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