Course. Math 514, Number Theory I (fall 1995)

Course location. 117 Taft Hall Course hours. MWF 12–1

Instructor. D. J. Bernstein

E-mail. djb@math.uic.edu

Office. 209 Science and Engineering Offices Office phone. 312–996–0752 (but e-mail is much more reliable) Office hours. MWF 11:30–12, MWF 1–1:30. Other hours by appointment.

Prerequisites. Prior exposure to groups, rings, and fields. The text contains all necessary Galois theory in an appendix. Galois theory in general can be rapidly acquired from D. J. H. Garling, A Course in Galois Theory (Cambridge, 1986).

Text. D. A. Marcus, Number Fields (Springer, 1977). On reserve at the library. Several copies should show up at the bookstore soon.

Contents. Introductory algebraic number theory. Major concepts: ring of integers, class group, unit group, norm, trace, different, discriminant, ramification, decomposition group, inertia group. Major theorems: prime ideal factorization, class group finiteness, Dirichlet’s unit theorem. Computational skills to handle any number field, including standard examples of quadratic and cyclotomic fields.

Grading policy. No examinations. Frequent homework assignments. Your final grade will be determined exclusively by your performance on the homework. Each homework is due by 5 p.m. one week after it is assigned. After I return your homework, if you have lost points on a problem, you may attempt to regain some points by redoing the problem. Your redone solution is due by 5 p.m. one week later.

Feedback. I reserve two minutes at the end of each class for you to tell me, in writing, your reactions to the lecture; constructive criticism is strongly encouraged. This is in addition to the usual mechanisms of oral feedback and formal evaluation.

Auditing policy. Feel free to sit in. If you plan to submit homework, please enroll. The drop deadline is 1 September 1995.