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Teaching Calculus through Nonstandard Analysis

2025-12-05 17:45:27.92163+01 by Dan Lyke 0 comments

This is fascinating to me because the calculus (and, indeed, the linear algebra) I was taught was so much drudgery and remembering rules, and it took other means to build a better intuitive feel for what was actually happening.

Daniel Lakeland @dlakelan@mastodon.sdf.org

Found this article thanks to a Reddit comment. Every day or so there's someone asking in math reddits what "dy/dx" means or why there's a "dx" in the integral notation, and then an army of people come out of the woodwork to push the orthodoxy of limits like some stockholm syndrome prisoners... And a small number of people point out that nonstandard analysis is actually a real thing and works... Anyway, back before I was born Sullivan did an actual experiment on teaching

The paper is The Teaching of Elementary Calculus Using the Nonstandard Analysis Approach Kathleen Sullivan (Wayback Machine link) from The American Mathematical Monthly, Vol. 83, No. 5 (May, 1976), pp. 370-375

http://www.jstor.org/stable/2318657

[ related topics: Mathematics ]

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