Topology
Math 131  Harvard University
Required Texts
 Munkres,
Topology,
2nd edition, PrenticeHall 2000
Prerequisites:
Acquaintance with metric spaces (Math 25, 55, 101 or 112)
and groups (Math 101 or 122).
Intended for undergraduate math majors.
Topics.
This course will cover the basics of topological spaces,
fundamental groups and covering spaces.
Topics include the following:

General Topology
 Set theory
 Topological spaces
 Connectedness
 Compactness
 Countability
 Metric spaces
 Baire category

Fundamental group
 Homotopy theory
 Fundamental group
 Jordan curves
 Groups and gluing
 Graphs
 Surfaces
 Covering spaces
Reading and Lectures.
Students are responsible for all topics covered in
the readings and lectures. Lectures may go beyond the
reading, and not every topic in the reading will be
covered in class.
Grades.
Grades will be based on weekly homework (40%), the midterm (20%)
and the takehome final (40%).
The two lowest homework grades will be dropped.
Homework.
Homework will be assigned every week.
Late homework will not be accepted.
Collaboration between students is encouraged, but you
must write your own solutions, understand them and
give credit to your collaborators.
