97-XX MATHEMATICS EDUCATION
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In this paper we report on an application of computer algebra in which mathematical puzzles are generated of a type that had been widely used in mathematics contests by a large number of participants worldwide.
The algorithmic aspect of our work provides a method to compute rational solutions of single polynomial equations that are typically large with 10^2 ... 10^5 terms and that are heavily underdetermined.
It was possible to obtain this functionality by adding a number of new modules for a new type of splitting of equations to the existing package CRACK that is normally used to solve polynomial algebraic and differential systems of equations.
We present an efficient GPU-based method to generate virtual X-ray images from tetrahedral meshes which are
associated with attenuation values. In addition, a novel approach is proposed that performs the model deformation
on the GPU. The tetrahedral grids are derived from volumetric statistical shape and intensity models (SSIMs) and describe anatomical structures. Our research targets at reconstructing 3D anatomical shapes by comparing virtual X-ray images generated using our novel approach with clinical data while varying the shape and density of the SSIM in an optimization process. We assume that a deformed SSIM adequately represents an anatomy of interest when the similarity between the virtual and the clinical X-ray image is maximized. The OpenGL implementation presented here generates accurate (virtual) X-ray images at interactive rates, thus qualifying it for its use in the reconstruction process.
„Diskrete Mathematik, was ist das?“, ist eine typische Frage von Lehrern mit traditioneller Mathematikausbildung, denn dort kam und kommt diskrete Mathematik kaum vor. Die etwas Aufgeschlosseneren fragen: „Wenn (schon wieder) etwas Neues unterrichtet werden soll, was soll denn dann im Lehrplan gestrichen werden?“ Auf die zweite Frage wird hier nicht eingegangen. Das Ziel dieses Aufsatzes ist es, in diskrete Mathematik einzuführen, Interesse an diesem Fachgebiet zu wecken und dazu anzuregen, dieses auch im Schulunterricht (ein wenig) zu berücksichtigen. Die Schüler und Schülerinnen werden dafür dankbar sein – eine Erfahrung, die in vielen Unterrichtsreihen gemacht wurde.