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Episodes


13. Sparse regularity and the Green-Tao theorem

16. Graph limits III: compactness and applications

11. Pseudorandom graphs I: quasirandomness

9. Szemerédi's graph regularity lemma IV: induced removal lemma

19. Roth's theorem II: Fourier analytic proof in the integers

2. Forbidding a subgraph I: Mantel's theorem and Turán's theorem

26. Sum-product problem and incidence geometry

10. Szemerédi's graph regularity lemma V: hypergraph removal and spectral proof

8. Szemerédi's graph regularity lemma III: further applications

17. Graph limits IV: inequalities between subgraph densities

3. Forbidding a subgraph II: complete bipartite subgraph

18. Roth's theorem I: Fourier analytic proof over finite field

7. Szemerédi's graph regularity lemma II: triangle removal lemma

5. Forbidding a subgraph IV: dependent random choice

24. Structure of set addition IV: proof of Freiman's theorem

20. Roth's theorem III: polynomial method and arithmetic regularity

23. Structure of set addition III: Bogolyubov's lemma and the geometry of numbers

15. Graph limits II: regularity and counting

1. Introduction, Course Organization of MIT 7.016 Introductory Biology, Fall 2018
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