Lecture 1; Math 636
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
function(s) ß Most important
topological vector space
More modern models not so easily identified with a structure on a set
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