MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
4.0
(2)
27 learners
What you'll learn
This course includes
- 33.5 hours of video
- Certificate of completion
- Access on mobile and TV
Course content
1 modules • 26 lessons • 33.5 hours of video
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
26 lessons
• 33.5 hours
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
26 lessons
• 33.5 hours
- 1. A bridge between graph theory and additive combinatorics01:16:21
- 2. Forbidding a subgraph I: Mantel's theorem and Turán's theorem01:12:41
- 3. Forbidding a subgraph II: complete bipartite subgraph01:16:37
- 4. Forbidding a subgraph III: algebraic constructions01:19:45
- 5. Forbidding a subgraph IV: dependent random choice01:20:00
- 6. Szemerédi's graph regularity lemma I: statement and proof01:19:08
- 7. Szemerédi's graph regularity lemma II: triangle removal lemma01:14:51
- 8. Szemerédi's graph regularity lemma III: further applications01:21:21
- 9. Szemerédi's graph regularity lemma IV: induced removal lemma01:23:16
- 10. Szemerédi's graph regularity lemma V: hypergraph removal and spectral proof01:19:14
- 11. Pseudorandom graphs I: quasirandomness01:18:20
- 12. Pseudorandom graphs II: second eigenvalue01:19:48
- 13. Sparse regularity and the Green-Tao theorem01:19:06
- 14. Graph limits I: introduction01:17:09
- 15. Graph limits II: regularity and counting01:21:09
- 16. Graph limits III: compactness and applications01:19:52
- 17. Graph limits IV: inequalities between subgraph densities01:19:41
- 18. Roth's theorem I: Fourier analytic proof over finite field01:14:17
- 19. Roth's theorem II: Fourier analytic proof in the integers01:20:09
- 20. Roth's theorem III: polynomial method and arithmetic regularity01:20:51
- 21. Structure of set addition I: introduction to Freiman's theorem01:14:36
- 22. Structure of set addition II: groups of bounded exponent and modeling lemma01:19:57
- 23. Structure of set addition III: Bogolyubov's lemma and the geometry of numbers01:18:06
- 24. Structure of set addition IV: proof of Freiman's theorem01:19:31
- 25. Structure of set addition V: additive energy and Balog-Szemerédi-Gowers theorem01:14:46
- 26. Sum-product problem and incidence geometry01:14:14
