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 the classical example of calculating the value of \pi by throwing darts. Estimating pi Suppose we take a square board and inscribe a quarter of a circle into it. We then proceed to throw darts at the…
"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 other people. And that's for members of the nobility, not some bumpkin on a remote farm. "The Pickled City: The Story of New York pickles" by Paul Van Ravenstein and Monique Mulder - yes, a book about…
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 finding educational examples of this pattern in the Rust standard library and other well-known projects. Without repeating the original article (please read it first!), here's the gist of it. Consider…
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. Relative velocity and its components Suppose we …
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 …
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