# Calendar

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 Lp 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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assignment Problem Sets