Nonstandard Analysis - The Comeback of Infinitesimals

The early Calculus of Newton and Leibniz made heavy use of infinitesimal quantities and flourished for over a hundred years until it was superseded by the more rigorous epsilon-delta formalism. It took until the 1950's for A. Robinson to find a proper way to construct a number system containing actual infinitesimals -- the Hyperreals *|R. This talk outlines their construction and possible applications in modern analysis.