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How best can a mathematics program be strengthened by the availability of software tools? I will discuss, through concrete examples, some possible uses of Mathematica in various facets of the collegiate mathematics curriculum. It is my belief that technological tools indeed have a vital role in education but that their use should be carefully tailored to the educational goals of the institution. Their use, ideally, will be natural for both the students and professors and will infuse vast areas of the curriculum while being only rarely required.
At my home institution (Randolph-Macon College), we offer Mathematica-intensive courses in elementary modeling, calculus, linear algebra, differential equations, and numerical analysis. I have been gradually writing my favorite ideas for incorporating technology in these courses into Mathematica packages, and the resulting suite of packages I call the RMC packages (named for my home institution). In this presentation, I will demonstrate some of the commands defined in these packages and how I use them in the classroom, and I will attempt to engage in a productive dialogue on the best uses of technology in university-level mathematics. I will speak about what I consider my greatest successes (and failures) in this endeavor over the past decade and I will give examples drawn from elementary (precalculus) courses through upper-division undergraduate courses. I hope to make the presentation useful for novices and power users alike.
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