MM509: Topology II (5 ECTS)

STADS: 13005701

Level
Bachelor course

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

Teacher responsible
Email: szymanski@imada.sdu.dk

Timetable
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Comment:
Ubegrænset deltagerantal. 3. kvartal. Fælles undervisning med MM813.

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 will be able to:

• give an oral presentation of the statement and proofs related to any subject on a previously given list of topics within the course's syllabus
• formulate the oral presentation in a mathematically correct way
• answer supplementary questions from the teacher and external examiner on definitions and results from the course syllabus

Subject overview
1) Metric and topological spaces.
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 spaces.
8) Existence and uniqueness of solutions to 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) Mandatory assignments. Pass/fail, internal evaluation by teacher.
The assignments must be passed in order to take the exam.
b) Oral exam. External marking. Marks according to the 7-point grading scale.

Reexamination after 4th quarter.

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

Forelæsninger (32 timer). Eksaminatorier (18 timer).
Educational activities

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.