In our vigorous teaching of concepts and skills to
students, we may cover (hide) more than we uncover,
obscuring significant relationships between mathematical
models and their associated chemical concepts with excessive
mathematical derivations. To set the record straight, I find
that mathematical treatments of physical phenomena are
beautiful and elegant. Students should know from where the
equations and simplifications leading to them arise. They
should know the limits of the equations in order to use them
properly. However, this can be the Siren's song. For example,
the mathematical representation of the Fourier transform and
its significance as presented in most texts are too brief to
convey understanding to the typical undergraduate student.
Furthermore, a few hand calculations would not permit
deeper probing of the method and its intimate link to
spectroscopy. The Fourier transform is a very good example of how
symbolic equation software can help to uncover the science
by making the mathematical manipulations easier and the
mathematical concepts more accessible.
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