MM846: Riemannian geometry, matrix manifolds and applications

Study Board of Science

Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N310023102
Censorship: Second examiner: Internal
Grading: 7-point grading scale
Offered in: Odense
Offered in: Spring
Level: Master

STADS ID (UVA): N310023101
ECTS value: 10

Date of Approval: 18-11-2019


Duration: 1 semester

Version: Approved - active

Comment

New course Fall 2018 (E2018)

Entry requirements

None

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 is not required

Course introduction

The course bridges pure and applied mathematics.

The aim of the course is to obtain knowledge about Riemannian manifolds, methods and tools of differential geometry and special applications that involve matrix manifolds. The student is enabled: 

  • to analyse, apply and modify these techniques by means of mathematical and numerical analysis 
  • to formulate the problems (including proofs) in a correct mathematical language
  • to make use of these techniques in practical applications

The course builds on the knowledge acquired in the Bachelor program. The course has connections to MM512: Curves and Surfaces. 
The course mediates between pure and applied mathematics and 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
  • The Stiefel and the Grassmann manifolds
  • Optimization and interpolation in matrix manifolds

Literature

See Blackboard for syllabus lists and additional literature references.

Examination regulations

Exam element a)

Timing

Autumn

Tests

Mandatory assignments and oral examination

EKA

N310023102

Censorship

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

10

Additional information

The examination form for re-examination may be different from the exam form at the regular exam.

Indicative number of lessons

84 hours per semester

Teaching Method

At the faculty of science, teaching is organized after the three-phase model ie. intro, training and study phase.

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 study phase:

  • Reading of suggested literature
  • Preparation of exercises in study groups
  • Contributing to online learning activities related to the course

Teacher responsible

Name E-mail Department
Ralf Zimmermann zimmermann@imada.sdu.dk

Timetable

Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Registration & Legality

NAT

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