*Fall 2011*

*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.

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 August 22

Lecture August 24

Lecture August 26

Lecture August 29

Lecture August 31

Lecture September 02

Lecture September 07

Lecture September 09

Lecture September 12

Lecture September 14

Lecture September 16

Lecture September 19

Lecture September 21

Lecture September 23

Lecture September 26

Lecture September 28

Lecture September 30

Lecture October 03

Lecture October 05

Lecture October 17

Lecture October 19

Lecture October 24 - 28

Lecture November 02 - 09

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 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

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.

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

The final grade will take into account the homework scores, the midterm, the research project, and the final oral exam.

*Collaboration*: Collaboration among
students to solve homework assignments is welcome. This is a good way
to learn mathematics. So is the consultation of other sources such as
other textbooks. However, *every student has to hand in his/her own set
of solutions*, and if you use other people's work or ideas you
*have to indicate the source in your solutions*.

(In any case, complete and correct homework receives full credit.)

However, from time to time there will be "controlled" problems, in which every student should work out his/her own solutions.