Number theory I.a - Algebraic number theory

MATH-482 / 5 crédits

Enseignant: Michel Philippe

Langue: Anglais

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

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

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