Abstract / Synopsis
In teaching infinitesimal calculus we sought to present basic concepts like continuity and convergence by comparing and contrasting various definitions, rather than presenting “the definition” to the students as a monolithic absolute. We hope that our experiences could be useful to other instructors wishing to follow this method of instruction. A poll run at the conclusion of the course indicates that students tend to favor infinitesimal definitions over epsilon-delta ones.
Mikhail Katz & Luie Polev, "From Pythagoreans and Weierstrassians to True Infinitesimal Calculus," Journal of Humanistic Mathematics, Volume 7 Issue 1 (January 2017), pages 87-104. DOI: 10.5642/jhummath.201701.07. Available at: https://scholarship.claremont.edu/jhm/vol7/iss1/7