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for MAS478 - Discrete Geometry - Spring 2012
Syllabus and course information.
We will use Part 1 from Igor Pak's book which can be downloaded
here.
The notes by Keith Ball will also be useful. They can be downloaded
here.
Chapter 4 of the book by Jirka Matousek can be downloaded
here.
pdf-file.
Course notes can be downloaded here.
Lecture notes
Here are lecture notes by Alfredo Hubard for Spring 2012.
Lectures
Monday - Wednesday - Friday : 15.00 - 15.50.
Room : E6-1 3433
February Guest Lecturer: Alfredo Hubard (alfhubard[at]gmail.com)
Progress
- Feb 6 A brief history of geometry.
- Feb 6. Sylvester's problem. Describe all finite set of points
with the following property: a line determined by any pair of points
of the set passes through a third point of the set.
- Feb 8. Unit distance graphs. What graphs can you
represent where the vertices are points in the plane and edges are
between points at unit distance apart?
- Feb 10. Results from extremal graph theory. Application to
the unit distance graph theorem
- Feb 13. Ramsey's theorem.
- Feb 15. Erdos-Szekeres theorem. proof by Ramsey's theorem
and the "cup-cap" proof.
- Feb 17. Colorful Caratheodory theorem. Radon's
lemma. Helly's theorem.
- Feb 20. Tverberg's theorem.
- Feb 22. Euler's formula. Planar graphs and Euler's
formula. Another proof of Sylvester's theorem.
Problem solving
Throughout the course we will suggest many problems for you to work
on. Some will be simple, and some will be harder problems. It is not
mandatory to submit solutions, but you should come to the office hours
to discuss strategies for solving the more difficult problems.
Grading
Grading will be based on your midterm project, your final exam, and
your participation in problem solving.
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