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 I want to provide examples of some simple uses of Monte Carlo simulations. We'll start with

"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 (pre-Victorian England); whole lives spent within a tiny area, interacting with a handful of oth

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 Rust programming language (the original post uses Haskell). I was particularly interested in fin

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 square bracket notation to denote samples: x[n] is the n-th sample of sign

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 a factorial reasonably accurately. This post will start by stating how to do the estimate, and if you’re curious you can read o