# Ramsey theory, fall 2016

**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).

## News

- The course has a Moodle page that will be used for exercises, news, etc. It is now available (although not in final shape).
- Note that exercises start already the first week (i.e. Friday 9.9.)
- Due to the University's opening ceremony there will be no lecture on Monday 5.9.

## Teaching schedule

Weeks 36-42 and 44-50, Monday 14-16 and Tuesday 10-12 in room C123, exercises Friday 10-12 in room C122.

## Exams

Exam lasts 2,5 hours.

You can use (lecturer will fill in) in the exam.

## Course material

We will mainly follow the book Graham, Rothschild, Spencer, Ramsey Theory (second edition).

## Registration

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## Exercises

### Assignments

will be published on the Moodle page of the course

### Exercise classes

Group | Day | Time | Room | Instructor |
---|---|---|---|---|

1. | Friday | 10-12 | C122 | Åsa Hirvonen |

## Course feedback

Course feedback can be given at any point during the course. Click here.