University of Liverpool

University of Liverpool

Mathematical Sciences

Research is structured around the following 9 clusters: Algebraic Geometry; Applied Probability, statistics and Operational Research; Dynamical Systems; Financial and Actuarial Mathematics; Mathematical Biology; Quantum Field Theory and Applications; Singularity Theory and its Applications; String Theory; Waves and Continuum Mechanics. The Department of Mathematical Sciences offers a wide range of opportunities for postgraduate research in four key areas: Applied Mathematics, Pure Mathematics, Theoretical Physics, and Financial and Actuarial Mathematics and Applied Probability.

Entry requirements

Good Honours and/or Master's degree in a relevant subject.

Course modules

Core modules: Maple-latex project; preliminary dissertation; main dissertation; optional modules: linear differential operators in mathematical physics; introduction to string theory; quantum field theory; mathematical biology; waves; mathematical modelling; introduction to modern particle theory; representation theory of finite groups; curves and singularities; elliptic curves; Galois theory; probability essentials for financial calculus; stochastic analysis and its applications; chaos and dynamical systems; Cartesian tensors and mathematical models of solids and viscous fluids; quantum mechanics; relativity; mathematical economics; population dynamics; number theory; group theory; combinatorics; differential geometry; analysis and number theory; applied stochastic models; linear statistical models; applied probability; mathematical risk theory; networks in theory and practice.

Sponsorship information

Some scholarships may be available for home and international students.


Qualification Study mode Start month Fee Course duration
PhD Full-time - 3 years
PhD Part-time - 6 years
MPhil Full-time - 2 years
MPhil Part-time - 4 years

Campus details

Campus name Town Postcode Region Main campus Campus Partner
City Centre Campus Liverpool L3 5PS North West

Get in touch

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Key information

Postgraduate Recruitment
Telephone number: 
0151 794 5927