- December 8, 2020–December 9, 2020
Dr. Randall Pruim, Chair of the Math & Statistics Department, will present a talk entitled “Calculus The Way It Might Have Been.”
The Math & Statistics Department Colloquium on Tuesday, December 8 will be presented by the Chair of the department, Dr. Randy Pruim. Join us virtually at 3:45 to hear his talk about “Calculus The Way It Might Have Been.”
The brief history of calculus is well known: development by Newton and Leibniz based on infinitesimals, concerns that the calculus was not well-founded, and the Σδ “solution” a century later. Less well known is the work of Abraham Robinson in the 1960’s, which showed that the Σδ approach is not the only solution.
The hyperreal numbers are an elementary extension of the reals that can be used as a basis for calculus that is much closer to the spirit of Leibniz and Newton than is our usual approach. The result is infinitesimal calculus (also called non-standard analysis). This talk will provide an introduction to the hyperreal number system, some of its properties, and what first-year calculus might have looked like had the hyperreal system been developed before Σδ limits.