An introduction to algebraic number theory. Dedekind domains, unique factorization of prime ideals. Number fields, splitting of primes, class group. Lattice methods, finiteness of the class number, Dirichlet's units theorem. Local fields, ramification, discriminants. Background in elementary number theory (e.g., 18.781) strongly recommended.
Prerequsites: 18.100 and 18.702
- Samuel, Algebraic Theory of Numbers
- Milne, Notes on algebraic number theory
[05.09.2013] The Take-home final has been posted.