Counting arguments (pigeonhole principle, double counting, first moment method) and applications (density of 0-1
matrices, the Lovász-Stein theorem, systems of distinct representatives).
Set systems (intersecting families, chains and antichains, blocking sets and duality, designs).
The probabilistic method (linearity of expectation, second moment method, Lovász local lemma, Shannon’s entropy
function) and applications (graph coloring, k-SAT, clique covers, independent sets, Erdős-Ko-Rado theorem).