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Prof Martin Anthony

This course is available on the BSc in Business Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Economics, BSc in Mathematics, Statistics, and Business and BSc in Statistics with Finance. This course is available with permission as an outside option to students on other programmes where regulations permit and to General Course students.

Students must have passed MA103 Introduction to Abstract Mathematics and, ideally, have taken MA211 Algebra and Number Theory. Students who have not taken MA211 may, in some cases, take the course with the lecturer's permission. (A small amount of additional reading on their part will be required).

The aim of the course is to continue the study of abstract algebraic structures and show how these structures can be used to solve concrete problems. There are three strands: Group actions; Rings, polynomials and fields; Applications, including coding and cryptography. Group actions; revision of permutation groups; orbits and stabilizers, the orbit-stabilizer theorem; applications to counting problems. Rings, polynomials and fields: revision of rings; quotient rings; polynomial rings and the Euclidean algorithm for polynomials; irreducible polynomials and factorisation of polynomials. fields; fields as quotients of polynomial rings; construction and properties of finite fields: Applications: Designs and orthogonal latin squares ; Error-correcting codes, including linear codes, cyclic codes and perfect codes; cryptography.

22 hours of lectures and 10 hours of classes in the LT.

Written answers to set problems will be expected on a weekly basis.

Lecture notes will be provided but additional reading is recommended.

Discrete Mathematics, N L Biggs, (specifically Chapters 20-24, together with some introductory material from earlier chapters).

Introduction to Algebra, Peter J Cameron (OUP 1988);

Rings, Fields and Groups: Introduction to Abstract Algebra, Reg Allenby (Butterworth-Heinemann, 2nd edition 1991).

Codes and Cryptography, D J A Welsh (Clarendon Press 1988)

Codes, N.L. Biggs (Springer, 2008).

Exam (100%, duration: 2 hours) in the summer exam period.