MM865: Riemannian Geometry
Study Board of Science
Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N310079102
Assessment: Second examiner: Internal
Grading: 7-point grading scale
Offered in: Odense
Offered in: Autumn
Level: Master
STADS ID (UVA): N310079101
ECTS value: 10
Date of Approval: 25-01-2024
Duration: 1 semester
Version: Approved - active
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 or MM505
- Have knowledge of the contents of MM533
- Knowledge of MM512 is recommended but not required
Course introduction
The aim of the course is to obtain knowledge about Riemannian manifolds, methods and tools of differential geometry. The student is enabled :
- to analyse, apply and modify these techniques by means of mathematical analysis
- to formulate the problems (including proofs) in a correct mathematical language
- to make use of these techniques in new problem settings
The course builds on the knowledge acquired in the Bachelor program. The course has connections to MM512: Curves and Surfaces. The course gives an academic basis for Master theses.
In relation to the competence profile of the degree it is the explicit focus of the course to:
- Give the competence to analyse and apply mathematical models
- 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 manifolds, tangent spaces and curvature
- compare and contrast the methods introduced in the course
- transfer the learning content to new problems and applications
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
January
Tests
Oral examination
EKA
N310079102
Assessment
Second examiner: Internal
Grading
7-point grading scale
Identification
Student Identification Card
Language
Normally, the same as teaching language
Examination aids
To be announced during the course.
ECTS value
10
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. These teaching activities are reflected in an estimated allocation of the workload of an average student as follows:
- Intro phase (lectures) - 56 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
Teacher responsible
Additional teachers
Timetable
Administrative Unit
Team at Educational Law & Registration
Offered in
Recommended course of study
Transition rules
Transitional arrangements describe how a course replaces another course when changes are made to the course of study.
If a transitional arrangement has been made for a course, it will be stated in the list.
See transitional arrangements for all courses at the Faculty of Science.