In this snapshot of modern mathematics we describe some of the most prevalent waves and patterns that can arise in mathematical models and which are used to describe a number of biological, chemical, physical, and social ...

How can we fairly divide a necklace with various types of beads? We use this problem as a motivating example to explain how geometry naturally appears in solutions of non-geometric problems. The strategy we develop to solve ...

Uncertainty - as opposed to risk - is used to describe events to which we are not able to assign a probability due to lack of information. Instead of assigning a probability to an uncertain event, we only assume that such ...

Everyone loves a good game, but when the players can access the counterintuitive world of quantum mechanics, watch out!

Nowadays, there are different medical imaging techniques to collect data about the progression of Alzheimer's disease in a patient's brain. These data describe different phenomena which are still not understood from a ...

The geometry of lines is a fundamental part of mathematics and the way we interact with the physical world. Core concepts such as distance and angle, and the accompanying theory of trigonometry, have been studied since ...

In this snapshot, we introduce the study of slices of polytopes – geometric shapes with flat sides – and examine the area of these slices. This is connected to combinatorics and polynomials and is surprisingly complex, ...