Analysis I: Real Analysis

1. Set Theory (2 lectures)

  • Sets and Relations
  • Cardinality

2. Real Numbers (3 lectures)

3. Metric Spaces (5 lectures)

4. Topological Spaces (3 lectures)

  • definitions, basic results
  • compactness
  • continuous functions on compact sets: Arzelà-Ascoli, Stone-Weierstrass

5. Linear Algebra (1 lecture)

6. Hilbert and Banach Spaces (6 lectures)

7. Differentiation and Integration (10 lectures)

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