Math 748-Algebraic Number Theory
Professor Amanda Folsom
Tues/Thurs 11:00am-12:15pm
B131 Van Vleck Hall
Course Description:
This course is a graduate level introduction to algebraic number theory, in which we will cover fundamentals of the subject. Topics include: rings of integers, Dedekind domains, factorization of prime ideals, lattices, Minkowski's theorem, finiteness of the class number, Dirichlet's unit theorem, cyclotomic extensions, the Chebotarev density theorem, and time permitting, valuations and topics from local fields.
Texts:
- J.S. Milne, Algebraic Number Theory, available at http://www.jmilne.org/math
- D.A. Marcus, Number Fields Universitext, Springer-Verlag, New York-Heidelberg, 1977.
-
J. Neukirch*, Algebraic Number Theory, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 322. Springer-Verlag, Berlin, 1999.
*optional
Prerequisites:
Math 741-742 or equivalent, or by consent of instructor