English

MM508: Topology I (5 ECTS)

STADS: 13006401

Level
Bachelor course

Teaching period
The course is offered in the autumn semester.
2. quarter.

Teacher responsible

Email: njn@imada.sdu.dk

Timetable

Group	Type	Day	Time	Classroom	Weeks
Common	I	Monday	12-14	U26	45-51
Common	I	Tuesday	08-10	U20	45-46
Common	I	Tuesday	12-14	U140	50
Common	I	Thursday	10-12	U140	45-50
M1	TE	Tuesday	08-10	U49d	50-51
M1	TE	Wednesday	16-18	U130	51
M1	TE	Thursday	14-16	U69	45-50
S1	TE	Tuesday	08-10	U49c	50-51
S1	TE	Wednesday	16-18	U142	51
S1	TE	Thursday	14-16	U49c	45-50

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Comment:
Ubegrænset deltagerantal. Kurset kører i 2. kvartal.

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.

Expected learning outcome
By the end of the course the students are expected to be able to:

-- solve (written) problems (including "proof problems") concerning the course topics, including in particular
* open and closed sets in metric and topological spaces
* convergence of sequences and series
* continuity
* compact sets
* connected sets
* completeness
-- formulate the answers in a correct mathematical language.

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:
(a) Mandatory exercises, pass/fail, internal evaluation by teacher. The exercises must be passed in order to take the written exam.
(b) 4 hours written exam. Marks according to the 7-point marking scale. External examinator.

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.