Induction. Basic count and count by inclusion-exclusion, recurrence (Catalan numbers) and generating functions. Sums, binomial numbers, asymptotic notation and estimates. Double Counting (Sperner's Theorem + Littlewood-Offord Problem). Graphs (basic notions, trees, cycles, bipartite graphs, pairings, Eulerian and Hamiltonian graphs, planar graphs). Introduction to the extreme theory of graphs (Mantel, Turán and the extreme number of the size 4 cycle). Introduction to Ramsey's theory (party with 6 people, higher quota for Ramsey numbers). Introduction to the discrete probability and the probabilistic method (lower quota for the Ramsey number).
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