E-Learning

PLAY! - Mathematics at your fingertips

In a project funded by the Exploratory-Teaching-Space (ETS) of RWTH Aachen in 2013 several dynamic and interactive mathematics modules had been developed.

The idea is to provide an ultra-low-threshold approach to certain key concepts of mathematics, like continuity or eigenvalues, by using dynamic and touchable applets in which the students can change a given scenario with their fingers by adjusting points, buttons and rulers. Haptics combined with visual feedback gives an immediate path to understand mathematics.

Original Technical Realization

Major aspect of the project was to not only provide an easy access for the students but the modules must also be easy to program by the lecturers. The computer-algebra software Wolfram Mathematica provides dynamic and interactive programming with easy-to-use top-level command combined with very powerful visualization. Wolfram also provides a 'Computable Document Format' (CDF) with which Mathematica-Notebooks can be viewed and interacted with using a stand-alone CDF-Player. In 2013 this player was available as NPAPI plugin for all common web browsers, hence, CDF-documents were easily accessible online after downloading a plugin. The interactive programs were executed on the local machine allowing a low-latency, highly responsive interaction with the applet. Unfortunately, NPAPI plugin are being deprecated since 2015 and the CDF-plugin is not available anymore.

Current Technical Realization

While it is still possible to download the CDF-files and view them with the CDF-player, this requires to install a 1.4GB program which is not exactly low-threshold. Wolfram advocates to use the Wolfram Cloud which provides full access to the tools of Mathematica online after a free registration. However, storing, up- and download of files requires a paid plan.

Compatibility of the old CDF-files is not straight-forward and the files are being converted gradually to be published in the Wolfram Cloud. Those published files are accessible by everyone online without cost or registration. Major disadvantage is the very high latency of the cloud which makes many interactive material much less fun.

Available Modules

Note: Several applets are only available in German language. If you have questions, please contact Manuel Torrilhon

Analysis

  • PLAY Complex Plane ! - Complex Numbers and Gaussian Plane (link in Wolfram Cloud)
  • PLAY Continuity ! - Continuous and Discontinuous Functions (download as cdf)
  • PLAY Fixpoint-Iteration ! - Fixpoints und Fixpoint-Iteration (download as cdf)
  • PLAY Functions in Higher Dimensions ! - Planes and Parametrized Surfaces (link in Wolfram Cloud)

Linear Algebra

  • PLAY Vector-Norms ! - Vectors and their Different Norms (download as cdf)
  • PLAY Matrix-Norms ! - Matrices und their Different Norms (download as cdf)
  • PLAY Gram-Schmidt ! - Orthogonalisation of Vectors (download as cdf)
  • PLAY Eigenvectors ! - Eigenvalues and Eigenvectors of Matrices (download as cdf)
  • PLAY Singulärwertzerlegung ! - Singular-Value-Decomposition of Matrices (download as cdf)

Numerical Methods

  • PLAY Regression ! - Parameter Estimation and Fitting (download as cdf)
  • PLAY Interpolation ! - Approximation von Funktionen durch Polynom-Interpolation (link in Wolfram Cloud)
  • PLAY Quadrature ! - Numerical Integration of Functions (download as cdf)
  • PLAY Explicit Euler-Method ! - Solution of Ordinary Differential Equations (download as cdf)

Mechanik

  • PLAY Rigid Bodies ! - Interacting Bodies in Gravity (download as cdf)
  • PLAY Spring Pendulum ! - Resonance Phenomenon with a Damped Pendulum (download as cdf)
  • PLAY Beam ! - Shapes and Deformation of Beams (download as cdf)
  • PLAY Mohr's Circle ! - Visualization of Cauchy Stresses (link in Wolfram Cloud)


Further Development

If you know of a tool which allows to program such dynamic applets using high-level commands and competitive visualization and deployes them online such that they can be opened in a browser with near-zero delay and executed in an ultra-snappy way - without any additional costs - please do not hesitate to contact us.