Your paper should contain the following components:

- The definition of a Markov chain.
- The definition of a transition matrix.
- The definitions of a regular transition matrix and a regular chain.
- A discussion of steady states.
- An argument that 1 is an eigenvalue of the transition matrix for any Markov chain.
- Examples of Markov chains and transition matrices.
- Applications of Markov chains to population distributions and/or other models of situations in biology, business, chemistry, engineering, economics, physics, or elsewhere.

Your first task in this project is to work out the mathematical details of Markov chains, and the second is to make sense of those details and organize them in a coherent written narrative. Your final paper may include symbols, computations, graphs, and matrices; however, these will need to be accompanied by generous verbal explanations that explain the mathematical ideas. You will be graded both on mathematical accuracy and written clarity. You must cite any sources that you use in proper bibliographic format.

You can find information on Markov chains in our textbook (Section 1.7), in the standard reference texts that I've posted on the General Information page, or by searching for information on the internet and/or in the library. Again, you must cite any sources that you use in proper bibliographic format.

Your final paper must be turned in by