The principal requirement for entry to the TSM-CDT is a first class Bachelor's or Master's degree in an appropriate subject within the physical sciences or engineering. The course is multidisciplinary in nature, so applicants from a wide range of backgrounds are encouraged to apply. However the theoretical nature of the course means that the study of mathematics to a high level is required. The list below gives the minimum mathematical pre-requisites for the course.

  • Complex algebra: roots of polynomials, de Moivre's theorem, hyperbolic functions.
  • Vector algebra: scalar, vector and triple products; basis vectors; vector geometry.
  • Matrix algebra: representation of simultaneous linear equations, matrix inversion, determinants, eigenproblems and diagonalisation.
  • Ordinary differential equations: solution of separable first-order and linear first-order equations; solution of linear second-order equations with constant coefficients.
  • Fourier analysis: Fourier series and transforms; Dirac delta function; convolution theorem.
  • Partial differential equations: solution of second-order equations by separation of variables; Fourier methods for applying boundary conditions.
  • Vector calculus: gradient, divergence, curl and Laplacian in Cartesians; line, surface and volume integrals' divergence and Stokes' theorems; spherical and cylindrical polar coordinates.