# P.S.Pankov, B.J.Bayachorova INTERACTIVE VISUAL STUDYING OF MATHEMATICAL OBJECTS

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## P.S.Pankov, B.J.Bayachorova INTERACTIVE VISUAL STUDYING OF MATHEMATICAL OBJECTS

Definition of any mathematical object yields many consequences (the object itself has many properties). The common logical way to derive these properties is very complex while interactive searching them with visual computer presentation of results is rapid and interesting for students, involves human geometrical imagination and may assist to discover new theoretical results. Such virtual environment may also use ideas of computer games.

As the main example, we consider topological spaces. Using a computer to perform four-dimensional (4D-) spaces was proposed for the first time by S. Ulam (1960) but without any concrete way of presentation. We introduce some definitions (A.A.Borubaev and P.S.Pankov, 1998). Let G be a topological space, S be a rectangle (screen of display) and J be a set of (black on white screen) images of points of G (some closed subsets of S).

Definition 1. If for any g in G the union of all images of g is a neighborhood of g and does not contain the complement of any other (broader) neighborhood of g then J is said to be a natural presentation of G.

Definition 2. A computer program is said to be a kinematical presentation of a connected metric space G on the display if it gives the opportunity of continuous transition from the image of any point to one of any other point and the minimal time of such transition is equal to the distance between these points.

J.R. Weeks (1985) proposed such presentations for some 2D- and 3D- locally Euclidean (without singular points) topological spaces (Klein bottle etc.). Pankov P.S., Bayachorova B.J. (GraphiCon96) treated locally non-Euclidean (with singular points and lines) topological spaces including Riemann surfaces (RS), and, with A.V.Terehin (GraphiCon98) treated 4Dspaces.

Remark. Well-known presentations of RS as surfaces with self-crossings in Euclidean space do not fulfil Definition 1.

## Y.V. Suslov PRIMARY-FLIGHT TRAINING COMPUTERISED SYSTEM

The report contains the results of investigation concerning the application of computerised systems during the primary flight training.

It is emphasised that at present there is no integral and universal theory of primary flight training computerised systems elaboration, but the existing theoretical principles embrace only some of the aspects of this problem and don’t take into con-sideration the vital aims of the primary flight training.

Some recommendations are suggests on primary flight training computerised systems elaboration which are based on the results of computer flight and ATC controller’s simulators development.

The author has worked out and substatiated the methodological principles of the primary flight training computerised systems application during the initial stage of fly-ing higher schools and flying schools students’ training.

The report contains the experimental data concerning the YAK-18T computer simulator application and other primary flight training computerised systems compo-nent required for the primary flight training.

The author draws special attention to the advantages of computerised systems:

their positive effect on the flight safety and reduction of the primary flight training cost.

## Kuzin N.J., Imamutdinov I.F. DEVELOPMENT OF THE ELECTRONIC MANUAL "DESIGN AND CALCULATION OF STEEL FARMS OF COVERINGS OF INDUSTRIAL BUILDINGS" WITH USE OF WEB-TECHNOLOGIES

The modern information technologies allow considerably improving efficiency of training of the students. Use of electronic mail (E-mail), computer networks Intranet/Internet, electronic text-books, manuals and directories provide the remote access to various sources of knowledge to the students. One of the main tasks in distance education is to create and maintain information base that contains a course material in different forms and at different presentation levels.

The goal of this research is to develop the electronic manual "Design and calculation of steel farms of coverings of industrial buildings" for the students of the specialization 290300 "Industrial and civil construction".

The manual covers topics on design and calculation of the metal farms most used in construction. The manual presents the theoretical framework, design and calculation techniques, examples of computing parameters of farms.

The electronic manual is implemented in the form of HTML-files with an advanced user interface. The development has been done with the modern information technologies such as DHTML, CSS, JavaScript, VBScript. The recommended browser for viewing the manual is Internet Explorer 4.0/5.0 on a personal computer running MS Windows 95/98/NT.

The electronic manual is developed in two versions:

1. The networked version in a HTML-format intended for use on a campus intranet and on the Internet as an element of distance education.

2. The local version implemented in the form of a EXE-file and intended for use on any standalone machine running Internet Explorer 4.0/5.0. The transformation of the networked version to the EXE-file has been performed with the of the evaluation (free-of-charge) release of the HTML-compiler WebCompiler from the Oakley Data Services company.

Our approach of designing an electronic manual imposes the following advantages over a typical presentation of a course material on the Web in the from of HTML documents:

3. Operative explanatory references on the literature and SNIPs in a separate window.

4. The operative explanatory notes for the formulas and fragments of figures in a separate window.

5. Animation of the basic design and compute stages.

All files of the manual have been manually optimized in order to minimize the total size of the manual.