NMAK15007U Automorphic Forms and Fuchsian Groups ( FuchsGr)
MSc Programme in Mathematics
Motivated by a number of examples from number theory we study
Fuchsian
groups and in particular the modular group. Fuchsian groups are
discrete isometries of the hyperbolic plane. We examine
lattices, hyperbolic geometry, fundamental
domains, Eisenstein series, modular forms, Maass forms, L-series
and related
topics. Course participation could lead to several masters thesis
topics.
Knowledge:
At the end of the course the student is expected to have thourough
knowledge of the results and methods mentioned in the description
of the content.
Skills:
Relevant to the course subject matter the student should at the end
of the course be able to:
- reproduce key results and give rigorous and detailed proofs of them,
- compare key results,
- apply the basic techniques, results and concepts of the course to concrete examples and exercises.
Competences:
At the end of the course the student is expected to be able to
- apply the abstract concepts in the course to concrete problems,
- analyze and discuss which methods are appropriate for a specific mathematical problem relevant to the course,
- construct proofs of results at the level of the course.
- Category
- Hours
- Colloquia
- 15
- Exam
- 20
- Lectures
- 36
- Preparation
- 117
- Theory exercises
- 18
- Total
- 206
As
an exchange, guest and credit student - click here!
Continuing Education - click here!
- Credit
- 7,5 ECTS
- Type of assessment
- Continuous assessment2 hand-in exercises and a seminar talk.
- Aid
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
One internal examiner
- Re-exam
30 minutters oral exam with 20 min. preparation time. All aids allowed during the preparation time, no aids allowed during the examination. Several internal examiners.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Course information
- Language
- English
- Course code
- NMAK15007U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 2
- Schedule
- B
- Course capacity
- No limit
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Morten S. Risager (7-746b7563696774426f63766a306d7730666d)