Teaching

Fundamental Mathematics in Engineering I

Differential equations from the ground up: first-order equations and the modelling they come from, second-order equations, resonance and stability, Laplace transforms, and linear systems — eigenvalues, phase planes, and what happens when the system stops being linear. The course closes on complex analysis: analytic functions, contour integration, and the residue calculus that turns hard real integrals into bookkeeping.

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 — the heat, wave, and Laplace equations, separation of variables, Fourier series and transforms, Sturm–Liouville theory, and boundary-value problems. Where the first course asks how a system evolves in time, this one asks how it evolves in space and time at once.

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. The evidence lower bound and the two directions of KL divergence, mean-field and amortized approximations, stochastic gradients and the reparameterization trick, and normalizing flows as the expressive family — with hands-on labs and a team project.

Interactive demonstrations

• Which KL you minimise decides what you get wrong

Deep Generative Models

Normalizing flows, variational autoencoders, generative adversarial networks, and diffusion models — the probabilistic foundations they share, maximum likelihood versus adversarial training, and what an exact likelihood buys that a sample cannot. Previously offered.