LEC # | TOPICS | KEY DATES |
---|---|---|
1 | Basic Banach Space Theory | |
2 | Bounded Linear Operators | Assignment 1 due |
3 | Quotient Spaces, the Baire Category Theorem and the Uniform Boundedness Theorem | |
4 | The Open Mapping Theorem and the Closed Graph Theorem | Assignment 2 due |
5 | Zorn’s Lemma and the Hahn-Banach Theorem | |
6 | The Double Dual and the Outer Measure of a Subset of Real Numbers | Assignment 3 due |
7 | Sigma Algebras | |
8 | Lebesgue Measurable Subsets and Measure | Assignment 4 due |
9 | Lebesgue Measurable Functions | |
10 | Simple Functions | Assignment 5 due |
11 | The Lebesgue Integral of a Nonnegative Function and Convergence Theorems | |
Midterm Exam | Midterm Exam due | |
12 | Lebesgue Integrable Functions, the Lebesgue Integral and the Dominated Convergence Theorem | |
13 | L^{p} Space Theory | |
14 | Basic Hilbert Space Theory | Assignment 6 due |
15 | Orthonormal Bases and Fourier Series | |
16 | Fejer’s Theorem and Convergence of Fourier Series | Assignment 7 due |
17 | Minimizers, Orthogonal Complements and the Riesz Representation Theorem | |
18 | The Adjoint of a Bounded Linear Operator on a Hilbert Space | Assignment 8 due |
19 | Compact Subsets of a Hilbert Space and Finite-Rank Operators | |
20 | Compact Operators and the Spectrum of a Bounded Linear Operator on a Hilbert Space | Assignment 9 due |
21 | The Spectrum of Self-Adjoint Operators and the Eigenspaces of Compact Self-Adjoint Operators | |
22 | The Spectral Theorem for a Compact Self-Adjoint Operator | Assignment 10 due |
23 | The Dirichlet Problem on an Interval | |
Final Assignment | Final Assignment due |
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