Introduction to Functional Analysis

Four nested, non-concentric circles representing topological space, metric spaces, normed, and inner product spaces.

A hierarchy of mathematical spaces: The inner product induces a norm. The norm induces a metric. The metric induces a topology. (Image by Jhausauer,on Wikimedia Commons. Public domain.)


MIT Course Number

18.102 / 18.1021

As Taught In

Spring 2021


Undergraduate / Graduate

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Course Description

Course Features

Course Description

Functional analysis helps to solve problems where the vector space is no longer finite-dimensional, a situation that arises very naturally in many concrete problems. Topics will include normed spaces, completeness, functionals, Hahn-Banach theorem, duality, operators; Lebesgue measure, measurable functions, integrability, completeness of Lp spaces; Hilbert spaces; compact and self-adjoint operators; and the spectral theorem.

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Casey Rodriguez. 18.102 Introduction to Functional Analysis. Spring 2021. Massachusetts Institute of Technology: MIT OpenCourseWare, License: Creative Commons BY-NC-SA.

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