| Week | Topics | Reading |
| 1 | Metric Spaces, ordered fields, number systems, induction, countability | Introduction, 1.1 |
| 2 | Sequences, convergence, least upper bounds, Cauchy condition, completeness, Bolzano-Weierstrauss theorem | 1.2, 1.3, 1.4, 1.5 |
| 3 | Norms, inner product spaces, Cauchy-Schwartz inequality, contractions, Banach fixed point theorem, open & closed sets | 1.7, 2.1, 2.2, 2.3 |
| 4 | Set closure & boundary, sequences and closed & complete spaces, convergence of series | 2.4, 2.5, 2.6, 2.7, 2.8, 2.9 |
| 5 | Compactness, Heine-Borel theorem, nested sets | 3.1, 3.2, 3.3 |
| 6 | Midterm May 5, Connectedness | 3.4, 3.5 |
| 7 | Continuity, intermediate value theorem | 4.1, 4.2, 4.3, 4.4, 4.5 |
| 8 | Uniform continuity, differentiation and integration in one real variable | 4.6, 4.7, 4.8 |
| 9 | Pointwise and uniform convergence, Weierstrauss M-test | 5.1, 5.2 |
| 10 | Integration and differentiation of series, the space of continuous functions | 5.3, 5.5 |