Suggested preparation: Real analysis, linear algebra and proof-writing.
Optional preparation: Free MIT Course: Real Analysis and Mathematical Proofs.
About this course
Develop the foundations of functional analysis through Banach spaces, extension theorems, measurable functions, Lp spaces and Hilbert-space methods. The emphasis is on rigorous reasoning.
Topics and lesson examples
- Lecture 3: Quotient Spaces, the Baire Category Theorem and the Uniform Boundedness Theorem
- Lecture 5: Zorn’s Lemma and the Hahn-Banach Theorem
- Lecture 12: Lebesgue Integrable Functions, the Lebesgue Integral and the Dominated Convergence…
- Lecture 16: Fejer’s Theorem and Convergence of Fourier Series
- Lecture 17: Minimizers, Orthogonal Complements and the Riesz Representation Theorem
Course at a glance
| Provider | MIT |
|---|---|
| Platform | YouTube · MIT OpenCourseWare |
| Access | Free Video |
| Level | Professional — WikiFree study-level assessment |
| Language | English |
| Available lessons | 23 |
| Video duration | 30h 16m · self-paced |
| Details checked | 10 October 2026 |
Preparation and study approach
Suggested preparation: Real analysis, linear algebra and proof-writing.
Follow the available videos in sequence, pausing to summarize the main argument or reconstruct a worked example. Keep a short list of assumptions, unfamiliar terms and questions to revisit. Additional reading, problem solving and practice will take time beyond the listed video duration.
Using this video classroom
Select a lesson from the list, or search for a topic. Previous and Next move through the sequence. You can mark lessons complete; progress is stored in this browser without a WikiFree account.
Free access and course scope
The public MIT OpenCourseWare videos in this classroom are free to watch. This listing provides the available playlist recordings, which may include selected lectures, recitations, demonstrations or supporting discussions rather than every component of the original campus course. Textbooks, equipment, software licenses, supervised labs, graded assignments and instructor feedback are not supplied by WikiFree. No purchase is required to watch the videos or use the note-based study approach above.
WikiFree independently organizes these resources for self-paced study. Watching does not award an MIT certificate, academic credit or admission to MIT.
Video provider and credit: MIT OpenCourseWare on YouTube. WikiFree titles, descriptions and cover artwork are independently prepared.
Related courses for your next step
- Review a lower-level optionFree MIT Course: Real Analysis and Mathematical Proofs
Focus: Lecture 2: Introduction to Real Numbers (cont.) · Lecture 8: Convergence Tests for Series; Power Series
Intermediate - Review a lower-level optionFree MIT Course: Metric Spaces and Mathematical Analysis
Focus: MIT Course: Metric Spaces and Mathematical Analysis
Intermediate - Review a lower-level optionFree MIT Course: Linear Algebra: Matrices, Eigenvalues and Vector Spaces
Focus: An Interview with Gilbert Strang on Teaching Linear Algebra · 8. Solving Ax = b: Row Reduced Form R
Intermediate
Compare course focus, level and study time
| Course | Level | Focus | Study time |
|---|---|---|---|
| This course — Free MIT Course: Functional Analysis and Hilbert Spaces | Professional | Lecture 3: Quotient Spaces, the Baire Category Theorem and the Uniform Boundedness Theorem · Lecture 5: Zorn’s Lemma and the Hahn-Banach Theorem · Lecture 12: Lebesgue Integrable Functions, the Lebesgue Integral and the Dominated Convergence... | 30h 16m of video; practice time is additional |
| Free MIT Course: Real Analysis and Mathematical Proofs | Intermediate | Lecture 2: Introduction to Real Numbers (cont.) · Lecture 8: Convergence Tests for Series; Power Series · Lecture 12: Convergence in Metric Spaces; Operations on Sets | 32h 56m of video; practice time is additional |
| Free MIT Course: Metric Spaces and Mathematical Analysis | Intermediate | MIT Course: Metric Spaces and Mathematical Analysis | 6h 46m of video; practice time is additional |
| Free MIT Course: Linear Algebra: Matrices, Eigenvalues and Vector Spaces | Intermediate | An Interview with Gilbert Strang on Teaching Linear Algebra · 8. Solving Ax = b: Row Reduced Form R · 17. Orthogonal Matrices and Gram-Schmidt | 35h 49m of video; practice time is additional |
Provider: MIT. Videos play from the MIT OpenCourseWare channel on YouTube.
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