MM516: Geometry of Surfaces (5 ECTS)
STADS: 13001601Level
Bachelor course
Teaching period
The course is offered in the spring semester.
3rd quarter.
Teacher responsible
Email: svensson@imada.sdu.dkTimetable
| Group | Type | Day | Time | Classroom | Weeks | Comment |
|---|---|---|---|---|---|---|
| Common | I | Monday | 10-12 | U44 | 05-11 | |
| Common | I | Wednesday | 12-14 | U44 | 05-11 | |
| Common | I | Friday | 08-10 | U44 | 05-06 | |
| S1 | TE | Thursday | 14-16 | U44 | 05-09, 11 | |
| S1 | TE | Friday | 08-10 | U44 | 08 | |
| S1 | TE | Friday | 08-10 | U17 | 10 |
Show personal time table for this course.
Comment:
Ubegrænset deltagerantal.
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 introduction
The course introduces some important aspects of the interplay between geometry and topology for surfaces in 3-space, in particular the Gauβ-Bonnet Theorem.
Expected learning outcome
After the course the student is expected to:
• (after 1/2 hour's preparation time) select essential definitions and results from a given subtopic of the relevant course material and present these in a precise mathematical language including formal proof(s) of at least 1 essential (sub)result. This part of the examination is expected to last 15 -10 minutes.
• (without time for preparation) give correct and exhaustive answers to questions concerning central definitions and/or results chosen among all topics treated in the course. This part of the examination is expected to last 5 – 10 minutes and proofs can be touched upon only in a very sketchy way.
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.
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:
Oral exam. Danish 7 mark scale, external examiner.
Reexamination after 4. quarter.
Expected working hours
The teaching method is based on three phase model.
Forelæsninger (32 timer), eksaminatorier (16 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.
