Math 25: The Final Project

Updates

• 11/17/2011: Information on practice presentation scheduling and final presentations are available now.
• 11/12/2011: You can introductory find information on preparing a LaTeX document.

Summary

The final project for this class consists of two parts: a short, 15-20 minute presentation, to be given either during the final exam time allocated for this class, or on the last day of class (we will need multiple days), and a short paper, about 3-4 pages in length. You will work with a randomly assigned partner. The topic can be about anything remotely related to number theory; a list appears below, or you can come up with your own and run it by the instructor and TA.

Deadlines

There are three deadlines for this project. Only the last counts for any grade, but the other two deadlines are concrete and you must meet them.

1. Decide on a topic. You should meet with your partner and decide on a topic to work on. This should be completed by Friday, November 11. You should arrange a meeting with the instructor and TA to briefly discuss your choice of topic and a vague sketch of what you plan on presenting and writing about prior to this deadline. We will not let groups present identical topics, so topic selection is first come, first serve!
2. Prepare a first draft of the paper and give a practice version of the presentation to the instructor and TA. This should be completed by Wednesday, November 30. We will need to schedule this over multiple weeks, so you should email the instructor as soon as possible to schedule a time. (See below for more information)
3. Give the final presentation and submit the paper. The final paper will be due on Tuesday, December 6, and the final presentation will either occur on the last day of class or the day the final exam for this class is scheduled. We will provide a schedule of who is presenting when in early November. Attendence during presentation sessions which you are not presenting at will be optional, but we encourage you to listen to your fellow classmates talk.

On the paper

The paper should be written at a level so that other students in the class can understand and learn something from them. In other words, you should assume the reader has some knowledge of number theory vocabulary, but is not an expert at your subject. You do not necessarily need to give proofs in your paper, although in some situations proofs would be nice.

Ideally, the paper you write should be a well-written and educational exposition on the topic you chose. The style should probably be not quite like a textbook, and not quite like an encyclopedia article, but perhaps a cross of the two. Part of the purpose of submitting a rough draft is so the instructor and TA can provide feedback on the style and structure of the paper.

In theory, you could typeset your paper using a conventional wordprocessor, but we strongly suggest that you learn and use LaTeX, a document markup language that is used for typesetting mathematics. LaTeX is almost universally used amongst mathematicians, theoretical physicists, and computer scientists. You can find more information on preparing a document using LaTeX here (this information is more or less identical to something posted for Math 75 a year and a half ago.)

Possible topics

The following are some suggestions for possible topics. They are only meant as a starting point, so feel free to modify them or think of your own topics entirely.

• Topics that are covered in the textbook but which we did not cover in class. Highlights might include a brief exposition on the Riemann zeta function, representing numbers as sums of squares, or Pythagorean triples.
• Cryptographic applications of number theory. Topics which are approachable include classical ciphers, such as the Caesar cipher or the Vigenere cipher. More modern topics which are still approachable include Diffie-Hellman key exchange and the discrete logarithm problem.
• Computational algorithms in number theory that we didn't cover. For example, some simple primality testing algorithms which we will not discuss include Pocklington's test, the Lucas-Lehmer method for Mersenne primes, or the Solovay-Strassen test. Possible factorization algorithms include the Pollard rho algorithm, p-1, and p+1 algorithms.
• Not all topics have to be "mathematical". For example, you can present biographies of mathematicians whose work we have studied, such as Fermat, Euler, or Gauss. Or you can discuss some of the history behind some of the theorems we have encountered.
• Of course, you can also write and present about whatever you think is interesting, as long as it is tangentially related to number theory.

Practice presentation schedule

The following are dates for the practice presentations. For now, we will hold them in Kemeny 343. If you plan on using a computer projector, you should bring whatever video adapters you have, especially if you have a Mac (you will probably need an adapter that can connect to a VGA or DVI display). Each group will have a total of 20 minutes to present, after which we will provide comments for about 5-10 minutes. It is important that you stay under the time limit so we can review everyone's presentation in a timely fashion.

Last updated: Monday Nov 28 1:00am

Actual presentation schedule

The scheduled final exam time for this class is Saturday, 12/3/2011, from 8:00am - 11:00am. Since this is not enough time to accomodate every group, we will have a second presentation session. The Friday time is 12/2/2011, 2:30pm - 5:00pm. Eight groups will present on Saturday, and six on the other day. You are not required to attend presentations during the session you will not be presenting in, but you are required to stay and listen to your fellow students' presentations during the session you do present in. Both presentations will be held in the usual classroom of 108 Kemeny.

If you need to present during a particular session (because of schedule conflicts), email me as soon as possible with your restriction.