Difference between revisions of "MAT3213"
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| − | + | '''Catalog entry''': | |
| − | Introduction to Real Analysis by Bartle and Sherbert | + | |
| + | ''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. | ||
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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]. | ||
| Line 259: | Line 266: | ||
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| − | * [[Sequences:Convergence]] | + | * [[Real Numbers:Sequences|Sequences:Convergence]] |
* [[Sequences:Subsequences]] <!--- 3213-3.4 ---> | * [[Sequences:Subsequences]] <!--- 3213-3.4 ---> | ||
| Line 284: | Line 291: | ||
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| − | * [[Sequences:Convergence]] <!--- 3213-3.1 ---> | + | * [[Real Numbers:Sequences|Sequences:Convergence]] <!--- 3213-3.1 ---> |
* [[Sequences:Limits]] <!--- 3213-3.1 ---> | * [[Sequences:Limits]] <!--- 3213-3.1 ---> | ||
| − | * [[Sequences | + | * [[Real Numbers:Sequences|The Cauchy Criterion]] <!--- 3213-3.5 ---> |
|| <!--Student Learning Outcomes--> | || <!--Student Learning Outcomes--> | ||
| Line 308: | Line 315: | ||
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| − | * [[Sequences:Convergence]] <!--- 3213-3.1 ---> | + | * [[Real Numbers:Sequences|Sequences:Convergence]] <!--- 3213-3.1 ---> |
* [[Sequences:Limits]] <!--- 3213-3.1 ---> | * [[Sequences:Limits]] <!--- 3213-3.1 ---> | ||
| − | * [[Sequences | + | * [[Real Numbers:Sequences|The Cauchy Criterion]] <!--- 3213-3.5 ---> |
|| <!--Student Learning Outcomes--> | || <!--Student Learning Outcomes--> | ||
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|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| − | * [[Sequences:Convergence]] <!--- 3213-3.1 ---> | + | * [[Real Numbers:Sequences|Sequences:Convergence]] <!--- 3213-3.1 ---> |
* [[Sequences:Limits]] <!--- 3213-3.1 ---> | * [[Sequences:Limits]] <!--- 3213-3.1 ---> | ||
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|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| − | * [[ | + | * [[The Limit of a Function|Limits of Real Functions]] |
* [[Divergence Criteria]] | * [[Divergence Criteria]] | ||
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 |
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| Week 2 |
1.2 & 1.3 |
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| Week 3 |
2.1-2.2 |
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| Week 4 |
2.3-2.4 |
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| Week 5 |
2.5 & 3.1 |
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| Week 6 |
3.2 |
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| Week 7 |
|
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| Week 8 |
3.3 |
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| Week 9 |
3.4 |
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| Week 10 |
3.5-3.6 |
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| Week 11 |
3.7 |
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| Week 12 |
4.1 |
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| Week 13 |
4.2 |
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| Week 14 |
4.3 |
|
