### Mathematical Modelling

Real-life phenomena, from traffic flow to the effect of greenhouse gases, are
usually too complex to be analyzed quantitatively without idealization and
simplification. It is just not feasible to follow the individual motions of
dollars into and out of all the banking systems of the world, or the paths of
individual water molecules in the ocean, as ways to understand the economy
or the world's climate. When we simplify things, for example by neglecting
the gravitational pull of Jupiter on the motion of an airplane, we are making
a * model * of reality.
In some sense, the construction of useful mathematical models, for such prosaic
things as flow of fluids through porous media (such as diapers, as was done in
a study by our department for Johnson and Johnson) or for the motion of wood particles
in fluid for the pulp and paper industry (David Jeffrey studies this because there
is great interest in mechanical pulping because it is so much cleaner and easier
on the environment than chemical pulping), is the very essence of applied mathematics.

We offer a third year course in this---not first year because the rudiments of the
usual language for modelling, namely the calculus, must be mastered first---but it
is not until graduate school that modelling really comes into its own in our department.
Whether the models are for the physics of elementary particles, really getting down
to fundamentals, or for the motion of blood in arteries, or for the number of people
infected with HIV, the creation of useful and accurate models is as much an art
as a science---imagination, judgement, taste, reasoning, experience, and skill
all play a part. It is this which distinguishes applied from pure mathematics, because
pure mathematicians care little for where the mathematics comes from, or for what
it means. For us, what the equations * mean * is the heart of the matter.