Governor's School for the Sciences 2006

Math 251 - Final Project

Project Details

The final project for our class has two components: a short (5-15 minute) in-class presentation on the last Thursday (or Friday if needed) and a 2-5 page write up.

You are allowed and encouraged to work with a partner on this project.

We will have the last Wednesday open for you to work on your project but you should pick something out before then and begin doing some work.

There are two main options for projects. The first is to take one of the application labs we did in class and to do either a more detailed example or to do some variation on the lab. I've listed some examples of those below. The other is to find either in our book or some other linear algebra book some theory or concept that we didn't cover and investigate it.

Some Project Suggestions
There are lots of possibilities with Markov Chains (Labs 5, 10). You could model an existing board game or some made up game. You could do random movement on a large 2D maze. You could model an existing or made up disease with many states.

The growth models of Lab 6 are like Markov Chains and thus have lots of available variations to other situations.

In graphics, you could study fractals (Mandelbrot and Julia Sets) and how they relate to what we did in Labs 9 and 11. Or you could extend Lab 12 by learning how to incorporate perspective as a the projection.

The network and economic models of Lab 3 and 4 have obvious possibilities to extend to larger or more complex problems. You might try and find data on Leontief's original problem.

You could figure out and explain how the Fast Fourier Transform works (Lab 14).