Difference between revisions of "MAT3333"
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* Field axioms. | * Field axioms. | ||
* Order of ℝ. | * Order of ℝ. | ||
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| − | Appendix J. | + | 1.2. Appendix J. |
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| + | * Intervals: open, closed, bounded and unbounded. | ||
* Upper and lower bounds of subsets of ℝ. | * Upper and lower bounds of subsets of ℝ. | ||
* Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ. | * Least upper (supremum) and greatest lower (infimum) bound of a subset of ℝ. | ||
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3 | 3 | ||
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| − | + | 2.1, 2.2 | |
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Basic topological notions in the real line. | Basic topological notions in the real line. | ||
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* Continuous functions on ℝ (global continuity). | * Continuous functions on ℝ (global continuity). | ||
* Continuous functions on subsets of ℝ. | * Continuous functions on subsets of ℝ. | ||
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| + | |- | ||
| + | <!-- Week # --> | ||
| + | 5 | ||
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| + | <!-- Sections --> | ||
| + | --- | ||
| + | || | ||
| + | <!-- Topics --> | ||
| + | Review. First midterm exam. | ||
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| + | <!-- SLOs --> | ||
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| + | |- | ||
| + | <!-- Week # --> | ||
| + | 6 | ||
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| + | <!-- Sections --> | ||
| + | 4.1, 4.2 | ||
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| + | <!-- Topics --> | ||
| + | Convergence of real sequences. | ||
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| + | <!-- SLOs --> | ||
| + | * Sequences in ℝ. | ||
| + | * Convergent sequences. | ||
| + | * Algebraic operations on convergent sequences. | ||
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| + | |- | ||
| + | <!-- Week # --> | ||
| + | 7 | ||
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| + | <!-- Sections --> | ||
| + | 4.3, 4.4 | ||
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| + | <!-- Topics --> | ||
| + | The Cauchy criterion. Subsequences. | ||
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| + | <!-- SLOs --> | ||
| + | * Sufficient conditions for convergence. Cauchy criterion. | ||
| + | * Subsequences. | ||
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Revision as of 14:08, 25 March 2023
Course name
MAT 3333 Fundamentals of Analysis and Topology.
Catalog entry: MAT 333 Fundamentals of Analysis and Topology. Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor. Topology of the real line. Introduction to point-set topology.
Prerequisites: MAT 1224 and MAT 3003.
Sample textbooks:
- John M. Erdman, A Problems Based Course in Advanced Calculus. Pure and Applied Undergraduate Texts 32, American Mathematical Society (2018). ISBN: 978-1-4704-4246-0.
- Jyh-Haur Teh, Advanced Calculus I. ISBN-13: 979-8704582137.
Topics List
(Section numbers refer to Erdman's book.)
5 6 7| Week | Sections | Topics | Student Learning Outcomes |
|---|---|---|---|
|
1 |
1.1. Appendices C, G & H. |
Operations, order and intervals of the real line. |
|
|
2 |
1.2. Appendix J. |
Completeness of the real line. Suprema and infima. |
|
|
3 |
2.1, 2.2 |
Basic topological notions in the real line. |
|
|
4 |
3.1–3.3 |
Continuous functions on subsets of the real line. |
|
|
--- |
Review. First midterm exam. |
||
|
4.1, 4.2 |
Convergence of real sequences. |
| |
|
4.3, 4.4 |
The Cauchy criterion. Subsequences. |
|
