The PhD degree usually involves a qualifying dissertation submitted during the second year of study, which is helpful training for writing the PhD thesis. There are opportunities for postgraduate research in Pure Mathematics, especially in the areas of algebra, analysis, combinatorics and graph theory. Training is provided through individual supervision of research, by advanced seminar courses and conferences, and by generic courses. We are internationally renowned for our world-leading research, which involves international and multidisciplinary collaboration. We have strong research groups in algebra, analysis, combinatorics, continuum mechanics, initiatives and infrastructures, mathematical biology, nonlinear systems, numerical analysis, statistics, and theoretical and computational optimization.