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, lattices in R^n
- Dedekind rings
- The ring of integers of a number field
- Application to Galois theory
- 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
Dans les plans d'études
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Number theory I.a - Algebraic number theory
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
Semaine de référence
Lu | Ma | Me | Je | Ve | |
8-9 | |||||
9-10 | |||||
10-11 | |||||
11-12 | |||||
12-13 | |||||
13-14 | |||||
14-15 | |||||
15-16 | |||||
16-17 | |||||
17-18 | |||||
18-19 | |||||
19-20 | |||||
20-21 | |||||
21-22 |
Légendes:
Cours
Exercice, TP
Projet, Labo, autre