Geometry 2 (Geom2)
Course content
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
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
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
- ECTS
- 7,5 ECTS
- Type of assessment
-
Oral examination, 30 minutes
- Type of assessment details
- 30 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.
- Aid
- 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
- Re-exam
-
Same as the ordinary exam.
If the assignment was not approved before the ordinary exam, the assignment must be handed in and approved three weeks before the re-exam.An approved mandatory assignment is valid for the re-exam in the year it was approved and for exam and re-exam the following year, but no longer.
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)
- Category
- Hours
- Lectures
- 35
- Preparation
- 142
- Theory exercises
- 28
- Exam
- 1
- English
- 206
Kursusinformation
- Language
- English
- Course number
- NMAA06062U
- ECTS
- 7,5 ECTS
- Programme level
- Full Degree Master
- Duration
-
1 block
- Placement
- Block 2
- Schedulegroup
-
B
- Capacity
- No limit
The number of seats may be reduced in the late registration period - Studyboard
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinator
- Henrik Schlichtkrull (8-76666b6f6c666b77437064776b316e7831676e)
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