Winter 2014
Math 467: Modern Geometry

Frank Sottile

Paper policies

This is a W class, and one way that we fulfill that attribute is by writing papers. There will be two papers for this class. The first will be on a topic related to the book Flatland by Edwin Abbott Abbott, and the second will be either I will give more information in the second half of the semester, in general, I urge creativity.
Second paper: This is to be either Historical/Expository or Mathematical. By Historical/Expository, I mean an exposition on a topic from the class, on a historical figure, or on the evolution of an idea. Our book is full of a lot of additional material which can help you get started. A mathematical paper should involve the exposition of a significant result that is interesting. Proofs, definitions, ilustrataions, etc. need to be included when appropriate. See Notes on choice of topic below for more information, Flatland: The book Flatland is a classic that has piqued the imagination of readers for 130 years. I want you to write a paper inspired by Flatland; there are many possible and legitimate directions to take. Simplistically (for the purpose of this paragraph), Flatland is both a social satire and an exploration of the meaning of space and dimension. One direction that you could take is to compare it to other well-known satires, either modern or classical, or both. You could use it as a point de départ to discuss education, or class, or education of Women in either Victorian England or contemporary US or elsewhere. You could explore its mathematical aspects, or mathematics that it touches on (geometry in higher-dimensional space). Flatland has inspired a lot of other works, including other books, movies, and articles, you could write about some of these, or about its affects on how people think. It is possible to argue a line from Flatland to special and general relativity. You could write additional chapetrs/sections for Flatland. The possibilities are limited only by your imagination.
I will expect multiple sources in addition to the book Flatland, and solely on-line sources will not cut it, unless you can make a good argument.

Each paper should exceed five pages and 1500 words. You will need at least this much in order to do your topic justice. In past semesters, I have found that shorted papers are often too sketchy to receive high marks. If you happen to do an excellent job with fewer words, I could lighten this requirement, the standards will be quite high for that.
Papers will be marked out of 160 points, with 10 points for timely and complete submission of topic and sources, 30 for the rough draft, 20 for the peer-review, and 100 for the final product.
Topic and sources: Give a (preliminary) title, and a short (2 sentences to 1 paragraph) description of your topic, e.g. an abstract.
Historical/Expository require multiple sources, severeal of which must be longer than the paper itself. I want to see at least one source that is not a web page. Remember that Web items usually have authors and titles, not just URLs, and need to be cited accordingly. (Giving the date of access is also considered desirable, since the Web changes constantly.)
Mathematical papers need not have sources, if it is self-contained, but they would be improved by your knowing something of the context. In fact an important part of the mathematical paper will be its introduction (for context if that is warranted) and the clarity/justification of any definitions.
Draft: This will be handed in to Frank, who will look at them and make some comments. While they need not be in final form, they should be complete, and will be marked on that basis.
Peer Review: We will spend one day of class time working in small groups to read and discuss your writing. Your drafts must also be handed in to members of your group.
Here is an approximate breakdown:

Criterion Expository Mathematical

Choice of topic 5% 5%

Correctness and depth 25% 50%

Exposition 35% 20%

Mechanics (punctuation, etc.) 25% 20%

References 10% 5%
Don't expect perfect scores. In serious writing the threshold of perfection is infinite.
A note on Plagiarism: Finding information in books or on the Internet is praiseworthy; lying (even by silence) about where it came from is academic dishonesty. Whenever you copy from, or "find the answer" in, some other source, give a footnote or reference. Otherwise, you are certifying that it is your own work.
Guidelines for Authors. This is borrowed from Steve Fulling
Notes on choice of topic: This is borrowed, with premission, from Steve Fulling
- Any "major exercise" or "project" from the textbook is allowable, with the qualifications below.
- You can choose a topic from outside the book's lists, but it would be prudent to consult me about it first.
- In Ch. 1, major exercise 4 is harder than it looks. I'll accept a paper that does 2 of the 3 parts (e.g., assumes (a) and uses it to prove (b) and (c)).
- Poject 5 in Ch. 1 (Morley's theorem) to be historical. (The solution is hard to work out but easy to find on the web.) So, put some history into it. (One paper found and compared two proofs.) I would shy away from this topic.
- Ch. 1, project 13: Beware that Russell has been misquoted here (and many other places). The correct quotation, which has different connotations, is here.
- In Ch. 2, regular exercises 14, 15, 16, and 19 are "major" in my opinion (hence suitable for papers).
- In Ch. 3, major exercise 6 is quite long. Part (a) alone (done well) makes a good 5-page paper.
- All exercises in Ch. 7 are considered "major".
- All essay topics in Ch. 8 are considered "major" (but some may also be "historical"; consult me if you're not sure).
These major papers should be individual work. (The "Joint work" policy is not a license to turn in a paper that is a clone of someone else's.) Exception: Two (or more) different papers on closely related topics that form a single project, with a different author taking primary responsibility for each. (Example: Exercises 5-8 of Chapter 4, pp. 202-205. Or regular exercise 14 and major exercise 3 in Chapter 2. Or essays 2 and 18 in Ch. 8.)

Criterion	Expository	Mathematical
Choice of topic	5%	5%
Correctness and depth	25%	50%
Exposition	35%	20%
Mechanics (punctuation, etc.)	25%	20%
References	10%	5%

Winter 2014 Math 467: Modern Geometry

Frank Sottile

Paper policies

Winter 2014
Math 467: Modern Geometry