Difference between revisions of "MAT3213"

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The textbook for this course is
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'''Catalog entry''':
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Introduction to Real Analysis by Bartle and Sherbert
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''Prerequisites'': MAT 1224 and MAT 3013.
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''Content'': Axiomatic definition of real numbers, including order properties and completeness; infinite sequences and their convergence; basic notions related to series and their convergence; functions and function limits. Introduction to topology of the real line. Emphasis on theorem proving.
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''Sample textbook'': Introduction to Real Analysis by Bartle and Sherbert
  
 
A comprehensive list of all undergraduate math courses at UTSA can be found [https://catalog.utsa.edu/undergraduate/coursedescriptions/mat/  here].
 
A comprehensive list of all undergraduate math courses at UTSA can be found [https://catalog.utsa.edu/undergraduate/coursedescriptions/mat/  here].
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* [[Real Numbers:Sequences|Sequences]]
 
* [[Real Numbers:Sequences|Sequences]]
 
* [[Real Numbers:Sequences|Sequences:Convergence]]
 
* [[Real Numbers:Sequences|Sequences:Convergence]]
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* [[Real Numbers:Sequences|Sequences:Limits]]
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* [[Sequences:Limits]]
  
 
|| <!--Prerequisite Skills-->  
 
|| <!--Prerequisite Skills-->  
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* [[Real Numbers:Sequences|Sequences:Tails]]
 
* [[Real Numbers:Sequences|Sequences:Tails]]
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* [[Real Numbers:Sequences|Sequences:Limit Laws]]
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* [[Sequences:Limits|Sequences:Limit Laws]]
 
* [[Real Numbers:Sequences|Sequences:Bounded when Convergent]]
 
* [[Real Numbers:Sequences|Sequences:Bounded when Convergent]]
 
* [[Real Numbers:Sequences|Sequences:Squeeze Theorem]]
 
* [[Real Numbers:Sequences|Sequences:Squeeze Theorem]]
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* [[Real Numbers:Sequences|Sequences:Convergence]]
 
* [[Real Numbers:Sequences|Sequences:Convergence]]
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* [[Real Numbers:Sequences|Sequences:Limits]]
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* [[Sequences:Limits|Sequences:Limits]]
  
 
|| <!--Student Learning Outcomes-->  
 
|| <!--Student Learning Outcomes-->  
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* [[Proofs:Induction]] <!--- 3213-1.2 --->
 
* [[Proofs:Induction]] <!--- 3213-1.2 --->
 
* [[Real Numbers:Bounded Subsets|Bounded Sets]]
 
* [[Real Numbers:Bounded Subsets|Bounded Sets]]
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* [[Real Numbers:Sequences|Sequences:Limit Laws]]
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* [[Sequences:Limits|Sequences:Limit Laws]]
  
 
|| <!--Student Learning Outcomes-->  
 
|| <!--Student Learning Outcomes-->  
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* [[Real Numbers:Sequences|Sequences:Monotone]]
 
* [[Real Numbers:Sequences|Sequences:Monotone]]
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* [[Real Numbers:Sequences|Sequences:Limit Laws]]
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* [[Sequences:Limits|Sequences:Limit Laws]]
  
 
|| <!--Student Learning Outcomes-->  
 
|| <!--Student Learning Outcomes-->  
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* [[Real Numbers:Sequences|The Cauchy Criterion]]
 
* [[Real Numbers:Sequences|The Cauchy Criterion]]
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* [[Sequences:Contractive]]
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* [[Real Numbers:Sequences|Sequences:Contractive]]
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* [[Sequences:Divergent]]
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* [[Properly Divergent Sequences]]
  
 
|| <!--Prerequisite Skills-->  
 
|| <!--Prerequisite Skills-->  
  
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* [[Sequences:Convergence]]
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* [[Real Numbers:Sequences|Sequences:Convergence]]
 
* [[Sequences:Subsequences]] <!--- 3213-3.4 --->
 
* [[Sequences:Subsequences]] <!--- 3213-3.4 --->
  
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|| <!--Prerequisite Skills-->  
 
|| <!--Prerequisite Skills-->  
  
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* [[Sequences:Convergence]] <!--- 3213-3.1 --->
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* [[Real Numbers:Sequences|Sequences:Convergence]] <!--- 3213-3.1 --->
 
* [[Sequences:Limits]] <!--- 3213-3.1 --->
 
* [[Sequences:Limits]] <!--- 3213-3.1 --->
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* [[Sequences:Cauchy|The Cauchy Criterion]] <!--- 3213-3.5 --->
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* [[Real Numbers:Sequences|The Cauchy Criterion]] <!--- 3213-3.5 --->
  
 
|| <!--Student Learning Outcomes-->  
 
|| <!--Student Learning Outcomes-->  
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|| <!--Topics-->  
 
|| <!--Topics-->  
  
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* [[Neighborhoods in 𝐑]]
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* [[Neighborhoods in R]]
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* [[Cluster Points in 𝐑]]
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* [[Cluster Points]]
 
* [[The Limit of a Function|Limits of Real Functions]]
 
* [[The Limit of a Function|Limits of Real Functions]]
  
 
|| <!--Prerequisite Skills-->  
 
|| <!--Prerequisite Skills-->  
  
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* [[Sequences:Convergence]] <!--- 3213-3.1 --->
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* [[Real Numbers:Sequences|Sequences:Convergence]] <!--- 3213-3.1 --->
 
* [[Sequences:Limits]] <!--- 3213-3.1 --->
 
* [[Sequences:Limits]] <!--- 3213-3.1 --->
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* [[Sequences:Cauchy|The Cauchy Criterion]] <!--- 3213-3.5 --->
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* [[Real Numbers:Sequences|The Cauchy Criterion]] <!--- 3213-3.5 --->
  
 
|| <!--Student Learning Outcomes-->  
 
|| <!--Student Learning Outcomes-->  
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* [[Real Function Limits:Sequential Criterion|The Sequential Criterion for Limits]]
 
* [[Real Function Limits:Sequential Criterion|The Sequential Criterion for Limits]]
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* [[Real Function Limits:Divergence Criteria|Divergence Criteria]]
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* [[Divergence Criteria]]
  
 
|| <!--Prerequisite Skills-->  
 
|| <!--Prerequisite Skills-->  
  
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* [[Sequences:Convergence]] <!--- 3213-3.1 --->
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* [[Real Numbers:Sequences|Sequences:Convergence]] <!--- 3213-3.1 --->
 
* [[Sequences:Limits]] <!--- 3213-3.1 --->
 
* [[Sequences:Limits]] <!--- 3213-3.1 --->
  
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* [[Real Function Limits:One-Sided|One-Sided Limits of Functions]]
 
* [[Real Function Limits:One-Sided|One-Sided Limits of Functions]]
 
* [[Real Function Limits:Infinite|Infinite Limits of Functions]]
 
* [[Real Function Limits:Infinite|Infinite Limits of Functions]]
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* [[Real Function Limits:At Infinity|Limits of Functions at Infinity]]
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* [[Real Function Limits:Infinite|Limits of Functions at Infinity]]
  
 
|| <!--Prerequisite Skills-->  
 
|| <!--Prerequisite Skills-->  
  
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* [[Real Functions:Limits|Limits of Real Functions]]
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* [[The Limit of a Function|Limits of Real Functions]]
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* [[Real Function Limits:Divergence Criteria|Divergence Criteria]]
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* [[Divergence Criteria]]
  
 
|| <!--Student Learning Outcomes-->  
 
|| <!--Student Learning Outcomes-->  
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Latest revision as of 20:56, 24 March 2023

Catalog entry:

Prerequisites: MAT 1224 and MAT 3013.

Content: Axiomatic definition of real numbers, including order properties and completeness; infinite sequences and their convergence; basic notions related to series and their convergence; functions and function limits. Introduction to topology of the real line. Emphasis on theorem proving.


Sample textbook: 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


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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