Func. Analysis·Course
Functional Analysis
Functional analysis: normed spaces, Banach and Hilbert spaces, operators, and spectral theory
Part of the Mathematics track — finish it for a verifiable diploma →
§ 01 — Orientation
New here?
What you'll be able to do, who this is for, how long it takes, and where to begin.
By the end, you will be able to
- 01Reason in metric and normed spaces.
- 02Work in Hilbert spaces.
- 03Analyze linear operators.
- 04Approach spectral theory.
- 05See the backbone of quantum theory and PDEs.
Who this is for
How long it takes
- Quick orientationSkim the opening module and the cheatsheet to get the shape of it.~2 h
- Full read-throughRead every article once, in order.~2 h
- Mastery pathRead, take the quizzes, and space out your reviews.~2 weeks
- APA
Stoa. (2026). Functional Analysis [Online course]. Stoa. https://stoa.school/course/functional-analysis
- MLA
Stoa. “Functional Analysis.” Stoa, 2026, https://stoa.school/course/functional-analysis.
- Chicago
Stoa. “Functional Analysis.” Stoa. Accessed September 1, 2026. https://stoa.school/course/functional-analysis.
§ 02 — Curriculum
5 modules.
Each module is a small unit. Most read in sequence — but a determined reader can begin anywhere.
- M IMetric and Normed SpacesMetrics, norms, completeness, and convergence in function spaces3 articles
18 minBegin → - M IIHilbert SpacesInner product, orthogonality, and Fourier series3 articles
18 minBegin → - M IIIOperator TheorySpectral theory, compact operators, and Fredholm equations3 articles
18 minBegin → - M IVVariational MethodsWeak solutions, the Lax–Milgram theorem, and Sobolev spaces3 articles
18 minBegin → - M VFourier Transforms and DistributionsFourier transform, Plancherel’s theorem, and generalized functions3 articles
18 minBegin →
§ 03 — Learning outcomes
4 outcomes.
Work with metric, normed, and Banach spaces
Understand orthogonality, bases, and projections in Hilbert spaces
Analyze bounded and closed operators and apply the Hahn–Banach theorem
Study operator spectra and compact and self-adjoint operators
§ 04 — Practices