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Interactive Internet Based Multivariable Calculus


Thomas Banchoff
June 26-29, 2005
Brown University
Providence, RI

Registration Fee $250 by May 3

Visualizing graphs of functions of two and more variables is a key skill needed to deal with the main ideas of multivariable calculus. Internet-based tools make it possible to engage students in the interplay between analysis, algebra, and geometry in ways that lead to deeper appreciation of the underlying principles and of real-world applications.

New software developed by the workshop leader and his students provides accessible and powerful tools for interactively investigating curves and surfaces, and enables students to share their own demonstrations with the instructor and with other students. Communication software provides easy ways for students to respond online to homework assignments and even examinations, and for instructors to submit online comments that can be shared, after a  time delay, with other members of the class.

One student, describing her experience in the class, wrote: “In the beginning I really did not like the system of reading other students’ homework. It made me feel really nervous and exposed and it made me want to leave problems blank rather than put an incorrect answer.  As the semester progressed I realized what a useful tool it could be and I started reading other people's homework responses more and more and felt more comfortable with mine being read.”

This workshop is intended for teachers of multivariable calculus who wish to explore the possibilities of new software for helping students develop a full range of geometric intuitions as well as formal skills in algebra, in abstract concepts in calculus (including continuity, differentiability, and curvature) and in effective writing. Prior computer experience is not required. The workshop will use Java applet software and laboratory materials that will be available for the participants to use in their courses in the fall.

In addition to the three-day intensive workshop, there will be online follow-up activities at least once a month during the fall, concentrating on different ways that the participants experiment with the software in their courses.  Members of the workshop will be invited to participate in a session at the joint MAA-AMS national meeting in January 2006 to share their experiences. For more information, please visit the workshop webpage at

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