Topology

Math 131 - Harvard University
Required Texts
  • Munkres, Topology, 2nd edition, Prentice-Hall 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 take-home 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.


Course home page: http://math.harvard.edu/~ctm/math131