Kursussøgning, efter- og videreuddannelse – Københavns Universitet

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Kursussøgning, efter- og videreuddannelse

Geometry 2 (Geom2)

Practical information
Study year 2016/2017
Block 2
Programme level Full Degree Master
Course responsible
  • Hans Plesner Jakobsen (8-7067717568796b744673677a6e34717b346a71)
Phone +45 35 32 06 89, office 04.4.15
  • Department of Mathematical Sciences
Course number: NMAA06062U

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. 

Learning outcome


  • Central definitions and theorems from the theory


  • 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


  • 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

Recommended prerequisites

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

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MSc Programme in Mathematics


Study Board of Mathematics and Computer Science

Course type

Single subject courses (day)


1 block


---- SKEMA LINK ----

Teaching and learning methods

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


No limit




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


Type of assessment

Oral examination, 30 minutes
30 minutes of preparation before the exam


All aids allowed

Marking scale

7-point grading scale

Criteria for exam assessment

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

Censorship form

External censorship


Same as ordinary. 

If the requirement is not fulfilled, it can be fulfilled before the re-examination.

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