# NMAA06062U  Geometry 2 (Geom2)

Volume 2018/2019
Education

MSc Programme in Mathematics

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 (cursory)

7 Differential forms.

8 Integration; Stokes' Theorem

Learning Outcome

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
Analyse 1 (An1), Geometri 1 (Geom1) and Topologi (Top) or similar.
5 hours of lectures and 4 hours of exercises per week for 7 weeks
Credit
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
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
Marking 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 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.

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