Nach positiver Absolvierung der Lehrveranstaltung sind Studierende in der Lage, Ramsey-Phänomene in verschiedenen Gebieten der Mathematik zu erkennen, sowie Verbindungen zwischen kombinatorischen und dynamischen Begriffen in diesem Kontext anzuwenden.
Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that focuses on the appearance of order in a substructure given a structure of a known size.
More precisely, it is the study of quesions of the following type: given a combinatorial structure (e.g. a graph or a subset of the integers), how large does the structure have to be to guarantee the existence of some substructure (e.g. subgraph, subset) with a given property?
We investigate connections of such questions with various branches of mathematics such as topological dynamics, and applications e.g. to arithmetics, universal algebra, or theoretical computer science.
Each student gives about 2 lectures on selected topics.
Continuous assessment.
Nicht erforderlich
Logik oder Algebra.
