Course Outcomes
Learning Outcomes
Students should know all relevant definitions, correct statements of the major theorems (including their hypotheses and limitations), and examples and non-examples of the various concepts. The students should be able to demonstrate their mastery by solving non-trivial problems related to these concepts, and by proving simple (but non-trivial) theorems about the concepts below, related to, but not identical to, statements proven by the text or instructor. For more detailed information visit the Math 554 Wiki page.
Overview
- The Fundamental Group
- The topology of the plane
- Jordan Curve Theorem
- Seifert-van Kampen Theorem
- Classification of Surfaces
- Classification of Covering Spaces
- Group Theory
- Free groups
- Free abelian groups
- Presentations of groups
- Subgroups of free groups