Math 751R: Advanced Special Topics in Topology - Revision history

Cpg at 17:04, 14 October 2022

2022-10-14T17:04:11Z

2016-06-13T21:58:34Z

‎Prerequisite

2013-04-03T22:47:15Z

2010-07-28T16:42:55Z

‎Minimal learning outcomes

2010-07-16T15:59:17Z

‎Minimal learning outcomes

2010-07-16T15:58:59Z

‎Minimal learning outcomes

2010-07-16T15:56:03Z

‎Minimal learning outcomes

2010-07-16T15:33:40Z

‎Minimal learning outcomes

2010-07-16T15:32:52Z

‎Minimal learning outcomes

2010-07-16T15:29:11Z

‎Minimal learning outcomes

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 === Prerequisite ===
-[[Math 551]]
 === Description ===

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 === Prerequisite ===
-[[Math 655]] and [[Math 656|656]], or instructor's consent.
+[[Math 551]]
 === Description ===

← Older revision		Revision as of 16:42, 28 July 2010
Line 44:		Line 44:

	</div>		</div>
		+	=== Textbooks ===
		+
		+	Possible textbooks for this course include (but are not limited to):
		+
		+	*

	=== Additional topics ===		=== Additional topics ===

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 === 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, successful students will know terminology, statements and approaches to 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 participating in other activities expected of more advanced graduate students.
+Minimal learning outcomes cannot be specified for a course in which topics will vary from year to year.  However, regardless of the topic, successful students will know terminology, statements and approaches to 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 participating in 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.

@@ Line 21: / Line 21: @@
 === 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 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.
+Minimal learning outcomes cannot be specified for a course in which topics will vary from year to year.  However, regardless of the topic, successful students will know terminology, statements and approaches to 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 participating in 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.

← Older revision	Revision as of 22:47, 3 April 2013
(No difference)

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 <div style="-moz-column-count:2; column-count:2;">
 #Link complements as 3-manifolds
 #*Polyhedral decomposition associated with a link diagram
 #*Alternating versus non-alternating links

@@ Line 32: / Line 32: @@
 #*Subdivision into tetrahedra, cusp triangulations
 #Geometric structures on manifolds, particularly hyperbolic structures
-#*developing map, holonomy
+#*Developing map, holonomy
-#*Complete and incomplete structures, Mostow-Prasad rigidity
+#*Complete and incomplete structures
-#*Gluing and completeness equations, ideal hyperbolic tetrahedra
+#*Mostow-Prasad rigidity
-#*Hyperbolic Dehn surgery, hyperbolic Dehn surgery space
+#*Gluing and completeness equations
 #Examples of hyperbolic links and their geometric properties
 #*Volumes, embedded geodesic surfaces, etc.