MM803: de Rham cohomology I (5 ECTS)

STADS: 13003001

Level
Master's level course

Teaching period
The course is offered in the autumn semester.

Teacher responsible
Email: swann@imada.sdu.dk

Timetable
There is no timetable available for the chosen semester.

Comment:
Ubegrænset deltagerantal. 3. kvartal.

Prerequisites:
None

Academic preconditions:
Basic command of calculus, linear algebra, point set topology and curves and surfaces is assumed, e.g. corresponding to MM501, MM502, MM505, MM508, MM509 and MM512.

Course introduction
To study properties of smooth manifolds by means of differential forms and linear algebra.

Expected learning outcome
At the end of the course the student is supposed to be able to:

- Present definitions and results, including their proofs, from course syllabus
- Apply these results to problems in de Rham cohomology based on the course syllabus
- use correct and complete mathematical terminology

Subject overview
The alternating algebra. de Rham cohomology. Chain complexes and their cohomology. The Mayer Vietoris sequence. Homotopy. Applications of de Rham cohomology. Smooth manifolds. Differential forms on smooth manifolds. Integration on manifolds. Degree, linking numbers and index of vector fields.

Literature
There isn't any litterature for the course at the moment.

Syllabus
See syllabus.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
Oral exam. Danish 7 mark scale, internal examiner.

Reexams will be offered according to the rules adopted by the study board.

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

Forelæsninger, antal timer 32.
Eksaminatorietimer/opgaveregning, antal timer 18.
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.

Remarks
The course is offered when the need and the possibility coincide.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.