MM508: Topology I (5 ECTS)

STADS: 13000801

Level
Bachelor course

Teaching period
The course is offered in the autumn semester.

Teacher responsible
Email: hjm@imada.sdu.dk

Timetable
Show entire timetable
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Comment:
14.09.2007: Skemaændring S1.

Ubegrænset deltagerantal.

Prerequisites:
None

Academic preconditions:
The contents of Calculus I (MM501) and Calculus II (MM502) must be known.

Course introduction
Topological properties are used in most mathematical areas and the aim of the course is to provide knowledge of the fundamental topological properties of metric and topological spaces, in particular the Euclidian spaces.

Qualifications
The students shall learn the techniques of a mathematical proof and will be introduced to various subjects in the basic theory of metric and topological spaces. In particular the course will concentrate on the topology of the Euclidian spaces. After having followed the course the students are expected to
• understand the fundamental topological concepts such as open and closed sets, compact sets and continuity of functions.
• be able to use topological arguments, including compactness arguments, in concrete situations in mathematics and in areas where mathematics is applied.

Expected learning outcome


Subject overview
1. The topological properties of the Euclidian spaces, metric and topological spaces.
2. Continuity of functions.
3. Convergence of sequences and series.
4. Compact sets, including the characterization of compact subsets of the Euclidian spaces (the theorem of Heine-Borel).
5. Connected sets.
6. Completeness of the Euclidian spaces.

Literature

Meddeles ved kursets start.

Syllabus
See syllabus.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
Study progammes where only Topology I is compulsary: A 2 hours written exam. Marks according to the 7-point marking scale. External examinator. Study programmes where both Topology I and Topology II are compulsary: A common exam with Topology II, consisting of a 2 hours written exam and a 30 minutes oral exam with preparation. Marks according to the 7-point marking scale. External examinator.
Examination only when the course(s) has been taugth. Examination in opposition terms only after acceptance from the study board.

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

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

Language
No recorded information about the language used in the course.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.