# Functional Analysis

Canonical: https://manyspace.aporia.systems/subjects/mathematics/functional-analysis-45
Updated: 2026-10-13

Functional Analysis: about 39 hours. Each topic lists what you need first and what it unlocks.

## Banach & Hilbert Spaces

- [Normed & Banach Spaces](https://manyspace.aporia.systems/topics/normed-banach-spaces-mth-func-315)
- [Hilbert Spaces](https://manyspace.aporia.systems/topics/hilbert-spaces-mth-func-316)
- [Bounded Linear Operators](https://manyspace.aporia.systems/topics/bounded-linear-operators-mth-func-317)

## Theorems & Applications

- [Fundamental Theorems](https://manyspace.aporia.systems/topics/fundamental-theorems-mth-func-318)
- [Spectral Theory Intro](https://manyspace.aporia.systems/topics/spectral-theory-intro-mth-func-319)
- [Distributions & Sobolev Spaces](https://manyspace.aporia.systems/topics/distributions-sobolev-spaces-mth-func-320)