"You're Doing Simulations with Your Students, so Why Are You Using Mathematica?"

Phil Ramsden
Department of Mathematics, Imperial College of Science, Technology and Medicine, London, UK

At Imperial College, staff from the Mathematics and Chemistry departments have set up computer-based "Mathematics Laboratories" for first year Chemistry undergraduates. We´ve provided several types of activity in these laboratories, but one of the most important kinds involves students? setting up and studying models and simulations of chemical conditions and processes. Dedicated simulation software exists for this sort of thing, much of it offering a lot of presentational sophistication and dynamic interactivity. But actually, all our simulations are implemented entirely in Mathematica; moreover, our presentation style is simple and stark in the extreme. Mathematica works for us as simulation and modelling software because it allows us to be open in our approach to design. All the code that is used to set up and run the simulations is visible to the students, and indeed we require them to engage with it directly. The relationships between the underlying mathematics, the chemistry that is being modelled, and the computer code that implements the model can be explicit rather than hidden. Students can be encouraged to adopt a critical attitude towards mathematical models and to develop their own ideas and approaches. On the other hand, Mathematica´s power and range enable us to set up fairly realistic and uncontrived problems, and to place some mathematical elements of these problems firmly in the background if we choose. I illustrate these strengths of Mathematica for our purposes using the example of a series of assessed problems. These concern the forces between ions (modelled as Newtonian point charges) and the chemical dynamics to which these forces give rise. I show examples of closed and open-ended tasks, and present excerpts of students? work on these tasks.