# Math 497A - Introduction to Ramsey Theory

Fall 2011

### Overview

Lectures: MWF 10:10-11am, Room 113 McAllister
Instructor: Jan Reimann
Office: 318B McAllister
Office hours: Tu 1:30-2:30, We 3-4
Email:
Personal Website: http://math.psu.edu/reimann/

Course blog: Links to supplementary material, hints to homework problems etc will be posted on http://massramsey2011.wordpress.com.

### Content

The course will cover some central results of Ramsey Theory. The basic paradigm of Ramsey theory is that if a structure is sufficiently large, it will have very regular substructures of a certain size. We will illustrate this principle by means of a number of results from graph theory, number theory, and combinatorial geometry. Along the way, we will encounter a phenomenon typical of Ramsey theory -- sufficiently large often means really large. We will investigate this phenomenon and see that it has some interesting consequences concerning the foundations of mathematics.

### Lecture Notes

There will be no required text for this class. Lecture notes will be made available during the course of the semester.
For further reading, I recommend the following:

• Graham, Rothschild, and Spencer – Ramsey Theory, 1990
• Nesetril – Ramsey Theory, in: Handbook of Combinatorics, 1995

### Homework

Homework will be assigned each Monday and will be due in class the following Monday in class. Homework will be graded and the two lowest scores will be dropped. Late homework will not be accepted. There will be no exception to this rule. Of course it may happen that you cannot turn in homework because you were ill or for some other valid reason. This is why the two lowest scores will be dropped.

Homework 1, due August 29, 2011 (Solutions)
Homework 2, due September 7, 2011 (Solutions)
Homework 3, due September 12, 2011 (Solutions)
Homework 4, due September 19, 2011 (Solutions)
Homework 5, due September 26, 2011 (Solutions)
Homework 6, due October 3, 2011 (Solutions)
Homework 7, due October 24, 2011
Homework 8, due October 31, 2011
Homework 9, due November 7, 2011
Homework 10, due November 14, 2011 (Solutions)
Homework 11, due December 5, 2011

### Research Project

Each participant is required to complete a research project on a specific topic. This will usually include reading original research papers. As part of the final exam, each participant will give a 20 minute representation on his/her project. Furthermore, participants are required to prepare a 5-10 page written report.

I will make available a list of possible projects in October. However, I welcome suggestions from students. So, look around, read a bit, maybe you will find a topic that interests you particularly.

### Exams

There will be a midterm: Monday, Oct 10, 10:10-12.
Midterm preparation sheet (Oct 5, 2011)
This exam will be a closed book exams. No cheat sheets! Bring blue books.

The final exam will, according to MASS tradition, be an individual 1 hour oral exam for each participant.