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DESCRIPTION;ENCODING=QUOTED-PRINTABLE: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.”=0D=0A=0D=0AThe 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.=0D=0AThe 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.
SUMMARY;ENCODING=QUOTED-PRINTABLE:Math Colloquium: Calculus the Way It Might Have Been
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