NMAK14025U The Geometry of Numbers

Volume 2014/2015
Education
MSc Programme in Mathematics
MSc Programme in Statistics
MSc Programme in Mathematics-Economics
Content

Lattices, Quadratic forms, Convex bodies, Successive minima, Minkowski's theorems, The space of lattices, Mahler's compactness theorem, Siegel's mean value formula, Packings and coverings, The Minkowski-Hlawka theorem, Gauss circle problem and its generalizations, The Epstein zeta function.

Learning Outcome

Knowledge: After completing the course the student is expected to have a thorough knowledge of definitions, theorems and examples related to the topics mentioned in the description of the course content.

Skills: At the end of the course the student is expected to have the ability to use the acquired knowledge to follow arguments and proofs of advanced level as well as to solve relevant problems.

Competences: At the end of the course the student is expected to be able to
1. reproduce key results presented in the course together with detailed proofs thereof, 
2. construct proofs of results in the geometry of numbers at the level of this course,
3. use the course content to study relevant examples and to solve concrete problems.  

Complex analysis (KomAn).
Four hours of lectures and two hours of exercise sessions per week for 9 weeks.
  • Category
  • Hours
  • Exam
  • 40
  • Lectures
  • 36
  • Preparation
  • 112
  • Theory exercises
  • 18
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Continuous assessment
4 mandatory homework assignments to be returned in weeks 3,5,7 and 9 of
the course. No second hand-in allowed. At least one assignment will be
assessed in part by an individual oral presentation.
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner.
Re-exam
Oral examination (30 minutes).
Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.