NMAA06062U Geometry 2 (Geom2)

Volume 2015/2016
Education
MSc Programme in Mathematics
Content

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.

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


Competences:

  • In general to perform logical reasoning within the subject of the course
  • Give an oral presentation of a specific topic within the theory
Analyse 1 (An1), Geometri 1 (Geom1) and Topologi (Top) or similar.
5 hours of lectures and 4 hours of exercises per week for 7 weeks
  • Category
  • Hours
  • Exam
  • 1
  • Lectures
  • 35
  • Preparation
  • 142
  • Theory exercises
  • 28
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
30 minutes of preparation before the exam
Exam registration requirements
A mandatory assignment must be approved before the exam.
If the requirement is not fulfilled, it can be fulfilled before the re-examination. The assignment is to be handed in no later than two weeks before the registration period for the re-examination ends. The assignment has to be approved before the reexamination.
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
External censorship
Criteria for exam assesment

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