Destiné aux étudiants de premier et deuxième cycle des études universitaires scientifiques comme aux candidats au CAPES de mathématiques, cet ouvrage traite de probabilités, de variables, de fonctions caractéristiques et de convergences.
Des rappels de cours sans démonstration sont suivis d'exercices, de problèmes et de corrigés.
The contributions in this proceedings volume offer a new perspective on the mathematical ties between France and Italy, and reveal how mathematical developments in these two countries affected one another. The focus is above all on the Peninsula's influence on French mathematicians, counterbalancing the historically predominant perception that French mathematics was a model for Italian mathematicians. In the process, the book details a subtle network of relations between the two countries, where mathematical exchanges fit into the changing and evolving framework of Italian political and academic structures. It reconsiders the issue of nationalities in all of its complexity, an aspect often neglected in research on the history of mathematics.
The works in this volume are selected contributions from a conference held in Lille and Lens (France) in November 2013 on Images of Italian Mathematics in France from Risorgimento to Fascism. The authors include respected historians of mathematics, philosophers of science, historians, and specialists for Italy and intellectual relations, ensuring the book will be of great interest to their peers.
Numerous scientists have taken part in the war effort during World War I, but few gave it the passionate energy of the prominent Italian mathematician Volterra. As a convinced supporter of the cause of Britain and France, he struggled vigorously to carry Italy into the war in May 1915 and then developed a frenetic activity to support the war effort, going himself to the front, even though he was 55. This activity found an adequate echo with his French colleagues Borel, Hadamard and Picard. The huge correspondence they exchanged during the war, gives an extraordinary view of these activities, and raises numerous fundamental questions about the role of a scientist, and particularly a mathematician during WW I. It also offers a vivid documentation about the intellectual life of the time ; Volterra's and Borel's circles in particular were extremely wide and the range of their interests was not limited to their field of specialization. The book proposes the complete transcription of the aforementioned correspondence, annotated with numerous footnotes to give details on the contents. It also offers a general historical introduction to the context of the letters and several complements on themes related to the academic exchanges between France and Italy during the war.
This book is a consequence of the international meeting organized in Marseilles in November 2018 devoted to the aftermath of the Great War for mathematical communities. It features selected original research presented at the meeting offering a new perspective on a period, the 1920s, not extensively considered by historiography.
After 1918, new countries were created, and borders of several others were modified. Territories were annexed while some countries lost entire regions. These territorial changes bear witness to the massive and varied upheavals with which European societies were confronted in the aftermath of the Great War. The reconfiguration of political Europe was accompanied by new alliances and a redistribution of trade - commercial, intellectual, artistic, military, and so on - which largely shaped international life during the interwar period. These changes also had an enormous impact on scientific life, not only in practice, but also in its organization and communication strategies.
The mathematical sciences, which from the late 19th century to the 1920s experienced a deep disciplinary evolution, were thus facing a double movement, internal and external, which led to a sustainable restructuring of research and teaching. Concomitantly, various areas such as topology, functional analysis, abstract algebra, logic or probability, among others, experienced exceptional development. This was accompanied by an explosion of new international or national associations of mathematicians with for instance the founding, in 1918, of the International Mathematical Union and the controversial creation of the International Research Council. Therefore, the central idea for the articulation of the various chapters of the book is to present case studies illustrating how in the aftermath of the war, many mathematicians had to organize their personal trajectories taking into account the evolution of the political, social and scientific environment which had taken place at the end of the conflict.
Comment les mathe´maticiens ont-ils mis leurs compe´tences, leurs connaissances et leur renomme´e au service de l'action militaire lors de diffe´rents conflits des XIXe et XXe sie`cles ?
Leur intervention a pu être de´cline´e de bien des fac¸ons et se faire de manie`re plus ou moins volontaire, et avec des convictions variables, allant de l'engagement total jusqu'au refus de toute compromission.
Le présent livre, issu d'un colloque tenu a` Paris en fe´vrier 2012 a` l'Institut des sciences de la communication du CNRS (ISCC), se concentre sur différents modes d'implication des mathe´maticiens dans les guerres des deux derniers sie`cles.