Geometry 2 (Geom2)

Course content

The following nine subjects are covered. Two of these will, however, only be treated in a cursory manner.

 

1. Differentiable manifolds in Euclidean spaces.
2. Abstract differentiable manifolds.
3. Tangent spaces, differentiable maps and differentials.
4. Submanifold, immersion and imbedding.
5. Topological properties, compactness, connectedness and components.
6. Vector fields.
7. Lie groups and Lie Algebras.

8. Differential forms.

9. Integration. 

Education

MSc Programme in Mathematics

Learning outcome

Knowledge:

  • Central definitions and theorems from the theory


Skill:

  • Decide whether a given subset of R^n is a manifold
  • Determine the differential of a smooth map
  • Work with tangent vectors, including the Lie algebra of a Lie group
  • Utilize topological concepts in relation with manifolds
  • Find the Lie bracket of given vector fields
  • Work with exterior differentiation and pull-back of differential forms


Competences:

  • In general to perform logical reasoning within the subject of the course
  • Give an oral presentation of a specific topic within the theory as well as a strategy for solving a specific problem

5 hours of lectures and 4 hours of exercises per week for 7 weeks

Analyse 1 (An1), Geometri 1 (Geom1) and Topologi (Top) or similar.

ECTS
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
30 minutes of preparation before the exam
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
External censorship
Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 35
  • Theory exercises
  • 28
  • Preparation
  • 142
  • Exam
  • 1
  • English
  • 206