MM816: Geometry of Surfaces (5 ECTS)
STADS: 13005901
Level
Master's level course
Teaching period
The course is offered in the spring semester.
3rd quarter.
Teacher responsible
Email: svensson@imada.sdu.dk
Timetable
Group |
Type |
Day |
Time |
Classroom |
Weeks |
Comment |
Common |
I |
Monday |
10-12 |
U49D |
06-12 |
|
Common |
I |
Wednesday |
12-13 |
U49C |
06-09 |
|
Common |
I |
Thursday |
12-14 |
U26a |
06-12 |
|
S1 |
TE |
Tuesday |
08-10 |
U37 |
06-12 |
|
S1 |
TE |
Wednesday |
13-14 |
U49C |
09-12 |
|
Show entire timetable
Show personal time table for this course.
Comment:
Ubegrænset deltagerantal. 3. kvartal.
Prerequisites:
None
Academic preconditions:
Basic knowledge concerning point set topology as well as curves and surfaces is required. Basic knowledge of complex function theory is recommended.
Course introductionThe course introduces some important aspects of the interplay between geometry and topology for surfaces in 3-space, in particular the Gauâ-Bonnet Theorem.
Expected learning outcomeAt the end of the course the student will be able to:
- reproduce the definitions within the scope of the course’s syllabus in a precise mathematical language
- reproduce results, together with complete proofs, within the scope of the course’s syllabus
- relate the results within the scope of the course’s syllabus to each other
- apply the theory to solve problems within the scope of the course's syllabus
- combine concepts from differential geometry, topology and complex analysis to explain results within the scope of the course's syllabus
Subject overview- Surfaces in 3-space.
- The Inverse Function Theorem.
- Change of coordinates for surfaces.
- Level curves and level surfaces.
- Orientation, area and isometries.
- Minimal surfaces and the Weierstrass representation.
- Theorema Egregium.
- The Gauss-Bonnet Theorem and the classification of compact surfaces.
LiteratureMeddeles ved kursets start.
Syllabus
See syllabus.
Website
This course uses
e-learn (blackboard).
Prerequisites for participating in the exam
None
Assessment and marking:
Oral examination, grades according to the danish 7-point scale and external censorship.
Mandatory assignments, pass/fail, internal evaluation by the teacher.
Reexamination after 4th quarter.
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.