NMAA06062U Geometry 2 (Geom2)

Volume 2013/2014
Education
MSc program 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
An1, Geom1 and 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
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.