Probability calculation in the courtroom and non-linear optimization

On Wednesday, September 25, 2019, a teacher training course on the above 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 25 euros per participant and will be charged via the KLBS.

Registration is possible athttp://vedab.nibis.depossible. Direct link:

https://vedab.de/veranstaltungsdetails.php?vid=110166

Dr. Raj Spielmann, Gymnasium Kirchenfeld, Bern
The theory of probability in the courtroom

The theory of probability is omnipresent in the courtroom, because there is not always conclusive evidence. Whether expressed in figures or as "certainty", judges and jurors must then formulate their conviction of guilt or innocence on the basis of probabilities. A number of obvious miscarriages of justice point to typical errors that lie in the interpretation of numbers or the model used. Some of them, including the murder trial of professional football player O. J. Simpson and the trial of Sally Clark for double infanticide, will be analyzed here. The results of DNA analysis are becoming increasingly important. It can be proven both theoretically and practically that the data sets from the trace analysis of real crimes do not allow the clear identification of individuals. This fact corresponds to the classic birthday paradox and is therefore referred to as the birthday paradox in the database. This makes it clear that the solving of crimes through so-called cold hits should be viewed with skepticism. Furthermore, "racial profiling" - a preventive observation of ethnic or religious minorities in the fight against crime, which is also practiced in Germany and Switzerland - is criticized from the perspective of probability theory. One aim of the lecture is to bridge the gap between mathematics, biology and the humanities. By illuminating familiar basic terms and concepts of probability theory in a new context, they become more vivid. At the same time, it becomes clear that probability theory is also indispensable for lawyers and social scientists.

Dr. Daniel Scholz, Volkswagen AG
From non-linear optimization to training artificial neural networks: Examples and applications with taramath

Optimization is primarily concerned with how to find the minimum (or maximum) of a function. Depending on the properties of the function to be analyzed, different solution methods are used. The lecture will discuss some of these methods and illustrate them with examples. An artificial neural network for recognizing handwritten digits will be presented as a special application: Here, too, non-linear optimization is used to train a neural network using training data in such a way that digits can subsequently be recognized. All examples of the lecture are presented using the taramath JavaScript library, so that the solution methods can be applied and deepened independently afterwards.

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