Difference between revisions of "Math 751R: Advanced Special Topics in Topology"
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== Desired Learning Outcomes == | == Desired Learning Outcomes == | ||
| + | Students should become familiar with a specific area of topology undergoing current research. | ||
| + | |||
=== Prerequisites === | === Prerequisites === | ||
| + | Graduate level differential and algebraic topology at the level of [[Math 655]] and [[Math 656|656]]. | ||
=== Minimal learning outcomes === | === Minimal learning outcomes === | ||
| + | Minimal learning outcomes cannot be specified for a course in which topics will vary from year to year. However, regardless of the topic, students will be expected to know terminology, statements and approaches to motivating problems undergoing active research, and major results in the area and techniques used to prove them. Students will demonstrate this knowledge by working suitable problems and developing their own proofs, by presenting and writing work inside and outside of class, and other activities expected of more advanced graduate students. | ||
| + | |||
| + | As an example of the level and type of material covered, the following topics were required for the course when it covered hyperbolic knot theory. | ||
<div style="-moz-column-count:2; column-count:2;"> | <div style="-moz-column-count:2; column-count:2;"> | ||
| + | #Link complements as 3-manifolds, polyhedral decomposition | ||
| + | #Geometric structures on manifolds, particularly hyperbolic structures | ||
| + | #Complete and incomplete structures | ||
| + | #Gluing and completeness equations | ||
| + | #Hyperbolic Dehn filling | ||
| + | #Examples of hyperbolic links and their geometric properties | ||
</div> | </div> | ||
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=== Courses for which this course is prerequisite === | === Courses for which this course is prerequisite === | ||
| + | |||
| + | None. | ||
[[Category:Courses|751]] | [[Category:Courses|751]] | ||
Revision as of 09:20, 16 July 2010
Contents
Catalog Information
Title
Advanced Special Topics in Topology.
Credit Hours
3
Prerequisite
Math 655 and 656, or instructor's consent.
Description
This course covers current topics of research interest.
Desired Learning Outcomes
Students should become familiar with a specific area of topology undergoing current research.
Prerequisites
Graduate level differential and algebraic topology at the level of Math 655 and 656.
Minimal learning outcomes
Minimal learning outcomes cannot be specified for a course in which topics will vary from year to year. However, regardless of the topic, students will be expected to know terminology, statements and approaches to motivating problems undergoing active research, and major results in the area and techniques used to prove them. Students will demonstrate this knowledge by working suitable problems and developing their own proofs, by presenting and writing work inside and outside of class, and other activities expected of more advanced graduate students.
As an example of the level and type of material covered, the following topics were required for the course when it covered hyperbolic knot theory.
- Link complements as 3-manifolds, polyhedral decomposition
- Geometric structures on manifolds, particularly hyperbolic structures
- Complete and incomplete structures
- Gluing and completeness equations
- Hyperbolic Dehn filling
- Examples of hyperbolic links and their geometric properties
Additional topics
Courses for which this course is prerequisite
None.
