Teaching

For the thinking behind these pages, see How I teach.

Most of my teaching material started out as Jupyter notebooks: exercises for the Theoretical Neuroscience lecture at Goethe University Frankfurt, and a webinar I gave for the German Neuroscience Olympiad in 2020. Notebooks are great for a course, but they are a hassle to open just to look at one plot. So I have moved the parts that benefit most from playing around onto these pages, where they run directly in the browser.

Each page has one small simulation and a handful of sliders. The simulation keeps running while you move a slider, so you can watch what a parameter does rather than read about it. The text is meant to make sense on its own, but it is not a replacement for the book. The exercises come from Dayan and Abbott’s Theoretical Neuroscience, and the format is borrowed from Dirk Brockmann’s Complexity Explorables.

The leaky integrate-and-fire neuron

The simplest model of a spiking neuron: a live membrane trace, a dose of noise, and an f-I curve that fills in as you explore.
Principal component analysis

Four measurements per flower, boiled down to two: what PCA does to the iris data, and why standardising the variables matters.
Sampling and the discrete Fourier transform

What happens to a signal when you only measure it at discrete points: the Nyquist frequency, aliasing, leakage, and rebuilding a signal from a few frequencies.
Recurrent networks: from kernel to pattern

How local excitation and wider inhibition single out one spatial frequency, and how a ring of neurons wired that way turns random input into stripes.
Hebbian learning in the weight plane

Why plain Hebbian learning runs away, and two ways to stop it: hard bounds and Oja’s rule, drawn as trajectories in the plane of two synaptic weights.
Stochastic differential equations

How to add noise to a differential equation without angering the mathematicians: an ensemble of sample paths, the Euler–Maruyama scheme, and the odd rule that noise scales…
Eigenmodes of a recurrent network

Why a linear network is easier to read in the basis of its eigenvectors: every mode decays or grows at its own rate, and the slowest one is the one that lasts.
Two coupled neurons

Two spiking neurons wired to each other through synapses: why mutual inhibition makes them fire together, mutual excitation makes them alternate, and the synaptic time…
The Hodgkin–Huxley neuron

The model that explains where the spike comes from: a live membrane trace with its three gating variables, sliders for the sodium and potassium conductances, and an f-I…
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