Presentation: written work should be done on one side only of 8.5''x11'' paper with smooth edges. Each problem should begin on a new page.
Deadlines: papers should be turned in outside of Jones 130 by 5pm. Extensions may be granted if requested at least twenty-four hours before the due date. Late homework will not be accepted.
| Date | Topic | Assignments | |
| 1 | 1/25 | Overview, general ideas | Homework 0 and a solution |
| 2 | 1/30 | Metric spaces, elements of topology | |
| 2/01 | Completeness | Homework 1 and a solution | |
| 3 | 2/06 | $\ell^p$ spaces | |
| 2/08 | More examples, uniform continuity | ||
| 4 | 2/13 | Completion of a metric space | |
| 2/15 | Compactness in $C(X)$: Arzelà-Ascoli | Homework 2 and a solution | |
| 5 | 2/20 | More on compactness | |
| 2/22 | The Baire Category Theorem | Homework 3 and a solution | |
| 6 | 2/27 | Normed linear spaces: subspaces, quotients, bases | |
| 3/01 | Normed linear spaces: bounded operators | ||
| 7 | 3/06 | Series in Banach spaces, quotients - Finite dimension | |
| 3/07 | No Class | Midterm 1 | |
| 3/08 | Riesz' compactness theorem | ||
| 3/11-19 | Spring Break | ||
| 8 | 3/20 | The Open Mapping and Bounded Inverse Theorems | Homework 4 and a solution |
| 3/22 | The Closed Graph Theorem | Homework 5 and a solution | |
| 9 | 3/27 | Duality | |
| 3/29 | Analytic Hahn-Banach | ||
| 10 | 4/03 | Geometric Hahn-Banach | Homework 6 and a solution |
| 4/05 | Hilbert spaces: orthogonality | ||
| 11 | 4/10 | Projections | |
| 4/12 | The Riesz Representation Theorem, Hilbert bases | ||
| 12 | 4/17 | More duality, adjoints | |
| 4/18 | Midterm 2 | ||
| 4/19 | Fourier series: $L^2$-theory | ||
| 13 | 4/24 | Fourier series: convergence questions | Homework 7 and a solution |
| 4/26 | Applications of Hilbert techniques | ||
| 14 | 5/01 | Introduction to the theory of distributions, I | |
| 5/03 | Introduction to the theory of distributions, II | ||
| ★ | 5/16 | Final Examination |