Suggested preparation: Combinatorics, probability and mathematical proof-writing.
Optional preparation: Free MIT Course: Discrete Applied Mathematics.
About this course
Explore the interplay between graph theory and additive combinatorics. Advanced lectures develop regularity methods, removal lemmas and arithmetic-structure results through detailed proofs.
Topics and lesson examples
- 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
- 19. Roth's theorem II: Fourier analytic proof in the integers
- 26. Sum-product problem and incidence geometry
Course at a glance
| Provider | MIT |
|---|---|
| Platform | YouTube · MIT OpenCourseWare |
| Access | Free Video |
| Level | Professional — WikiFree study-level assessment |
| Language | English |
| Available lessons | 26 |
| Video duration | 33h 54m · self-paced |
| Details checked | 10 October 2026 |
Preparation and study approach
Suggested preparation: Combinatorics, probability and mathematical 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
- Related learningFree MIT Course: Discrete Applied Mathematics
Focus: Lecture 16: Data Compression and Shannon’s Noiseless Coding Theorem · Lecture 18: Transmitting Information Reliably over a Noisy Channel & Shannon’s Noisy Coding Theorem
Intermediate - Related learningFree MIT Course: Discrete Mathematics for Computer Science
Focus: MIT Course: Discrete Mathematics for Computer Science
Intermediate - Related learningFree MIT Course: Probabilistic Methods in Combinatorics
Focus: Large Bipartite Subgraph · Extremal Set Theory: Sperner's Theorem
Professional
Compare course focus, level and study time
| Course | Level | Focus | Study time |
|---|---|---|---|
| This course — 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: Discrete Applied Mathematics | Intermediate | Lecture 16: Data Compression and Shannon’s Noiseless Coding Theorem · Lecture 18: Transmitting Information Reliably over a Noisy Channel & Shannon’s Noisy Coding Theorem · Lecture 19: Error-Correcting Codes—Hamming Codes | 24h 42m of video; practice time is additional |
| Free MIT Course: Discrete Mathematics for Computer Science | Intermediate | MIT Course: Discrete Mathematics for Computer Science | 31h 40m of video; practice time is additional |
| 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 |
Provider: MIT. Videos play from the MIT OpenCourseWare channel on YouTube.
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