Deriving Single-Element Reservoir Sampling
Introduction Reservoir sampling is a method of selecting a random subset from a collection of a priori unknown size. Here, we consider the problem of selecti...
Posts by Tag
Mathematics
Transformations of normals under parametric scalings
Introduction Consider a surface in \(\R^3\) defined parametrically by
Fourier Transforms
This post is inspired by a lecture series given by David Skinner in 2016. In particular, for further reading on Fourier transformations, see chapter 8 of the...
Superellipses
This post is inspired by Matt Parker’s “What is the area of a Squircle?” video.
Special Functions: Gamma, Beta, and Zeta
Gamma Function Let \(z \in \mathbb C\) and define, for \(\operatorname{Re}(z) > 0\),
Parametrisation and Integration over \(n\)-spheres
In this post, we begin by considering how we can parametrise points on a circle, and exploit this to perform a change of variables in 2D. Then, we perform th...
Fourier Series, Parseval’s Identity, and \(\zeta(2)\)
This post is inspired by a lecture series given by David Skinner in 2016. In particular, for further reading on Fourier series, see chapter 1 of the Mathemat...
Computing
Deriving Single-Element Reservoir Sampling
Introduction Reservoir sampling is a method of selecting a random subset from a collection of a priori unknown size. Here, we consider the problem of selecti...