1,308 research outputs found

    Teaching University-Level Mathematics Using Mathematica

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    This paper considers the use of the computer algebra system Mathematica for teaching university-level mathematics subjects. Outlined are basic Mathematica concepts, connected with different mathematics areas: algebra, linear algebra, geometry, calculus and analysis, complex functions, numerical analysis and scientific computing, probability and statistics. The course “Information technologies in mathematics”, which involves the use of Mathematica, is also presented - discussed are the syllabus, aims, approaches and outcomes

    Preconditioning and convergence in the right norm

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    The convergence of numerical approximations to the solutions of differential equations is a key aspect of Numerical Analysis and Scientific Computing. Iterative solution methods for the systems of linear(ised) equations which often result are also underpinned by analyses of convergence. In the function space setting, it is widely appreciated that there are appropriate ways in which to assess convergence and it is well-known that different norms are not equivalent. In the finite dimensional linear algebra setting, however, all norms are equivalent and little attention is often payed to the norms used. In this paper, we highlight this consideration in the context of preconditioning for minimum residual methods (MINRES and GMRES/GCR/ORTHOMIN) and argue that even in the linear algebra setting there is a ‘right’ norm in which to consider convergence: stopping an iteration which is rapidly converging in an irrelevant or highly scaled norm at some tolerance level may still give a poor answer

    AI Education Matters: Data Science and Machine Learning with Magic: The Gathering

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    In this column, we briefly describe a rich dataset with many opportunities for interesting data science and machine learning assignments and research projects, we take up a simple question, and we offer code illustrating use of the dataset in pursuit of answers to the question

    Mapping legume roots can determine best performing crops

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    Legume plants have a mutually beneficial relationship with bacteria. These beneficial bacteria live in nodules found on plant roots. Until recently there was no way to systematically measure the roots the nodules are found on and to place accurately the nodules on these roots. The research team created software and a method to measure multiple root parameters which were not available previously. This allows different plant varieties to be compared with precise measurements of the root structure in order to figure out which plants will grow better

    Comparing Methods for Interpolation to Improve Raster Digital Elevation Models

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    Digital elevation models (DEMs) are available as raster files at 100m, 30m, and 10m resolutions for the contiguous United States and are used in a variety of geographic analyses. Some projects may require a finer resolution. GIS software offers many options for interpolating data to higher resolutions. We compared ten interpolation methods using 10m sample data from the Ouachita Mountains in central Arkansas. We interpolated the 10m DEM to 5m, 2.5m, and 1m resolutions and compared the absolute mean difference (AMD) for each using surveyed control points. Overall, there was little difference in the accuracy between interpolation methods at the resolutions tested and minimal departure from the original 10m raster
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