18.102 | Spring 2021 | Undergraduate

Introduction to Functional Analysis


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

Course Info

As Taught In
Spring 2021
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