Math. 656 Syllabus



Grading Policy

Grades in the course will be determined on the following basis:

Homeworks and class participation 100 points
Quizes 100 points
Take-home final 200 points



Syllabus and Calendar

The following syllabus is somewhat tentative. It is possible that there might be some slippage and some topics might be omitted. The precise quiz dates will be announced at least one week in advance.

Week of Topics Covered
Jan. 5 surfaces and manifolds
Jan. 12 classification of compact connected surfaces
Jan. 19 Quiz 1, homotopy and the fundamental group
Jan. 26 fundamental group of the circle and applications, free groups and presentations
Feb. 2 Quiz 2, Seifert-van Kampen Theorem
Feb. 9 calculations of fundamental groups
Feb. 16 Quiz 3, definition and examples of covering spaces
Feb. 23 Quiz 4, liftings of maps, relation to fundamental group, universal covers
Mar. 2 Quiz 5, applications to graphs and surfaces
Mar. 9 Quiz 6, genus of smooth projective curves