Algebraic structures are of fundamental importance in mathematics and play an increasingly significant role in many application areas, including computer science and communication. This course introduces the main algebraic structures: groups, rings and fields. Fundamental concepts and properties of these structures are studied, both in the abstract and in relation to concrete families of structures. Furthermore, algebra is an excellent vehicle for training students in mathematical rigour, proofs, and problem solving.
To explain algebraic properties of some important families of groups: permutation groups, dihedral groups, matrix groups
To be able to classify groups up to isomorphism
To discuss algebraic properties of rings and fields (particularly finite fields), and to be able to classify rings and fields up to isomorphism
To be able to write down formal mathematical proofs