Have you ever wondered why a group of interacting nations
often polarizes, i.e. divides quite unexpectedly into diametrically
opposed subsets of nations? What rules of interaction would lead to
such a division? Are tripolar and more complex configurations
possible? And how might an arbitrary configuration of friendly and
hostile relationshsips at one time evolve into a polar one at another
time?
Can you predict, given the density of cars on a road, when there will be a traffic jam at a light?
Is it possible to treat cars moving on a road as a continuous stream, like a fluid, or is it necessary to view each car as an individual entity?
Is is
possible to anticipate when two nations will become involved in an
ever escalating arms race, increasing their arms budgets at each turn
in reaction to similar escalations by their adversary? Are
configurations other than a run away arms race possible?
A mouse is running in a maze, with lighted and darken rooms, trap doors (the sky is the limit here), and a prize dish of succulent food at the end. Can one say anything reasonable about such a situation? How long might one expect it to take the mouse to get to the prize? On average, how often does the mouse remain in a lighted vs a darken room (i.e. is the mouse afraid of the dark)?
All of these questions, and their answers, flow from mathematical models of the problems involved. This course is concerned with providing the student with modeling skills as well as an appreciation of the different sides of modeling, including the use of different mathematical methods in modeling endeavors. We will
While mathematical background is flexible, exposure to differential equations would be a asset. In addition the course will have a distinctive Web approach, with the use of software essential.