Disclaimer + Overview

Over the last few years, I’ve been learning some elementary maths. I like writing up notes to help myself understand a new concept, or to help myself remember it later. Some of these notes are stand-alone summaries (e.g. these), others are just collections of useful facts (e.g. these). In both cases, there are almost certainly a lot of mistakes, both conceptual ones and typos.

The main principle I try to stick to with these notes is modularity, in the software design sense. For example, an explanation of the postulates of quantum physics should not itself contain an explanation of what a Hermitian operator is - it should outsource that a separate set of notes on linear algebra.

For me, at least, the lack of modular explanations makes learning much slower. Often I find an explanation of some subject confusing, but it’s usually because the thing being explained relies heavily on mathematical background that I don’t have (e.g. Fourier analysis). In these cases, I much prefer the “dependency” to be made explicit, and not implicitly crammed into the core narrative.