Discrete Mathematics Study Materials

Propositions, logical connectives, truth tables, tautology, contradiction, and equivalences.

Predicates, quantifiers (universal, existential), logical arguments, and proof techniques.

Sets, subsets, operations (union, intersection, difference, complement), Venn diagrams, and power sets.

Types of relations, properties (reflexive, symmetric, transitive), equivalence relations, and partial orders.

Injective, surjective, bijective functions, composition, inverse, and pigeonhole principle.

Types of graphs, paths, cycles, trees, Euler and Hamiltonian paths, graph colouring.

Permutations, combinations, inclusion-exclusion principle, binomial theorem, and generating functions.

Divisibility, GCD, LCM, modular arithmetic, Fermat's little theorem, and RSA basics.

Solving linear recurrences, homogeneous and non-homogeneous recurrences, and Masters theorem.

Boolean lattice, duality principle, Boolean functions, and algebraic simplification.

Partially ordered sets, Hasse diagrams, lattices, and their properties.

DFA, NFA, regular expressions, finite state machines, and introduction to Turing machines.