Analyse Non Standard - Nonstandard Analysis

est un groupement de chercheurs mathématiciens avec comme centre d'intérêt commun l'Analyse non standard.

Georges Reeb (1920-1992) était professeur de mathématique à l'Université de Strasbourg. Il a toujours cherché à rendre la mathématique plus simple et agréable. Dans de nombreux domaines mathématiques il a obtenu des progrès percutants, en appliquant des concepts et méthodes venus d'ailleurs.

This site is devoted to infinitesimals past and present, with a special emphasis on nonstandard analysis, the legacy of Abraham Robinson.

Ph.D., Yale University (1977) Professor of Economics and Mathematics

Associate Professor Ph.D. Mathematics, University of Kansas

Laboratoire J.-A. Dieudonné Université de Nice - Sophia Antipolis

My current research interests center on mathematical logic, foundations of mathematics, bounded arithmetic, and automatic proof verification . On-line writings on these and other topics will be posted under papers. Dynamical Theories of Brownian Motion has been posted at books, and more books will be added.

[[Eric Schechter, Vanderbilt University : "Nelson is the father of Internal Set Theory (IST), a variant of Nonstandard Analysis. IST has acquired a large following; some analysts are of the opinion that IST is the most intuitive approach to limits. (Personally, I suspect that most of those analysts were first trained as logicians, but that may be a reflection of my own ignorance.) Some of Nelson's writings are available online." ]]

MIT Dept. of Linguistics & Philosophy

Quantum algorithms, n-Categories, Applications of noncommutative harmonic analysis, Mathematical logic and its applications to computer science, Game Theory, Semantics and the study of information, Steganography.

urrently I am pursuing a long-held fascination with Nonstandard Analysis,

University of Denver

Professor Department of Mathematics Smith College. Northampton

Professor, Department of Mathematics, University of Illinois at Urbana-Champaign

University of Wisconsin

University of Illinois at Urbana-Champaign

Auteur: Alain Robert Presses Polytechniques et Universitaires Romandes

This book introduces the graduate mathematician and researcher to the effective use of nonstandard analysis (NSA).

edited by Peter A. Loeb Dept. of Mathematics, University of Illinois at Urbana, USA Manfred P.H. Wolff Mathematical Institute, University of Tübingen, Germany

On-line Edition, by H. Jerome Keisler (24 megabytes)

Edward Nelson Department of Mathematics at Princeton University.

Unfinished book on nonstandard analysis

Quelques articles publiés par les membres du réseau Georges Reeb

(Certains articles disponibles comme : On Tykhonov's theorem for convergence of solutions of slow and fast systems de Claude Lobry)

les autres pour ceux qui sont abonnés à : Bulletin of the Belgian Mathematical Society

André Deledicq. Extrait de Tangente hors série n° 13

Francine et Marc Diener

K. D. Stroyan

On-line Edition, by H. Jerome Keisler

This is a calculus textbook at the college Freshman level based on Abraham Robinson's infinitesimals, which date from 1960. Robinson's modern infinitesimal approach puts the intuitive ideas of the founders of the calculus on a mathematically sound footing, and is easier for beginners to understand than the more common approach vsa limitson of this book was published in 1976, and a revised Second Edition was published in 1986, both by Prindle, Weber & Schmidt.

The book is now out of print and the copyright has been returned to me as the author. I have decided (as of September 2002) to make the book available for free in electronic form at this site. These PDF files were made from the printed Second Edition. .

Véronique GAUTHERON Emmanuel ISAMBERT___« Nous tentons ici d'exposer, avec le minimum d'investissement théorique, les notions d'ANS qui nous paraissent essentielles a un mathématicien "classique" pour comprendre les idées à l'oeuvre dans un exposé non standard proche de leur spécialité. »

Bernard Gisin

« Voici un essai sur la construction des nombres hyperréels, qui étendent les nombres réels avec des nombres infiniment petits et infiniment grands. La construction se base sur un ultrafiltre non principal des entiers, qui est un ensemble de sous ensemble des entiers. Il ne peut pas être "construit", mais son existance est démontrée en utilisant l'axiome du choix. L'acceptation de cet objet est la partie la plus difficile, ensuite toute la construction des nombres surréels se fait de manière similaire à la construction des nombres réels avec des suites de Cauchy. »

Organizers Francine Diener, (University of Nice, France) Imme van den Berg & A. J. Franco de Oliveira, (University of Évora, Portugal) João Paulo Teixeira, (IST, Portugal) Keith Stroyan, (University of Iowa, USA) Vítor Neves, University of Aveiro, Portugal

Aveiro (Portugal), July 5-10, 2004

6 Oct. 1918 - 11 Avr. 1974

In 1966 Robinson published his famous text Non-standard analysis.

School of Mathematics and Statistics University of St Andrews, Scotland

A Biographical Memoir by Solomon Feferman. PDF