Number Theory – Mathematics 2530
Brown University – Spring, 2011
Professor Joseph Silverman

Text I'll mostly be using the following two books, but it's up to you whether you want to buy copies. (The Samuel books is only $8.17 from Amazon!)
  • Algebraic Number Theory (2nd ed.), Serge Lang, 1994.
  • Algebraic Theory of Numbers: Pierre Samuel, Dover Books on Mathematics, 2008. (Translated from the French by Allan J. Silberger)
But there are lots of good books that cover basic algebraic number theory in greater or lesser detail.
Office Mathematics Department, Kassar House, Room 202
Phone 863-1124
Email jhs@math.brown.edu
Web Site www.math.brown.edu/~jhs/MA0253/MA0253HomePage.html
Office Hours Monday 10:00–10:30am and Friday 3:30–3:30pm.
(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 download the Homework Problems for Math 253.
Note on Using Computers in Math 253 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, and also somewhat limited at doing calculations in algebraic number fields. You can download PARI by clicking here. A free alternative to PARI is SAGE, which you can get at the SAGE web site. (You can also use PARI from within SAGE.)

Tentative Syllabus:

  1. Algebraic Integers, Dedekind Domains, Unique Factorization
  2. Completions
  3. Ramification, Discriminants
  4. Ideal Class Groups
  5. Unit Groups, Dirichlet's Theorem
  6. Galois Theory, Decomposition and Inertia Groups, Splitting of Primes
    Additional Topics (as time permits) chosen from:
  7. Cyclotomic Fields
  8. Adeles and Ideles
  9. Zeta Functions and L-series
  10. Tchebotarev Density Theorem

Go to Professor Silverman's Home Page.