Course Identification

Introduction to Algebraic Number Theory
20194111

Lecturers and Teaching Assistants

Prof. Dmitry Gourevitch
Devika Sharma

Course Schedule and Location

2019
First Semester
Monday, 11:15 - 14:00, Jacob Ziskind Building, Rm 155

Tutorials
Thursday, 10:15 - 11:00, Jacob Ziskind Building, Rm 155
05/11/2018

Field of Study, Course Type and Credit Points

Mathematics and Computer Science: Lecture; Elective; 3.00 points

Comments

N/A

Prerequisites

Good knowledge of linear algebra and basic Galois theory.

Restrictions

100

Language of Instruction

English

Attendance and participation

Expected and Recommended

Grade Type

Pass / Fail

Grade Breakdown (in %)

50%
50%

Evaluation Type

Take-home exam

Scheduled date 1

N/A
N/A
-
N/A

Estimated Weekly Independent Workload (in hours)

3

Syllabus

The course will cover part one of Lang's book "Algebraic Number theory". This includes:

  1. Algebraic Integers
  2. Completions of number fields
  3. Discriminants 
  4. Cyclotomic fields
  5. Parallelotopes
  6. Ideals, ideal classes, and the ideal function
  7. Ideles and Adeles
  8. Elementary Properties of the Zeta Function and L-series

Learning Outcomes

Upon successful completion of this course, students should be able to:

  1. Demonstrate knowledge of the basics of algebraic number theory.
  2. Approach the advanced algebraic topics of class field theory and automorphic forms. 

Reading List

Serge Lang:

1.  "Algebraic Number Theory"

2. "Algebra"

Website