Over the course of the semester, we look in more or less detail at
many aspects of ancient and classical mathematics. However, the
field is far too enormous for a comprehensive account and we pass
rapidly over many topics and ignore many others. In order to give
you an opportunity to engage with one topic in more depth, you are to
work on a final project that wil culminate in both a brief presentation
to the class during finals week and a forma paper.

The paper should be about
7-10 pages, not including illustrations or figures, and must be
properly footnoted with a bibliography of sources cited at the end of
the paper. You may use whatever style of refernce you are
comfortable with (e.g., MLA, APA, etc.) so long as you are
consistent. In the paper you should introduce your topic, locate
it in its proper context and analyze its interest from both
mathematical and historical standpoints. That is, you need to
find a topic that is
significant both from an historical point of view and from a
mathematical point of view. You will be working with this paper for the
rest of the semester
-- choose something that interests you. Spend some time thinking about
possible
topics until you find something that you think will be both enjoyable
and
doable and for which you can obtain sufficient information. Do not
forget
to look ahead to topics we have not yet covered.

The presentation should
last approximately 7-10 minutes and explain to the class your topic,
why you chose it and what you found out. The presentatios will be
during our scheduled final exam time: 1:30 - 4:30 pm on Wednesday
December 14. Do not attempt to read your paper for the
presentation - think about how to present the most important points
clearly, without having to give all the detail you did in the
paper.

More particular suggestions include:

- Archaic metrological systems.
- The differing approaches to Sargonic mathematics.

- The development of the sexagesimal place value system.
- Analysis of some types of Old Babylonian problems and the techniques used.
- The scribal curriculum in the Old Babylonian period.
- Constructing and orienting pyramids.
- The Egyptian Mathematical Leather Roll.
- Egyptian scribal literature.
- The 2/n table in RMP.
- Analysis of a certain class of problems in RMP and the techniques used to solve them.
- The Moscow papyrus.
- The parallel postulate in Euclidean geometry.
- Eudoxus and the theory of proportion.
- Pythagoras and Pythagoreans.
- Mathematics and music in Greek period.
- The 'geometric algebra' debate.
- Archimedes: pick one aspect of his life and work
- Apollonius: analyse his conic constructions.
- Nicomachos.
- Hypatia.

Organize your material as well and as clearly as you can. Think through your arguments. Make sure you have supporting evidence. Every claim you make should be adequately backed up. Remember, this is an academic paper, not an article for a magazine. I expect details. I expect mathematics. And I also expect proper documentation of your sources. Every statement which is not either common knowledge or your own idea must be referenced.

Before you hand your paper in, write it, re-write it, have someone read it, re-write it. Repeat. It should be the best paper you can produce. Spend at least some time polishing away surface defects (grammar, punctuation, spelling, etc.) as they irritate the reader (me) and detract from an understanding of your argument.

When you write, think of the responses of the reader. If you have someone else read your paper, note their responses and be grateful. Good questions to keep in mind as you construct your paper include the following, among many others.

- Where could the paper be better organized?
- Where is the argument incomplete?
- Where is it inaccurate?
- Where is it unclear?
- Where do you need more or different evidence?
- Where are you too prolix?
- Where do you need more or less mathematics?
- Where do you need more or less history?
- Where should the focus be changed?

Up to Day
13.

Last modified: 5 October 2005

Comments to dmelville@stlawu.edu