Submitted by IMAGINARY on
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 an event is possible or that its probability is within some range. We illustrate the effects of the inclusion of uncertainty in modeling by looking at simple cases of an optimal investment problem.
Submitted by IMAGINARY on
This snapshot compares two techniques of shuffling a deck of cards, asking how long it will take to shuffle the cards until a “well-mixed deck” is obtained. Surprisingly, the number of shuffles can be very different for very similar looking shuffling techniques.
Submitted by IMAGINARY on
The Dutch catalog for the exhibition “Pracht en kracht van wiskunde,” which toured Belgium and the Netherlands in 2022 and 2023, is available here.
This gallery contains additional information about the exhibition, posters in English and Dutch, and other materials.
Submitted by IMAGINARY on
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 this problem has been used in several other contexts.
Submitted by IMAGINARY on
This snapshot compares two techniques of shuffling a deck of cards, asking how long it will take to shuffle the cards until a “well-mixed deck” is obtained. Surprisingly, the number of shuffles can be very different for very similar looking shuffling techniques.
Submitted by IMAGINARY on
The goal of inverse problems is to find an unknown parameter based on noisy data. Such problems appear in a wide range of applications including geophysics, medicine, and chemistry. One method of solving them is known as the Bayesian approach. In this approach, the unknown parameter is modelled as a random variable to reflect its uncertain value. Bayes’ theorem is applied to update our knowledge given new information from noisy data.
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Can we always mathematically formalise our taste and preferences? We discuss how this has been done historically in the field of game theory, and how recent ideas from logic and computer science have brought an interesting twist to this beautiful theory.
Submitted by Bianca Violet on
This paper describes the weaving technique of a traditional Colombian hat called sombrero vueltiao and some of its patterns. The making of the hat–and weaving in general–involves interesting mathematical thoughts and concepts and offers many learning opportunities, for all of which we provide examples in this paper.
Submitted by IMAGINARY on
Topological complexity is a number that measures how hard it is to plan motions (for robots, say) in terms of a particular space associated to the kind of motion to be planned. This is a burgeoning subject within the wider area of Applied Algebraic Topology. Surprisingly, the same mathematics gives insight into the question of creating social choice functions, which may be viewed as algorithms for making decisions by artificial intelligences.
Submitted by IMAGINARY on
We present some examples of optimal transport problems and of applications to different sciences (logistics, economics, image processing, and a little bit of evolution equations) through the crazy story of an industrial dynasty regularly asking advice from an exotic mathematician.