MTH3150 - Algebra and number theory II - 2017

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:

1. Formulate abstract concepts in algebra;
2. Use a variety of proof-techniques to prove mathematical results;
3. Apply advanced concepts, algorithms and results in algebra and number theory
4. Apply Diophantine equations, primitive roots, the Gaussian integers and the quaternions - the best known skew field;
5. Be aware of the links between algebra and number theory;
6. 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;
7. Perform calculations in the algebra of polynomials;
8. Use the Euclidean algorithm in structures other than integers;
9. Construct larger fields from smaller fields (field extensions);
10. 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

Dr Heiko Dietrich

Applied mathematics

Mathematical statistics

Mathematics

Pure mathematics

MTH2121 or MTH3121