Number Theory - Mathematics 254

Number Theory – Mathematics 2540
Brown University – Spring, 2011
Professor Joseph Silverman

Text	I'll be lecturing from various sources, so there won't be an official text (or texts) for the course. I've listed some references below.
Office	Mathematics Department, Kassar House, Room 202
Phone	863-1124
Email	jhs@math.brown.edu
Web Site	www.math.brown.edu/~jhs/MA0254/MA0254HomePage.html
Office Hours	TBA (Or send me an email to make an appointment. I tend to be in on MWF and not on TTh.)
Course Time	MWF 11:00–11:50am (D hour)
Course Location	Kassar 105
Homework	Homework assignments will be posted online. (I'll also try to announce them in class.) Click here to go to the Math 254 Homework Page.
Note on Using Computers in Math 254	I tend to use a computer program called PARI-GP to do number theory calculations. The good news about PARI is that it is free and very fast and powerful at doing number theoretic computations. The bad news is that it's not tremendouly user friendly. You can download PARI by clicking here. Another way to use PARI to do short calculations is to use the SAGE web site. You'll need to create a (free) account. Then you'll be able to type one or more PARI commands and type Shift-Return to perform the computation.

Tentative Syllabus (with some references):

Class Field Theory
- Class Field Theory, N. Childress, Springer, 2009.
- Algebraic Number Theory (2nd ed.), S. Lang, 1994.
- Local Fields, J.-P. Serre, Springer, 1980.
- Algebraic Number Theory (2nd ed.), J.W.S. Cassels and A. Frohlich, London Mathematical Society, 2010. (Chapters on local and global class field theory.)
Group Cohomology and Galois Cohomology
- Local Fields, J.-P. Serre, Springer, 1980.
- Galois Cohomology, J.-P. Serre, Springer, 2001.
- Algebraic Number Theory (2nd ed.), J.W.S. Cassels and A. Frohlich, London Mathematical Society, 2010. (Chapters on group and Galois cohomology.)
Elliptic Curves
- The Arithmetic of Elliptic Curves (2nd ed.), J.H. Silverman, Springer, 2009.