Topological
Methods in Combinatorics
Info
- Class:
Tuesday 16:00-18:00 Sh. 115
- Teacher - Nati
Linial, Room 215, Ross +2. No
official reception hour will be given. You can either send an e-mail to
nati@cs
or call 85237.
Course description
The course is based on the following book by Jiri
Matousek:
Using the Borsuk-Ulam theorem (Lectures on topological
methods in combinatorics and geometry) (Springer,
April 2003)
For general background in topology, we recommend reading in the
following
books:
- J. R. Munkres:
Topology (A first course), Prentice Hall, 2000 (this is the 2nd ed.,
the older one is also good); this is an introduction to general
topology and a just a little of algebraic topology
- J. R. Munkres:
Elements of algebraic topology, Addison-Wesley, Reading,
MA, 1984
- A. Hatcher: Algebraic Topology, Cambridge University Press, 2001.
Algebraic topology is generally useful and it
probably pays
off to study these books carefully. For the purposes of the course,
though, it
may be helpful even to read the beginning of one of these books once or
twice,
skimming over the details, in order to get used to the basic
topological
notions.
In particular, do not miss Chapter 0 in Hatcher's book, where many
things
are beautifully explained on an intuitive level! The next step in that
book
would be Chapter 2 (homology). We won't make much use of the
fundamental group,
which is the subject of Chapter 1.
Useful Links
Exercises:
- Exercise 1 (not
mandatory) ( pdf
, ps )
- Exercise 2 (pdf , ps)
- Exercise 3 (pdf , ps)
Grading Policy
All the exercises are mandatory except for the first one, and they will
make 20% of the final grade.
The grades for the exercises will be determined in an inteview. Each
student that submits exercises will have one interview during the
semester.