| Suggestions and Comments on Term Paper
for Math 401
Taken and Modified from Notes by Phill Schultz, University of Western
Revised by Martin Flashman, Humboldt State University
Suggestions on Explication
Initially, find a source from which the
text is extracted, and
read enough about your text to put it into its historical context. For
this, you will also have to consult other library books and Internet
But this background material should occupy not more than a quarter of your
essay. The main content should be a careful explanation of
the author is trying to do and how he or she does it. Try to put
into the shoes of the author, not assuming any more knowledge or a
background that he or she did not have. When you employ modern notation
or concepts in order to explain the text, make it clear that you are
Here are some points to bear in
mind when writing an explication:
- Sometimes it is important to discuss the actual
document and how
it was transmitted to us. This is especially important for documents
antiquity, or in cases that the original does not survive, or when the
text is a translation.
- Sometimes it is important to discuss biographical details
of the authors,
for example those which explain their mathematical development.
- It is essential to discuss the mathematical significance of
the text, for
example how it is linked to earlier and later mathematics.
- Discuss the historical, cultural, social or religious
background of the
author if this is relevant to the mathematics.
- Use your own ideas wherever possible, especially when you
do not agree
with statements in the references.
- Adequate referencing is essential. Whenever you make a
based on something you have read, give a complete reference including
or section number. There are several reasons for this. First, it is
for academic ethics. Second, it allows your readers to pursue a part of
your work which interests them. Third, you will eventually need to go
and check something, so adequate referencing the first time round saves
you time in the long run.
Presenting Your Talk.
|It is a new and sometimes frightening experience for
students to present
a talk in front of a class. Relax, and look on it as a unique
to talk about something on which you know more than anyone else,
me. You have already thoroughly prepared the material in much
more detail than you could possibly present in half an hour. In the
before your presentation, cull this material to the bare minimum needed
to explain the essence of the text, and practice it either before your
friends or in front of a mirror. It is a worse fault to go over time
to finish five minutes early.
If you would like the class to have materials for your presentation,
let me know and I will have them reproduced for the class.
Remember that your audience has the text
in front of them so there
is no need to write it on the blackboard. Begin by explaining precisely
what the author was trying to do, and then explain how he or she did
This should occupy about half or more of your talk. Your sources of
the same as those mentioned in the section Explication of Text above.
The remainder of your talk should
about placing your author in
the context of his own mathematical and social culture. What were the
concerns of mathematicians of the time? What was known about the
before the author tackled it? Is it a school text or new research? What
influence did it have on the author's contemporaries or on the History
General points to bear in mind:
- Your project is on the history of mathematics. It should be
neither all history
nor all mathematics but should contain a reasonably non-trivial piece
mathematics as well as the history and background of that mathematics.
- Enough expository material should be included so as to make
- You should use a variety of research materials and must
to your sources. Usually, a source consists of a book or article which
may refer to other sources. Give complete details!! For suitable
see any issue of the journals Archive for the History of the Exact
or Historia Mathematica.
- Your paper should include a Bibliography listing your
sources and they
should be cited in the body of your paper when appropriate. See the
mentioned above for the correct method. Do not use Footnotes but refer
in the body of the essay to specific page numbers or chapters of works
(including web sites) listed in your Bibliography. Sometimes you may
not be able to access the work referred to, which is cited in some
secondary source. In that case, your reference in the body of the essay
should say "cited in ..." and the Bibliography should include both
primary and secondary source.
- For projects that go beyond explication of a single source,
work may include a paraphrase of other people's ideas, but should
present your own point of view, or perhaps several opposing points of
with your reasoned arguments for supporting one of them. You are not
to make any startling new contributions to human knowledge (though such
would of course be welcome and suitably rewarded). However, you are
to produce a coherent presentation of your own ideas and opinions,
and crticising the opinions of others, conjecturing how mathematicians
may have been led to their discoveries, who may have influenced them,
they were affected by their social environment or personal background.
You are especially expected to make a judicious choice of texts to
and where necessary clarify them in modern terminology.
- What you write should
indicate that you understand what you are writing:
to the contrary include quotes out of context, abstruse language
"lifted" from elsewhere, and insufficient detail in a mathematical
- You are welcome to discuss
the progress of your essay, and any
you are having, with me at any time. I may be able to suggest
and references. However, I will not comment on a draft of your
essay. What you finally submit must be your own work.
- The grading of your paper will be based on a
including: the historical and mathematical content; the significance,
accuracy, and completeness of the material; the accuracy, scope and
of your references, and the sensitivity with which they are used and
and finally, the style in which it is written.
| According to the Random House College Dictionary
plagiarism is "the appropriation
or imitation of the language, ideas, and thoughts of another author,
representation of them as one's original work."
must be taken to avoid this in your writing. Naturally
the source of a direct quotation must be cited. But also when you take
the ideas of another and rephrase them you must cite your source. In historical
work everything except the common and readily available facts needs a
to the work where you learned this information.
|There are numerous texts on the History of Mathematics
in the HSU
Library. Apart from the source volumes mentioned above and our own text
by Katz, the texts I recommend:
Two other important sources of information
- Carl B. Boyer and Uta C.Merzbach, A History of
- Howard Eves, An Introduction to
the History of Mathematics.
- Victor J. Katz A History of Mathematics
In addition, you should become familiar
with C. C. Gillispie Dictionary of Scientific Biography
- Ivor Grattan-Guiness Companion Encyclopaedia of the
History and Philosophy
of the Mathematical Sciences
- Morris Kline Mathematical Thought from Ancient to
World Wide Web
|The Web is a useful source of information and
the History of Mathematics. However, it is not always reliable or
accurate. Do not accept at face value everything you read on the
Web. A useful link is http://flashman.neocities.org/mathhistorysites.html,
to find numerous links to other relevant sites.