Difference between revisions of "MAT4273"

From Department of Mathematics at UTSA
Jump to navigation Jump to search
(Added content to the table(weeks 1 and 2))
(Added content to the table(weeks 2 and 3))
Line 26: Line 26:
  
 
* [[Order of Operations]] <!-- 1073-Mod R -->
 
* [[Order of Operations]] <!-- 1073-Mod R -->
−
 
  
 
||
 
||
Line 98: Line 97:
 
* [[Intervals ]] <!-- 3213-2.5 -->  
 
* [[Intervals ]] <!-- 3213-2.5 -->  
 
* [[Suprema, Infima, and the Completeness Property]] <!-- 3213-2.3 -->  
 
* [[Suprema, Infima, and the Completeness Property]] <!-- 3213-2.3 -->  
 +
* [[Mathematical Induction]] <!-- 3213-1.2 -->
  
 
||
 
||
Line 118: Line 118:
 
    
 
    
  
−
[[Cauchy-Schwarz formula]]  
+
[[Cauchy-Schwarz Formula]]  
  
 
||
 
||
  
−
*  
+
* [[Absolute Value Functions| Absolute Value]] <!-- DNE (recommend 1073-1) -->
 +
* [[Inequalities ]] <!-- 3213-2.1 -->
  
 
||
 
||
  
−
*  
+
* The Cauchy-Schwarz Formula
  
 
||
 
||
−
 
  
  
Line 143: Line 143:
 
||
 
||
 
    
 
    
−
 
+
[[Distance Between Two Points in Higher Dimensions]]  
−
[[Distance between Two Points in Higher Dimensions]]  
 
  
 
||
 
||
  
−
*  
+
* [[Distance Between Two Points in the Real Numbers]] <!-- 4237-(30-31) -->
  
 
||
 
||
  
−
*  
+
* Distance formula for higher dimensions
  
 
||
 
||
Line 168: Line 167:
 
||
 
||
 
    
 
    
−
 
 
[[Open Subsets in Higher Dimensions]]
 
[[Open Subsets in Higher Dimensions]]
  
 
||
 
||
  
−
*  
+
* [[Intervals|Open Intervals ]] <!-- 3213-2.5 -->
 +
* [[Suprema, Infima, and the Completeness Property]] <!-- 3213-2.3 -->
  
 
||
 
||
  
−
*  
+
* Definition of an open set
 +
* Definition of an interior point
  
 
||  
 
||  
Line 190: Line 190:
  
 
<div style="text-align: center;">34-38</div>
 
<div style="text-align: center;">34-38</div>
 +
 +
|| 
 +
 +
[[Limit Points (or Cluster Points) in Higher Dimensions]]
 +
 +
||
 +
 +
* [[Open Subsets in Higher Dimensions]] <!-- 4237-(34-38) -->
 +
* [[Limit of a sequence in the Real Numbers]] <!-- 4237-(34-38) -->
 +
* [[Mathematical Induction]] <!-- 3213-1.2 -->
 +
 +
||
 +
 +
* Definition of a limit point (or cluster point)
 +
* The limit point as the limit of a sequence
 +
 +
||
 +
 +
 +
|-
 +
 +
 +
|Week&nbsp;3
 +
 +
||
 +
 +
<div style="text-align: center;">39-40</div>
 +
 +
||
 +
 +
[[Closed Subsets in Higher Dimensions]]
 +
 +
||
 +
 +
* [[Limit Points (or Cluster Points) in Higher Dimensions]]
 +
* [[Open Subsets in Higher Dimensions]]
 +
 +
||
 +
 +
* Definition of a closed set
 +
* Properties of a closed set
 +
 +
||
 +
 +
 +
|-
 +
 +
 +
|Week&nbsp;3
 +
 +
||
 +
 +
<div style="text-align: center;">39-40</div>
  
 
||
 
||
 
    
 
    
 +
[[Bounded sets in Higher Dimensions]]
 +
 +
||
 +
 +
* [[Closed Subsets in Higher Dimensions]]
 +
* [[Limit Points (or Cluster Points) in Higher Dimensions]]
 +
* [[Open Subsets in Higher Dimensions]]
 +
 +
||
 +
 +
* Definition of a bounded set
 +
* Properties of a bounded set
 +
 +
||
 +
 +
 +
|-
 +
 +
 +
|Week&nbsp;5
  
−
[[Limit Points (or Cluster Points) in Higher Dimensions]]
+
||
 +
 
 +
<div style="text-align: center;">39-40</div>
 +
 
 +
||
 +
 
 +
[[The Nested Interval Theorem in Higher Dimensions]]
 +
 
 +
||
 +
 
 +
* [[The Nested Interval Theorem for the Real Numbers]]
 +
* [[Bounded sets in Higher Dimensions]]
 +
 
 +
||
 +
 
 +
* The nested intervals theorem in higher dimensions
 +
 
 +
||
 +
 
 +
 
 +
|-
 +
 
 +
 
 +
|Week&nbsp;5
 +
 
 +
||
 +
 
 +
<div style="text-align: center;">39-40</div>
 +
 
 +
||
 +
 
 +
[[The Bolzano-Weierstrass Theorem in Higher Dimensions]]
 +
 
 +
||
 +
 
 +
* [[The Bolzano Weierstrass Theorem ]] <!-- 3213-3.4 -->
 +
* [[Bounded sets in Higher Dimensions]]
 +
 
 +
||
 +
 
 +
* The Bolzano Weierstrass Theorem in higher dimensions
 +
 
 +
||
 +
 
 +
 
 +
|-
 +
 
 +
 
 +
|Week&nbsp;5
 +
 
 +
||
 +
 
 +
<div style="text-align: center;"></div>
 +
 
 +
||
 +
 
 +
 
 +
[[]]
 +
 
 +
||
  
 +
*
 
||
 
||
  
 
*  
 
*  
  
 +
||
 +
 +
 +
|-
 +
 +
 +
|Week&nbsp;5
 +
 +
||
 +
 +
<div style="text-align: center;"></div>
 +
 +
||
 +
 
 +
 +
[[]]
 +
 +
||
 +
 +
*
 
||
 
||
  

Revision as of 15:08, 10 August 2020

The textbook(s) for this course is [1] Undergraduate Topology, by R. H. Kasriel; topics from [2] Introduction to Analysis by W. R. Wade (Stone-Weierstrass Theorem).

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

The Wikipedia summary of topology and its history.

Topics List

Date Sections Topics Prerequisite Skills Student Learning Outcomes
Week 1
30-31

Algebraic Structure of the Real Numbers

  • Review of algebraic properties of the Real Numbers


Week 1
30-31


Distance Between Two Points in the Real Numbers

  • The distance between two point on the real line
Week 1
30-31

Limit of a sequence in the Real Numbers

  • The definition of a limit of a sequence


Week 1
30-31

The Nested Interval Theorem for the Real Numbers

  • The nested intervals property in the real numbers


Week 2
34-38


Cauchy-Schwarz Formula

  • The Cauchy-Schwarz Formula


Week 2
34-38

Distance Between Two Points in Higher Dimensions

  • Distance formula for higher dimensions


Week 2
34-38

Open Subsets in Higher Dimensions

  • Definition of an open set
  • Definition of an interior point


Week 2
34-38

Limit Points (or Cluster Points) in Higher Dimensions

  • Definition of a limit point (or cluster point)
  • The limit point as the limit of a sequence


Week 3
39-40

Closed Subsets in Higher Dimensions

  • Definition of a closed set
  • Properties of a closed set


Week 3
39-40

Bounded sets in Higher Dimensions

  • Definition of a bounded set
  • Properties of a bounded set


Week 5
39-40

The Nested Interval Theorem in Higher Dimensions

  • The nested intervals theorem in higher dimensions


Week 5
39-40

The Bolzano-Weierstrass Theorem in Higher Dimensions

  • The Bolzano Weierstrass Theorem in higher dimensions


Week 5


[[]]


Week 5


[[]]


Week 5


[[]]


Retrieved from "https://mathresearch.utsa.edu/wiki/index.php?title=MAT4273&oldid=391"