Math 641: Functions of a Real Variable - Revision history

Ls5: /* Catalog Information */

2019-11-14T17:36:16Z

‎Catalog Information

Ls5: moved Math 641 to Math 641: Functions of a Real Variable

2013-04-03T22:44:38Z

moved Math 641 to Math 641: Functions of a Real Variable

Cpg: /* Minimal learning outcomes */

2010-07-28T16:38:06Z

‎Minimal learning outcomes

Cpg at 19:49, 4 June 2009

2009-06-04T19:49:09Z

Cpg: /* Description */

2008-12-02T17:53:41Z

‎Description

Cpg: /* Minimal learning outcomes */

2008-08-14T20:02:32Z

‎Minimal learning outcomes

Cpg: /* Prerequisites */

2008-08-14T20:01:00Z

‎Prerequisites

Cpg at 19:36, 14 August 2008

2008-08-14T19:36:57Z

Cpg: /* Courses for which this course is prerequisite */

2008-08-14T18:03:22Z

‎Courses for which this course is prerequisite

Cpg: /* Prerequisites */

2008-08-14T17:42:18Z

‎Prerequisites

← Older revision		Revision as of 17:36, 14 November 2019
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	=== Credit Hours ===		=== Credit Hours ===
	3		3
		+
		+	=== Offered ===
		+	W (odd years)

	=== Prerequisite ===		=== Prerequisite ===

← Older revision		Revision as of 16:38, 28 July 2010
Line 94:		Line 94:

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

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

@@ Line 2: / Line 2: @@
 === Title ===
-Functions of Real and Complex Variables 1.
+Functions of a Real Variable.
 === Credit Hours ===
@@ Line 8: / Line 8: @@
 === Prerequisite ===
-[[Math 542]] or instructor's consent
+[[Math 541]] or instructor's consent
 === Description ===
-Fundamentals of measure and integration, Borel measures, product measures, L<sup>p</sup> spaces, introduction to functional analysis, Radon Nikodym theorem, differentiation theory, Fourier transforms.
+Abstract measure and integration theory; L(p)(?) spaces; measures on topological and Euclidean spaces.
 == Desired Learning Outcomes ==
-Math 641 is a course in abstract measure and integration theory.  The official current course description mentions a couple of items that are not envisioned to be core topics in the renovated course:  functional analysis and Fourier transforms.  A new 500-level course in linear functional analysis would subsume functional-analytic material previously taught in Math 641, and Fourier transforms will be covered in [[Math 541]] and not repeated in Math 641.  There will be some repetition of topics between [[Math 541]] and Math 641, but it is felt that the repetition will help solidify student understanding, and there will be a difference in approach, with the lower-level course taking a concrete approach restricted to Lebesgue measure.
+Math 641 is a course in abstract measure and integration theory.  There will be some repetition of topics between [[Math 541]] and Math 641, but it is felt that the repetition will help solidify student understanding, and there will be a difference in approach, with the lower-level course taking a concrete approach restricted to Lebesgue measure.
 === Prerequisites ===
+We strongly recommend that students take [[Math 541]] prior to Math 641.
-It is proposed that the current prerequisite course, [[Math 542]], be deleted from the catalog and therefore as a prerequisite for Math 641.  We probably should strongly recommend that students take [[Math 541]] as a prerequisite.  At a minimum, students should have had a course equivalent to [[Math 316]].
 === Minimal learning outcomes ===
 Outlined below are topics that all successful Math 641 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.
 <div style="-moz-column-count:2; column-count:2;">
@@ Line 100: / Line 98: @@
 === Courses for which this course is prerequisite ===
 [[Category:Courses|641]]

@@ Line 11: / Line 11: @@
 === Description ===
-Fundamentals of measure and integration, Borel measures, product measures, L^ spaces, introduction to functional analysis, Radon Nikodym theorem, differentiation theory, Fourier transforms.
+Fundamentals of measure and integration, Borel measures, product measures, L<sup>p</sup> spaces, introduction to functional analysis, Radon Nikodym theorem, differentiation theory, Fourier transforms.
 == Desired Learning Outcomes ==
 Math 641 is a course in abstract measure and integration theory.  The official current course description mentions a couple of items that are not envisioned to be core topics in the renovated course:  functional analysis and Fourier transforms.  A new 500-level course in linear functional analysis would subsume functional-analytic material previously taught in Math 641, and Fourier transforms will be covered in [[Math 541]] and not repeated in Math 641.  There will be some repetition of topics between [[Math 541]] and Math 641, but it is felt that the repetition will help solidify student understanding, and there will be a difference in approach, with the lower-level course taking a concrete approach restricted to Lebesgue measure.

@@ Line 73: / Line 73: @@
 #* Fubini's Theorem
 # Measures on topological spaces
-#* Borel σ-algebra
+#* Borel σ-algebras
 #* Locally compact Hausdorff spaces
 #* Urysohn's Lemma

← Older revision	Revision as of 22:44, 3 April 2013
(No difference)

← Older revision		Revision as of 18:03, 14 August 2008
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	[[Category:Courses\|641]]		[[Category:Courses\|641]]
		+
		+	Math 641 is currently a prerequisite for [[Math 642]] and [[Math 645]]. It is being proposed that [[Math 642]], at least in its current form, be deleted from the catalog. There are also two new functional analysis classes being proposed that may replace [[Math 645]] and [[Math 646\|646]]; these new courses would not require Math 641 as a prerequisite. [[Math 647]] should probably have Math 641 as a prerequisite. Also, it is possible that a class on function spaces will be created in the future; such a class should have Math 641 as a prerequisite.

← Older revision		Revision as of 17:42, 14 August 2008
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	=== Prerequisites ===		=== Prerequisites ===
		+
		+	It is proposed that the current prerequisite course, [[Math 542]], be deleted from the catalog and therefore as a prerequisite for Math 641. We probably should strongly recommend that students take [[Math 541]] as a prerequisite.

	=== Minimal learning outcomes ===		=== Minimal learning outcomes ===