We want to talk about physical phenomena using
mathematical objects.
In these sheets, the objects are sets.^{1}

We call the mathematical objects which we use to reason (by analogy) about the physical phenomenon the model of the phenomenon. One often has a choice of model.

There are roughly two broad approaches to selecting a mathematical model for physical phenomena.

The first is deterministic. One constructs differential equations using physical principles and experiments. This is the method of Galileo and Newton for modeling moving rigid bodies. For example planets (i.e., balls).

The second is probabilistic. One specifies the probability of events using physical principles (e.g. the symmetry of noise) and experiments (e.g. the observed frequency of particular events).

- At present, this sheet deviates from the
analytical nature of the Bourbaki project. This
may change in future editions. In particular, we
may use physical models as
*motivation*for much of the mathematics. This sheet borrows from the notes of S. Lall. ↩︎