Presentation: written work should be done on one side only of 8.5''x11'' paper with smooth edges. Each problem should begin a new page.
Deadlines: papers should be turned in outside of Jones 130. 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 | 1/17 | Overview of the material | Homework 0 and a solution. |
| 2 | 1/22 | Metric spaces: generalities | |
| 1/24 | Metric topology | Homework 1 and a solution. | |
| 3 | 1/29 | $\ell^p$-norms | |
| 1/31 | Completeness | ||
| 4 | 2/05 | Completion of a metric space | |
| 2/07 | Compactness in $C(X)$: Arzelà-Ascoli | Homework 2 and a solution. | |
| 5 | 2/12 | More on compactness | |
| 2/14 | The Baire Category Theorem | Homework 3 and a solution. | |
| 6 | 2/19 | Normed linear spaces: subspaces, quotients, bases | |
| 2/21 | Normed linear spaces: bounded operators | ||
| 7 | 2/26 | Banach spaces | |
| 2/28 | Midterm 1 and a solution | ||
| 8 | 3/05 | Spring Break | |
| 3/07 | Spring Break | Homework 4 and a solution | |
| 9 | 3/12 | Series in Banach spaces, finite dimension | |
| 3/14 | Riesz Theorem, the Bounded Inverse Theorem | ||
| 10 | 3/19 | The Open Mapping Theorem | |
| 3/21 | The Closed Graph, complements | Homework 5, and a solution | |
| 11 | 3/26 | Duality | |
| 3/28 | Analytic Hahn-Banach | ||
| 12 | 4/02 | Midterm 2 | |
| 4/04 | No class | Homework 6, and a solution | |
| 13 | 4/09 | Hilbert spaces, orthogonality | |
| 4/11 | Projections, duality | ||
| 14 | 4/16 | Hilbert bases | |
| 4/18 | Adjoints, Fourier series: $L^2$ theory | ||
| 15 | 4/23 | Fourier series: convergence results | |
| 4/25 | Introduction to Harmonic Analysis | ||
| 5/02 | Final Examination, due by 4/30 at noon. |
