Mathematical Sciences

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. This PhD offers a wide range of research topics across several broad themes, with the flexibility for you to suggest your own topic within these areas. Research themes include: TheDepartment of Mathematical Sciencesfosters an active and collaborative research culture, with a diverse range of research groups focusing on both pure and applied mathematics. The department supports a dynamic learning environment where you can engage in cutting-edge research. Postgraduate researchers benefit f

IELTS: 6.5 overall, with no component below 5.5 TOEFL iBT: If you took a TOEFL test on or before 20 January 2026, you’ll need 88 overall, with minimum scores of listening 17, writing 17, reading 17 and speaking 19. If you took a TOEFL test from 21 January 2026 onwards, when a new scoring system was introduced, you’ll need 4.5 overall, with 4 or above in all components. TOEFL Home Edition not accepted. Pearson PTE Academic: 61 overall, with no component below 59 Your most recent IELTS score: Pre-sessional English course length 6.0 overall, with no component below 5.5: 6 weeks 5.5 overall, with no more than one component at 5.0: 10 weeks 5.5 overall, with no component below 5.0: 12 weeks 5.0 overall, with no component below 5.0: 20 weeks 5.0 overall, with no component below 4.5: 30 weeks 4.5 overall, with no more than one component at 4.0: 40 weeks

IELTS 6.5 overall, with no component below 5.5

International students: £5,238

UK students: £5,238

UK/Home: £5,238

International: £5,238

Year round

Rolling admissions - check project listing

• Liverpool, United Kingdom