Geometry 2 (Geom2)
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
7 Differential forms.
8 Integration; Stokes' Theorem
MSc Programme in Mathematics
MSc Programme in Statistics
MSc Programme in Mathematics with a minor subject
- 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
5 hours of lectures and 4 hours of exercises per week for 7 weeks
Analyse 1 (An1), Geometri 1 (Geom1), Topologi (Top), Advanced
Vector Spaces (AdVec) or similar.
Academic qualifications equivalent to a BSc degree is recommended.
Oral feedback will be given on students’ presentations in class
- 7,5 ECTS
- Type of assessment
Oral examination, 30 minutes
- Type of assessment details
- 30 minutes of preparation before the exam.
- All aids allowed
All aids are allowed during preparation. No aids are allowed during examination
- Marking scale
- 7-point grading scale
- Censorship form
- External censorship
Criteria for exam assessment
The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.
Single subject courses (day)
- Theory exercises
- Course number
- 7,5 ECTS
- Programme level
- Full Degree Master
- Block 2
- No limit
The number of seats may be reduced in the late registration period
- Study Board of Mathematics and Computer Science
- Department of Mathematical Sciences
- Faculty of Science
- Henrik Schlichtkrull (8-7a6a6f73706a6f7b4774687b6f35727c356b72)
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Courseinformation of students