Ramsey theory, fall 2016

Ramsey theory Moodle page

Teacher: Åsa Hirvonen 

Scope: 10 cr

Type: Advanced studies

Teaching: Four hours of lectures and two hours of exercises per week.

Topics: Ramsey theory considers unavoidable regularities in large structures: If all k-subsets of the integers are finitely coloured, then there is an infinite homogeneous set (Ramsey); if the positive integers are finitely coloured then one colour class contains arithmetic progressions of arbitrary length (van der Waerden); an n-dimensional cube (for n large enough) is r-coloured then there exists a monochromatic 'line' (Hales-Jewett theorem), etc. We will look at basic proof techniques of both finite and infinite Ramsey theory.

This is not really a logic course, although there are some applications to logic, but Ramsey theory is about phenomena that occur in areas as varied as combinatorics, algebra, analysis, geometry, set theory and logic.

Prerequisites: This course does not really require any logic background, but some 'mathematical routine' is assumed (this is an advanced course, so some intermediate courses such as Algebra I and Topology I are assumed).