# Geometry 2 (Geom2)

### Course content

The following subjects are covered.

Differentiable manifolds in Euclidean spaces

Abstract differentiable manifolds

Tangent spaces, differentiable maps and differentials

Submanifolds immersions and imbeddings

Vector fields

Lie groups and Lie Algebras

Differential forms

Integration; Stokes' Theorem

Education

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

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

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.

Written
Oral
Collective

Oral feedback will be given on students’ presentations in class

ECTS
7,5 ECTS
Type of assessment
Oral examination, 30 minutes (30-minute preparation time)
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
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 limitation – unless you register in the late-registration period (BSc and MSc) or as a credit or single subject student.
Studyboard
Study Board of Mathematics and Computer Science
##### Contracting department
• Department of Mathematical Sciences
##### Contracting faculty
• Faculty of Science
##### Course Coordinator
• Henrik Schlichtkrull   (8-78686d716e686d79457266796d33707a336970)
Phone +45 35 33 04 05, office 04.1.11
Saved on the 15-02-2024

### Are you BA- or KA-student?

Are you bachelor- or kandidat-student, then find the course in the course catalog for students:

Courseinformation of students