One of the most wonderful aspects of math is how deep we can get by studying seemingly trivial questions. Consider the roots of unity, where "unity" simply means the number 1.

Monte Carlo simulations (or methods) is the technique of applying randomness and the Law of large numbers to the solution of various scientific and engineering problems. One of its first documented uses was by Stanislaw Ulam and John von Neumann for nuclear weapon simulations after WWII [1].

In this post …

• "Wuthering Heights" by Emily Brontë - good writing, but the protagonists are quite something. There's barely a likable character in the whole story - they are all either crazy, evil, stupid or a combination of these. It's also remarkable to consider how small the world of some people in those times was …

Like many programmers, I find Alexis King's Parse, don't validate article fascinating, because it gives a name to an idiom that seems familiar and important - one I've observed and used in the past without naming it explicitly. This post is a review of the "Parse, don't validate" pattern applied to …

The following are my notes on discrete-time Fourier series (DTFS), as well as the discrete-time Fourier transform (DTFT). These topics serve as an important theoretical underpinning to the digital processing of signals by computers using the DFT (which will be covered in a future post).

For discrete-time signals, we use …

The other day, I found myself wondering how big 52! (52 factorial) is, and that led me to ponder how these could be estimated without a calculator or a computer.

It turns out there’s some fairly interesting math behind being able to estimate the size (number of digits) of …

This is part 8 in a series of posts on writing concurrent network servers. In this part, we'll switch to Go and see how it tackles the challenges described earlier in the series.

All posts in the series:

• Part 1 - Introduction
• Part 2 - Threads
• Part 3 - Event-driven
• Part 4 - libuv …

This is part 7 in a series of posts on writing concurrent network servers. In this part, we discuss how the challenges described in earlier parts are tackled in the Rust programming language.

All posts in the series:

• Part 1 - Introduction
• Part 2 - Threads
• Part 3 - Event-driven
• Part 4 - libuv …

In Physics simulations or game engines it’s sometimes useful to determine the speed with which two objects are approaching each other. This post will discuss the concept of closing speed, which is the normal component of the relative velocity of two objects.

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 …