Topic: Algebraic number theory from the global perspective covering number fields and their rings of integers and their discriminants and ideals and their norms and traces, the finiteness of an ideal class group and its applications to Diophantine equations, the Dirichlet Unit Theorem, the Dedekind Theorem for ramified primes over \(\mathbb{Q}\), the prime factorizations over a Galois extension and the Artin reciprocity law over \(\mathbb{Q}\) and its implication to the quadratic reciprocity law.

Prerequisites

Elementary number theory, module theory and Galois theory.