Logic, Boolean algebra, number theory, relations, order, and the discrete structures behind computation.
Discrete mathematics studies finite and countable structures and the reasoning used to work with them. Start with the proof language in Mathematical Foundations. The logic sequence then moves from Boolean functions to formal semantics and natural deduction, followed by propositional and first-order automated reasoning. Number theory, relations and order, and graph theory develop other discrete structures.
Boolean identities, function representations, functional completeness, and simplification through algebra, Karnaugh maps, and Quine–McCluskey.
Syntax, models, entailment, natural deduction, quantifier rules, and the distinction between consistency and completeness.
Model checking, Horn clauses, forward and backward chaining, resolution refutation, and DPLL with explicit guarantees.
Substitution, unification, Skolemization, factoring, and a complete resolution proof, with search strategies and termination limits.
Divisibility, modular arithmetic, number representations, prime algorithms, congruences, and elementary cryptography.
Binary relations, closures, equivalence classes, partial orders, and searching in ordered arrays.
An explicit migration scaffold for Graph Theory, preserved from the archived Math-for-Computer-Science outline until the mathematical exposition is written and reviewed.