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The Mathematical Laboratory: Using Mathematica
with Science Students
Phil Ramsden
Imperial College
Download talk material:
Presenter's website: http://metric.ma.ic.ac.uk
The traditional model of mathematics teaching for science students
goes a bit like
this: first we teach them a set of mathematical concepts and skills,
and then the students
"apply" those concepts and skills to their subjects. This works fine some of the
time and for some
students, but it has a well-known drawback, namely, that for many
students the mathematics
stays forever separate from the science and never gets
"applied" at all.
Moreover, the way science uses mathematics is changing. At one time
the mathematics that
scientists used was generally explicit but often, outside certain
disciplines, routine.
Scientists in many fields now use techniques of analysis that reflect
increasingly
sophisticated mathematical models, but these models are often implicit
in the technology
of the lab. The scientist of the 21st century needs to have
access to, and
understanding of, the mathematical models that underlie her work: she
needs that just as
much as, if not more than, mastery of traditional pen-and-paper
algorithms.
Here at Imperial, the departments of mathematics and chemistry are
working on a joint
teaching project based on Mathematica. The governing philosophy
of the project is
that students should, from early on in their first year, encounter
math as an integral
part of chemistry and that they should be encouraged to examine,
amend, devise, and
reflect upon mathematical and statistical models of chemical systems.
Without computer
power, such a project would have foundered because without computer
power the students
would have access only to trivial, tractable models that don't
adequately
describe the science. With the wrong kind of computer power, it would
have foundered for
another reason: if, for example, we had merely written a collection of
"simulations," then the mathematics would have remained
hidden behind an opaque
user interface.
What Mathematica gives us is power plus explicitness: the
ability to set up
relatively sophisticated models in a way that allows students to
ungroup and amend them
and then to set up their own. The typesetting features of the new
front end have helped us
to get students into the mathematics quickly and smoothly without
needing first to master
an arcane syntax.
I will demonstrate some examples of the materials we are devising at
Imperial, together with
some preliminary findings from a systematic evaluation of them in use
that is being carried out by the
Institute of Education in London.
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