An e-learning environment for elementary analysis: combining computer algebra, graphics and automated reasoning

Abstract

CreaComp is a project at the University of Linz, which aims at producing computer-supported interactive learning units for several mathematical topics at introductory university level. The units are available as Mathematica notebooks. For student experimentation we provide computational, graphical and reasoning tools as well. This paper focuses on the elementary analysis units. The computational and graphical tools of the CreaComp learning environment facilitate the exploration of new mathematical objects and their properties (e.g., boundedness, continuity, limits of real valued functions). Using the provided tools students should be able to collect empirical data systematically and come up with conjectures. A CreaComp component allows the formulation of precise conjectures and the investigatation of their validity. The Theorema system, which has been integrated into the CreaComp learning environment, provides full predicate logic with a user-friendly twodimensional syntax and a couple of automated reasoners that produce proofs in an easy-to-read and natural presentation. We demonstrate the learning situations and the provided tools through several examples.

A Collaboratively-Derived Research Agenda for E-assessment in Undergraduate Mathematics

“…Both contain proofs, but they look very different. Such variety is a significant challenge in general, although it is certainly possible to assess proof in particular constrained areas of mathematics using specially-designed tools (e.g., Gruttmann et al, 2008;Vajda, 2009;Vajda et al, 2009).…”