Math 490 Section M2 (Topology of Surfaces)
The subject of this topics course is geometric/combinatorial topology.
As such it complements the two other advanced undergraduate courses in
topology and geometry (Math 423: Differential Geometry of Curves and
Surfaces, and Math 432: Set Theory and Topology). The highlight of the
course and our principal aim is the classification theorem for compact
surfaces, which we will prove by an explicit combinatorial argument.
Along the way we will encounter applications of ideas and techniques
from geometric topology in a variety of other contexts: differential
equations and vector fields, algebra, knot theory, graph theory and
map colorings, to name a few.
- Instructor: Prof. Jeremy Tyson
- Office Location: 330 Illini Hall
- Office Phone: 244-4132
- Office Hours: Mon 10:00-11:00, Tue 11:00-12:00, Wed
2:00-3:00, or by appointment
- Lecture Times: TueThu 9:00-10:30
- Lecture Location: 343 Altgeld Hall
- Course web site:
- Textbook: A First Course in Geometric Topology and
Differential Geometry by E. D. Bloch (Birkhauser, 1997)
- Other recommended texts:
- A Combinatorial Introduction to Topology by M. Henle
(Freeman and Co., 1979; reprinted by Dover, 1994)
- Topology of Surfaces by L. C. Kinsey (Springer, 1993)
- The Knot Book by C. Adams (Freeman and Co., 1994): on
reserve at the Math Library
- Intuitive Topology by V. V. Prasolov (American
Mathematical Society, 1995)
- Homework and projects: There will be regular homework
assignments (approximately three per month). In addition, there will
be one long-term project. Topics for the projects can come from a list
which I will draw up; you are welcome to design your own project as
well although it must receive my OK first.
You are encouraged to work on the homework in groups, although each
student should submit a separate set of solutions. (Please indicate
which other students you collaborated with, if any.) Class
participation and discussion will be an important component of your
- Exams: There will be one midterm exam and a cumulative
final exam. Either of these exams may be takehome exams.
- Grading Policy: Grades will be computed according to the
| Midterm (Tue 3/14 in class)
Note: extra class session on Wed, 4/26 from 5 - 5:30 pm.