This information is for the 2020/21 session.
Teacher responsible
Prof Martin Anthony
Availability
This course is available on the BSc in Business Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Economics and BSc in Mathematics, Statistics and Business. This course is available with permission as an outside option to students on other programmes where regulations permit and to General Course students.
Pre-requisites
MA103 Introduction to Abstract Mathematics and MA211 Algebra and Number Theory.
Course content
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.
Teaching
Teaching will consist of 22 hours of lectures and 10 hours of classes, in the LT. Some of this might be delivered through a combination of virtual classes and lectures delivered as online videos
Formative coursework
Written answers to set problems will be expected on a weekly basis.
Indicative reading
Lecture notes will be provided. No additional reading is required, but the following books are recommended for further reading.
Introduction to Algebra, Peter J Cameron (OUP 2007);
Codes, N.L. Biggs (Springer, 2008).
Assessment
Exam (100%, duration: 2 hours) in the summer exam period.
Key facts
Department: Mathematics
Total students 2019/20: 12
Average class size 2019/20: 12
Capped 2019/20: No
Value: Half Unit
Personal development skills
Important information in response to COVID-19
Please note that during 2020/21 academic year some variation to teaching and learning activities may be required to respond to changes in public health advice and/or to account for the situation of students in attendance on campus and those studying online during the early part of the academic year. For assessment, this may involve changes to mode of delivery and/or the format or weighting of assessments. Changes will only be made if required and students will be notified about any changes to teaching or assessment plans at the earliest opportunity.