Number theory I.a - Algebraic number theory
Summary
Algebraic number theory is the study of the properties of solutions of polynomial equations with integral coefficients; Starting with concrete problems, we then introduce more general notions like algebraic number fields, algebraic integers, units, ideal class groups...
Content
- Basics on rings and modules (especially finitely generated ones)
- Dedekind rings
- The ring of integers of a number field
- Application to Galois theory
- Lattices in R^n
- Finiteness of the ideal class group
- Dirichlet's units theorem
- Applications
Keywords
Rings, Fields, integers, ideals, lattices
Learning Prerequisites
Required courses
MATH-215
Recommended courses
MATH-311
MATH-313
MATH-317
Learning Outcomes
By the end of the course, the student must be able to:
- Quote the main results of the course
- Use the main results of the course
- Prove the main results of the course
Teaching methods
ex-cathedra
Expected student activities
attendance to the course and active participation to the exercises sessions
Assessment methods
written exam
Supervision
| Assistants | Yes |
| Others | moodle page |
Resources
Notes/Handbook
a pdf of the course will be provided
Moodle Link
Prerequisite for
MATH-417
MATH-489
MATH-494
Fields medal
In the programs
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Number theory I.a - Algebraic number theory
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks