The Mathematical Laboratory: using Mathematica with Science Students

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The Mathematical Laboratory using Mathematica
with Science Students

• Phil Ramsden
• METRIC Project
• Imperial College, London

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Experiments in Undergraduate Mathematics

• Innovative in its approach to learning
• Highly conventional in its content.

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Math for science students

• We teach them a set of concepts and skills, then
• they apply them to their subjects.

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What math do scientists do?

• Explicit and sophisticated?
• Explicit but routine?
• Sophisticated but hidden?

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Current work at Imperial

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

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Assessed project

• Makes explicit the idea of model.
• Based on a simulation (but an explicit one).
• Mathematica 3.0 out of the can.

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Mathematical modelling

• Students lack technical proficiency, so...
• models tend to be fairly trivial, so
• its hard to do real science with them.

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Lecturers comments

• my tutorial group have some really great
  stuff . They hardly asked for help and two of
  them dont have A level maths, but some of
  their work shows real critical thinking. Here is
  an example

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Excerpt from a students 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. Im 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
  reactionif so, bye-bye model.

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Lecturers comments

• My groups scripts are full of this stuff, its
  not always correct but one can really figure out
  whats going on in their heads. Its really
  amazing.

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METRIC Project

• Phil Ramsden and Phillip Kent
• metric-proj_at_ic.ac.uk
• http//metric.ma.ic.ac.uk/