Propositional and first order logic, sets, relations, functions, partial orders, lattices, monoids, groups, graphs (connectivity, matching, coloring), counting, recurrence relations, generating functions, Boolean algebra.
Formal logic: propositions, predicates, quantifiers, logical connectives.
Collection of distinct objects.
Subset of Cartesian product representing connections.
Special relation where each input maps to exactly one output.
Partial orders (reflexive, antisymmetric, transitive). Lattices are partial orders with greatest lower bound and least upper bound.
Algebraic structure: semigroup with identity element.
Monoid with inverses for every element.
Graph connectivity: vertices reachable via paths.
Set of edges with no common vertices.
Assigning colors to vertices (or edges) so adjacent vertices have distinct colors.
Combinatorics: permutations, combinations, inclusion-exclusion, pigeonhole principle.
Equations defining sequence recursively.
Formal power series encoding sequence coefficients.