Suggested preparation: Probability, combinatorics and proof-writing.
Optional preparation: Existence Theorems in Calculus: Free Course.
About this course
Learn how probability can establish combinatorial results. The videos work through expectations, extremal questions and concentration bounds, illustrating the probabilistic method through mathematical examples.
Topics and lesson examples
- Large Bipartite Subgraph
- Extremal Set Theory: Sperner's Theorem
- Independent Sets and Turán's Theorem
- Markov, Chebyshev, and Chernoff
- Existence of Graphs with High Girth and High Chromatic Number
Course at a glance
| Provider | MIT |
|---|---|
| Platform | YouTube · MIT OpenCourseWare |
| Access | Free Video |
| Level | Professional — WikiFree study-level assessment |
| Language | English |
| Available lessons | 11 |
| Video duration | 3h 36m · self-paced |
| Details checked | 10 October 2026 |
Preparation and study approach
Suggested preparation: Probability, combinatorics 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
- Compare another approachFree MIT Course: Graph Theory and Additive Combinatorics
Focus: 1. A bridge between graph theory and additive combinatorics · 7. Szemerédi's graph regularity lemma II: triangle removal lemma
Professional - Compare another approachFree MIT Course: Projection Theory and Geometric Combinatorics
Focus: Lecture 14: The Bourgain Projection Theorem Part 1 (over the Real Numbers) · Lecture 16: The Bourgain Projection Theorem, Part 3
Professional - Review a lower-level optionExistence Theorems in Calculus: Free Course
Focus: Intermediate value theorem · Extreme value theorem
Intermediate
Compare course focus, level and study time
| Course | Level | Focus | Study time |
|---|---|---|---|
| This course — Free MIT Course: Probabilistic Methods in Combinatorics | Professional | Large Bipartite Subgraph · Extremal Set Theory: Sperner's Theorem · Independent Sets and Turán's Theorem | 3h 36m of video; practice time is additional |
| Free MIT Course: Graph Theory and Additive Combinatorics | Professional | 1. A bridge between graph theory and additive combinatorics · 7. Szemerédi's graph regularity lemma II: triangle removal lemma · 13. Sparse regularity and the Green-Tao theorem | 33h 54m of video; practice time is additional |
| Free MIT Course: Projection Theory and Geometric Combinatorics | Professional | Lecture 14: The Bourgain Projection Theorem Part 1 (over the Real Numbers) · Lecture 16: The Bourgain Projection Theorem, Part 3 · Lecture 19: Random Walks on Finite Groups, Part 3 | 31h 32m of video; practice time is additional |
| Existence Theorems in Calculus: Free Course | Intermediate | Intermediate value theorem · Extreme value theorem · Mean value theorem | 1h 16m of video; practice time is additional |
Provider: MIT. Videos play from the MIT OpenCourseWare channel on YouTube.
Report a correction
Questions & discussion
Share a useful question or correction. Comments appear after moderation. Please avoid personal or sensitive information.