NMAK13003U Automorphic Forms and Fuchsian Groups ( FuchsGr)

Volume 2013/2014
Education
MSc Programme in Mathematics
Content
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.
Learning Outcome
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:
  1. reproduce key results and give rigorous and detailed proofs of them,
  2. compare key results,
  3. 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
  1. apply the abstract concepts in the course to concrete problems,
  2. analyze and discuss which methods are appropriate for a specific mathematical problem relevant to the course,
  3. construct proofs of results at the level of the course.
KomAn
4 hours of lectures and 2 hours of exercise sessions each week for 9 weeks
  • Category
  • Hours
  • Colloquia
  • 15
  • Exam
  • 20
  • Lectures
  • 36
  • Preparation
  • 117
  • Theory exercises
  • 18
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Continuous assessment
2 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 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.