Teaching

Fundamental Mathematics in Engineering I

Differential equations from the ground up: first-order equations and the modelling they come from, second-order equations and their stability, Laplace transforms, and linear systems — eigenvalues, phase planes, and what happens when the system stops being linear. The course closes on complex analysis, which is where the spectral thinking behind much of the lab's research begins.

Interactive demonstrations

Coming soon.

Fundamental Mathematics in Engineering II

The sequel, and the step up in dimension: partial differential equations and the analytical machinery they demand. Where the first course asks how a system evolves in time, this one asks how it evolves in space and time at once — which is the setting every model in this lab eventually lives in.

Interactive demonstrations

• A shape that keeps its shape is an eigenvector — spring-chain modes
• The overtones you hear are the modes you see — string overtones, with sound

Variational Inference

A graduate course on approximate Bayesian inference: how to reason about a posterior you cannot compute, by replacing it with one you can and being precise about what that costs. Taught as a flipped classroom — a recorded lecture before class, and the in-person session spent on problems, labs and team projects rather than on transcription.

This is the course closest to what the lab actually does. Students who enjoy it tend to be the ones who enjoy the research.

Interactive demonstrations

• Which KL you minimise decides what you get wrong

Deep Generative Models

Normalizing flows, latent-variable models, and the generative machinery that the lab uses as measuring instruments rather than as products — an exact likelihood is a diagnostic before it is a loss function. Previously offered.