Lecture 2; Math 636


Natural vs. ad hoc models revisited


Metatheorem: The more you match the structure of the problem, the better the model.


System – varies with application but generally coincides with the object being modeled*




Manifold = variables + equations between them (Differential Geometry)


Static vs dynamic models revisited


Group = generators + equations between them (Abstract Algebra)


Arguments from scale:

            Groups acting on sets -- symmetries

            Scaling: Group of similitudes (homotheties, multiples of the identity)

            Alias vs. alibi in group actions – the two halves of chapter 2

                        Example: the rotation group on R2

                                                      Given an orthogonal matrix, is it a linear map or a change of basis?


            Allometric models


            Units and dimensional analysis



*Image from http://energy.sdsu.edu/testcenter/testhome/Test/problems/images/ch01/piston-coil.jpg