Mathematics 254B Number Theory

Prof. Bjorn Poonen Spring 2000

CLASSES: Mondays, Wednesdays and Fridays 12:10-1:00 in 9 Evans.

OFFICE HOURS: Wednesdays 11:10-12:00 and Fridays 2:10-3:00 in 703 Evans, or by appt., or whenever my office door is open. My phone number is 642-5229, but the best way to reach me is to send e-mail to poonen@math

PREREQUISITE: 254A.

TEXTBOOK: None required, but some of the topics will be based on material in Serre, A course in arithmetic, and Cassels & Fröhlich, Algebraic number theory.

COURSE DESCRIPTION: Rather than concentrate on a single topic (such as the proof of class field theory), we will survey many different topics within number theory, perhaps some subset of {Galois cohomology, some analytic number theory (e.g., modular forms at the level of A course in arithmetic, and the Hardy-Littlewood circle method), quadratic forms, the Hasse principle and its failure, Brauer groups of local and global fields, and undecidability in number theory (Hilbert’s 10th problem)}.

GRADING: There will be no exams. Grades will be based on weekly homework.

HOMEWORK: Assignments will be due in class on Mondays. The first one will be due Jan. 24. Late homeworks will not be accepted. You are free to consult any sources (animate or inanimate) while doing your homework, but if you use anything (or anyone) other than your class notes or the texts listed above, you should say so on your homework. Staple loose sheets!!!