Difference between revisions of "MAT3213"
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(Topics until Week 4.) |
(Added bullets everywhere.) |
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|| <!--Topics--> | || <!--Topics--> | ||
| − | [[Sets:Definitions]] | + | * [[Sets:Definitions]] |
| − | [[Sets:Operations]] | + | * [[Sets:Operations]] |
| − | [[Functions:Definition]] | + | * [[Functions:Definition]] |
| − | [[Functions:Domain]] | + | * [[Functions:Domain]] |
| − | [[Functions:Range]] | + | * [[Functions:Range]] |
| − | [[Functions:Injective]] | + | * [[Functions:Injective]] |
| − | [[Functions:Bijective]] | + | * [[Functions:Bijective]] |
| − | [[Functions:Composition]] | + | * [[Functions:Composition]] |
| − | [[Functions:Inverse]] | + | * [[Functions:Inverse]] |
| − | [[Functions:ForwardImage]] | + | * [[Functions:ForwardImage]] |
| − | [[Functions:InverseImage]] | + | * [[Functions:InverseImage]] |
| − | [[Functions:Restriction]] | + | * [[Functions:Restriction]] |
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| Line 50: | Line 50: | ||
|| <!--Topics--> | || <!--Topics--> | ||
| − | [[NaturalNumbers:Well Ordering]] | + | * [[NaturalNumbers:Well Ordering]] |
| − | [[Proofs:Induction]] | + | * [[Proofs:Induction]] |
| − | [[Induction:Variants]] | + | * [[Induction:Variants]] |
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| Line 74: | Line 74: | ||
| − | [[Finite and Infinite Sets]] | + | * [[Finite and Infinite Sets]] |
| − | [[Countable Sets]] | + | * [[Countable Sets]] |
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| − | [[Sets:Operations]] | + | * [[Sets:Operations]] |
| − | [[NaturalNumbers:Well Ordering]] | + | * [[NaturalNumbers:Well Ordering]] |
| − | [[Proofs:Induction]] | + | * [[Proofs:Induction]] |
| − | [[Functions:Injective]] | + | * [[Functions:Injective]] |
| − | [[Functions:Bijective]] | + | * [[Functions:Bijective]] |
|| <!--Student Learning Outcomes--> | || <!--Student Learning Outcomes--> | ||
| Line 100: | Line 100: | ||
|| <!--Topics--> | || <!--Topics--> | ||
| − | [[Real Numbers]] | + | * [[Real Numbers]] |
| − | [[RealNumbers:Algebraic Properties]] | + | * [[RealNumbers:Algebraic Properties]] |
| − | [[RealNumbers:Order]] | + | * [[RealNumbers:Order]] |
| − | [[RealNumbers:Inequalities|Inequalities]] | + | * [[RealNumbers:Inequalities|Inequalities]] |
| − | [[RealNumbers:Absolute Value|Absolute Value]] | + | * [[RealNumbers:Absolute Value|Absolute Value]] |
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| Line 125: | Line 125: | ||
|| <!--Topics--> | || <!--Topics--> | ||
| − | [[RealNumbers:Completeness]] | + | * [[RealNumbers:Completeness]] |
| − | [[RealNumbers:Archimedean Property|Archimedean Property]] | + | * [[RealNumbers:Archimedean Property|Archimedean Property]] |
| − | [[RealNumbers:Suprema of Subsets|Suprema of Subsets]] | + | * [[RealNumbers:Suprema of Subsets|Suprema of Subsets]] |
| − | [[RealNumbers:Infima of Subsets|Infima of Subsets]] | + | * [[RealNumbers:Infima of Subsets|Infima of Subsets]] |
| − | [[RealNumbers:Suprema of Subsets|Suprema of Subsets]] | + | * [[RealNumbers:Suprema of Subsets|Suprema of Subsets]] |
| − | [[RealNumbers:Rational]] | + | * [[RealNumbers:Rational]] |
| − | [[RealNumbers:Irrational]] | + | * [[RealNumbers:Irrational]] |
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| − | [[RealNumbers:Algebraic Properties]] | + | * [[RealNumbers:Algebraic Properties]] |
| − | [[RealNumbers:Inequalities|Inequalities]] | + | * [[RealNumbers:Inequalities|Inequalities]] |
| − | [[RealNumbers:Order]] | + | * [[RealNumbers:Order]] |
| − | [[RealNumbers:Absolute Value|Absolute Value]] | + | * [[RealNumbers:Absolute Value|Absolute Value]] |
|| <!--Student Learning Outcomes--> | || <!--Student Learning Outcomes--> | ||
| Line 154: | Line 154: | ||
|| <!--Topics--> | || <!--Topics--> | ||
| − | [[RealNumbers:Intervals|Intervals]] | + | * [[RealNumbers:Intervals|Intervals]] |
| − | [[RealNumbers:Cardinality]] | + | * [[RealNumbers:Cardinality]] |
| − | [[RealNumbers:Decimal Representation|Decimal Representation]] | + | * [[RealNumbers:Decimal Representation|Decimal Representation]] |
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| − | [[RealNumbers:Completeness|Completeness]] <!--- 3213-2.1 ---> | + | * [[RealNumbers:Completeness|Completeness]] <!--- 3213-2.1 ---> |
| − | [[RealNumbers:Archimedean Property|Archimedean Property]] | + | * [[RealNumbers:Archimedean Property|Archimedean Property]] |
| − | [[RealNumbers:Bounded Subsets|Bounded Sets]] | + | * [[RealNumbers:Bounded Subsets|Bounded Sets]] |
| − | [[RealNumbers:Suprema of Subsets|Suprema of Subsets]] | + | * [[RealNumbers:Suprema of Subsets|Suprema of Subsets]] |
| − | [[RealNumbers:Infima of Subsets|Infima of Subsets]] | + | * [[RealNumbers:Infima of Subsets|Infima of Subsets]] |
|| <!--Student Learning Outcomes--> | || <!--Student Learning Outcomes--> | ||
| Line 180: | Line 180: | ||
|| <!--Topics--> | || <!--Topics--> | ||
| − | [[RealNumbers:Sequences|Sequences]] | + | * [[RealNumbers:Sequences|Sequences]] |
| − | [[Sequences:Tails]] | + | * [[Sequences:Tails]] |
| − | [[Sequences:Limits]] | + | * [[Sequences:Limits]] |
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| − | [[RealNumbers:Inequalities|Inequalities]] | + | * [[RealNumbers:Inequalities|Inequalities]] |
| − | [[RealNumbers:Absolute Value|Absolute Value]] | + | * [[RealNumbers:Absolute Value|Absolute Value]] |
|| <!--Student Learning Outcomes--> | || <!--Student Learning Outcomes--> | ||
| Line 203: | Line 203: | ||
|| <!--Topics--> | || <!--Topics--> | ||
| − | [[Sequences:Limit Laws]] | + | * [[Sequences:Limit Laws]] |
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| − | [[Sequences:Limits]] | + | * [[Sequences:Limits]] |
|| <!--Student Learning Outcomes--> | || <!--Student Learning Outcomes--> | ||
| Line 223: | Line 223: | ||
|| <!--Topics--> | || <!--Topics--> | ||
| − | [[Sequences:Monotone]] | + | * [[Sequences:Monotone]] |
| − | [[Euler's Number]] | + | * [[Euler's Number]] |
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| − | [[Proofs:Induction]] <!--- 3213-1.2 ---> | + | * [[Proofs:Induction]] <!--- 3213-1.2 ---> |
| − | [[RealNumbers:Bounded Subsets|Bounded Sets]] | + | * [[RealNumbers:Bounded Subsets|Bounded Sets]] |
| − | [[Sequences:Limit Laws]] | + | * [[Sequences:Limit Laws]] |
|| <!--Student Learning Outcomes--> | || <!--Student Learning Outcomes--> | ||
| Line 247: | Line 247: | ||
|| <!--Topics--> | || <!--Topics--> | ||
| − | [[Subsequences]] | + | * [[Subsequences]] |
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| Line 268: | Line 268: | ||
|| <!--Topics--> | || <!--Topics--> | ||
| − | [[The Bolzano Weierstrass Theorem]] | + | * [[The Bolzano Weierstrass Theorem]] |
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| Line 290: | Line 290: | ||
|| <!--Topics--> | || <!--Topics--> | ||
| − | [[The Limit Superior and Limit Inferior]] | + | * [[The Limit Superior and Limit Inferior]] |
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| Line 312: | Line 312: | ||
|| <!--Topics--> | || <!--Topics--> | ||
| − | [[The Cauchy Criterion for Convergence]] | + | * [[The Cauchy Criterion for Convergence]] |
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| Line 334: | Line 334: | ||
|| <!--Topics--> | || <!--Topics--> | ||
| − | [[Properly Divergent Sequences]] | + | * [[Properly Divergent Sequences]] |
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| Line 356: | Line 356: | ||
|| <!--Topics--> | || <!--Topics--> | ||
| − | [[Introduction to Infinite Series]] | + | * [[Introduction to Infinite Series]] |
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| Line 378: | Line 378: | ||
|| <!--Topics--> | || <!--Topics--> | ||
| − | [[Cluster Points]] | + | * [[Cluster Points]] |
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| Line 400: | Line 400: | ||
|| <!--Topics--> | || <!--Topics--> | ||
| − | [[The Definition of the Limit of a Function]] | + | * [[The Definition of the Limit of a Function]] |
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| Line 422: | Line 422: | ||
|| <!--Topics--> | || <!--Topics--> | ||
| − | [[The Sequential Criterion and Divergence Criteria]] | + | * [[The Sequential Criterion and Divergence Criteria]] |
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| Line 444: | Line 444: | ||
|| <!--Topics--> | || <!--Topics--> | ||
| − | [[The Limit Theorems for Functions]] | + | * [[The Limit Theorems for Functions]] |
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| Line 466: | Line 466: | ||
|| <!--Topics--> | || <!--Topics--> | ||
| − | [[One Sided Limits]] | + | * [[One Sided Limits]] |
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
| Line 487: | Line 487: | ||
|| <!--Topics--> | || <!--Topics--> | ||
| − | [[Infinite Limits and Limits at Infinity]] | + | * [[Infinite Limits and Limits at Infinity]] |
|| <!--Prerequisite Skills--> | || <!--Prerequisite Skills--> | ||
Revision as of 14:11, 14 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 |
| ||
| Week 3 |
1.3 |
|
| |
| Week 3 |
2.1-2.2 |
| ||
| Week 3 |
2.3-2.4 |
| ||
| Week 4 |
2.5 |
| ||
| Week 5 |
3.1 |
| ||
| Week 6 |
3.2 |
| ||
| Week 7 |
3.3 |
| ||
| Week 5 |
3.4 |
| ||
| Week 5 |
3.4 |
| ||
| Week 5/6 |
3.4 |
| ||
| Week 6 |
3.5 |
| ||
| Week 6 |
3.6 |
| ||
| Week 6/7 |
3.7 |
| ||
| Week 12 |
4.1 |
| ||
| Week 12 |
4.1 |
| ||
| Week 12/13 |
4.1 |
| ||
| Week 13 |
4.2 |
| ||
| Week 14 |
4.3 |
| ||
| Week 14/15 |
4.3 |
|
