Expository Papers, References, Internet Sites
(MATH 464)
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Papers - the Process
- Written Outline, including your topic and a broad plan for the paper. Choose something you like! Be prepared to verbally explain to me (and maybe the class too) what you think your paper will cover. Include a list of at least 3 printed references you are looking at. Each student must have a different topic. Try to use original sources as much as possible, i.e., "Learn from the Masters!" Look at the references and bibliographies of your sources for further related sources! This is detective work; follow the clues, stick to the truth.
- Many Drafts improves the paper immeasurably. REVISE! The First Draft Deadline in any case must be met. There will be a grade penalty if no First Draft is received by that date. A Draft should be at least half to three-quarters of the paper, in draft form of course. Type, please. Draw or write by hand any mathematics or pictures if necessary. Don't give a draft "for show". If there's nothing there, it is not acceptable.
- Previous Drafts. Always return the previous marked-up draft with the current draft, so I can recognize changes.
- Final Paper. See below for style, presentation, Title page, Reference page, 10+ internal pages, 10 or 12 pt font, 1 inch margins, etc.
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General Notes on Class Papers
- This semester you will be required to write two (2) 10-page papers. These are "internal" pages, not including the title and bibliography pages.
- The first paper is due by mid-term, and the second at the end of the course.
- For each paper you will turn in at least two DRAFTS, and then later the paper. The drafts will not be graded, but I will return them to you promptly with written comments, and discuss these with you verbally. More than two drafts are recommended. (If these drafts are not received before the final paper, 10% of your grade on the paper will be forfeited.)
- All topics must be approved by me beforehand, and each person must have a different topic. The First Paper usually covers a pre-1650 (before the invention of calculus) topic. The Second Paper usually covers post-1650 (after the invention of calculus). Of course these dates are flexible. Try to find a topic of particular interest to yourself.
- A paper must have a carefully explicated proof somewhere in it, possibly several. This will depend on your topic, of course; some papers will consist entirely of one "classic" proof, others will contain a series of smaller proofs. Discuss this with me.
- The papers should be roughly at least 50% (or more) mathematics. The English parts must be typed with a word-processor. The mathematics portions should be typed using a mathematical word processor such as Microsoft's Equation Editor. Diagrams can be hand-drawn if needed.
- Do not be too broad. Restrict to a few well-chosen and thoroughly explicated theorems as the core of your paper. The analysis of mathematics should be the core of your paper. Biographical, historical lead-in and conclusions are just the frame.
- The level of discourse in your paper should be at least that of a student at this 400 (senior) level of mathematics.
- The notation of Katz, Dunham, and this course should be the notation you use in your papers, and should otherwise be standard. Ask me if you have doubts.
- I expect a Title page (title, name, course, date), and a Bibliography page as the last page. Within your paper please refer to your numbered Bibliography references by numbers within square brackets, such as: [8] or, [17, p.242]. References to books should always have page references.
- A paper should have at least 5 references, among them original sources in some form. Quoting actual documents for illustration or flavor is a good idea. Web site references are discouraged.
- Your paper should be double-spaced, with 1 inch margins, and 12 pt. font or smaller.
A few ideas (not complete!) for papers:
- Start with a modern statement of a theorem or problem and its proof. Research its history: Various early proofs, counterexamples, errors, people and dates, variations, context, and so on.
- Start with a theory, or collection of ideas, and choose representative theorems to explicate.
- Start with a person and choose his or her specific important theorems to explicate.
- Look over titles of papers written by previous students in this course.
- For ideas note that Katz has Exercises, References, and Notes at the end of chapters, as well as General References at the end of the text. Dunham has a Bibliography at the end. Of course the Source Book by Smith is excellent. Look ahead in all the textbooks too; do not limit yourself to what we have already covered in class.
- The Linda Hall Library of Science, Engineering, and Technology is a major resource. Review back issues of Historia Mathematica or Scripta Mathematica. Great articles and ideas! Also visit UMKC's Miller Nichols Library.
- The Internet (see below) may be a source of ideas, but be highly critical of the information you find. Always confirm it in printed references.
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Good History of Mathematics Internet Sites
Many have Links to other sites of interest.
Be critical of the information you find!
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