Mathematics + computer science = key digital technologies

On Wednesday, March 19, 2025, a teacher training course on the above-mentioned
topic will take place at the Institute of Mathematics at Clausthal University of Technology,
Erzstraße 1, from 9.30 am to 4.30 pm, in cooperation with the Competence Center for Teacher Training Braunschweig (KLBS)
, to which we cordially invite you. The cost of participation is 12.50 euros per
participant and will be charged via the KLBS.

Registration is possible at nlc.info
direct link: nlc.info/app/edb/event/46854

Program (subject to change):
The Mathematics and Computer Science Day will feature four presentations by experts
followed by a discussion:

Dr. Henning Behnke
Numerical integration
Numerical integration (quadrature) is the approximate calculation of certain single and multiple proper or improper integrals. Since there are many functions whose definite integral cannot be specified exactly in closed form, numerical integration is of particular importance. Among the many applications of numerical quadrature, the best known is the finite element method. In fact, numerical integration is one of the oldest disciplines of numerical mathematics and the literature dealing with it is correspondingly large. However, we will only deal with the better known methods that can be applied to larger classes of integrals. Some aspects that will be considered in more detail are the derivation of quadrature methods, error estimation, adaptive methods, suitable choice of grid points and simple example programs (Python) for illustration.

Prof. Dr. Andreas Potschka
How artificial neural networks learn
Artificial intelligence - few other terms are currently associated with so much hope for progress. This hope is based on breakthroughs in the fields of image and speech recognition, machine language translation and even protein folding (AlphaFold from Google DeepMind, 2024 Nobel Prize in Chemistry for Baker, Hassabis and Jumper). Even the 2024 Nobel Prize in Physics was awarded to Hopfield and Hinton for machine learning with artificial neural networks. In the lecture, we want to get to know the basics of training artificial neural networks.

Prof. Dr. Robert Bredereck
Elections from a computer science perspective
Elections and voting are an integral part of the democratic process and play an important role in the school community. Yet how often are elections and votes conducted in everyday school life without much consideration of the underlying information and the potential risks of manipulation? In this talk, we will look at modeling elections from a computer science perspective and discuss the various applications and goals for which different voting methods are suitable. We will also look at the computational problems that can arise when conducting elections and how these can be solved. In addition, we will discuss the possibilities of election manipulation and present ways to prevent it. We will also analyze different electoral systems and discuss which are fair under which conditions and answer the question of whether there can be a "best electoral system". Finally, we will present some online voting tools that can be used in practice. The aim of the presentation is to provide teachers with a more nuanced understanding of elections and voting and to enable them to make informed decisions when conducting elections and voting.

Prof. Dr. Rüdiger Ehlers
From Sudoku to the timetabling problem - Using SAT solvers to make it practically understandable what difficult computational problems are and how they can be solved today
Almost all of today's computer science applications only use algorithms that solve comparatively simple computational problems. At the same time, algorithms that solve problems that are demonstrably difficult to solve work in the background of some applications. Intuitively speaking, provably difficult means that all (known) algorithms for solving these problems either provide suboptimal or incorrect solutions for a few inputs of moderate size or take an impractically long time to calculate, up to computing times that can last for years. An example of such a demonstrably difficult optimization problem is the distribution of a company's deliveries to several delivery vehicles so that their routes are as short as possible in total. Although the practically relevant variants of this problem are provably difficult, the problem does not disappear simply because it is characterized as difficult. In practice, algorithms with known weaknesses are used for such problems. In this program item, we show ways of making it possible to understand what it means for a computational problem to be provably difficult. While in the research field of complexity theory this notion of difficulty is formalized and the difficulty (then called complexity) of many practical computational problems is characterized, in this program item the focus is on conveying the intuition of how a computational problem can be difficult at all and how to deal with such provably difficult computational problems in practice. The solving of Sudoku puzzles is used as the main example. These are also demonstrably difficult to solve (in the generalization beyond 9x9 fields). To solve these, tricks for inserting a few safe values can be combined with systematic guessing and trying out other values. In practice, the many tricks for using safe values in Sudokus ensure that often only a few guesses have to be made, which motivates why in practice Sudokus can often be solved quickly despite the proven difficulty of solving them. The basic ideas of solving Sudokus are then transferred to the world of Boolean formulas and form the algorithmic core of the so-called SAT solvers, in whose input language many practical search problems can be coded, and which also solve a provably difficult calculation problem, namely finding a satisfying assignment of a Boolean formula. Finally, it is shown how to try out the modeling and solving of such practical problems with the help of solvers with little effort.

Program: