Topic Hub
Mathematics
Foundations of mathematics through to its modern frontiers — algebra, analysis, geometry, topology, probability, number theory — and the Fields Medal and Abel Prize that honour the field’s deepest contributions.
8 courses
Linear Algebra →
Vector spaces, linear maps, eigenvalues, inner products, spectral theorem, and applications across the sciences.
Differential Geometry →
Manifolds, tangent spaces, differential forms, Lie groups, Riemannian geometry, fibre bundles, and connections.
Numerical Methods →
Numerical linear algebra, root finding, ODE/PDE integration, spectral methods, optimisation, and scientific computing in practice.
Probability & Statistics →
Probability spaces, random variables, limit theorems, statistical inference, Bayesian methods, and stochastic processes.
History of Mathematics & Physics →
A unified history of mathematics and physics from antiquity through quantum mechanics — ideas, instruments, and people.
Biogeometry →
Geometric structures in biology: protein topology, membrane curvature, tissue mechanics, and biological pattern formation.
Music & Mathematics →
The mathematical structure of music: tuning systems, harmonic analysis, group theory of pitch, signal processing, and instrument physics.
Fields Medal & Abel Prize →
A history of mathematics through its highest honours: the Fields Medal (since 1936) and the Abel Prize (since 2003). Laureates, theorems, and the ideas that reshaped mathematics.