All Topics

Set notation, membership, subsets, power sets, and set equality.

Union, intersection, complement, difference, and symmetric difference.

Cardinality, countable vs uncountable infinity, and Cantor's theorem.

Propositions, connectives, truth tables, and logical equivalence.

Quantifiers, predicates, bound variables, and logical inference.

Direct proof, contradiction, contrapositive, and mathematical induction.

Addition and multiplication principles, pigeonhole principle.

Ordered and unordered selections, with and without repetition.

Binary relations, properties: reflexive, symmetric, transitive, antisymmetric.

Equivalence classes, partitions, and the quotient set.

Posets, Hasse diagrams, lattices, and total orders.

Injections, surjections, bijections, and function composition.

Recursive definitions, solving recurrence relations, the Master theorem.

Vertices, edges, degree, paths, cycles, and graph isomorphism.

BFS, DFS, shortest paths, Euler and Hamilton paths.

Rooted trees, binary trees, tree traversals, spanning trees.