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 HahnBanach 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 FiniteRank Operators  
20  Compact Operators and the Spectrum of a Bounded Linear Operator on a Hilbert Space  Assignment 9 due 
21  The Spectrum of SelfAdjoint Operators and the Eigenspaces of Compact SelfAdjoint Operators  
22  The Spectral Theorem for a Compact SelfAdjoint Operator  Assignment 10 due 
23  The Dirichlet Problem on an Interval  
Final Assignment  Final Assignment due 
Calendar
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As Taught In:  Spring 2021 
Level: 
Undergraduate

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