Topics in Algebra and Number Theory

Course content

We will cover various topics in contemporary Algebra and Number Theory, such as Arithmetic Geometry, special functions, explicit methods, rational points, moduli problems in arithmetic, with the precise content depending on the modern questions asked in these fields.

Education

MSc Programme in Mathematics

Learning outcome

Knowledge: To display knowledge of the course topics and content, at the level of a beginning researcher.

Skills: To be able to use the acquired knowledge to obtain proofs.

Competences: To be able to produce independent proofs in extension of
the acquired knowledge.

4 hours of lectures.
Lectures will be given by the professor and some talks will be prepared and given by the students.

See Absalon for a list of course literature.

This course definitely fits in the circle of ideas presented in these other courses: Algebra 3, Algebraic Number Theory, Analytic Number Theory, Algebraic Geometry, Elliptic curves. Nevertheless, these courses are not requirements, the course will be self-contained.

Academic qualifications equivalent to a BSc degree is recommended.

Oral
Collective
Continuous feedback during the course of the semester
ECTS
7,5 ECTS
Type of assessment
Oral examination, 30 min under invigilation
The exam will be a 30 minutes oral exam with 30 minutes of preparation time.
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner.
Criteria for exam assessment

In order to obtain the grade 12 the student should convincingly and accurately demonstrate the knowledge, skills and competences described under Learning Outcome.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 28
  • Preparation
  • 177
  • Exercises
  • 14
  • Exam
  • 1
  • English
  • 220