The course projects should be handed in before Thursday, April 25 (midnight).

On the request of some of the students in the class, I plan to post the student projects on this web site so you can all have access to them (as well as the rest of the world...) If you object to your work being publicly posted, just let me know when you submit your project and I will not post it.

Here are some of the projects:

Henri Darmon: MW 2:00-3:00, or by appointment, in room 1111.

You may also avail yourself of the services of the Math Help Desk, which is open Monday-Friday from 12:00 to 5:00 PM, in BH 911.

Andrew Granville, Introductions to Gauss's Number Theory, together with the appendices.

To quote the author himself, "This is the first draft of an introductory book of number theory, where the focus is on trying to explain proofs so that they are easily accessible. I need your help, especially in knowing which parts are not easy to understand. Please email me with your comments, good and bad, on this (and any other suggestions) to andgranville@gmail.com. Thanks, Andrew Granville"

William J. LeVeque, Fundamentals of Number Theory, Dover Books.

Winfried Scharlau and Hans Opolka, From Fermat to Minkowski: Lectures on the Theory of Numbers and its historical development.

The corrections to the midterm are now available.

Computation and experimentation are an important facet of Number Theory, a tradition that does back at least to Gauss who was a prodigious calculator. Because of this, Number Theory is the branch of pure mathematics that is perhaps the closest to physics. (This may seem surprising in light of Number Theory's reputation as the purest part of pure mathematics, well removed from the "real world".)

Unlike physics where experiments often rely on costly apparatus that can only be carried out in well-endowed laboratories, the requirements for experimentation in number theory are modest: a personal computer running a symbolic algebra package is all that you will need. A number of questions in the assignments will rely on calculations on such a symbolic algebra system. Pari/GP, which is freely available on the web, is the system I recommend. (But you are free to use an equivalent system, like Maple, Mathematica or Magma if you prefer.)

Before writing Assignment 1, you should download Pari onto your computer. You might want to seek help from a classmate if you have trouble in doing this. I am told that the operation is relatively simple and painless if you work in a Windows environment, but if you are part of the swelling crowds of Mac afficionados, it can be a bit more compicated. Xiangyu Wu has been through the installation successfully, and has kindly sent me these instructions:

1) Download and install XCode by going to

http://connect.apple.com/.

You need to register for apple developer, it is free. Once registered, login to the developer portal and search for XCode.

2) Download and install Mac Ports:

http://www.macports.org/install.php.

3) Download the file Pari from:

http://pari.math.u-bordeaux.fr/download.html

4) Download and install Command Line Developer Tools from the same site as XCode.

5) Launch Terminal and type "xcodebuild -license" from the command line prompt.

6) Then, type "ports install pari" from the Terminal command line prompt.