The Mathematical Laboratory using Mathematica with Science Students

The Mathematical Laboratory: using Mathematica with Science Students Phil Ramsden METRIC Project Imperial College, London

Experiments in Undergraduate Mathematics • Innovative in its approach to learning • Highly conventional in its content.

Math for science students • We teach them a set of concepts and skills, then… • … they “apply” them to their subjects.

What math do scientists do? • Explicit and sophisticated? • Explicit but routine? • Sophisticated but hidden?

Current work at Imperial • Departments of Mathematics and Chemistry. • Math as an integral part of (physical) chemistry. • Examine, amend, devise and reflect upon models.

Assessed project • Makes explicit the idea of model. • Based on a simulation (but an explicit one). • Mathematica 3. 0 “out of the can”.

Mathematical modelling • Students lack technical proficiency, so. . . • … models tend to be fairly trivial, so… • … it’s hard to do “real” science with them.

Lecturer’s comments: … my tutorial group have some really great stuff…. They hardly asked for help and two of them don’t have ‘A’ level maths, but some of their work shows real critical thinking. Here is an example:

Excerpt from a student’s work: … this one could be more complex, but no way am I giving up. The potential energy is basically shown by area under the force-time graph [sic]. An option is therefore to integrate the expression force/time. … I’m simply going to work out an equation for the potential energy of each particle (using Integrate) and substitute that equation into my Plot command… I can then combine the two graphs for potential and kinetic energy and see if it varies during the reaction—if so, bye-bye model.

Lecturer’s comments: My group’s scripts are full of this stuff, it’s not always correct but one can really figure out what’s going on in their heads. It’s really amazing.

METRIC Project Phil Ramsden and Phillip Kent metric-proj@ic. ac. uk http: //metric. ma. ic. ac. uk/