Introduction to Algebraic Number Theory

Introduction to Algebraic Number Theory
Algebraic integers; different and discriminant; decomposition of primes; class group; Dirichlet unit theorem; Dedekind zeta function; cyclotomic fields; valuations; completions.
MATH
586
 Hours3.0 Credit, 3.0 Lecture, 0.0 Lab
 PrerequisitesMath 372 or equivalent.
 TaughtFall Contact Department, Winter Contact Department, Spring Contact Department, Summer Contact Department
Course Outcomes

Learning Outcomes

Students should achieve an advanced mastery of the topics listed on the 586 Math Wiki page. This means that they should know all relevant definitions, correct statements and proofs of the major theorems (including their hypotheses and limitations), and examples and non-examples of the various concepts. The students should be able to demonstrate their mastery by solving difficult problems related to these concepts, and by proving theorems about the below concepts, even if the theorems go beyond the material in the text.

Overview

  1. Number Fields
  2. Prime decomposition in rings of integers
  3. Ideal Class Group
  4. Dirichlet's unit theorem
  5. Cebotarev Density Theorem (Statement)
  6. Dedekind zeta function