The goal of this project is to improve the calculus sequence at San Francisco State University by making modern symbolic and numeric calculation an integral part of the course. Our Mathematics Department is committed to including mathematical computing as part of calculus. We propose to revamp our calculus sequence so that student use of Mathematica becomes a key part of the course. However, the present computing facilities of the Mathematics Department are not capable of supporting most modern mathematical software. Thus we propose to re-equip our computing facility with new computers that can run Mathematica. Our philosophy for using Mathematica in calculus is that the existence of such software changes what and how we teach. For example, knowing how to integrate a rational function by using the partial fraction decomposition is no longer a marketable skill because Mathematica can perform the calculation with ease. However, understanding what an integral is and knowing which integration to perform is more important than ever now that huge computational power is available. Thus we envision shifting the calculus course away from algorithmic skills and toward more problem solving, more applications, and a deeper understanding of the objects being manipulated. Mathematica will allow us to drop some training in computations that are better performed by machines than by people. With the time freed by dropping a few such topics, we expect to spend more time emphasizing the key ideas and applications of calculus. Thus the use of Mathematica will make our calculus course more demanding, not easier. In return, we expect to produce students who can use their calculus (and Mathematica) skills in other courses and in their professional lives.
