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• CAS-aided visualization in LATEX documents for mathematical education

  1-18

  Masataka Kaneko

  Takayuki Abe

  Kenji Fukazawa

  Masayoshi Sekiguchi

  Yuuki Tadokoro

  Satoshi Yamashita

  Setsuo Takato

  Views:

  9

  We have been developing KETpic as a macro package of a CAS for drawing fine LATEX-pictures, and we use it efficiently in mathematical education. Printed materials for mathematics classes are prepared under several constraints, such as "without animation", "mass printings", "monochrome", and "without halftone shadings". Because of these constraints, visualization in mathematical education tends to be unsatisfactory. Taking full advantages of LATEX and CAS, KETpic enables us to provide teaching materials with figures which are effective for mathematical education. The effects are summarized as follows:
  (1) The plottings of KETpic are accurate due to CAS, and enable students to deduce mathematical laws.
  (2) KETpic can provide adequate pictures for students' various interest. For example, when some students who understand a matter try to modify it, KETpic can give them appropriate and experimental figures.
  (3) Even though CAS can draw 3D-figures beautifully and automatically, it is expensive for mass printings and the figures are sometimes not easy to understand. Oppositely, 3D-graphics by KETpic are monochrome, but are richly expressive.
  In this paper, we give various examples of LATEX-pictures which we drew by using KETpic. For instance, the picture which is used in order to explain the convergence theorem of Fourier series makes it easier for students to understand the idea that function series converge to another function. Also the picture of skeleton is endowed with clear perspective. KETpic gives us great potential for the teaching of combinatorial mathematics. Through these examples, we claim that KETpic should have great possibilities of rich mathematical expressions under the constraints above mentioned.

• WMI2: interactive mathematics on the web

  393-405

  Zoltán Kovács

  Views:

  2

  After 5 years of experiments and feedback we decided to continue the software development on WebMathematics Interactive, a web-based e-learning tool, rewriting it from scratch. The demonstration version of WebMathematics Interactive 2 (WMI2) has been shown to the expert audience on the CADGME conference. In this article we summarize the development goals and results.

• Interactive web portals in mathematics

  347-361

  Róbert Vajda

  Zoltán Kovács

  Views:

  6

  Many of the recent problems in higher education (less contact seminars, the heterogeneity and the increasing number of our students) call for new instructional methods. At University of Szeged we have developed a mathematical web portal which can offer a solution for such problems among the changing circumstances. This freely available, easy-to-use web-surface supports interactive mathematical problem-solving and student self assessment. Our computer program cooperates with a lot of free software (computer algebra systems, formula parsers, converters, word processors). WebMathematics Interactive has been available for the public since June 2002 on its web page http://wmi.math.u-szeged.hu.