Topic selection (10 points): The topic for your research project is to be selected by you, in consultation with me, by 9 a.m., Thursday, April 10. The topic should be a great theorem from mathematics history which can be developed into a chapter of Journey Through Genius. Note that Journey Through Genius chapters generally include historical information providing a context for the great theorem (much mathematics history and some general history), biographical information about the mathematicians involved, the great theorem itself together with a clear and lucid presentation of its proof, and an Epilogue describing subsequent ramifications and applications of the great theorem.

Preliminary reports (60 points): These consist of any 2-3 consecutive pages of your paper, not including the title page or the bibliography. Your bibliography to date must be included with each preliminary report. Your first preliminary report may be a detailed 2-3-page outline or description of what you intend for your paper to include, or it may be any 2-3 pages of your paper. Preliminary reports are due Friday, April 18, and Friday, April 25 (30 points each).

The paper itself (170 points): Your paper, of course, should be carefully prepared, organized and presented. It must include a title page and a bibliography, but otherwise should be organized as are the chapters in Journey Through Genius. The style also should be similar to that of Journey Through Genius---that is, it should be clear and lively. Number definitions, theorems, examples, and figures. You may find it helpful to number some or all of your equations as well. Be consistent in your numbering scheme and in your use of notation.

At least four (4) sources must be cited in the body of the paper. Cite these references by number (e.g. [3], where [3] refers to the third reference in your list, also labeled [3]) or author (e.g. (Smith, 1988)), rather than using footnotes. The paper must include a list of references, or bibliography. The list of sources you actually cite should appear first, followed (if you wish) by a list of additional sources consulted and/or recommended to the reader.

How much detail should you provide? Use Dunham's Journey Through Genius
as your model. More specifically, your goal should be to make the material you are presenting clear to a sophomore mathematics major who has not previously studied this material. Clear and correct explanations and arguments are essential; illustrative examples and diagrams are always helpful.

Criteria for evaluation include the accuracy of the history and the mathematics you present, the organization and clarity of your presentation, your use of appropriate and illustrative examples, your use of mathematical notation, and your use of the English language (this includes style and grace, as well as grammar and spelling).

The first draft is due Friday, May 2 (30 points); and the final draft is due Monday, May 12 (140 points).

The paper should be word processed and laser printed. In order to save time later, I recommend that you type up sections of your paper as you work on them. In particular, be sure to compile your bibliography as you find and use references.

Oral presentation (60 points): No more than 20 minutes, please! Tips will be given in class beforehand. Rehearsal required. Presentations will be given in class Thursday, May 8, Tuesday, May 13, and Thursday, May 15.

Suggested paper topics: Perfect numbers and the Euclid-Euler formula, Pythagorean triples, FLT n=4 case, sums of squares, Fibonacci sequence, properties of "Pascal" triangle, Stirling's formula, Wallis's formula, logarithm as an integral, logarithms of negative numbers, Konigsburg Bridge Problem and Euler circuits, Euler's formula, Four Color Theorem, Cauchy's "wrong" theorems and proofs, etc., etc.


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