Projects for Math on the Web (Math 645-543)

Instructions

The two main projects for the term are listed below.

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 an absolute necessity.
  • Any mathematics involved must be valid.
  • Any markup (such as LaTeX or HTML) must be free of errors.
• Clarity. Your work should be well-organized, executed with good style, and appropriate for its intended audience.
• Creativity.

Your work will benefit 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. I expect to see several drafts for each project.

Preliminary drafts of the projects are due October 6. The final versions of all three projects are due one week before the last class of the semester.

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 to another web page.
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. I may be able to suggest to you some faculty member who would like to have a website.

Project B

As your major 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 (error correcting codes? cryptography? fractals? chaos? mathematics in astronomy? 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, a mathematical graphic of your devising---perhaps a 3D Mapleplot). 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. Uses for graphics in mathematics (or math instruction) on the web: try web sites of math organizations or math-oriented companies -- American Mathematical Society, Mathematical Association of America, Mathematica, Maple, or math department web sites, e.g., UPenn Math, etc.
7. Putting math on the web directly (without using .PDF files, which require the viewer to use Acrobat Reader or another PDF viewer). There are at least two projects based on XML (eXtensible Markup Language) -- GELLMU (by Bill Hammond, my recitation instructor in freshman math, which was called "Magic Math" by the engineering students), and MathML (by Robert Miner, at University of Michigan, if I recall, and by a second author whose name escape me now.) What are the advantages and disadvantages? How far along is it (MathML is being used expermentally at Hindawi Press)? What does it look like? etc.
8. Including graphics files in PDF documents.I will do a little on this, but it would be easy to write a short paper on this subject --or even a long paper.
9. Generating graphics for use on the web.
   1. Bill Casselman's web site has a lot of examples of graphics and a PDF book on using PostScript to produce graphics.
   2. Graphics Editors: on Unix systems there is xfig (available directly on the command line on crab and probably on clam as well), and there is a newer and more versatile editor called skencil, which is probably buried on our servers, but if so, can be accessed by giving the full path to the file.
10. 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. For example, it may be possible for you to create interactive lessons for the Calculus on the Web program at Temple University, which uses PERL to process what a student types as an answer to a question, generate valid input for the computer algebra package Maple, feeds the input to Maple, which compages the student's answer with the correct answer, and again uses PERL to give feedback to the student by creating a web page. A detailed description of the module would go on your home page. A somewhat less demanding project might be to create web pages that would provide students with feedback in a less sophisticated way, allowing students to choose between several choices, and then presenting the student with information based on which choice the student made.

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Last modified: October 27, 2004