Difference between revisions of "Math 554: Foundations of Topology 2"
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Latest revision as of 16:42, 3 April 2013
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, Seifertvan 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
 Seifertvan 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):