The Fourier series is a great tool for analyzing periodic functions. But what about functions that don’t repeat? We’ve seen that we can compute Fourier series for a non-periodic function defined on a finite interval, as long as we don’t care about its behavior beyond that interval …

The goal of this post is to answer a simple question: why are the following two definitions of the vector dot product in Euclidean space [1] equivalent for vectors \vec{a} and \vec{b}:

• Component definition: \vec{a}\cdot\vec{b}=\sum_{i=1}^{n}a_i b_i
• Geometric definition: \vec …

• "The Nuremberg Trial" by John Tusa and Ann Tusa - a detailed, meticulously researched account of the Nuremberg Trials. There's not a whole lot of side questing in this book - it's all focused on the trials themselves. Interesting read overall, though somewhat dry and academic.
• "Things Become Other Things: A Walking …

Recently I came upon Pluggy, a Python library for developing plugin systems. It was originally developed as part of the pytest project - known for its rich plugin ecosystem - and later extracted into a standalone library. You're supposed to reach out for Pluggy if you want to add a plugin system …

A few months ago I wrote about using LLM agents to help restructuring one of my Python projects. It's worth beginning by saying that the rewrite has been successful by all reasonable measures; I've been able to continue maintaining that project since then without an issue.

In this post, I …

The trigonometric Fourier series is a beautiful mathematical theory that shows how to decompose a periodic function into an infinite sum of sinusoids. These are my notes on the subject, with some examples and the connection to linear algebra in Hilbert space.

This is a brief and simple [1] explanation of how to adjust the standard sinusoid sin(x) to change its amplitude, frequency and phase shift. More precisely, given the general function: \[s(x)=A\cdot sin(w\cdot x+\theta)\] We’ll see how adjusting the parameters , and affect the …