MM564: Riemannian geometry
Study Board of Science
Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N300047102
Assessment: Second examiner: Internal
Grading: 7-point grading scale
Offered in: Odense
Offered in: Spring
Level: Bachelor
STADS ID (UVA): N300047101
ECTS value: 5
Date of Approval: 02-10-2019
Duration: 1 semester
Version: Archive
Entry requirements
Academic preconditions
Students taking the course are expected to:
- Have knowledge of the contents of MM536
- Have knowledge of the contents of MM540, MM505 or MM568
- Have knowledge of the contents of MM533
- Have knowledge of the contents of MM512
Course introduction
The aim of the course is to obtain basic knowledge about Riemannian manifolds, methods and tools of differential geometry. The student is enabled :
- to understand and apply these techniques
- to formalize statements in a correct mathematical language
- to make use of these techniques in default problem settings
The course has connections to MM512: Curves and Surfaces.
In relation to the competence profile of the degree it is the explicit focus of the course to:
- Give the competence to work with mathematical models and theory
- Give basic understanding on how to work with geometric ideas and manifold structures
Expected learning outcome
The learning objective of the course is that the student demonstrates the ability to:
- understand the basic principles of Riemannian geometry
- understand and work with manifolds, tangent spaces and curvature
- compare and contrast the methods introduced in the course
Content
The following main topics are contained in the course:
- Topological and differential manifolds
- Tangent spaces
- Riemannian metrics
- Covariant derivatives
- Geodesics
- Curvature
Literature
Examination regulations
Exam element a)
Timing
Spring
Tests
Mandatory assignments and oral examination
EKA
N300047102
Assessment
Second examiner: Internal
Grading
7-point grading scale
Identification
Full name and SDU username
Language
Normally, the same as teaching language
Examination aids
To be announced during the course
ECTS value
5
Indicative number of lessons
Teaching Method
At the faculty of science, teaching is organized after the three-phase model ie. intro, training and study phase. In order to enable students to achieve the learning objectives for the course, the teaching is organised in such a way that there are 48 lectures, class lessons, etc. on a semester. These teaching activities are reflected in an estimated allocation of the workload of an average student as follows:
- Intro phase (lectures, class lessons) - 28 hours
- Training phase: 14 hours, including 14 hours tutorials
Teaching is centred on interaction and dialogue. In the intro phase, concepts, theories and models are introduced and put into perspective. In the training phase, students train their skills through exercises and dig deeper into the subject matter. In the study phase, students gain academic, personal and social experiences that consolidate and further develop their scientific proficiency. Focus is on immersion, understanding, and development of collaborative skills.
Activities during the studyphase:
- Reading of suggested literature
- Preparation of exercises in study groups
- Contributing to online learning activities related to the course