MATH 323: Fall 2005
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
topics until you find something that you think will be both enjoyable
doable and for which you can obtain sufficient information. Do not
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
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
not have time even to mention. For example, we covered only a small
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
Elements, we will only consider a fraction of the work of Archimedes
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:
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.
- 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
- 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
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.
Proposals/Abstracts and Preliminary Bibliography: Due October 24.
I will need a proposed title and a 1 paragraph abstract of your topic
basic outlines of what you expect to say and why you think it is a
interesting subject. Include comments on both mathematical and
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
reference in your favorite format, together with a brief summary of the
of each work and why it is relevant to your topic. The bibliography for
final paper will not need the annotations, but you will find them
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,
an article for a magazine. I expect details. I expect mathematics. And
also expect proper documentation of your sources. Every statement which
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
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
All this probably sounds like a lot of work. It is, so pick a topic you
- 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?
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Last modified: 5 October 2005
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