6 ECTS credits
150 h study time

Offer 1 with catalog number 4013329FNR for all students in the 2nd semester of odd academic years (e.g. 2013-2014) at a (F) Master - specialised level.

Semester
biennial: 2nd semester of an odd academic year (e.g. 2013-2014)
Enrollment based on exam contract
Impossible
Grading method
Grading (scale from 0 to 20)
Can retake in second session
Yes
Taught in
Dutch
Faculty
Faculty of Science and Bio-engineering Sciences
Department
Mathematics
Educational team
Michel Van Den Bergh (course titular)
ALAIN VERSCHOREN
Activities and contact hours

30 contact hours Lecture
30 contact hours Seminar, Exercises or Practicals
Course Content

The content of the course is variable. We explore the boundary area between number theory, algebraic geometry and analysis. We emphasize in particular the special role of the zeta-function and the more general L-series, and we explain in this context the relevance of the "Riemann-Hypothesis" and the Birch-Swinnerton-Dyer conjecture, both "millenium problems" http://www.claymath.org/millennium-problems). 

Part of the course is devoted to an introduction to elliptic curves (plane curves defined by a third degree equation). In this area of mathematics the synergy of ideas from different domains has been extremely fruitful. Elliptic curves are very important in modern cryptography and through the theory of L-series they form also an important part of the proof of Fermat's theorem by Andrew Wiles.

In the course we will occasionally use the language of algebraic geometry as well as some elementary complex analysis. The necessary background information is introduced but is not part of the exam.

Course material
Digital course material (Required) : Syllabus dat steunt op aanbevolen boek
Handbook (Recommended) : A course in Number Theory and Cryptography, Neal Koblitz, 2de, Springer, 9781461264422, 2012
Additional info

There is a syllabus.

Learning Outcomes

General competencies

After following this course the student will have a clearer idea about some principles of modern number theory.

Grading

The final grade is composed based on the following categories:
Oral Exam determines 100% of the final mark.

Within the Oral Exam category, the following assignments need to be completed:

  • Mondeling examen with a relative weight of 1 which comprises 100% of the final mark.

Additional info regarding evaluation

Oral exam with written preparation.

Allowed unsatisfactory mark
The supplementary Teaching and Examination Regulations of your faculty stipulate whether an allowed unsatisfactory mark for this programme unit is permitted.

Academic context

This offer is part of the following study plans:
Master of Mathematics: Fundamental Mathematics (only offered in Dutch)
Master of Mathematics: Education (only offered in Dutch)