Tim McCarty

Teaching Calculus Using Infinitesimals

Date: 2/20/2019
Time: 3:30PM-4:30PM
Place: 315 Armstrong Hall

Abstract:Calculus has traditionally been taught with an understanding that epsilon-delta limits are its foundation. The publication of Robinson’s Nonstandard Analysis (1961) has shown that this understanding is not absolute and that an infinitesimal-based calculus is
equally valid. In this seminar, I wish to present an argument for teaching first-year calculus with a nonstandard, infinitesimal-based approach. I will begin by briefly discussing the highlights of the historical development of both standard and nonstandard analysis and
then summarize Robinson’s presentation of formal infinitesimals as well as a formal construction of infinitesimals, in the hopes of giving the audience a more-formal understanding of infinitesimals beyond “they’re small.” Next, I will show and discuss textbooks, studies, and papers that teach or address the teaching of infinitesimal-based calculus, and conclude with arguments for why I believe such teaching should be attempted. I hope to end with enough time remaining for brief discussion and audience questions.

All are welcome – this talk is meant to be general-audience and not limited to the RUME community.

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