I believe the hardest part of the term paper will be selecting material that is difficult enough to be interesting and simultaneously easy enough to master and explain to your classmates.

To that end, one of the things you must provide are a few problems to solve. They can be computations that illustrate theorems, or simple things to prove based on what you've presented.

Your assignment this week is to find a topic, and collect at least some of the papers you'll be working on.

Soon I'll ask for an outline of what you plan to present, then possibly a rough draft.

I'll schedule presentations by working backwards from the end of the semester, seeing how many class periods we'll need to fit them all in.

You can work on the term paper as part of a team of two if you wish.

Here are some possible topics:

• Continued fractions and Pell's Equation.

• Angle Trisection, the Heptagon, and the Triskaidecagon at JSTOR. Here's a link to a local copy.

• The proof of the law of quadratic reciprocity from Friedberg's book.

• The Lucas-Lehmer test for Mersenne primes. The Wikipedia entry is a place to start. See too J. W. Bruce's A Really Trivial Proof of the Lucas-Lehmer Test, The American Mathematical Monthly, Vol.100, No.4, pp.370.371. April 1993. (I have a hard copy of this article.) Giedrius Alkauskas' A Curious Proof of Fermat's Little Theorem, American Mathematical Monthly, April 2009, pp 362-364.

• Juan Sabia and Susana Tesauri's The Least Prime in Certain Arithmetic Progressions, American Mathematical Monthly, Volume 116, Number 7, August-September 2009 , pp. 641-643(3). The direct link above is not free but you can get the article free through the Healey library. And I have a hard copy.

• Juan Pablo Pinasco's New Proofs of Euclid's and Euler's Theorems . American Mathematical Monthly, Volume 116, Number 2, February 2009 , pp. 172-174(3). I have a hard copy of this paper.

  This is the beginning of analytic number theory - the Euler theorem referred to is the one that says that the sum of the reciprocals of the primes diverges.