André Deledicq

André Deledicq is a contemporary french teacher of mathematics, specialist — among other things — of Non-Standard Analysis.

Roughly speaking, mathematics are divided into pure mathematics and applied mathematics. These two names explain by themselves what they refer to. In particular, pure mathematics do not care about use of results in practical life.

Roughly speaking, pure mathematics are divided into algebra and analysis. The separation of fields is less easy. One can say that a mathematician does analysis as soon as limits are involved. Set theory is an anavoidable tool which is basically used in both fields.

Non-standard analysis (or NSA — no link with the famous organization) is a new way to view mathematical analysis, in fact a new approach of old ideas. The trick is in thinking that a number can be infinitely small and that one can perform calculations with infinitely small numbers almost like calculations with ordinary numbers. This seems to be simple but in order to have no gaps in proofs, one must begin theory with a big amount of logical considerations.

Personnally I know only a few things in non-standard analysis; the change in mind this new view requires is too important for a person who has already other habits. My book on the subject is

Leçons de calcul INFINITÉSIMAL
by André Deledicq and Marc Diener
ed. Armand Colin, 1989
ISBN 2-200-21068-X

This book can be used by a student in sciences in second year of university.

It is not impossible that, in the future, non-standard analysis become as familiar to all people who use mathematics as is (or should be) today set theory.

P. M.

(alphacode : deledicqandre ; numcode : 396)

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