ALGEBRA

On successful completion of this course, students will be able to: - define basic algebraic structures ( groupoids, semigroups, monoids, groups, rings, fields) - describe the algebra of sets, relations, mappings, natural numbers - describe semigroups with the proof of the Representation theorem (regular, idempotent, inverse) in detail - describe lattices (distributive, modular, with complements) - examine the structure of groups in detail and define subgroups, normal subgroups, quotient groups, cyclic groups, symmetric group with the proof of the Cayley theorem , direct product of groups and prove the Fundamental theorem on homomorphisms of groups - examine the structure of rings in detail and define subrings, ideals, quotient rings, direct product of rings and prove the Fundamental theorem on homomorphisms of rings - describe the ring of polynomials and polynomial functions and prove the basic theorems about the factorization of polynomials with applications