MATH-322 / 5 credits

Teacher: Cossarini Marcos

Language: English

## 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:

## In the programs

• Semester: Fall
• Exam form: Written (winter session)
• Subject examined: Introduction to differentiable manifolds
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks

## Reference week

 Mo Tu We Th Fr 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

Tuesday, 8h - 10h: Lecture MAA330

Tuesday, 10h - 12h: Exercise, TP MAA330