Difference between revisions of "Math 554: Foundations of Topology 2"
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| − | == | + | == Catalog Information == |
| − | === | + | === Title === |
| + | Foundations of Topology 2. | ||
| + | |||
| + | === (Credit Hours:Lecture Hours:Lab Hours) === | ||
| + | (3:3:0) | ||
| + | |||
| + | === Offered === | ||
| + | W | ||
| + | |||
| + | === 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 === | === Minimal learning outcomes === | ||
<div style="-moz-column-count:2; column-count:2;"> | <div style="-moz-column-count:2; column-count:2;"> | ||
| + | |||
| + | # 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 | ||
</div> | </div> | ||
| + | === Textbooks === | ||
| + | |||
| + | Possible textbooks for this course include (but are not limited to): | ||
| + | |||
| + | * | ||
=== Additional topics === | === Additional topics === | ||
Latest revision as of 11:07, 14 November 2019
Contents
Catalog Information
Title
Foundations of Topology 2.
(Credit Hours:Lecture Hours:Lab Hours)
(3:3:0)
Offered
W
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):
