The Project.

You will prepare a three page paper explaining a potential application of some higher mathematics to a physical problem. I will not be worried so much about any actual math which appears as about your explanation of the problem and how to solve it. Your English will count!

Your first assignment, for Friday, May 18th, is to read Chapters 7.6, 8.8, and 8.9. Focus on the examples, not necessarily yet the actual mathematics. You will be asked to choose a couple of these applications to explain in your project, so look for ones which are interesting to you. By all means look for ones from elsewhere in the book, or others you know of, as well. For instance, if you are interested in computers, complex numbers and Boolean algebras (neither of which are discussed in our class) are likely candidates for a project. I will try to have other resources available for you as well if you come in for office hours.

Let's be a little more specific, now that you're thinking about your projects, about the details.

1) The math involved needs to be relatively sophisticated. That means differential equations, interesting applications of series, parametric equations, or something else you couldn't really have learned before this quarter. Finding the area under a curve or the speed of a ball dropped from a building is not enough.

2) It should be a real physical problem. You may need to be inventive to come up with one, or to simplify your area of interest to make it tractable in the time we have. Still, the paper needs to be more than just proving an interesting theorem.

3) Within the 3 pages or so of the paper, I would like both a good description of the physical situation (in idiomatic English) and full mathematical justification of any more difficult results you use. You are free, of course, to mention further refinements of the problem and how more advanced techniques we couldn't hope to cover in this class would be used, but the main ones should be suitably explained.

4) When you write the paper, assume you are writing to someone who has had basic integral and differential calculus, but isn't familiar with either the full physical situation or the (more sophisticated) techniques you are using. Maybe imagine you are writing to yourself several years down the road, when you have forgotten a lot of the things you are learning here, but want to refresh your memory. There's a reason why there are so many books in stores about 'Forgotten Calculus'...

5) Don't stress out. If you are stuck, the WORST!!!! thing you can do is not tell me. That almost guarantees getting very few of the ten percentage points of your grade this project is worth. I am going out on a limb to put in the time and energy to do this too, but I thought it would be more profitable for you than yet another midterm. Prove me right.

Your second assignment, which should be ready Friday, May 25th, will involve a paragraph long proposal of precisely what you will investigate, as well as a description of the mathematics involved. So be prepared to have a pretty good idea of what you will be describing.

A preliminary version of the actual project will be due a week before the final. If you wish, you can hand in a blank piece of paper; however, you will probably want my input on a rough draft! The final version will be due at the beginning of the final exam; this is a firm deadline.

Those of you who handed in rough drafts may pick them up in my box near my office in Eckhart basement. I hope they all turn out as well as they seem to be developing. These are just rough drafts, but they already look pretty good.