NMAA06062U Geometry 2 (Geom2)
MSc Programme in Mathematics
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.
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
- Category
- Hours
- Exam
- 1
- Lectures
- 35
- Preparation
- 142
- Theory exercises
- 28
- Total
- 206
As
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- Credit
- 7,5 ECTS
- Type of assessment
- Oral examination, 30 minutes30 minutes of preparation before the exam
- Exam registration requirements
A mandatory assignment must be approved before the exam.
The assignment is to be handed in no later than two weeks before the re-exam week. The assignment has to be approved before the reexamination.
- Aid
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- External censorship
- Re-exam
Same as ordinary.
If the requirement is not fulfilled, it can be fulfilled before the re-examination.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome.
Course information
- Language
- English
- Course code
- NMAA06062U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 2
- Schedule
- B
- Course capacity
- No limit
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Hans Plesner Jakobsen (8-756c767a6d7e70794b786c7f73397680396f76)