The programme aims to offer knowledge and expertise for a career in the academic world, or to pursue a variety of other opportunities in which a strong mathematical background is important. Past students are on the staff of universities in the UK and abroad, and senior statisticians and managers in industry and business. Available research areas number theory functional analysis and spectral theory of ordinary and partial differential operators calculus of variations and partial differential equations numerical analysis theoretical and computational fluid dynamics operator algebras and non commutative geometry algebraic topology algebraic geometry combinatorics quantum field theory and statistical mechanics conformal field theory and vertex operator algebras image processing operational research time series analysis probability theory and statistics. Distinctive features Lively research environment, extensive seminar programme. Conference and workshop support, including annual Welsh Mathematics Colloquium. Optional participation in undergraduate teaching, including HEA accreditation. Colloquia are held regularly and each research group has a weekly research seminar. The School hosts and participates in frequent workshops organised by WIMSC research clusters, with which the research groups are associated. The many collaborative projects with groups in other institutions in the UK and abroad, bring a steady stream of distinguished visitors to the School.