Probabilistic Method, 5 credits

Sannolikhetsmetodik

Course information

Language of instruction: English
Course period: 2026 HT
Course structure: 20 x 2hr lectures, 4 x 2hr problem sessions, including student presentations.

Recommended prerequisites

None, since students of differing backgrounds may apply. We will ask students to give examples of random models used in their area of research.

Learning outcomes

Problem solving, presenting to peers at a blackboard, understanding of random models in a variety of fields.

Learning outcomes for doctoral degree

Problem solving, close to research since some presented results will be of applications made in last one or two years.

Course contents

First moment method, Second moment method, Lovasz Local Lemma, Phase Transition in G(n, p), Correlation and concentration including, Clique and chromatic number of G(n, p), Random network models (preferential attachment, stochastic block models), entropy methods.

Instruction

Lecturing at the blackboard; encourage student participation with questions and predictions of behaviour of newly introduced systems.

Assessment

3 assignments for PhD students, 2 for master’s students. Each student presents a problem in front of the group. Accommodations will be made if required.

Course examiner

Annika Heckel annika.heckel@math.uu.se

Department with main responsibility

Mathematics Department

Contact person

Fiona Skerman fiona.skerman@math.uu.se

Application

Submit the application for admission to: Fiona Skerman & Annika Heckel
Submit the application not later than: 15th May 2026