Topics in Algebraic Number Theory
MIT OpenCourseWare offers this advanced graduate course covering the core machinery of algebraic number theory. Topics include Dedekind domains, unique factorization of prime ideals, number fields, the splitting of primes, the class group, lattice methods, finiteness of the class number, Dirichlet's unit theorem, local fields, ramification, and discriminants. Materials consist of lecture notes and problem sets that build from the structure of rings of integers toward the analytic and geometric tools used to study them, including Minkowski's lattice methods and local field theory. The course assumes prior exposure to abstract algebra and is meant for students who already know the basics of ring and field theory. As with other MIT OCW offerings, all materials are free to access and there is no certificate track.