DE

Modul

Riemann Surfaces [M-MATH-106466]

Credits
8
Recurrence
Unregelmäßig
Duration
1 Semester
Language
German
Level
4
Version
1

Responsible

Organisation

  • KIT-Fakultät für Mathematik

Part of

Bricks

Identifier Name LP
T-MATH-113081 Riemann Surfaces 8

Competence Certificate

Oral examination of ca. 30 minutes.

Competence Goal

Students know

  • essential structural properties of Riemann surfaces,
  • topological, analytic and algebraic methods for the investigation of Riemann surfaces, and are able to apply them.

Prerequisites

None

Content

  • Definition of Riemann surfaces
  • holomorphic and meromorphic functions on Riemann surfaces
  • Compact Riemann surfaces
  • The Riemann-Roch theorem
  • Uniformization, Fuchsian groups and hyperbolic metric
  • Classification of compact Riemann surfaces

Recommendation

Some knowledge of complex analysis (e.g. "Analysis 4") is strongly recommended as well as the modules "Elementary Geometry" and "Introduction to Algebra and Number Theory".

Workload

Total workload: 240 hours

Attendance: 90 h

  • lectures, problem classes  and examination

Self studies: 150 h

  • follow-up and deepening of the course content,
  • work on problem sheets,
  • literature study and internet research on the course content,
  • preparation for the module examination