Students might be capable of write mathematical proofs and reason abstractly in exploring properties of groups and jewelry
use the division algorithm, euclidean algorithm, and modular arithmetic in computations and proofs about the integers
outline, construct examples of, and explore homes of agencies, inclusive of symmetry groups, permutation agencies and cyclic corporations
determine subgroups and component agencies of finite organizations, determine, use and apply homomorphisms among companies
define and assemble examples of rings, which include crucial domains and polynomial jewelry.
organizations: ancient background
definition of a group with a few examples
order of an detail of a set
subgroup, turbines and relations
unfastened companies, cyclic companies
group of permutations: cayley’s theorem on permutation businesses
cosets and lagrange’s theorem
simplicity, normalizers, direct products.
homomorphism: element agencies
outline and assemble examples of earrings
necessary domains and polynmial earrings.