Mathematical structures
BS BT BN BB DT BC BP BDT
Dr John Arkinstall
3 points * First semester * 2 hours per week * Gippsland/Distance * Prerequisites: GAS1611 (and GAS1612 is desirable) * Prohibitions: Not available to students who have previously passed subject 7162 (offered pre-1992)
This subject introduces students to the formal mathematics of proof, through an algebraic study of abstract structure in various branches of mathematics. Fundamental material on sets, proof and logic. Relations, including equivalence relations, mappings and order relations. Binary operations and semigroups. Groups including subgroups, cyclic groups, cosets and Lagrange's theorem. Rings and fields, including finite fields and field extensions (quadratic). For the Gippsland class, a single two-hour class, a hybrid of lecture/tutorial, each week for fourteen weeks. For the distance class, five two-hour problem-solving and expository classes are held over the semester to supplement a full set of notes, with tutorial activities and exercises.
Assessment
Assignments: 40% * Examination: 60%
Prescribed texts
Fraleigh J B A first course in abstract algebra