MSc Mathematics (Research)

The University of Buckingham is:

• Home of the two-year degree, the University of Buckingham, based in the South East of England, is ranked 6th for Student Satisfaction in the UK (National Student Survey, 2020).

• We are proudly independent and not-for-profit, and offer courses in Allied Health, Business, Computing, Education, Humanities, Law, Medicine, Psychology and Security and Intelligence. We are one of the few universities in the UK that offer September and January start dates for almost all of our courses.

• Based in Buckingham on a riverside campus, we are only 20 minutes’ from Milton Keynes central station and a short drive from Bicester, Aylesbury, Banbury and Northampton. There is free parking on-site and we are within easy reach of London and Oxford.

• Our award-winning small class tutorials ensure every student is known by name and supported throughout their studies, including by dedicated personal tutors.

• As pioneers of the two-year degree, we offer a condensed version of the traditional three-year degree, meaning you can gain a full honours degree and complete your studies a whole year earlier. Alternatively, you can complete both your undergraduate and master’s degree with us in just three years: saving you time and money.

Research programmes can be full-time or part-time with starting dates in January, April, July and September.

This programme aims to engage energetic and motivated Mathematics students in innovative research in pure Mathematics and its application in Computer Science. The programme is suitable for students with a solid background in Mathematics or in a closely related discipline. This programme, in particular, is a stepping stone for students to join research institutes and universities as PhD students and researchers.

Some of our research projects will seek new directions towards neural networks and AI, and potentially towards industrial application. The significance of interdisciplinary research is emphasised in the UK’s Research and Development Roadmap, which includes innovative proposals for interactions between mathematical sciences, biomedical research, and the Computing industry.

The main research areas of interest include, but are not limited to:

Model theory is a branch of mathematical logic, and its applications in a wide range of subjects such as algebra, topological dynamics, combinatorics, and theoretical Computer Science. Specifically, the projects are focused on Fraïssé construction method, automorphism groups of countable homogeneous structures, structural Ramsey theory, asymptotic classes, ultraproducts, and infinite constraint satisfaction problems in theoretical Computer Science. Research proposals in a wider range of areas in mathematical logic, philosophy of Mathematics, pure Mathematics and theoretical Computer Science are also welcome. These include research areas such as formal methods, type theory, set theory, higher-order logics and fuzzy logics.

Applied Computational Topology and Geometry is a relatively recent and fast-growing field of mathematics that emerged from applying well-established theories in algebraic topology and geometry. Specific projects focus on applications of data-driven Machine Learning and Artificial Intelligence in the fields of computer vision, medical diagnostics, and multimedia security for image tampering and fake videos. These applications employ Topological Data Analysis (TDA) and its growing list of tools (Persistent Homology, Mapper, etc.) to infer relevant (topological) class discriminating features from high dimensional and complex data. Other projects involve the use of TDA for interpreting Deep Learning (DL) decisions and dealing with the problem of overfitting of DL models.