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Pure mathematics

Research Pure mathematics with The Open University.

The Pure Mathematics Group in the School of Mathematics and Statistics is highly respected and has world-renowned researchers in the areas of analysis and geometry, and combinatorics.

Analysis is the study of sets, functions and limiting processes; geometry is the study of shape, position and space. The Open University is currently home to the largest research group in complex analysis in the UK. Researchers in the group are particularly active in complex analysis, complex iteration theory, continued fraction theory, dynamical systems, geometric measure theory and toric topology.

Combinatorics is the mathematics of discrete structures, such as graphs, permutations or designs. Researchers in the group have particular interests in graph theory, permutation patterns, combinatorial designs and the theory of symmetric maps on surfaces.

Qualifications available:

PhD or MPhil


For detailed information on current fees visit Fees and funding.

Entry requirements:

Minimum 2:1 (or equivalent), ideally with a significant project component indicating aptitude for mathematical research

Potential research projects

Applicants are strongly encouraged to apply for one of the research projects listed on the School of Mathematics and Statistics’ PhD recruitment page. The themes listed below indicate general areas where research projects may be available.

Analysis and geometry

  • Complex dynamics: the structure of the escaping set and dimensions of Julia sets of transcendental entire functions
  • Complex analysis: the boundary behaviour of analytic and subharmonic functions
  • Continued fraction theory
  • Hyperbolic geometry in complex analysis
  • Fractal geometry: the structure of sets and measures in Euclidean spaces
  • Applied analysis: renormalization theory and nonlinear dynamical systems
  • Toric topology


  • Graph theory: well-quasi-ordering; degree-diameter problem and cages
  • Combinatorial designs, including their automorphisms and embeddings
  • Pattern avoiding permutations; enumeration and connections with graph theory
  • Theory of symmetric maps on surfaces

Further information

If you have an enquiry specific to this research area please contact:

Director of Research, School of Mathematics and Statistics
+44 (0)1908 655552

For general enquiries please contact the Research Degrees Team via the link under 'Your Questions' on the right of the page.