Our MINT-EC Math-Talent-School 2023

Prime numbers are the basic building blocks of the integers. Everyone knows them, they have applications everywhere: from gears to fractions to encryption – and they still raise many questions. Currently, the best-known applications of prime numbers are in cryptography. Many have heard of RSA, but what about Diffie-Hellman or ElGamal? How exactly does something like that work? How secure is it?

In this project we will look at many properties of prime numbers, starting with finding them in the first place. The normal methods don't work anymore if we want to have prime numbers with 100 or even 1000 digits. This then also goes hand-in-hand with the question of how many prime numbers are there, or how rare are they?

The aim is, depending on the interest, to investigate these and other questions practically, if necessary up to »complete cryptosystems« and attacks on them.

The group is supervised by Prof. Dr. Claus Fieker and Prof. Dr. Max Horn from the Department of Mathematics (AG Algebraic Geometry) at the University of Kaiserslautern-Landau.

Body fat percentage is a good first indicator to assess your health. However, not only too high a body fat percentage can have health consequences, but also too low a percentage. Accordingly, it is of interest for everyone to know their body fat percentage. But can I determine my body fat percentage at home without a special body fat scale, just by using a measuring tape?
 

Linear Regression Using the Programming Language R

In this project we will learn the answers to these questions from a theoretical point of view. After first insights into the theory of linear regression, you will attend a programming course in R, a language that is especially popular in statistics. This programming course is suitable for both beginners and more experienced programmers. Afterwards, you will be able to apply the methods you have learned to a data set in R.

The group is supervised by Christian Gib from the Department of Mathematics at the University of Kaiserslautern-Landau.

Are you wondering where a Start-Up should position its headquarters, where a large supermarket chain should open its next branch or where the best place to station a rescue helicopter is?

All these questions have something in common:

1. they are looking for one or more locations from which all customers can be reached as quickly as possible.
2. they are relevant, topical and their answers must be very well thought out.
3. they can be answered with mathematical location planning.

In this project we learn how to transform such questions into a mathematical model, solve them and visualise them. The students will also take part in a Python programming course and receive an introduction to the Gurobi software. 

The group is supervised by Dr Florentine Kämmerer, Nils Hausbrandt and Kathrin Prinz from the Department of Mathematics (AG Optimisation) at the University of Kaiserslautern-Landau.

In 2019, Google solved a mathematical problem with a quantum computer in a few minutes, for which it was previously assumed to take several thousand years. This triggered a hype from which quantum researchers are still profiting today: Billions of dollars are invested in researching and promoting these machines.
 

So How Much Potential Is There in These Machines?

This project is about testing the capabilities of quantum computers. The team will work on formulating known problems suitable for the machine and then test them against conventional algorithms. The goal is to see how far we can get with the current hardware and, if necessary, »help« the quantum computer with correction algorithms. 

The group is supervised by our colleague Dominic Leib from the division »Optimisation« at Fraunhofer ITWM.

Nonwovens are structures made of fibres/ threads that have been joined together to form a fibre layer. Nonwovens have many applications, for example as filters in hoovers, as insulation material or in the medical field, where they are used, for example, as wound dressings. 

To produce such nonwovens, silica gel is first made malleable and pressed through nozzles. This creates threads that are laid down on a base. A special movement of the backing then creates a nonwoven fabric. After production, the fabric is cut to size and can then be further processed into a wound dressing. The quality of the fabric depends on the uniformity, the number of threads.

In this project, the participants calculate the optimal movement of the pad in order to produce the highest quality fleece possible.

The group is supervised by our colleague Cymoen O'Reilly from the department »Transport Processes« at the Fraunhofer ITWM.

Since Corona at the latest, infectious diseases and their spread have become the focus of public attention. Mathematical models and their simulation can help to predict the course of an epidemic based on a variety of factors and to design and test control measures on the computer.

Zombies and Difference Equations

The factors to be considered are manifold. Decisive for the spread of a disease are, for example, the rate of spread, external factors and possible intervention actions.

In our project we will learn some mathematical tools and model a zombie pandemic using difference equations. 

The group is supervised by Prof. Dr. Christina Surulescu from the Department of Mathematics (AG Biomathematik) at the University of Kaiserslautern-Landau.