Mathematical NetBooks

Vladimir Batagelj and Matjaz Zaversnik
University of Ljubljana, FMF, Dept. of Mathematics
Jadranska 19, 1000 Ljubljana, Slovenia

Multimedia PCs widely opened the possibility to prepare and use notebooks containing dynamic elements (animation, video, sound, simulations, programmed actions, ...). Combined with the network they also lost their closeness -- their parts can be located at different places (computers), sometimes they are spread over the network and there is no clear boundary.
In the paper we discuss different technical possibilities that we have when creating such netbooks: HTML, use of (special) helper applications or plug-ins, support libraries written in Java, Javascript templates, transformers to VRML, service programs at servers, ... The emphasis is on the development of netbooks with mathematical contents. Our main goal is to provide a teacher with a collection of easy-to-use elements to build their own netbooks.
All the discussed possibilities are illustrated with examples.


With a multimedia personal computer, at the beginning of the nineties, the education finally got a computer suitable for its needs. Besides the computational power it offers also an integration of different media. Connected to the Internet it opened a vast and unexplored space of new possibilities. In this paper we shall discuss its impact to the presentation of mathematical subjects.

There are several possibilities to produce a (mathematical) notebook on a computer:
General tools: TeX, Word, Acrobat, Corel Draw, PowerPoint, ...;
Authoring programs: Asymetrix ToolBook, Macromedia Director, ...;
Special purpose programs: Mathcad, DERIVE, Cabri, Mathematica, Maple, ...;
These tools gave birth to desktop publishing and allowed to everyone to produce her/his own materials. The use of colors became cheap. Since the text stays in author's hands it is easy to adapt and to improve. The ease of multiplying the text by copying encourage the cooperation and interchange of materials.

The expansion of WWW after 1993 offered another possibility with its solutions (HTTP, HTML, servers, browsers, ...). Besides providing, by HTML, standard means for formatting hypertext and interactivity it also facilitates the availability and distribution of materials (documents, data, programs, multimedia), and communications among users (mail, conferences, chat, collaboration, ...). The WWW solutions, realized in HTML and extensions, offer several benefits in respect to the 'classical' tools and are becoming very popular among the authors of e-text materials.

Basic HTML and Mathematics

The characteristics of HTML are: The formatting is described in HTML by the use of tags - markup. The current version of HTML offers limited possibilities for a mathematical markup: we can write simple indexes and exponents and we can include special characters:
<font color=red size=5> <font face=symbol>&#242;</font> <i>x<sup>n</sup></i> d<i>x</i> = <i>x<sup>n+1</sup></i> / (<i>n+1</i>) &nbsp; &nbsp; &nbsp; <font face=symbol>&#216;</font>(p <font face=symbol>&#217;</font> q) <font face=symbol>&#219;</font> <font face=symbol>&#216;</font>p <font face=symbol>&#218;</font> <font face=symbol>&#216;</font>q </font>
produces (on Windows)
ò xn dx = xn+1 / (n+1)       Ø(p Ù q) Û Øp Ú Øq
To include complex mathematical expressions we can use figures (as in LaTeX2HTML) or solutions based on Java (see WebEQ). But, we can expect a regular solution in a near future (see MathML).

There exist programs to transform documents from 'classical' to web formats: LaTeX2HTML, HyperTex, W2CSS, PDFLaTeX.

HTML extensions

We can enhance and adapt the basic HTML to our needs using: Eventually, to support some special functions (for example: infos about conferences, dictionary, quiz base and collection of answers), we have to provide supporting programs at server side. These programs are mostly written in Perl or C. For some of these functions program packages were produced ( Trubar - catalog tools) that allow also to nonprogrammers to build server supported services.


A netbook usually consists of several units (pages) organized by a navigation structure. Typical navigation elements are represented by 'buttons' for movement (next, previous, up, detail), global view / jumps (contents, index), infos (author, copyright, help), interaction (password, simulation, quiz, test, notes, bookmarks), communication / mail (author, instructor, other students), display (picture, animation, video, sound). The new XML ( Extensible Markup Language) standard offers, with its linking elements, a possibility to build advanced (personalized) navigation structures.

Some nice examples of netbooks can be found on the Internet: MegaMath, Graph Theory, Euclid's Elements (based on The Geometry Applet), Introductory Statistics, HyperStat online, Statistics UCLA. Looking at these examples we can see that the range of means used by their authors spans from basic HTML to the use of programs written in Java and Javascript, and special server services.

Yes, hyperlinks and the use of multimedia allow us to produce fancier texts - often the materials found on the web are merely transformations of paper-text into a web form. But, the real difference is in the interactivity - ability of the netbook to interact with the user, to adapt to her/his needs.

Although the knowledge of programming is losing its importance in the use of computers, the old saying Most teachers are bad programmers, and most programmers are bad teachers is still valid also in new circumstances - and we have to add the artist to the group. There are some ways to bridge this gap. Professional production by a team of experts is reasonable for materials of broad use and is very expensive. The other possibility is the use of authoring tools by teachers ( WebTutor, HyperWave). Somewhere in between is a 'Lego' approach - to provide teachers with necessary skills and a large collection of building blocks (pictures, sounds, videos, applets, templates, ...) which they can combine in their own educational materials. For some examples of such blocks see: Quiz, Problem, Interactive Algebra, Geometry, Functions, Graph, Rules VR_Logo.

We expect that the 'Lego' approach will give in the following years a solid basis of blocks for the main mathematical subjects.


Because of limited space available for the printed version of this paper we were unable to give the URLs of underlined resources in the text - you will find them in the extended and in the HTML versions of this paper, available at