Development of Mathematics, 1950–2000
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Development of Mathematics, 1950–2000

Development of Mathematics, 1950–2000


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About the Book

Le projet de ce livre etait une gageure. lIs' agissait de rendre compte du developpement des mathematiques depuis cinquante ans a un public mathematique aussi large que possi- ble, sans viser l'exhaustivite, mais sans se bomer a un apen;u superticiel. Pour tenter de realiser cette ambition, Ie comite de lecture a fait appel a des mathematiciens actifs dans divers domaines des mathematiques. II a recru une trentaine de contributions qui forment la matiere de ce livre. En outre, il a auditionne plusieurs mathematiciens qui donnent leur point de vue personnel. Entin il a reuni quelques documents, soit statistiques, soit bibliographiques, pour completer les references donnees par les auteurs et signaler les ar- ticles de synthese. Le resultat ne pouvait etre ni complet, ni homo gene, et nous sommes evidemment conscients de ses insuftisances. Nous y reviendrons, mais nous voulons com- mencer par in sister sur ce qui fait l'interet et l' importance de ce livre. D'abord, et c'est la raison d'etre de ce vaste projet, ce livre correspond a un be- soin. Le livre precedent, Development of Mathematics 1900-1950 (Birkhauser, Bale, 1994), en depit de son caractere incomplet et de son inhomogeneite, a connu un grand succes, et s'avere d'interet durable pour ceux qui veulent explorer les matMmatiques de la premiere moitie du siecle.

Table of Contents:
Guided tour.- Diagram.- Dynamical systems.- Singularity theory.- The magnet and the butterfly.- La théorie des graphes.- Géométrie riemannienne.- Sampling theory of signal analysis.- Le problème du sous-espace invariant.- The geometry of algebraic varieties.- The calculus of variations, nonsmooth analysis and optimal control.- L’école mathématique française du XXe siècle.- Variétés et espaces analytiques complexes.- Geometrie aspects of stochastic analysis.- Cinquante ans de théorie analytique des nombres.- Du pourquoi au comment: la théorie de la démonstration de 1950 à nos jours.- Percolation.- Marches aléatoires sur les groupes.- Décomposition en ondelettes.- Rapport sur la K-théorie (1956–1997).- Plurisubharmonic functions and potential theory in several complex variables.- Comments on the development of topos theory.- La statistique mathématique depuis 1950.- Processus de branchement, arbres et superprocessus.- Some mathematical questions arising in fractal geometry.- Les processus stochastiques de 1950 à nos jours.- Arithmétique et cryptographie.- Autour du théorème de Morley.- Statistique et génétique.- La théorie des modèles, et un petit problème de Hardy.- Géométrie algébrique réelle.- Microlocal analysis.- Information, entropy and Bernoulli systems.- Game theory 1950–2000.- Some developments on Navier-Stokes equations in the second half of the 20th century.- Moscow Mathematics 1950–1975.- Un demi-siècle de transcendance.- Le mouvement brownien: quelques développements de 1950 à 1995.- Interview: Adrien Douady.- Interview: Mickhael Gromov.- Interview: Friedrich Hirzebruch.- Fields medalists and Rolf Nevanlinna prize winners.- International Congresses of Mathematicians.- Bulletin of the American Mathematical Society.- Uspehi Matematiceskii Nauk.- Elements of a bibliography on contemporary history of mathematics.- List of names.

Review :
"This impressive book covers…the major mathematical discoveries -- from the fundamentals of the applications in physics, in computer science and in biology -- of the second half of the twentieth century the subject is well motivated, the main ideas are demonstrated on instructive examples, the really deep problems are stressed, and the l’art pour l’art ones are avoided. It is an amazing experience to read each article, as an introduction and as an overview for a mathematician of general interest and a specialist, respectively." -ASM "…This is a very valuable book…with a valuable preliminary bibliography on the history of mathematics in the last twenty years." --MAA Online


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Product Details
  • ISBN-13: 9783764362805
  • Publisher: Birkhauser Verlag AG
  • Publisher Imprint: Birkhauser Verlag AG
  • Language: English
  • Returnable: Y
  • ISBN-10: 3764362804
  • Publisher Date: 01 Sep 2000
  • Binding: Hardback
  • No of Pages: 1372
  • Weight: 1760 gr


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