Projects for Mathematical Communication and Technology (Math 689-604)

Instructions

The three main projects for the term are listed below. These projects are intentionally open-ended: that's how life is. I expect you, as graduate students, to be at the level of working on somewhat vague problems that have no single correct answer.

One of my jobs as your instructor is to give you guidance, so if you have questions about the projects, or you need further direction, please ask me. Here are some of the criteria that I will use in evaluating your work:

• Correctness. This is the sine qua non!
  • The mathematics involved must be valid.
  • The computer code (Maple, LaTeX, html) must be free of errors.
• Clarity. Your work should be well-organized, executed with good style, and appropriate for its intended audience.
• Creativity.

Quality work benefits by going through multiple drafts. I hope that you will start working on these projects right away. As your skills improve over the course of the semester, you will be able to refine and improve your work.

Preliminary drafts of two projects are due by October 20. The final versions of all three projects are due December 4.

Project A

1. Make yourself a home page on the World-Wide Web. Your page must contain at least one image (for instance, a picture of yourself) and at least one link.
2. Help someone else create a home page. For example, this could be a faculty member, a friend, or your home town chamber of commerce. Include a link on your home page to the other person's page.

Project B

Look through the Maple Help Browser, pick out some item or package that interests you, and write a Maple lab (suitable for undergraduates) that illustrates and explains that topic. The topic should be something beyond what is covered in the CalcLabs with Maple V manual.

Examples of possible topics are: Grobner bases; Euler-Maclaurin summation; the Mellin transform; permutation groups; amortization schedules; the simplex algorithm; projective geometry; Sylow subgroups; p-adic numbers; normal forms of matrices; Fermat numbers; Euler's constant; continued fractions; Bessel functions; fitting data via least squares. There are lots and lots of other possibilities.

Project C

As your third project, choose one of the following.

1. Write an essay about the number pi, suitable for first-year college students. Make both a hypertext version (with a link to your home page) and a paper version (in LaTeX). For example, you could find out who holds the record for computing digits of pi, how was the computation done, where on the Internet can one get a million digits of pi. I expect the paper version to be five to ten pages long.
2. As above, but address the topic of prime numbers. (For example, what is the largest prime number known, what are the largest twin primes known, how were they found, etc.)
3. As above, but some other topic (fractals? chaos? the Poincaré conjecture?). Please get my approval for the topic ahead of time. Keep in mind the intended audience of first-year college students.
4. Design a letterhead for the Department of Mathematics. The idea is that someone should be able to start off a letter with

                 \documentclass[12pt]{letter}
                 \input letterhead
                 \begin{document}

   and have the letterhead appear at the right place at the top of the letter. The letterhead should contain an image (for instance, the TAMU seal, or a mathematical graphic of your devising---perhaps a 3D Maple plot). Also, the letterhead needs to work with all of the options [10pt], [11pt], and [12pt]. Write instructions about how to use the letterhead, and put a link to them on your home page.
5. Lamport says that each LaTeX installation is supposed to have a Local Guide. This should describe the idiosyncrasies of the local system, how to print and preview, local availability of packages and fonts, and so forth. The Department of Mathematics does not have a Local Guide. Write one. Make a hypertext version with a link to your home page, and a paper version (in LaTeX, of course).
6. Other projects are possible and encouraged. If you have an idea for a project that you would like to do, please discuss it with me ahead of time.

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Last modified: Wed Sep 6 16:09:10 1995