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Mathematics III - Foundations of Analysis - Summer 24
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Summer courses ST24
MM5021 ST24
2. Metric spaces and compact sets
Metric Spaces
Metric Spaces
Axioms of metric spaces and first examples
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Metric Spaces
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◄ Quiz: Week 2
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Topics Oral Exam
ST24 Homework-1-DUE:June 29th
ST24 Homework-2-DUE: 14/07 23:59 AM
ST24 Homework-3-DUE: 28/07
Old Exams
Lecture 1
Some comments on sets
Quiz: Week 1
Lecture Slides
Lecture 2
Quiz: Week 2
Open Balls of a metric space
Interior points and Open sets
Open covers and compact sets: Definition
Lecture SLides 2
Lecture SLides 1
Lecture 3
Quiz: Week 3
Theorem: Every compact set is closed and bounded
Theorem: Infinite sets of compact sets have limit points
Lecture Slides
Lecture 4
Quiz: Week 4
The Cauchy construction of the real numbers
An old lecture on sequences
Notes of the video on Sequences
Lecture Slides
Lecture 5
Quiz: Week 5
Lecture Slides
Lecture 6
Quiz: Week 6
Some video-lectures on differentability for real valued functions
Rudin Chpt 6 pages 120-134
Lecture Slides
Lecture 7
Quiz: Week 7
Lecture Slides
Lecture 8
Quiz 8
Lecture 9
Quiz 9
Statement of The implicit function Theorem
An interpretation of the Implicit Function Theorem
Statement of the Inverse Function Theorem
Proof of the Inverse Function Theorem from the Implicit Function Theorem
Proof of the Implicit Function Theorem (Step 1/5)
Proof of the Implicit Function Theorem (Step 2/5)
Proof of the Implicit Function Theorem (Step 3/5)
Proof of the Implicit Function Theorem (Step 4/5)
Proof of the Implicit Function Theorem (Step 5/5)
Lecture 10
Oral Exams
Oral Re-Exam
Open Balls of a metric space ►