Markov chains, which are introduced in Problem Set 6, #6,
have a huge range of applications. For example, they are used in
chemistry to model reactions, in economics to model asset pricing, and
in biology to model population processes. A less serious
application is to use this math to figure out which
squares in the game Monopoly are landed on most frequently.
Here are a couple of Scientific American articles which
explain more: "How Fair Is Monopoly?" and "Monopoly
Revisited". You should see that the math here is basically the same as that in Problem Set 6, #6.
The articles mention that "eigenvectors" are a fast way to do some
of the computations; we'll be talking about those in a few weeks!