What is a Mathematical Model?
This course is centered around the idea of mathematical models. A mathematical model is a mathematical object --- be it a graph, a matrix, a finite state diagram, a Markov Chain, or any other mathematical construct --- that is used to represent a process that appears in the world. The model has to be complicated enough to approximate reality well, but at the same time it needs to be simple enough to be analyzable. The key idea is to have a way to analyze behavior of the process by looking at the analogous behavior in the mathematical model.