NMAK23008U Invitation to Combinatorics

Volume 2023/2024
Education

MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject

Content

Discrete Mathematics is the study of discrete, as opposed to continuous objects. Often also called combinatorics, it is primarily associated with counting questions.

Importantly, however, it also finds application and stands in relation to other areas, such as representation theory and algebraic geometry. The idea of the course is to provide a panorama of such relations and interplays, ideally giving glimpses into current research. 

A particular focus is on learning algebraic, geometric as well as probablistic methods in combinatorics. Specific topics are selected based on current research. Topics discussed include

Probablistic methods and extremal combinatorics,

Algebraic methods and formal power series

Geometric combinatorics and discrete geometry.

Learning Outcome

Knowledge: To display knowledge and understanding of the course topics
and content at a level suitable for further studies in Combinatorics.

Skills: At the end of the course the student is expected to be able to
follow and reproduce arguments at a high abstract level corresponding to
the contents of the course.

Competences: At the end of the course the student is expected to be
able to apply basic techniques and results to concrete examples.

General knowledge in basic algebra and analysis. Additional basic knowledge in probability theory, groups and rings is ideal.
Lineær algebra i de matematiske fag (LinAlgMat) and Analyse 1 (An1).
4 hours lectures and 3 hours exercises/recitation for 9 weeks
  • Category
  • Hours
  • Lectures
  • 36
  • Preparation
  • 116
  • Theory exercises
  • 27
  • Exam
  • 27
  • Total
  • 206
Oral
Credit
7,5 ECTS
Type of assessment
Continuous assessment
Type of assessment details
3 in-class oral presentations of 45 minutes each. The assessment will be based on the two best oral presentations. The in-class oral presentations are weighted the same.
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner
Re-exam

Oral exam
30 minutes oral exam without preparation time and without aids.
 

Criteria for exam assesment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.