| Week | Date | Topic & Assignments | Reading |
| Week 1 | Sep 4 (Thu) | Review: Vector Spaces and syllabus overview. Instructor’s notes Homework Set 0 | Vector space |
| Week 2 | Sep 9 (Tue) | Introduction to Metric Spaces Homework Set 1 | Pages 31–41 |
| Sep 11 (Thu) | Convergence and Completeness in Metric Spaces Homework Set 2 | Pages 42–50 | |
| Week 3 | Sep 16 (Tue) | Topology in Metric Spaces — Part 1 Homework Set 3 | Pages 53–54 |
| Sep 18 (Thu) | Topology in Metric Spaces — Part 2 Homework Set 3 | Pages 55–57 | |
| Week 4 | Sep 23 (Tue) | Closed Sets and Accumulation Points Homework Set 4 | Pages 62–64 |
| Sep 25 (Thu) | Closure, Density, and Separability Homework Set 4 | Pages 66–70 | |
| Week 5 | Sep 30 (Tue) | Compactness Homework Set 5 | Pages 75–78 |