Tag Archives: computation

Fifteen awesome cross-platform math apps

So much of my learning mathematics happened by tinkering around with mathematics software. Here are fifteen applications I think are really cool, with eleven of them being free. 1. SageMath Free: Yes Platforms: Windows, MacOS, Linux Website: https://www.sagemath.org/ Top on our list is Sage. Sage is a command line and Jupyter notebook based mathematics system […]

Calculation of an Orbital Integral

In the Arthur-Selberg trace formula and other formulas, one encounters so-called ‘orbital integrals’. These integrals might appear forbidding and abstract at first, but actually they are quite concrete objects. In this post we’ll look at an example that should make orbital integrals seem more friendly and approachable. Let $k = \mathbb{F}_q$ be a finite field […]

Graphing the Mandelbrot Set

A class of fractals known as Mandelbrot sets, named after Benoit Mandelbrot, have pervaded popular culture and are now controlling us. Well, perhaps not quite, but have you ever wondered how they are drawn? Here is an approximation of one: From now on, Mandelbrot set will refer to the following set: for any complex number […]