Suggested preparation: Graduate-level analysis, algebra and mathematical maturity.
Optional preparation: Free MIT Course: Real Analysis and Mathematical Proofs.
About this course
Explore advanced connections between projection theory, incidence geometry, additive combinatorics and random walks. The emphasis is on mathematical arguments and research-level techniques, not introductory geometry.
Topics and lesson examples
- 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
- Lecture 21: Homogeneous Dynamics, Part 2
- Lecture 24: Sharp Projection Theorems, Part 3: Combining Different Scales
Course at a glance
| Provider | MIT |
|---|---|
| Platform | YouTube · MIT OpenCourseWare |
| Access | Free Video |
| Level | Professional — WikiFree study-level assessment |
| Language | English |
| Available lessons | 24 |
| Video duration | 31h 32m · self-paced |
| Details checked | 10 October 2026 |
Preparation and study approach
Suggested preparation: Graduate-level analysis, algebra and mathematical maturity.
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: Probabilistic Methods in Combinatorics
Focus: Large Bipartite Subgraph · Extremal Set Theory: Sperner's Theorem
Professional - 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
Compare course focus, level and study time
| Course | Level | Focus | Study time |
|---|---|---|---|
| This course — 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 |
| 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: 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: 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 |
Provider: MIT. Videos play from the MIT OpenCourseWare channel on YouTube.
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