eli.thegreenplace.net

Notes on the complex roots of unity

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

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 aft...

Summary of reading: July - September 2026

Re-reads:

Rusty thoughts on "Parse, don't validate"

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"...

Notes on discrete-time Fourier series and transform

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...

How big are factorials?

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.

Concurrent Servers: Part 8 - Go

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.

Concurrent Servers: Part 7 - Rust

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.

Relative velocity and closing speed

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.