Suggestions and Comments on Term Paper for Math 401
Taken and Modified from Notes by Phill Schultz, University of Western Austarlia
Revised by Martin Flashman, Humboldt State University

Suggestions on Explication of Text

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 sources. But this background material should occupy not more than a quarter of your essay. The main content should be a careful explanation of exactly what the author is trying to do and how he or she does it. Try to put yourself into the shoes of the author, not assuming any more knowledge or a cultural 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 doing so.

 Here are some points to bear in mind when writing an explication:

  1.  Sometimes it is important to discuss the actual document and how it was transmitted to us. This is especially important for documents from antiquity, or in cases that the original does not survive, or when the text is a translation.
  2. Sometimes it is important to discuss biographical details of the authors, for example those which explain their mathematical development.
  3. It is essential to discuss the mathematical significance of the text, for example how it is linked to earlier and later mathematics.
  4. Discuss the historical, cultural, social or religious background of the author if this is relevant to the mathematics.
  5. Use your own ideas wherever possible, especially when you do not agree with statements in the references.
  6. Adequate referencing is essential. Whenever you make a statement that is based on something you have read, give a complete reference including page or section number. There are several reasons for this. First, it is essential 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 back and check something, so adequate referencing the first time round saves you time in the long run.

Suggestions on 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 opportunity to talk about something on which you know more than anyone else, including me. You have already thoroughly prepared the material in much more detail than you could possibly present in half an hour. In the week 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 than 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 it. This should occupy about half or more of your talk. Your sources of information are 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 main concerns of mathematicians of the time? What was known about the problem 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 of Mathematics?

Other Suggesions

General points to bear in mind:

  1. 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 of mathematics as well as the history and background of that mathematics.
  2. Enough expository material should be included so as to make your paper self-contained.
  3. You should use a variety of research materials and must give careful references to your sources. Usually, a source consists of a book or article which may refer to other sources. Give complete details!! For suitable formats, see any issue of the journals Archive for the History of the Exact Sciences or Historia Mathematica.
  4. Your paper should include a Bibliography listing your sources and they should be cited in the body of your paper when appropriate. See the journals 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.
  5. For projects that go beyond explication of a single source, your work may include a paraphrase of other people's ideas, but should present your own point of view, or perhaps several opposing points of view with your reasoned arguments for supporting one of them. You are not expected to make any startling new contributions to human knowledge (though such would of course be welcome and suitably rewarded). However, you are expected to produce a coherent presentation of your own ideas and opinions, comparing and crticising the opinions of others, conjecturing how mathematicians may have been led to their discoveries, who may have influenced them, how they were affected by their social environment or personal background. You are especially expected to make a judicious choice of texts to quote and where necessary clarify them in modern terminology.
  6. What you write should indicate that you understand what you are writing: indications to the contrary include quotes out of context, abstruse language "lifted" from elsewhere, and insufficient detail in a mathematical argument.
  7. You are welcome to discuss the progress of your essay, and any difficulties you are having, with me at any time. I may be able to suggest new ideas and references. However, I will not comment on a draft of your completed essay. What you finally submit must be your own work.
  8. The grading of your paper will be based on a number of factors, including: the historical and mathematical content; the significance, interest, accuracy, and completeness of the material; the accuracy, scope and significance of your references, and the sensitivity with which they are used and cited; and finally, the style in which it is written.

Plagiarism.

According to the Random House College Dictionary plagiarism is "the appropriation or imitation of the language, ideas, and thoughts of another author, and representation of them as one's original work."

Scrupulous care 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 reference to the work where you learned this information.

REFERENCES

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:
  1. Carl B. Boyer and Uta C.Merzbach, A History of Mathematics
  2. Howard Eves, An Introduction to the History of Mathematics.
  3. Victor J. Katz A History of Mathematics
Two other important sources of information are:
  1. Ivor Grattan-Guiness Companion Encyclopaedia of the History and Philosophy of the Mathematical Sciences
  2. Morris Kline Mathematical Thought from Ancient to Modern Times
In addition, you should become familiar with C. C. Gillispie Dictionary of Scientific Biography

World Wide Web

The Web is a useful source of information and entertainment concerning 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://users.humboldt.edu/flashman/mathhistorysites.html, to find numerous links to other relevant sites.

Last update: June 7, 2011

Author: Phill Schultz, schultz@maths.uwa.edu.au
Revised for use in Math 401 at Humboldt State University by Martin Flashman