Lecture 1; Math 636

Math Modeling

1. Discovery and exploitation of mathematical structures in phenomena

2. Theoretical science

3. The art of crafting mathematics to match measurements

“Mathematics is a language” – J.W. Gibbs (1st US scientist of world renown; 1839-1903)

Iterative process – expand domain / improve accuracy

What constitutes “good enough” in any area is strongly dependent on prior art

Math structures on a set

graph

function(s) ß Most important

group

vector space

topology

metric space

topological vector space

measure

…

More modern models not so easily identified with a structure on a set

games

automata

information

The new feature seems to be the notion of “agent”.

Models can be

static – dynamic

deterministic – stochastic

discrete – continuous

robust – fragile

natural – ad hoc

Two hat model of a modeler: work in pairs (groups?).

Learn to speak mathematics and applications.

Variables vs. parameters