MATH-322 / 5 crédits

Enseignant: Cossarini Marcos

Langue: Anglais

## Summary

Differentiable manifolds are a certain class of topological spaces which, in a way we will make precise, locally resemble R^n. We introduce the key concepts of this subject, such as vector fields, differential forms, integration of differential forms etc.

## Keywords

differentiable manifold, tangent space, vector field, differential form, Stokes

## Required courses

Espaces métriques et topologique, Topologie, Analyse III et IV

## Important concepts to start the course

Topological spaces, multivariate calculus (implicit function theorem etc.)

## Learning Outcomes

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

• Define and understand the key concepts (differentiable structure, (co)tangent bundle etc.)
• Use these concepts to solve problems
• Prove the main theorems (Stokes etc.)

## Transversal skills

• Continue to work through difficulties or initial failure to find optimal solutions.
• Demonstrate a capacity for creativity.
• Access and evaluate appropriate sources of information.
• Demonstrate the capacity for critical thinking
• Assess one's own level of skill acquisition, and plan their on-going learning goals.

## Teaching methods

2h lectures + 2h exercises

## Expected student activities

Attend classes and solve exercises, revise course content / read appropriate literature to understand key concepts.

## Assessment methods

Written exam.

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l¿examen qu¿il communique aux étudiants concernés.

## Bibliography

John M. Lee: Introduction to Smooth Manifolds (e-book:

## Dans les plans d'études

• Semestre: Automne
• Forme de l'examen: Ecrit (session d'hiver)
• Matière examinée: Introduction to differentiable manifolds
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines

## Semaine de référence

 Lu Ma Me Je Ve 8-9 MAA330 9-10 10-11 MAA330 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 21-22

Mardi, 8h - 10h: Cours MAA330

Mardi, 10h - 12h: Exercice, TP MAA330