Students should know the technical terms, and be able to implement the methods taught in the course to work associated problems, including proving results of suitable accessibility. See the minimal learning outcomes section of the Math 686R Wiki page for a clear indication of the level of difficulty appropriate to the course.

1. Generalization of the Unique Factorization Theorem from rationals to number fields; Basic definitions:
2. Geometry of numbers:
3. Ramification Theory:
4. Splitting of Primes:
5. Arithmetic of cyclotomic fields, and the Kronecker-Weber Theorem
6. Dedekind zeta function