Difference between revisions of "Math 554: Foundations of Topology 2"
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Revision as of 10:28, 28 July 2010
Contents
Catalog Information
Title
Foundations of Topology 2.
(Credit Hours:Lecture Hours:Lab Hours)
(3:3:0)
Prerequisite
Math 553 or instructor's consent.
Description
Fundamental group, retractions and fixed points, homotopy types, separation theorems, classification of surfaces, Seifert-van Kampen Theorem, classification of covering spaces, and applications to group theory.
Desired Learning Outcomes
Students should gain a familiarity with surfaces, fundamental group, and covering spaces.
Minimal learning outcomes
- The Fundamenatal 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
Textbooks
Possible textbooks for this course include (but are not limited to):
