| Pure Mathematics | Algebra, analysis, geometry, topology, number theory, combinatorics, logic | Cambridge DPMMS, Oxford Math Institute, Imperial, Warwick, Edinburgh, UCL. |
| Applied Mathematics | PDEs, fluid mechanics, math biology, math physics, optimisation | Cambridge DAMTP, Oxford OCIAM, Imperial, Bristol, Manchester, Warwick. |
| Statistics | Bayesian, frequentist, high-dimensional, time series, spatial, survival | LSE Statistics, Oxford Stats, Cambridge Stats Lab, Imperial Stats, UCL. |
| Probability | Stochastic analysis, random matrices, percolation, SLE, queueing | Cambridge DPMMS, Oxford, Warwick, Bath, Bristol. |
| Statistical ML | Bayesian ML, kernel methods, GPs, deep learning theory | Cambridge MLG, UCL Gatsby, Imperial DSI, Manchester, Oxford OxCSML. |
| Mathematical Finance | Stochastic calculus, derivative pricing, risk modelling | Imperial, Oxford Mathematical & Computational Finance, LSE, Warwick. |
| Operational Research | Optimisation, simulation, decision theory, queueing | LSE OR, Lancaster Management Science, Edinburgh, Strathclyde, Warwick. |
| Data Science & Stats | Causal inference, ML for science, FAccT, statistical learning | Imperial DSI, Edinburgh Bayes Centre, Oxford OII, Cambridge MLG. |