Suggested preparation: Single-variable calculus and willingness to write proofs.
About this course
Move from intuitive calculus toward rigorous analysis. The lectures develop real-number properties, convergence, continuity, differentiation and uniform convergence through definitions and mathematical proofs.
Topics and lesson examples
- Lecture 2: Introduction to Real Numbers (cont.)
- Lecture 8: Convergence Tests for Series; Power Series
- Lecture 12: Convergence in Metric Spaces; Operations on Sets
- Lecture 16: Rolle’s Theorem; Mean Theorem; L’Hôpital’s Rule; Taylor Expansion
- Review for the 18.100B Real Analysis Final Exam
Course at a glance
| Provider | MIT |
|---|---|
| Platform | YouTube · MIT OpenCourseWare |
| Access | Free Video |
| Level | Intermediate — WikiFree study-level assessment |
| Language | English |
| Available lessons | 25 |
| Video duration | 32h 56m · self-paced |
| Details checked | 10 October 2026 |
Preparation and study approach
Suggested preparation: Single-variable calculus and willingness to write proofs.
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.
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Intermediate
Compare course focus, level and study time
| Course | Level | Focus | Study time |
|---|---|---|---|
| This course — 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 |
| Infinite Series and Convergence: Free Course | Intermediate | Convergence tests · Power series · Taylor polynomials | 7h 38m of video; practice time is additional |
| 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: Metric Spaces and Mathematical Analysis | Intermediate | MIT Course: Metric Spaces and Mathematical Analysis | 6h 46m of video; practice time is additional |
Provider: MIT. Videos play from the MIT OpenCourseWare channel on YouTube.
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