Rosalio G. Artes Jr.
Modern information technology is implemented in hardware, networks, and software, but many of its correctness guarantees are algebraic. Boolean algebras describe switching logic; monoids and semigroups describe sequential composition; finite fields and vector spaces support cryptography and error-correcting codes; and lattices model information ordering. This paper provides a concise account of these structures and proves elementary results that demonstrate how closure, associativity, distance, homomorphism, order, and inverses yield digital representation, reliable transmission, structure-preserving encoding, and public-key inversion.