Math 656: Algebraic Topology - Revision history

Cpg at 17:03, 14 October 2022

2022-10-14T17:03:34Z

2019-11-14T17:42:33Z

‎Catalog Information

2014-09-03T20:24:13Z

‎Prerequisite

2014-09-03T20:23:44Z

‎Prerequisite

2014-03-10T16:05:16Z

‎Prerequisite

2013-04-03T22:46:21Z

2011-05-03T19:01:03Z

‎Title

2010-07-16T15:54:13Z

‎Courses for which this course is prerequisite

2010-07-16T15:53:28Z

‎Desired Learning Outcomes

2010-07-16T15:51:29Z

‎Desired Learning Outcomes

@@ Line 20: / Line 20: @@
 === Prerequisites ===
-Topology of manifolds, tensors, and orientation is assumed from [[Math 655]].  A basic knowledge of fundamental groups and covering spaces, as in [[Math 554]], will also be required.
+Topology of manifolds, tensors, and orientation is assumed from [[Math 655]].
 === Minimal learning outcomes ===

@@ Line 8: / Line 8: @@
 === Prerequisite ===
-[[Math 553]].
+[[Math 371]] (or equivalent) and [[Math 553]].
 === Description ===

@@ Line 8: / Line 8: @@
 === Prerequisite ===
-[[Math 554]].
+[[Math 553]].
 === Description ===

@@ Line 8: / Line 8: @@
 === Prerequisite ===
-[[Math 655]].
+[[Math 554]].
 === Description ===

← Older revision	Revision as of 22:46, 3 April 2013
(No difference)

@@ Line 2: / Line 2: @@
 === Title ===
-Algebraic Topology 2.
+Algebraic Topology.
 === Credit Hours ===

← Older revision		Revision as of 15:54, 16 July 2010
Line 49:		Line 49:

	=== Courses for which this course is prerequisite ===		=== Courses for which this course is prerequisite ===
		+
		+	[[Math 751R]]

	[[Category:Courses\|656]]		[[Category:Courses\|656]]

@@ Line 25: / Line 25: @@
 <div style="-moz-column-count:2; column-count:2;">
-# Fundamental group
+# Fundamental group and homotopy
-#* Constructions, homotopy
+#* Constructions
 #* Van Kampen Theorem
 #* Covering spaces and group actions
 # Homology
 #* Simplicial, singular, cellular
@@ Line 39: / Line 40: @@
 #* Cup product
 #* Poincare duality
-# Homotopy
-#* Constructions
-#* Whitehead's theorem
 </div>
@@ Line 47: / Line 46: @@
 === Additional topics ===
-At the discretion of the instructor as time allows.  Possible topics include de Rham cohomology and the de Rham theorem, additional duality theorems, including Alexander and Lefschetz duality, the Hurewicz theorem, fiber bundles, fibrations, obstruction theory.
+At the discretion of the instructor as time allows.  Possible topics include de Rham cohomology and the de Rham theorem, additional duality theorems, including Alexander and Lefschetz duality, additional homotopy theory, including Whitehead's theorem, the Hurewicz theorem, fiber bundles, fibrations, obstruction theory.
 === Courses for which this course is prerequisite ===
 [[Category:Courses|656]]

@@ Line 21: / Line 21: @@
 === Minimal learning outcomes ===
-Outlined below are topics that all successful Math 656 students should understand well.  As evidence of that understanding, students should be able to demonstrate mastery of all relevant vocabulary, familiarity with common examples and counterexamples, knowledge of the content of the major theorems, understanding of the ideas in their proofs, and ability to make direct application of those results to related problems, including calculations.
+Outlined below are topics that all successful Math 656 students should understand well.  Students should be able to demonstrate mastery of relevant vocabulary, and use the vocabulary fluently in their work.  They should know common examples and counterexamples, and be able prove that these examples and counterexamples have properties as claimed.  Additionally, students should know the content (and limitations) of major theorems and the ideas of the proofs, and apply results of these theorems to solve suitable problems, or use techniques of the proofs to prove additional related results, or to make calculations and computations.
 <div style="-moz-column-count:2; column-count:2;">