Coursebooks

Algebraic number theory

MATH-482

Lecturer(s) :

Michel Philippe

Language:

English

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...

Learning Prerequisites

Required courses

Rings and fields

 

 

Recommended courses

Galois Theory

Introduction à la théorie analytique des nombres

Rings and modules

Learning Outcomes

By the end of the course, the student must be able to:

Teaching methods

cours ex-cathedra et exercices

Expected student activities

De part sa nature, la théorie algébrique des nombres combine des techniques provenant de plusieurs domaines (algebre lineaire, algebre commutative, analyse, geometrie). Il est indispensable d'avoir une bonne maitrise de chacun d'eux. On attend une présence active aux séances de cours et surtout aux séances d'exercices. On demandera notamment aux étudiants de venir presenter leurs solutions au tableau.

Assessment methods

examen ecrit

Supervision

Office hours No
Assistants Yes
Forum No
Others moodle

Resources

Bibliography

Samuel, algebraic number theory

Ressources en bibliothèque

Prerequisite for

Topics in number theory.

Applications of number theory: eg. cryptography

Solving the Birch-Swinnerton-Dyer conjecture and win one of the Millenium Prizes (1M USD) from the  Clay Mathematics Institute.

Receiving the Fields medal

In the programs

Reference week

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Under construction
 
      Lecture
      Exercise, TP
      Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German