Will Yesterday's Calculus Education Survive Mathematica?
Keith D. Stroyan
University of Iowa
Calculus is one of the greatest inventions of the human intellect. It has proved itself
over centuries by acting as the "language of continuous change" in subjects
ranging from physics to finance. Calculus will continue to be important, but Mathematica
has changed what educated people need to know in order to make calculus a useful part of
their lives.
I will discuss three ways Mathematica is impacting calculus
instruction: Calculus
WIZ, NetMath Calculus, and Calculus: The Language of Change.
These three highly developed experiments show how students can begin learning calculus
with Mathematica, resulting in faster mastery of skills, deeper involvement in the
mathematical development, and solution of more compelling and interesting problems.
Mathematica contains a vast body of "classical mathematical" knowledge.
The challenge to instructors is to make our students "educated users" of this
knowledge without having them earn Ph.D.'s in math. The potential is that
"ordinary" people will be able to apply this new organization of knowledge going
far beyond traditional calculus.
Keith Stroyan is Professor of Mathematics at the University of Iowa. Professor
Stroyan wrote the research monographs Introduction to the Theory of Infinitesimals and
Foundations of Infinitesimal Stochastic Analysis as well as numerous research articles on
Robinson's modern theory of infinitesimals. He has also taught a full spectrum of
mathematics courses including remedial algebra, high school analytical geometry, most of the
undergraduate math curriculum, graduate courses, and researchlevel topics courses such as
mathematical ecology and stochastic differential equations.
