NMAK21013U Invitation to Combinatorics

Volume 2021/2022
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 3 weeks
  • Category
  • Hours
  • Lectures
  • 36
  • Preparation
  • 116
  • Theory exercises
  • 27
  • Exam
  • 27
  • Total
  • 206
Written
Oral
Individual
Collective
Continuous feedback during the course of the semester
Credit
7,5 ECTS
Type of assessment
Continuous assessment
2-4 in-class oral presentations (depending on the number of enrolled students). The in-class oral presentations are weighted the same and the course performance is assessed as a whole.
Aid
All aids allowed
Marking scale
passed/not passed
Censorship form
No external censorship
One internal examiner
Re-exam

Oral exam
30 minutes oral exam without preparation time and without aids.
No external censorship. Several internal examiners.

Criteria for exam assesment

See learning outcome