Paper launch

MATH 323: Fall 2005

Final Project

Introduction

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.

Topic Suggestions

Possible categories of topics include: biographies of individual mathematicians or schools or institutions; history or evolution of a particular mathematical concept; various social, cultural or political influences on and uses of mathematics; mathematical education in a particular period and place; analysis of particular theorems, problems or problem types. You may go into a topic we covered in class in more depth, or work on a topic that we did not have time even to mention. For example, we covered only a small portion of Old Babylonian mathematics; you could use the tools we developed to analyze other problems. Similarly, we only considered a few problems from Rhind Mathematical Papyrus, we will look only at a few small portions of Euclid's Elements, we will only consider a fraction of the work of Archimedes and will not even mention many other mathematicians apart from Apollonius. A deeper analysis of a focussed topic is better than a superficial overview of a wide and complex issue. If the topic is sufficiently complex that you could write a book on it, then a 10-page paper probably won't do it justice.

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.

There are many, many more possible topics. This list is only meant to give you some ideas. Other good sources of topics are the readings, the DSB, the Companion Encyclopedia and the ancient chapters in history of mathematics textbooks.

Proposals/Abstracts and Preliminary Bibliography: Due October 24.

I will need a proposed title and a 1 paragraph abstract of your topic including basic outlines of what you expect to say and why you think it is a sufficiently interesting subject. Include comments on both mathematical and historical relevance and an annotated proposed bibliography. Research, reading and thinking take time. You need to get started finding possible sources of information, reading them, finding more sources, and ordering ILLs. For each entry in the preliminary bibliography you should give a complete bibliographical reference in your favorite format, together with a brief summary of the contents of each work and why it is relevant to your topic. The bibliography for the final paper will not need the annotations, but you will find them helpful in the process of writing the paper.

Actual Paper: Due December 14 by 4:30 pm.

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?

All this probably sounds like a lot of work. It is, so pick a topic you will enjoy.

Up to Day 13.

Last modified: 5 October 2005
Duncan J. Melville

Comments to dmelville@stlawu.edu