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).
Weeks 36-42 and 44-50, Monday 14-16 and Tuesday 10-12 in room C123, exercises Friday 10-12 in room C122.
Exam lasts 2,5 hours.
You can use (lecturer will fill in) in the exam.
We will mainly follow the book Graham, Rothschild, Spencer, Ramsey Theory (second edition).
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