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 Dieudonne Une breve histoire de la topologie.- 1 L'apport de Riemann.- 2 Les notions topologiques dans les espaces ?n.- 3 Espaces metriques et espaces topologiques.- 4 Homeomorphismes et dimension.- 5 Levolution de la Topologie generale.- 6 La prehistoire de la Topologie algebrique, de Riemann a Poincare.- 7 Les idees de Poincare et l'intervention de l'algebre.- 8 Les debuts de l'homologie.- 9 Les premieres applications de l'homologie.- 10 La formation de l'armature algebrique.- 11 Les diverses theories homologiques.- 12 Produits et coproduits.- 13 Constructions topologiques.- 14 L'aspect algebrique de l'homotopie.- 15 Premieres relations entre homotopie et homologie.- 16 Fibrations.- 17 Applications des fibrations.- 18 L'homologie et la cohomologie generalisees.- 19 La topologie geometrique des varietes lisses.- 20 La theorie generale des varietes.- 21 Les varietes de dimension infinie.- 22 Les varietes 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 the birth of functional analysis.- Marcel Guillaume La Logique Mathematique en sa jeunesse>.- Avant-Propos.- Table des Matieres.- Les premiers fruits du dix-neuvieme siecle.- Les temps optimistes.- Les premieres maturations de l'ere de la connaissance limitee.- Du developpement de la theorie de la demonstration, apres 1930.- De la theorie des ensembles, de 1930 a la veille de la fin de la premiere moitie du vingtieme siecle.- De la notion de modele, jusqu'aux temps de la semantique.- De la formation de la province de la recursivite, jusqu'en 1950.- Des progres et controverses, posterieurs a 1930, touchant mathematiques et logique intuitionnistes.- Des avances, apres 1930, au carrefour entre logique propositionnelle, algebre et topologie.- Des theoremes et methodes generaux issus des debuts de la theorie des modeles.- 18. Sur les modeles de la theorie des types simple et de la theorie des ensembles, durant les quinze dernieres annees avant 1950.- Des premieres applications mathematiques et des premieres notions theoriques de la theorie des modeles.- Postface, sur l'etat 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 prehistoire des conjectures de Weil.- H. Kornblum.- E. Artin.- F.K. Schmidt.- H. Hasse.- A. Weil.- Bibliographie.- Jean-Pierre Kahane Des series de Taylor au mouvement brownien, avec un apercu sur le retour.- Les travaux de Borel de 1896-1897 sur les series de Taylor, tels que Borel les analyse en 1912.- Que veut dire "en general"?.- Le point de vue de Steinhaus.- A la rencontre du mouvement brownien.- Le nouveau role moteur des probabilites.- References.- Andre Lichnerowicz Geometrie et relativite.- 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 Integration 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 Vallee-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 Mobius 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: 9783764328214
  • Publisher: Birkhauser Verlag AG
  • Publisher Imprint: Birkhauser Verlag AG
  • Edition: Bilingual edition
  • Language: English
  • Weight: 1450 gr
  • ISBN-10: 3764328215
  • Publisher Date: /07/1994
  • Binding: Hardback
  • Height: 240 mm
  • Returnable: N


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