Development of Mathematics 1900–1950
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Development of Mathematics 1900–1950

Development of Mathematics 1900–1950


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About the Book

This volume grew out of the preparation and achievements of the Symposium organized by the Luxembourg Mathematical Society in June 1992, at Chateau Bourglinster (Luxembourg). We express our best thanks to Monsieur Marc Fischbach, ministre de I 'Education nationale, Luxembourg Monsieur Rene Steichen, ministre delegue aux Affaires culturelles, Luxem- bourg, Academie des sciences, Paris, Academie roya1e des sciences, des lettres et des beaux-arts de Belgique, Section des sciences de l'Institut grand-ducal, Luxembourg, and all lecturers and participants. We hope that this contribution may ease a better understanding of the vitality in mathematics during the first half of the present century and provide clues for the explanation of its influence on later developments. We say our gratitude to persons who assisted us with their advice and help for the technical realization of the volume, especially Mrs. Suzanne D' Addato-Mues, Mr. Fran~ois Gaillard, Mr. Hubert Glesener. We are also grateful to Birkhauser- Verlag for having accepted this publication. Now the book should speak for itself ...

Table of Contents:
Guidelines 1900–1950.- Jean Dieudonné Une brève histoire de la topologie.- 1 L’apport de Riemann.- 2 Les notions topologiques dans les espaces ?n.- 3 Espaces métriques et espaces topologiques.- 4 Homéomorphismes et dimension.- 5 Lévolution de la Topologie générale.- 6 La préhistoire de la Topologie algébrique, de Riemann à Poincaré.- 7 Les idées de Poincaré et l’intervention de l’algèbre.- 8 Les débuts de l’homologie.- 9 Les premières applications de l’homologie.- 10 La formation de l’armature algébrique.- 11 Les diverses théories homologiques.- 12 Produits et coproduits.- 13 Constructions topologiques.- 14 L’aspect algébrique de l’homotopie.- 15 Premières relations entre homotopie et homologie.- 16 Fibrations.- 17 Applications des fibrations.- 18 L’homologie et la cohomologie généralisées.- 19 La topologie géométrique des variétés lisses.- 20 La théorie générale des variétés.- 21 Les variétés de dimension infinie.- 22 Les variétés de petite dimension.- Joseph L. Doob The Development of Rigor in Mathematical Probability, (1900–1950).- 1 Introduction.- 2 What is the real world (nonmathematical) problem?.- 3 The law of large numbers.- 4 What is probability?.- 5 Mathematical probability before the era of precise definitions.- 6 The development of measure theory.- 7 Early applications of explicit measure theory to probability.- 8 Kolmogorov’s 1933 monograph.- 9 Expansion backwards of the Kolmogorov basis.- 10 Uncountable index sets.- 11 Reluctance to accept measure theory by probabilists.- 12 New relations between functions made possible by the mathematization of probability.- 13 What is the place of probability theory in measure theory, and more generally in analysis?.- Gaetano Fichera Vito Volterra and thebirth of functional analysis.- Marcel Guillaume La Logique Mathématique en sa jeunesse>.- Avant-Propos.- Table des Matières.- Les premiers fruits du dix-neuvième siècle.- Les temps optimistes.- Les premières maturations de l’ère de la connaissance limitée.- Du développement de la théorie de la démonstration, après 1930.- De la théorie des ensembles, de 1930 à la veille de la fin de la première moitié du vingtième siècle.- De la notion de modèle, jusqu’aux temps de la sémantique.- De la formation de la province de la récursivité, jusqu’en 1950.- Des progrès et controverses, postérieurs à 1930, touchant mathématiques et logique intuitionnistes.- Des avances, après 1930, au carrefour entre logique propositionnelle, algèbre et topologie.- Des théorèmes et méthodes généraux issus des débuts de la théorie des modèles.- 18. Sur les modèles de la théorie des types simple et de la théorie des ensembles, durant les quinze dernières années avant 1950.- Des premières applications mathématiques et des premières notions théoriques de la théorie des modèles.- Postface, sur l’état de la logique vers 1950.- Bibliographie.- Walter K. Hayman Function Theory 1900–1950.- 1 Introduction.- 2 Entire functions.- 3 Meromorphic functions and Nevanlinna Theory.- 4 Functions in the unit disk.- Christian Houzel La préhistoire des conjectures de Weil.- H. Kornblum.- E. Artin.- F.K. Schmidt.- H. Hasse.- A. Weil.- Bibliographie.- Jean-Pierre Kahane Des séries de Taylor au mouvement brownien, avec un aperçu sur le retour.- Les travaux de Borel de 1896–1897 sur les séries de Taylor, tels que Borel les analyse en 1912.- Que veut dire «en général»?.- Le point de vue de Steinhaus.- A la rencontre du mouvement brownien.- Le nouveau rôlemoteur des probabilités.- Références.- André Lichnerowicz Géométrie et relativité.- Jean Mawhin Boundary value problems for nonlinear ordinary differential equations: from successive approximations to topology.- Introdution.- Picard’s pioneering work.- Sharp existence and uniqueness conditions using successive approximations.- Variational methods.- Topological methods.- Continuation and Leray-Schauder methods.- Lower and upper solutions and related results.- References.- Louis Nirenberg Partial Differential Equations in the First Half of the Century.- I. General Equations.- II. Elliptic Equations.- III. Elliptic Equations and Calculus of Variations.- IV. Hyperbolic Equations.- V. Other Topics.- Jean-Paul Pier Intégration et mesure 1900–1950.- Bibliographie.- Wolfgang Schwarz Some Remarks on the History of the Prime Number Theory from 1896 to 1960.- 1 Introduction.- 2 The Nineteenth Century.- 3 Hadamard and de la Vallée-Poussin.- 4 Other Proofs of the Prime Number Theorem.- 5 Improvement of the Remainder Term.- 6 Primes in Arithmetic Progressions.- 7 The Riemann Conjecture.- 8 The Möbius Function.- 9 Concluding Remarks.- 10 Bibliography.- 11 Facsimiles.- Journals.- References.- Index of Names.

Review :
"… leading mathematicians describe the development of various areas of mathematics during the first half of this century...The book contains several extensive bibliographies and many unique photos of mathematicians." Sefi Math (1995)


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Product Details
  • ISBN-13: 9783034899130
  • Publisher: Springer Basel
  • Publisher Imprint: Springer Basel
  • Height: 244 mm
  • No of Pages: 734
  • Returnable: Y
  • ISBN-10: 3034899130
  • Publisher Date: 16 Sep 2011
  • Binding: Paperback
  • Language: English
  • Returnable: Y
  • Width: 170 mm


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