Postmodern Analysis - Jost, Jürgen

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Résumé :
What is the title of this book intended to signify, what connotations is the adjective ?Postmodern? meant to carry? A potential reader will surely pose this question. To answer it, I should describe what distinguishes the - proach to analysis presented here from what has by its protagonists been called ?Modern Analysis?. ?Modern Analysis? as represented in the works of the Bourbaki group or in the textbooks by Jean Dieudonn? e is characterized by its systematic and axiomatic treatment and by its drive towards a high level of abstraction. Given the tendency of many prior treatises on analysis to degenerate into a collection of rather unconnected tricks to solve special problems, this de?nitely represented a healthy achievement. In any case, for the development of a consistent and powerful mathematical theory, it seems to be necessary to concentrate solely on the internal problems and structures and to neglect the relations to other ?elds of scienti?c, even of mathematical study for a certain while. Almost complete isolation may be required to reach the level of intellectual elegance and perfection that only a good mathem- ical theory can acquire. However, once this level has been reached, it can be useful to open one?s eyes again to the inspiration coming from concrete external problems.

Biographie:
J?rgen Jost is Codirector of the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany, an Honorary Professor at the Department of Mathematics and Computer Sciences at Leipzig University, and an External Faculty Member of the Santa Fe Institute for the Sciences of Complexity, New Mexico, USA. He is the author of a number of further Springer textbooks including Postmodern Analysis (1997, 2002, 2005), Compact Riemann Surfaces (1997, 2002, 2006), Partial Differential Equations (2002, 2007, 2013), Differentialgeometrie und Minimalfl?chen (1994, 2007, 2014, with J. Eschenburg), Dynamical Systems (2005), Mathematical Concepts (2015), as well as several research monographs, such as Geometry and Physics (2009), and many publications in scientific journals....

Sommaire:
J?rgen Jost studierte von 1975 bis 1980 Mathematik, Physik, Volkswirtschaftslehre und Philosophie an der Universit?t Bonn. Er promovierte 1980 in der Mathematik und wurde nach verschiedenen internationalen Forschungsaufenthalten 1984 als Professor f?r Mathematik an die Ruhruniversit?t Bochum und 1996 als Direktor an das neu zu gr?ndende Max-Planck-Institut f?r Mathematik in den Naturwissenschaften in Leipzig berufen. Er ist auch Honorarprofessor an der Universit?t Leipzig und externes Fakult?tsmitglied des Santa Fe Institute for the Sciences of Complexity in den USA. 1993 erhielt er den Gottfried-Wilhelm-Leibniz-Preis der DFG und 2010 einen Advanced Grant des European Research Council. Er ist Autor von mehr als 20 Forschungsmonographien und Lehrb?chern und von ?ber 400 wissenschaftlichen Fachpublikationen. In seinen Forschungen verbindet er eine Vielzahl von mathematischen Disziplinen und Methoden mit einer allgemeinen Theorie komplexer Systeme und vielf?ltigen Anwendungen in der mathematischen und theoretischen Biologie und Neurobiologie....