Mathematical structures
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), MAP2021
Objectives The objectives of this subject are for students to achieve an understanding of, and skill in, the processes of proof and in formal mathematical expression; develop skill in (abstract) algebraic manipulation; categorise examples using the abstract algebraic structures of equivalence relations, orders, semigroups, groups, rings, integral domains, fields, and interpret properties as those of such.
Synopsis 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
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