6 points, SCA Band 2, 0.125 EFTSL
Undergraduate - Unit
Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.
- Second semester 2018 (On-campus)
Rings, fields, ideals, algebraic extension fields. Coding theory and cryptographic applications of finite fields. Gaussian integers, Hamilton's quaternions. Euclidean Algorithm in rings.
On completion of this unit students will be able to:
- Formulate abstract concepts in algebra;
- Use a variety of proof-techniques to prove mathematical results;
- Apply advanced concepts, algorithms and results in algebra and number theory
- Apply Diophantine equations, primitive roots, the Gaussian integers and the quaternions - the best known skew field;
- Be aware of the links between algebra and number theory;
- Work with the most commonly occurring rings and fields: integers, integers modulo n, rationals, reals and complex numbers, more general structures such as algebraic number fields, algebraic integers and finite fields;
- Perform calculations in the algebra of polynomials;
- Use the Euclidean algorithm in structures other than integers;
- Construct larger fields from smaller fields (field extensions);
- Apply field theory to coding and cryptography.
Examination (3 hours): 60% (Hurdle)
Continuous assessment: 40%
Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.
Three 1-hour lectures and one 2-hour support class per week
See also Unit timetable information