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Colloquium, Spring 2006

Day: Monday, May 22nd Time: 4:00pm Place: BH 112 Title: Nonstandard Analysis Speaker: Salah Abed Abstract: Newton's and Liebniz's ideas of differentiability and continuity are two different things. One became the epsilon-delta definitions through Cauchy; the other uses "infinitesimal" numbers but on shaky ground. In 1966, Abraham Robinson used two languages, an ultrafilter, and some predicate calculus to rigorously construct a set of hyperreal numbers, which included these "infinitesimals." Using the ability to analyze this structure based on our knowledge of the real numbers, we can redefine continuity, differentiability, sequences, and real-line topology. We will discuss the ideas 300 years in the making behind this, properties of hyperreals, and how they boil continuity and differentiability proofs down to simple calculations. Tea: In BH 300 at 3:30pm.