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This is the study programme for 2019/2020. It is subject to change.

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.

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

### Method of work

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

### Open to

Master studies at the Faculty of Science and Technology.

### Course assessment

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

### Literature

K. Janich, "Topology", Springer, 1984.
K. Tapp, "Matrix Groups for Undergraduates", STML Volume 29, American Mathematical Society, 2005.

This is the study programme for 2019/2020. It is subject to change.

Sist oppdatert: 24.08.2019