A great deal of credit for this document goes to Mike Usher, who created an initial PDF of past UGA qual questions organized by topic. Here is a list of problems that Mike recommended reviewing during our problem sessions in Spring 2020:
- Section 1, Point-Set: 8, 10, 11, 14, 16, 19, 22, 23, 27 (Bolzano Weierstrass), 30 (Standard, see counterexamples), 31, 32, 38, 42, 44
- Section 2, Fundamental Group: 1
- Section 3, Covering Spaces: 1b and c, 2, 3, 6, 7, 8, 10 (not really about surfaces per se), 11, 12, 13, 14, 16
- Section 4, Homology/Degree Theory: 2, 4, 5, 8, 13, 19, 21, 22
- Section 5, Cell Complexes/Attaching: 1, 5, 10, 16
- Section 6, Surfaces: 3, 6, 7, 11, 14
- Section 7, Fixed Points: 4, 6, 12, 13, 14
- Section 8, Misc Algebraic Topology: 1, 3, 6, 8
Usually 30% of the problems on any given qual are related to point-set/general Topology. Note that this material is not covered in the course!