This term we will return to those foundations: the course will be initially a traditional first course in topology covering ``point-set topology'': the study of metric and topological spaces, continuity, compactness, connectedness, and other properties beginning with ``c''. This branch of the subject is really just a part of analysis, and it is very important for the foundations of the subject. Although it can seem quite abstract, it will help you learn to write proofs properly. I hope that the course will help you in general to appreciate and produce ``good mathematics'' at whatever level is appropriate.
The intended sequence of topics is:
1. Point-set topology
2. The fundamental group
3. Two-dimensional surfaces and their classification
4. Various topics: probably some hyperbolic geometry, some of the
theory of covering spaces, and some theory of
3-dimensional manifolds.
M. Armstrong, Basic Topology (1983, Springer-Verlag).
The second part on surfaces is contained in the notes for the course I gave in Edinburgh, which are available by clicking here.
My office hours are Monday 5.30 - 6.30 and Friday 11-12 in room
7210 in APM.
Midterm will be on February 9th in class.
Homeworks will be set most weeks on Mondays and be due the
following Monday in the lecture. The list of problems will be
maintained here: Homework problems
Grading will be 25% homework, 25% midterm, 50% final.
``Knots knotes'' in gzipped postscript.
``Knots knotes'' in pdf.
Additional Information
