Coursebooks

Introduction to differentiable manifolds

MATH-322

Lecturer(s) :

Kiesenhofer Anna

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.

Content

Keywords

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

Learning Prerequisites

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:

Transversal skills

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

Resources

Bibliography

John M. Lee: Introduction to Smooth Manifolds (e-book:
https://link.springer.com/book/10.1007%2F978-1-4419-9982-5)

Ressources en bibliothèque

In the programs

  • Mathematics, 2019-2020, Bachelor semester 5
    • Semester
      Fall
    • Exam form
      Written
    • Credits
      5
    • 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

MoTuWeThFr
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
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