NMAA06062U Geometry 2 (Geom2)
MSc Programme in Mathematics
The following subjects are covered.
1. Differentiable manifolds in Euclidean spaces.
2. Abstract differentiable manifolds.
3. Tangent spaces, differentiable maps and differentials.
4. Submanifolds immersions and imbeddings
5 Vector fields.
6 Lie groups and Lie Algebras (cursory)
7 Differential forms.
8 Integration; Stokes' Theorem
- 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
- 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 exam week.
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- External censorship
Same as the ordinary exam.
If the assignment was not approved before the ordinary exam, the assignment must be handed in two weeks before the re-exam and approved before the re-exam.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome.
- Theory exercises