As the days stretch on, my thoughts often wander back to the cherished moments spent at the Hicks Building at University of Sheffield, where everyone can unapologetically show the love of mathemati...

Let’s play a game with integer sequences. Observe the following sequence: [\begin{align} 1 11 21 1211 111221 312211 \vdots \end{align}] Can you tell the next number? ...

Motivation Recently, I came across an interesting application of the Lovász Local Lemma, a fundamental technique in the “probabilistic method” and a classic example of a non-constructive approach i...

Introduction There are, in general, two ways to construct things in mathematics. On the one hand, we can construct things explicitly, which tends to be difficult, if we don’t know exactly what the ...

Introduction In machine learning, cost functions play a crucial role in training and evaluating models. They quantify the discrepancy between the predicted values and the labels, guiding the model...