Abstract:

At present time, it is necessary to use computer technology in preparation of mathematics teachers. The article covers three areas of this preparation, namely in the area of mathematical statistics, algebra and solving mathematical problems with graphic method.

The immediate access to imaging methods, understandable processes and interesting examples plays an important role in teaching statistics (not only for mathematics but also for other branches). On our department, we started to use software tool Mathematica. This program allows to use at least four essential resources that are needed in statistics for creating interactive models which are:
1) It includes high-quality random numbers generator along with many random variables.
2) It includes the most advanced statistics tools (functions and procedures).
3) It allows to easily create interactive models even for the Internet.
4) It contains a huge amount of data from many different disciplines.

The first part of the article discusses some interactive models thus created not only for the students but also for the needs of others, for example, psychologists, sociologists, biologists, etc.

The second part of the article deals with LLL algorithm. The Gram-Schmidt process for orthonormalising a set of vectors is familiar to everyone who passed university mathematical studies. The orthonormal basis acquired this way is not usually “nice” although the original vectors had integer coordinates. The LLL algorithm in its common modification is able to produce certain reduced basis of integer lattice, in fact it is a integer approximation of Gram-Schmidt process. Many of its applications are quite interesting even in the ordinary school education (for example, finding rational approximations of real numbers, etc.).

In the third part of the article, graphic method of solving mathematical problems is reminded. Sometime, this method is being neglected but in some cases, it is quite easy and effective way of finding the solution. Especially in solving word problems about the movement (or simple optimizing word problems, too), it can be used not only as a supplement to classical solving process, but even completely separately.

Using some dynamic geometry software might be an advantage in the case, allowing the teacher or the student to change (in a certain level of interactivity) the input conditions and variables and then watch the changing output.

Keywords:

Statistics, Mathematica, Gram-Schmidt Orthogonalization, LLL Algorithm, Integer relation, graphic method, word problems, dynamic geometry.