MM813: Topology II (5 ECTS)

STADS: 13004501

Level
Master's level course

Teaching period
The course is offered in the spring semester.
3rd quarter

Teacher responsible
Email: szymanski@imada.sdu.dk

Timetable
Show entire timetable
Show personal time table for this course.

Comment:
Ubegrænset deltagerantal. 3. kvartal. Fælles undervisning med MM509.

Prerequisites:
None

Academic preconditions:
The content of the courses MM501 Calculus I, MM502 Calculus II and MM508 Topology I must be known.

Course introduction
Topological properties play an important role in most branches of mathematics. The purpose of the course is to develop further the concepts, which are introduced in Topology I, in more advanced settings.

Expected learning outcome
By the end of the course the student is expected to:
- Present and illustrate in a mathematically precise way definitions within.
- Present in a mathermatically precise way central results, including detailed proofs, within the syllabus of the course.
- Compare and relate central results from the course.
- Generalise concepts from earlier courses to general topological spaces.

Subject overview
1. Metric and topoligical space.
2. Compactness and sequential compactness.
3. Uniform continuity of functions.
4. The Riemann integral.
5. Completeness of metric spaces
6. The Banach fixed-point theorem.
7. Spaces of continuous functions viewed as topological spacea. 8. Existence and uniqueness of solutions ti certain types of differential equations.
9. Approximation of continuous functions, e.g. the Stone-weierstrass theorem.
10. Normal topological spaces.

Literature

Meddeles ved kursets start.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
a) Written project, marks on 7-point scale, external examiner.
b) Oral examination, marks on the 7-point scale, external examiner. The project will be weighted 20% and the oral examination 80 % in the final mark for the course. To pass the course, both parts must be passed individually.

Reexamination after 4th quater.

Expected working hours
The teaching method is based on three phase model.

Forelæsninger: 32 timer Eksaminatorietimer/opgaveregning: 18 timer
Educational activities

Language
This course is taught in English, if international students participate. Otherwise the course is taught in Danish.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.