Topics in Algebraic Number Theory
A first course in algebraic number theory from MIT OpenCourseWare. Covers number fields, class numbers, Dirichlet's unit theorem, cyclotomic fields, local fields, valuations, decomposition and inertia groups, ramification, basic analytic methods, and basic class field theory. Problem sets weave in computer algebra as a tool for investigating number-theoretic questions alongside the theoretical development. Materials include lecture notes and assignments following MIT's OCW format, free to access under a Creative Commons license with no certificate offered. Suited to students who already have background in ring and field theory and want to move into the machinery of algebraic number theory, from unit groups to ramification behavior in extensions.