the mathematical laboratory: using mathematica with science students phil ramsden metric project...
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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 for 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.
