Math 784 Algebraic Number Theory

Course Description: This course aims to provide an introductory exploration into algebraic numbers and algebraic integers. Algebraic number theory extends its focus beyond integers, particularly emphasizing number fields as finite algebraic extensions of Q. The following topics will be covered in the course as time permits: Algebraic Numbers/Integers, Number Fields, Quadratic Fields, Cyclotomic Fields, Dedekind Domains, Orders, Factorization of Ideals, Minkowski’s Theorem, Geometry of Numbers, Ideal Classes, Dirichlet’s Unit Theorem, Splitting of Prime Ideals, Artin Reciprocity, L-functions, Class Number Formulas, and Class Field Theory.

References:
1. Daniel A. Marcus, Number Fields. Springer Cham (2nd edition) 2018
2. Jürgen Neukirch, Algebraic Number Theory. Springer Berlin, Heidelberg 1999

Many others are highly recommended:
1. Michael Filaseta’s notes
2. J.S. Milne, Algebraic Number Theory
3. Fröhlich and Taylor, Algebraic Number Theory
4. Cassels and Fröhlich, Algebraic Number Theory

Course Website: Blackboard