Mathematics
Advanced Combinatorics & Graph Theory
Part of Advanced Combinatorics & Graph Theory, level 8. About 60 hours of study across the topics below.
Extremal & Probabilistic Methods
- Extremal CombinatoricsTurán-type problems, Ramsey theory, additive combinatorics intro10–17 h
- Probabilistic Methodexistence via probability, Lovasz local lemma, applications10–17 h
- Algebraic Methodspolynomial method, Combinatorial Nullstellensatz10–17 h
Graph Theory Advanced
- Spectral Graph Theoryadjacency/Laplacian spectra, Cheeger inequalities, expanders10–17 h
- Random GraphsErdos-Renyi model, thresholds, phase transitions10–17 h
- Structural Graph Theorygraph minors, treewidth, perfect graphs10–17 h