MAT3333 - Revision history

Eduardo.duenez: Spelling…

2023-03-25T21:57:00Z

Spelling…

2023-03-25T21:46:39Z

Typo.

2023-03-25T21:45:48Z

Make week 15 optional.

2023-03-25T21:45:30Z

Week 15

2023-03-25T21:43:11Z

Improving catalog entry.

2023-03-25T21:41:32Z

Shuffling…

2023-03-25T21:39:07Z

Shuffling…

2023-03-25T21:38:05Z

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2023-03-25T21:35:01Z

Shuffled/merged.

2023-03-25T21:30:26Z

Merging…

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 MAT 3333 Fundamentals of Analysis and Topology.
 Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
-Topological notions in the real line and in metric spaces. Convergent sequences. Continuious functions. Connected and compact sets. The Intermediate Value and Extreme Value theorems. Sequential compactness and the Heine-Borel Theorem.
+Topological notions in the real line and in metric spaces. Convergent sequences. Continuous functions. Connected and compact sets. The Intermediate Value and Extreme Value theorems. Sequential compactness and the Heine-Borel Theorem.
 '''Prerequisites:'''

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-Complete metric spaces
+Complete metric spaces.
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 <!-- Sections -->
-Chapter 18
+Chapter 18 (time permitting)
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← Older revision		Revision as of 21:45, 25 March 2023
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	* The Heine-Borel Theorem.		* The Heine-Borel Theorem.

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		+	15
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		+	Chapter 18
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		+	Complete metric spaces
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		+	* Cauchy sequences in metric spaces.
		+	* Metric completness.
		+	* Completeness and compactness.
	\|}		\|}

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 MAT 3333 Fundamentals of Analysis and Topology.
 Prerequisite: MAT 3003 Discrete Mathematics, or consent of instructor.
-Topological notions in the real line and in metric spaces. Convergence of sequences and functions. Continuity. Connectedness and compactness. The Intermediate Value and Extreme Value theorems. Sequential compactness and the Heine-Borel Theorem.
+Topological notions in the real line and in metric spaces. Convergent sequences. Continuious functions. Connected and compact sets. The Intermediate Value and Extreme Value theorems. Sequential compactness and the Heine-Borel Theorem.
 '''Prerequisites:'''

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-Continuous functions on subsets of the real line.
+Continuous functions on ℝ.
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-.1, 5.2
+Chapter 5
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-.1, 6.2, 6.3
+Chapter 6
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-.1, 7.2
+Chapter 7
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-.1-12.3
+Chapter 12
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-.1-14.3
+Chapter 14
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-.1, 4.2
+Chapter 4
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 Convergence of real sequences.
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 * Convergent sequences.
 * Algebraic operations on convergent sequences.
 * Sufficient conditions for convergence. Cauchy criterion.
 * Subsequences.