Overview
Offerings
Requisites
Contacts
Chief Examiner(s)
Unit Coordinator(s)
Learning outcomes
Formulate abstract concepts in algebra;
Use a variety of proof-techniques to prove mathematical results;
Work with the most commonly occurring rings and fields: integers, integers modulo n, matrix rings, rationals, real and complex numbers, more general structures such as number fields and algebraic extension fields, splitting fields, algebraic integers and finite fields;
Demonstrate understanding of different types of rings, such as integral domains, principal ideal domains, unique factorisation domains, Euclidean domains, fields, skew-fields; amongst these are the Gaussian integers and the quaternions - the best-known skew field;
Demonstrate understanding of the classification of finite fields;
Generalise known concepts over the integers to other domains, for example, use the Euclidean algorithm or factorisation algorithms in the algebra of polynomials;
Construct larger fields from smaller fields (field extensions and splitting fields);
Apply field theory to coding theory and understand the classification of cyclic codes.
Teaching approach
Assessment
Scheduled and non-scheduled teaching activities
Workload requirements
Learning resources
Other unit costs
Costs are indicative and subject to change.
Miscellaneous items required (Unit Course Reader, Printing, Stationery) - $120.
Availability in areas of study
Mathematical statistics
Mathematics
Pure mathematics