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• Examining continuity/discontinuity of a function by using GeoGebra

  241-257

  Ljubica Dikovic

  Views:

  26

  The possibility to visualize the things with the help of today's dynamic software (GeoGebra being one of them), enables the students to see and explore mathematical relations and concepts that were difficult to be presented in the past, prior to the state-of-the-art technologies. In methodological sense, the contribution of this paper lies in the presentation of a set of visualizations designed to help students better understand and explore the basic calculus concepts such as continuity at a point, to examine discontinuity at a point, to display discontinuities and the relations between continuity and differentiability of single variable functions. In technical sense, this paper presents creative GeoGebra applets which offer new possibilities that could be of a vital importance for the future development of e-learning of College mathematics.

• Das Konzept des Analysisunterrichts von Professor Igor Kluvánek – einige Ergebnisse der qualitativen Forschung

  349-361

  Ján Gunčaga

  Views:

  30

  A renowned Slovak mathematician Professor Igor Kluvanek (1931-1993) during his affiliation with the University of Adelaide in Australia (1968-1990) has worked out a unique course of mathematical analysis for future high school teachers of mathematics. The course has been tested in its conceptual form but, as a whole, it still awaits its publication in the form of a monograph. Along these lines, our aim is to present the way he has introduced some key notions of differential calculus and to discuss its advantages. Central is the continuity of a function via which the limit and the derivative of a function at a point is defined.

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

  13-34

  Róbert Vajda

  Views:

  34

  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.

• Gaussian iteration of mean values and the existence of 2^(1/2)

  35-42

  Zoltán Daróczy

  Views:

  33

  We propose a method for proving the existence of √2 and finding its approximate value in secondary education.