Differential Equations
- First-order ODEs, models and autonomy
- Second-order linear equations
- Fourier series and Laplace transforms
- Systems, phase plane and linearisation
In May 2026 I began a project to refamiliarise myself with some of the mathematics I haven’t touched since university. My intent is to get to grips with these subjects at the structural/conceptual level as much as the practical.
As such I’ve selected these courses to be interlocking, rigorous and free. You can assume that I strongly recommend any of the courses I’ve completed.
Lecture notes/problem sets are written by hand on a Remarkable2, then synced, OCR-indexed, compressed, and uploaded to Drive via cron job. From there they’re part of the regular content pipeline. Also, this has been a chance to get back to writing Python, so I’ve linked repos where relevant.
I’m using a (self-built) local LLM app to assist with these studies: every time I watch a lecture I paraphrase from my notes; the app then flags* any sloppiness or errors and helps me correct them. The key concepts are added to a browsable library once they’ve been explained properly.
*Since the content of these courses are very well defined, it’s relatively straightforward for an LLM to check mistakes with high accuracy.
Current courses
Completed courses
Intro to Algorithms
- Elementary data structures
- Sorting, graphs and dynamic programming
- Modelling computational problems
- Algorithm performance and analysis
Statistics & Probability
- Fundamentals of probability
- Random variables and distributions
- Conditioning and expectation
- Limit theorems
Linear Algebra
- Matrix operations and elimination
- Vector spaces and fundamental subspaces
- Orthogonality and matrix geometry
- Eigenvalues and eigenvectors
- Singular Value Decomposition
Learning from Data
- The theory of machine learning
- Vapnik–Chervonenkis generalisation
- Bias and variance
- Regularisation and validation
- Linear models and feature transforms