Sets, relations and functions: Basic set operations: Subsets, equality of sets, union of sets, intersection of sets, complement of a set, ordered pairs, cartesian product of sets. Relations: Equivalence relations, equivalence classes. Functions: Domain of a function, range, codomain, surjective functions, injective functions, bijective functions, composition of functions, inverse functions.
Elementary combinatorics: Permutations and combinations, elementary properties. Binomial coefficients: Properties of binomial coefficients, binomial theorem, counting nonnegative integer solutions of certain equations, Bertrand's postulate.
Principles of counting: Pigeonhole principle and applications. Inclusion-Exclusion principle and applications.
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