en_GB
Hold Ctrl-tasten nede. Trykk på + for å forstørre eller - for å forminske.

MAT600_1

Topology and Symmetry

This is the study programme for 2020/2021.


The course gives an introduction to topology, symmetry groups and their applications.

Learning outcome

The student should after a completed course have knowledge of the important fundamental concepts of topology, and should be able to use them to describe different topological spaces. The student should also have knowledge of the groups SO(3) and SU(2) and should be able to distinguish these topologically. Moreover, the student should have knowledge of the concepts of Lie groups and matrix groups, and should be familiar with the most common Lie groups and their properties.

Contents

The course gives an introduction to topology, symmetry groups and their applications. Topology includes general topological spaces, open and closed sets, separability, Hausdorff spaces, compactness, continuity, homeomorphic and connected spaces. In particular, an introduction to Euclidean and metric spaces will be given. The fundamental group will also be introduced as an example of a topological invariant. Furthermore, attention will be focussed on the important groups SO(3) (group of rotations), SU(2) and quaternions. The concept of Lie groups will be introduced with a special application to matrix Lie groups. Applications will be emphasised.

Required prerequisite knowledge

None.

Recommended previous knowledge

MAT100 Mathematical Methods 1, MAT110 Linear Algebra, MAT120 Discrete Mathematics, MAT250 Abstract Algebra

Exam

Weight Duration Marks Aid
Oral exam1/1 A - F

Course teacher(s)

Course coordinator
Paul Francis de Medeiros
Course teacher
Paul Francis de Medeiros
Head of Department
Bjørn Henrik Auestad

Method of work

4 hours of lectures and problem solving per week. Language of tuition: English.

Open to

City and Regional Planning - Master of Science
Computer Science - Master's Degree Programme
Environmental Engineering - Master of Science Degree Programme
Industrial economics - Master's Degree Programme
Robot Technology and Signal Processing - Master's Degree Programme
Engineering Structures and Materials - Master's Degree Programme
Mathematics and Physics - Master of Science Degree Programme
Mathematics and Physics, 5-year integrated Master's Programme
Offshore Field Development Technology - Master's Degree Programme
Industrial Asset Management - Master's Degree Programme
Marine- and Offshore Technology - Master's Degree Programme
Offshore Technology - Master's Degree Programme
Petroleum Geosciences Engineering - Master of Science Degree Programme
Petroleum Engineering - Master of Science Degree Programme
Technical Societal Safety - Master's Degree Programme
Risk Management - Master's Degree Programme (Master i teknologi/siviling.)

Course assessment

Use of evaluation forms and/or conversation for students' evaluation of the course and teaching, according to current guidelines.

Literature

Literatur will be published as soon as it has been prepared by the course coordinator/teacher


This is the study programme for 2020/2021.

Sist oppdatert: 22.09.2020

History