Difference between revisions of "MAT3213"
Jump to navigation
Jump to search
Jose.iovino (talk | contribs) |
|||
| (11 intermediate revisions by 4 users not shown) | |||
| Line 1: | Line 1: | ||
| − | + | '''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. | ||
| + | |||
| + | |||
| + | |||
| + | ''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 164: | Line 171: | ||
|| <!--Topics--> | || <!--Topics--> | ||
| − | * [[Sequences:Tails]] | + | * [[Real Numbers:Sequences|Sequences:Tails]] |
* [[Sequences:Limits|Sequences:Limit Laws]] | * [[Sequences:Limits|Sequences:Limit Laws]] | ||
* [[Real Numbers:Sequences|Sequences:Bounded when Convergent]] | * [[Real Numbers:Sequences|Sequences:Bounded when Convergent]] | ||
| Line 254: | Line 261: | ||
* [[Real Numbers:Sequences|The Cauchy Criterion]] | * [[Real Numbers:Sequences|The Cauchy Criterion]] | ||
| − | * [[Sequences:Contractive]] | + | * [[Real Numbers:Sequences|Sequences:Contractive]] |
| − | * [[ | + | * [[Properly Divergent Sequences]] |
|| <!--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 302: | Line 309: | ||
|| <!--Topics--> | || <!--Topics--> | ||
| − | * [[Neighborhoods in | + | * [[Neighborhoods in R]] |
| − | * [[Cluster Points | + | * [[Cluster Points]] |
* [[The Limit of a Function|Limits of Real Functions]] | * [[The Limit of a Function|Limits of Real Functions]] | ||
|| <!--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 328: | Line 335: | ||
* [[Real Function Limits:Sequential Criterion|The Sequential Criterion for Limits]] | * [[Real Function Limits:Sequential Criterion|The Sequential Criterion for Limits]] | ||
| − | * [[ | + | * [[Divergence Criteria]] |
|| <!--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 ---> | ||
| Line 355: | Line 362: | ||
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| − | * [[ | + | * [[The Limit of a Function|Limits of Real Functions]] |
| − | * [[ | + | * [[Divergence Criteria]] |
|| <!--Student Learning Outcomes--> | || <!--Student Learning Outcomes--> | ||
| Line 363: | Line 370: | ||
|- | |- | ||
| + | |||
| + | |} | ||
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 |
|
| |||
| 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 |
|
