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.
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.
There is a syllabus.
After following this course the student will have a clearer idea about some principles of modern number theory.
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:
Oral exam with written preparation.
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)