Difference between revisions of "MAT3213"

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(Fixed pacing to try and fit in 14 weeks.)
(Still fixing weekly schedule of topics.)
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* [[Proofs:Induction]]
 
* [[Proofs:Induction]]
 
* [[Induction:Variants]]
 
* [[Induction:Variants]]
−
* [[Finite and Infinite Sets]]
+
* [[Sets:Cardinality]]
−
* [[Countable Sets]]
+
* [[Sets:Finite]]
 +
* [[Sets:Countable]]
 +
* [[Sets:Uncountable]]
 +
 
  
 
|| <!--Prerequisite Skills-->  
 
|| <!--Prerequisite Skills-->  
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|| <!--Prerequisite Skills-->  
 
|| <!--Prerequisite Skills-->  
−
 
+
2
 
* [[RealNumbers:Algebraic Properties]]
 
* [[RealNumbers:Algebraic Properties]]
 
* [[RealNumbers:Inequalities|Inequalities]]
 
* [[RealNumbers:Inequalities|Inequalities]]
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|| <!--Sections-->  
 
|| <!--Sections-->  
  
−
2.5
+
2.5 & 3.1
  
 
|| <!--Topics-->   
 
|| <!--Topics-->   
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* [[RealNumbers:Intervals|Intervals]]
 
* [[RealNumbers:Intervals|Intervals]]
 
* [[RealNumbers:Cardinality]]
 
* [[RealNumbers:Cardinality]]
−
* [[RealNumbers:Decimal Representation|Decimal Representation]]
 
−
 
−
|| <!--Prerequisite Skills-->
 
−
 
−
* [[RealNumbers:Completeness|Completeness]] <!--- 3213-2.1 --->
 
−
* [[RealNumbers:Archimedean Property|Archimedean Property]]
 
−
* [[RealNumbers:Bounded Subsets|Bounded Sets]]
 
−
* [[RealNumbers:Suprema of Subsets|Suprema of Subsets]]
 
−
* [[RealNumbers:Infima of Subsets|Infima of Subsets]]
 
−
 
−
|| <!--Student Learning Outcomes-->
 
−
 
−
<!-- ------------------------------------------------------------ -->
 
−
 
−
|-
 
−
 
−
| <!--Date--> Week 6
 
−
 
−
|| <!--Sections-->
 
−
 
−
3.1
 
−
 
−
|| <!--Topics--> 
 
−
 
 
* [[RealNumbers:Sequences|Sequences]]
 
* [[RealNumbers:Sequences|Sequences]]
−
* [[Sequences:Tails]]
 
 
* [[Sequences:Convergence]]
 
* [[Sequences:Convergence]]
 
* [[Sequences:Limits]]
 
* [[Sequences:Limits]]
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|| <!--Prerequisite Skills-->  
 
|| <!--Prerequisite Skills-->  
  
 +
* [[Sets:Cardinality]]
 
* [[RealNumbers:Inequalities|Inequalities]]
 
* [[RealNumbers:Inequalities|Inequalities]]
−
* [[RealNumbers:Absolute Value|Absolute Value]]
+
* [[RealNumbers:Bounded Subsets|Bounded Sets]]
  
 
|| <!--Student Learning Outcomes-->  
 
|| <!--Student Learning Outcomes-->  
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|-
 
|-
  
−
| <!--Date--> Week 7
+
| <!--Date--> Week 6
  
 
|| <!--Sections-->  
 
|| <!--Sections-->  
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3.2
 
3.2
  
−
|| <!--Topics-->  
+
|| <!--Topics-->
−
 
 
  
 +
* [[Sequences:Tails]]
 
* [[Sequences:Limit Laws]]
 
* [[Sequences:Limit Laws]]
 
* [[Sequences:Bounded when Convergent]]
 
* [[Sequences:Bounded when Convergent]]
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|| <!--Prerequisite Skills-->  
 
|| <!--Prerequisite Skills-->  
  
 +
* [[Sequences:Convergence]]
 
* [[Sequences:Limits]]
 
* [[Sequences:Limits]]
  
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|-
 
|-
  
−
| <!--Date--> Week 8
+
| <!--Date--> Week 7
  
 
|| <!--Sections-->  
 
|| <!--Sections-->  
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|-
 
|-
  
−
| <!--Date--> Week 9
+
| <!--Date--> Week 8
  
 
|| <!--Sections-->  
 
|| <!--Sections-->  
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|-
 
|-
  
−
| <!--Date--> Week 10
+
| <!--Date--> Week 9
  
 
|| <!--Sections-->  
 
|| <!--Sections-->  
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|-
 
|-
  
−
| <!--Date--> Week 11
+
| <!--Date--> Week 10
  
 
|| <!--Sections-->  
 
|| <!--Sections-->  
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|-
 
|-
  
−
| <!--Date--> Week 12
+
| <!--Date--> Week 11
  
 
|| <!--Sections-->  
 
|| <!--Sections-->  
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|-
 
|-
  
−
| <!--Date--> Week 13
+
| <!--Date--> Week 12
  
 
|| <!--Sections-->  
 
|| <!--Sections-->  
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−
| <!--Date--> Week 14
+
| <!--Date--> Week 13
  
 
|| <!--Sections-->  
 
|| <!--Sections-->  
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* [[Sequences:Convergence]] <!--- 3213-3.1 --->
 
* [[Sequences:Convergence]] <!--- 3213-3.1 --->
 
* [[Sequences:Limits]] <!--- 3213-3.1 --->
 
* [[Sequences:Limits]] <!--- 3213-3.1 --->
 +
 +
|| <!--Student Learning Outcomes-->
 +
 +
<!-- ------------------------------------------------------------ -->
 +
 +
|-
 +
 +
| <!--Date--> Week 14
 +
 +
|| <!--Sections-->
 +
 +
4.3
 +
 +
|| <!--Topics-->
 +
 +
* [[RealFunctionLimits:One-Sided|One-Sided Limits of Functions]]
 +
* [[RealFunctionLimits:Infinite|Infinite Limits of Functions]]
 +
* [[RealFunctionLimits:At Infinity|Limits of Functions at Infinity]]
 +
 +
|| <!--Prerequisite Skills-->
 +
 +
* [[RealFunctions:Limits|Limits of Real Functions]]
 +
* [[RealFunctionLimits:Divergence Criteria|Divergence Criteria]]
  
 
|| <!--Student Learning Outcomes-->  
 
|| <!--Student Learning Outcomes-->  

Revision as of 17:14, 16 August 2020

The textbook for this course is Introduction to Real Analysis by Bartle and Sherbert

A comprehensive list of all undergraduate math courses at UTSA can be found here.

The Wikipedia summary of Real Analysis.

Topics List

Date Sections Topics Prerequisite Skills Student Learning Outcomes
Week 1

1.1


Week 2

1.2 & 1.3





Week 3

2.1-2.2


Week 4

2.3-2.4

2


Week 5

2.5 & 3.1


Week 6

3.2


Week 7
  • Review
  • Midterm exam


Week 8

3.3


Week 9

3.4


Week 10

3.5-3.6


Week 11

3.7


Week 12

4.1


Week 13

4.2


Week 14

4.3


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