lichnerowicz
Geometrie et relativite 431
Jean Maw h in
Boundary value problems for nonlinear ordinary differential equations:
from successive approximations to topology 443
1 Introdution 443
2 Picard s pioneering work 444
3 Sharp existence and uniqueness conditions using successive
approximations 448
4 Variational methods 454
5 Topological methods 461
6 Continuation and Leray Schauder methods 467
7 Lower and upper solutions and related results 470
References 472
Louis Nirenberg
Partial Differential Equations in the First Half of the Century 479
I. General Equations 483
II. Elliptic Equations 486
III. Elliptic Equations and Calculus of Variations 490
IV. Hyperbolic Equations 495
V. Other Topics 497
Bibliography 501
Jean Paul Pier
Integration et mesure 1900 1950 517
Bibliographic 560
Wolfgang Schwarz
Some Remarks on the History of the Prime Number Theory
from 1896 to 1960 565
1 Introduction 565
2 The Nineteenth Century 568
3 Hadamard and de la Vallee Poussin 575
4 Other Proofs of the Prime Number Theorem 583
5 Improvement of the Remainder Term 590
Table of Contents xi
6 Primes in Arithmetic Progressions 596
7 The Riemann Conjecture 601
8 The Mobius Function 604
9 Concluding Remarks 608
10 Bibliography 611
11 Facsimiles 614
Journals 617
References 624
Index of Names 715
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| isbn | 3764328215 9783034899130 0817628215 9783034891141 |
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| physical | XVII, 729 S. Ill., graph. Darst. |
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| spelling | Development of mathematics: 1900 - 1950 ed. by Jean-Paul Pier Basel [u.a.] Birkhäuser 1994 XVII, 729 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Geschichte 1900-2000 Geschichte 1900-1990 gnd rswk-swf Geschichte 1900-1950 gnd rswk-swf Mathématiques - Histoire - 20e siècle Wiskunde gtt Geschichte Mathematik Mathematics History 20th century Mathematik (DE-588)4037944-9 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1992 Bourglinster gnd-content Mathematik (DE-588)4037944-9 s Geschichte 1900-1990 z DE-604 Geschichte 1900-1950 z 1\p DE-604 Pier, Jean-Paul Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006358276&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Development of mathematics: 1900 - 1950 Mathématiques - Histoire - 20e siècle Wiskunde gtt Geschichte Mathematik Mathematics History 20th century Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)1071861417 |
| title | Development of mathematics: 1900 - 1950 |
| title_auth | Development of mathematics: 1900 - 1950 |
| title_exact_search | Development of mathematics: 1900 - 1950 |
| title_full | Development of mathematics: 1900 - 1950 ed. by Jean-Paul Pier |
| title_fullStr | Development of mathematics: 1900 - 1950 ed. by Jean-Paul Pier |
| title_full_unstemmed | Development of mathematics: 1900 - 1950 ed. by Jean-Paul Pier |
| title_short | Development of mathematics: 1900 - 1950 |
| title_sort | development of mathematics 1900 1950 |
| topic | Mathématiques - Histoire - 20e siècle Wiskunde gtt Geschichte Mathematik Mathematics History 20th century Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Mathématiques - Histoire - 20e siècle Wiskunde Geschichte Mathematik Mathematics History 20th century Konferenzschrift 1992 Bourglinster |
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