MATH 6220

Applied Functional Analysis

Course Description

Course information provided by the Courses of Study 2024-2025.

Functional analysis is a branch of mathematical analysis that mainly focuses on the study of infinite-dimensional vector spaces and the operators acting upon them. It builds upon results and ideas from linear algebra and real and complex analysis to develop general frameworks that can be used to study analytical problems. Functional analysis plays a pivotal role in several areas of mathematics, physics, engineering, and even in some areas of computer science and economics. This course will cover the basic theory of Banach, Hilbert, and Sobolev spaces, as well as explore several notable applications, from analyzing partial differential equations (PDEs), numerical analysis, inverse problems, control theory, optimal transportation, and machine learning.

When Offered Spring.

Prerequisites/Corequisites Prerequisite: a first course in real analysis, including exposure to Lebesgue integration (e.g., MATH 6110 or MATH 6210).

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