NMAA06062U Geometry 2 (Geom2)

Volume 2023/2024
Education

MSc Programme in Mathematics
MSc Programme in Statistics
MSc Programme in Mathematics with a minor subject

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

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), Topologi (Top), Advanced Vector Spaces (AdVec) or similar.

Academic qualifications equivalent to a BSc degree is recommended.
5 hours of lectures and 4 hours of exercises per week for 7 weeks
  • Category
  • Hours
  • Lectures
  • 35
  • Preparation
  • 142
  • Theory exercises
  • 28
  • Exam
  • 1
  • Total
  • 206
Written
Oral
Collective

Oral feedback will be given on students’ presentations in class

Credit
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 assesment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.