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Graduate Seminar
Will Boney Carnegie Melllon University Title: Nonstandard Analysis Abstract: Following last weeks talk on compactness, we give more details on one of its applications: nonstandard analysis. In the beginning, calculus was developed with infinitesimal instead of the modern notion of a limit. Infinitesimals were abandoned because they lacked rigor. In the 1960s, Abraham Robinson formalized this notion using model theory and compactness. We follow his treatment and introduce the equivalents of continuity, differentiation, and integration and also give a proof or two to show how the flavor of arguments differ. Date: Tuesday, October 5, 2010 Time: 5:30 pm Location: Wean Hall 8220 Submitted by: Daniel Spector 