Session 1O | Non-Traditional OERs for Teaching First-Year Calculus

Potter, Dustin
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Texas Digital Library

The power of mathematics lies in the formal definition and the rigorous logic used to extend these definitions into realms unimagined by their creators/discoverers. Calculus is a great example with applications reaching from distant stars to quantum particles. First-year students, however, often fail to find the beauty, let alone relevance, in the traditional definitions of calculus as formalized by Weierstrass and instead stumble through the course with little understanding. A more intuitive formalization of calculus relies on infinitesimals, a concept that can be traced back to ancient Greek mathematics. However, it was not until 1960 that Robinson demonstrated the definition of hyperreals (which contain infinitesimals) was as rigorous as any approach to calculus. Several textbooks have been written, with the first-year calculus student in mind, that incorporate the infinitesimal definition, and many of these texts are in the public domain. In this presentation, available OERs related to an infinitesimal approach to calculus will be discussed as well as a general introduction to MyOpenMath (MOM) and resources in MOM directly related to calculus using infinitesimal numbers.