2024

The interface construct in the Go language is one of its most immediately visible features. Interfaces in Go are ubiquitous, but I am afraid that the best way to use them has not yet fully been explored. Moreover, in practice, Go interfaces seem to be used in ways that were not intended, and are not necessarily entirely beneficial, such as an implementation shortcut to the classic Handle/Body idiom that hides interchangeable implementations behind a common, well, interface.

Let $G$ be a finite group with $n$ elements, and $H$ a subgroup of $G$ with $m$ elements. Then $m$ is a divisor of $n$: for a finite group, the order of any subgroup divides the order of the group.

What methods are there to connect an external (USB) drive or memory stick to a Linux box most conveniently?

In my previous post on one-dimensional heat flow, I encountered sums of the form:

$$ \sum_{n=0}^\infty \frac{\pm 1}{2n+1} \exp \left( - (2n+1)^2 x \right) $$

A plot (involving the first 1000 terms) is shown below, and looks reasonable enough. Is this curve, which forms the limit of the series, a known function?

Imagine a rod that is initially at temperature $T_1$ and then brought into an environment with a lower temperature $T_0 < T_1$. How quickly does the body cool down? When will it have reached the environment’s temperature? What is the temperature profile throughout the rod, as a function of time?

This is essentially a worked homework set: a complete, step-by-step solution of the diffusion (or heat) equation in one dimension.