Adam Polinski & Dr. Adam Roberts

ADAM B. POLINSKI

Infinitesimal Calculus in the Classroom

The concept of the limit is rather simple – while we get closer and closer to approaching one specific value, another value gets closer and closer to approaching a “limiting” value.  At calculus’ conception, a rather “intuitive” approach to evaluating the limit was discovered, a “concept of an infinitesimal, or an infinitely small number” (Keisler, 1986).  In determining the limiting value, we observe the infinitesimally small values that are infinitesimally close to the value in question.  The basic properties of algebra and computation hold, so we can manipulate and evaluate the limit by working infinitesimally close to the value in question.  At the time, this approach was not mathematically rigorous, so infinitesimals were passed over for the traditional, ‘ε-δ’ definition of the limit.  In 1960, Abraham Robinson’s work made the infinitesimal approach mathematically rigorous.  In my project, I will explore the mechanics and concept of infinitesimals as an alternate approach to traditional instruction.

Adam Polinski is from Sayre, PA.  He has majors in Secondary Mathematics Education and Mathematics.  He will receive a Bachelor of Science degree.  During his undergraduate career, he was awarded the Mary Walters Resident Assistant of the Year and was elected for membership in Phi Kappa Phi.  His career plans are to seek a teaching position in mathematics education.