Mathematical Sciences PhD / MPhil

The PhD in Mathematical Sciences at Liverpool provides a vibrant environment where postgraduate researchers engage in cutting-edge research across applied mathematics, pure mathematics, theoretical physics, and financial mathematics. With access to advanced resources and a collaborative community, you’ll contribute to pioneering work in areas like quantum theory, mathematical biology, and financial mathematics, while developing expertise that leads to impactful discoveries. The Mathematical Sciences PhD at Liverpool provides a comprehensive research experience, allowing you to work within one of the nine research groups across the department. The programme is designed to support you in developing both advanced mathematical techniques and critical research skills, with opportunities to contribute to pioneering research in areas like algebraic geometry, dynamical systems and mathematical biology. Liverpool offers a structured environment, combining independent research with professional development, including access to dedicated resources such as high-performance computing facilities and specialised workshops. You’ll benefit from the expertise of academic supervisors and collaborative research groups, enabling you to make significant contributions to international research efforts. Graduates leave with strong analytical skills and a deep understanding of mathematical theory, well-prepared for roles in academia or industry, as well as research-based positions in finance and technology.

Applications are welcome from students who have (or expect to obtain) a good Honours degree (first class or 2:1) or an equivalent qualification. Since a wide background in mathematics is required for success in research, students with a higher qualification (eg MSc, MMath, Cambridge Part III) will find they are better prepared for starting research. Those without this higher qualification may be required to follow some or all of the taught part of the Mathematical Sciences MSc.