Mathematics
Algebra, analysis, geometry, probability and modelling methods.
- StatisticsInference, hypothesis testing, bootstrap, and interval estimation.Coursework: double degree
- Linear algebraDecompositions, PCA, factor analysis, and the geometry of representation spaces.Coursework: double degree
- OptimizationGradient descent, regularisation, and principled hyperparameter tuning.
- ProbabilityProbabilistic models and stochastic processes applied to time series.Coursework: double degree
- Differential geometryPseudo-Riemannian manifolds and the exponential map, the core of my thesis.Coursework: double degree
- Abstract algebraGroups, rings, fields, extensions and Galois theory.Coursework: double degree
- Computational algebraPolynomial ideals, Gröbner bases and symbolic computation.Coursework: double degree
- Functional analysisNormed, Banach and Hilbert spaces, duality and operators.Coursework: double degree
- Calculus and analysisLimits, series, differential and integral calculus in one and several variables.Coursework: double degree
- Differential equationsOrdinary differential equations, systems and methods for studying their evolution.Coursework: double degree
- Multivariate statisticsDependencies between variables, dimensionality reduction and multivariate analysis.Coursework: double degree
- Statistical inferenceEstimation, confidence intervals and hypothesis testing.Coursework: double degree
- Numerical methodsError and stability, systems of equations, interpolation and numerical integration.Coursework: double degree
- Mathematical modellingDifference equations, population models, calculus of variations and reaction-diffusion.Coursework: double degree
- TopologyTopological spaces, continuity, compactness, fundamental groups and coverings.Coursework: double degree
- Complex analysisHolomorphic functions, complex integration and residues.Coursework: double degree



