Since the time of Gutenberg, World Wide Web seems to be the greatest invention in publishing. We can publish on the WWW books, articles, galleries of paintings, and all this information can be linked in a form of an incredibly large hypertext encyclopedia. We can design web pages full of color, pictures, video, music and unusual spectacular effects. Only one thing seems to be a problem - publishing mathematics on the web. This problem is vital for many educators who are going to publish on the WWW their tutorials, textbooks and assignments in mathematics, physics or any other discipline using extensively mathematical notation. In this article, I am going to show how using Scientific Notebook 3.5 we can display mathematical concepts on the web pages.
According to the popular science fiction concept of parallel worlds, many worlds can exist in parallel at the same time. Each world represents Earth but each is determined by a slightly different course of certain events. For example, imagine how different our world would be if Hitler had never been born. Two products from TCI Software Research (now MacKichan Software, Inc.), Scientific Notebook (SNB) 3.5 and Scientific WorkPlace (SWP) 3.5, remind me of such a parallel world, and I will call it the TCI-web. In this article, I concentrate on SNB 3.5; however, most of the information also pertains to SWP 3.5.
On the TCI-web, web pages are saved as LaTeX files. Certain enhancements make LaTeX documents work in this new environment. For example, on the web we need a way to code various kinds of links and set bookmarks inside documents. Also, both SNB 3.5 and SWP 3.5 use the Maple computing kernel; thus, we need commands that extend LaTeX and show where Maple should compute and display a plot or perform some numerical or symbolic calculations. This modified version of LaTeX I will call the TCI-LaTeX.
We can develop a web site with TCI-LaTeX documents, link them, make a base of articles or reference library just as on an HTML-based web site. SNB 3.5 can serve as an editor of these web pages, a previewer of these pages, and an Internet browser. The TCI-web is not a replacement for the traditional web based on HTML pages. It exists in parallel. From TCI-LaTeX pages, we can link to the HTML pages and vice versa.
SNB 3.5 is a very good word processor for documents with mathematical formulae and various kinds of graphs. Editing formulae in SNB is very easy. With the large number of keyboard shortcuts, we can type a formula using a few keystrokes. Typing formulae this way is much more convenient than using the mouse to select formula components from the menus and toolbars. We can type them just as we type text.
The quality of formulae displayed in SNB 3.5 is much better than in most of the programs used to publish mathematics on the web. To display mathematics, SNB uses a standard Windows True Type Times New Roman font and a few other fonts provided with the software (tci1, tci2, tci3, tci4, tciuni) that contain all mathematical symbols. These fonts are installed on our computer with SNB. According to my observations, SNB contains a very comprehensive set of mathematical symbols. Printing in SNB goes through standard Windows printing routines.
Formulae in SNB 3.5 documents are an integral part of the text. We can search for any part of the formula and we can perform the same editing operations (search/replace, copy, paste, etc.) on the formulae as we can on body text.
With the Maple computing kernel, we can insert in an SNB 3.5 document a graph of a function. That graph will be replotted each time we load the document. We can also ask SNB 3.5 to make a snapshot of the graph and insert the picture in an appropriate place. This may be convenient if plotting the graph requires a lot of time or readers use only the SNB Viewer.
In SNB 3.5 we are not restricted to what is defined in the styles included with SNB. If we have designed a new style in which, let's say, a page has a light blue background and brown text, then we have to save this style on the web site with documents using this new style. While downloading a document from the web, SNB downloads also the style used with this page.
TCI-LaTeX pages cannot use a picture as a background or a background color that is not defined in locally existing styles. Tables should be regular (i.e., NxM without spanned cells). We cannot put multiple paragraphs in table cells or use a picture background for a table cell. These things are missing in TCI-web pages.
On the TCI-web, there is one thing worth remembering. If we have a page with many pictures, we can save it as a RAP file so that all pictures and text are saved together in one file. In this case, we do not have hundreds of pictures on a web site and site maintenance is much easier. Unfortunately, the style used for creating the page will not be wrapped together with the rest of the page elements unless it's in the same directory as the document.
SNB 3.5 accepts many more graphics formats than HTML-based web browsers. In HTML pages we use mostly GIF or JPG files. The list of graphics formats that can be embedded into TCI-LaTeX files is very large and includes most of the known bitmap formats. According to my observations, pictures of various formats are displayed and printed by SNB very well; however, transparent GIF pictures are not displayed as transparent. Although we can use various graphics formats on the web, we have to remember that the size of these files is very important for timely transmission across the Internet. This practical consideration limits the palette of file formats for the web to those most compressed, such as GIF or JPG files.
On the TCI-LaTeX pages we cannot use Java applets or other animated objects. It is a pity that although SNB 3.5 has the Maple kernel, it does not have animated graphs, one of the most attractive features of educational web pages.
SNB 3.5 can be used as an Internet browser on the web sites with TCI-LaTeX or LaTeX documents. It works perfectly with TCI-LaTeX documents. Loading documents of some other TeX formats may result in problems due to format or missing style sheets. In most situations, a document is loaded in SNB; however, some elements will be displayed incorrectly.
The most important difference between SNB 3.5 and other web browsers is that in SNB all consecutive pages are loaded in separate windows on top of the earlier pages, while in HTML browsers a new page always replaces the previous page in a browser. This feature is very convenient when we wish to return to a page that was displayed some time ago. We can easily switch between pages, compare facts or pictures, decide which page should be closed, etc.
While loading a TCI-LaTeX page, SNB 3.5 replots all graphs, unless they are graphics images. SNB documents should be saved as read-only documents; otherwise, hypertext links in the document will not work, as usually, on a single click. In read-write documents we can insert new or customize existing links (you can make the links work with CTRL+click). This means that most of the TCI-web documents should be read-only; however, always we can save a document on the local HD as a read-write file, edit it, perform some calculations, replot existing graphs with new parameters or add new graphs. Such documents are like a live textbook. We can experiment with them. Students may open an assignment from the TCI-web, save it as a read-write file, add solutions of problems and save it as a RAP file on the local network or e-mail the assignment to the tutor.
The SNB 3.5 Viewer is a separate, free application that can be used as a TCI-web browser or simply to display TCI-LaTeX files locally. In most cases, it works in the same manner as a full copy of SNB; however, there are some important differences.
The SNB 3.5 Viewer does not include an editor. This means that we cannot use it for editing or saving files. It does not have the Maple kernel; thus, graphs will be missing from documents loaded from the TCI-web. For this reason, it may be better to include a graph in the TCI-LaTeX file as a picture, or "snapshot", rather than a graph to be plotted. Read-only documents displayed in the SNB Viewer can be printed and all printouts, with the exception of missing graphs, have the same quality as regular SNB documents.
While loading files from remote web servers, the SNB 3.5 Viewer fails if the appropriate style is missing on the local computer or there are some foreign elements in the file format. In such cases, the document is not loaded at all.
The TCI-web does exist in the world where other formats of web pages exist and other ways of displaying mathematics on the web pages are used. It is important to know how SNB 3.5 cooperates with the rest of that world.
From TCI-LaTeX documents, we can link to HTML pages. When we click on such a link, SNB 3.5 passes that link to Netscape, Internet Explorer or any other Internet browser installed on our computer. This part of the communication works well. On the other hand, when we click on a link to an SNB document from an HTML page, the Internet browser loads that document in the temporary Internet files folder and opens that file with SNB. In this case, the file is saved locally. All relative links are broken and any pictures embedded in the file are missing. A simple way to integrate SNB documents with HTML web pages is described in article .
The interaction between SNB 3.5 and IBM techviewer is much worse. In most cases, IBM techviewer doesn't recognize TCI-LaTeX format and refuses to load the documents. More often, SNB 3.5 is able to open files in techviewer format; however, due to some differences in file formats, many elements of the documents are not displayed properly.
Java applets and MathView live mathematical graphs cannot be embedded into TCI-LaTeX documents. This is perhaps one of the most important drawbacks of the TCI-web. I am sure that SNB 3.5 should accept Java applets on its pages or a way should be developed to display Maple animation of functions on a TCI-web page. We also cannot use animated GIFs in TCI-web pages. SNB doesn't display them properly. If we desperately need an animation to illustrate a problem, we have to put link from the SNB document to an HTML page containing the animation. This is rather unnatural solution and not very convenient, but it works.
SNB 3.5 documents can be used on a web site in the same way as HTML files. Using them we can develop a complete educational web site with mathematical or technical documents, assignments, tests, tutorials, etc.
SNB 3.5 displays and prints mathematical formulae very well and it contains a very large library of mathematical symbols.
SNB 3.5 and SWP 3.5 contain the Maple computing kernel, making it possible for users of TCI-web site to read documents, perform calculations in the downloaded documents, plot graphs, experiment and explore a topic as much as possible.
SNB 3.5 can be used as an editor and browser of TCI-web pages and may collaborate with browsers of HTML web pages.
SNB 3.5 documents are the only ones in which we can search for a formula on the page.
The SNB 3.5 editor has a somewhat limited set of page design functions.
Animation of graphs is missing both in SNB 3.5 and SWP 3.5 documents.
Animated GIF files are not displayed in SNB 3.5 as animation.
TCI-LaTeX is partially incompatible with other TeX formats used for publishing mathematical documents on the web.
Upon developing an educational web site, establishing a mathematical or technical journal on the Internet, or creating an Internet library of mathematical documents, you have to decide whether you are going to use the HTML-based web or the TCI-web. Both ways have a lot of advantages and a few drawbacks.
The HTML-based web is very attractive. You can design very colorful and eye-catching pages with a lot of valuable Java applets or MathView live objects. On the WWW, you can find large resources of Java applets and MathView objects. You can include them in your pages (with permission of the author) or use them as a source of inspiration to develop your own live mathematical objects. Making Java applets requires proficiency in Java programming, and this may be a little difficult. Thus, if you choose to create an HTML-based site, you need a lot of experience in Java programming, editing LaTeX formulae, and embedding them into HTML web pages.
MathView offers a much easier way of creating mathematical live objects. Many of your students will find this task very enjoyable. You may expect that after teaching mathematics or physics with MathView for one or two years, your web site will be full of such examples.
For creation of HTML pages, you can use one of the many professional or shareware editors; however, all embedded objects must be developed separately.
For browsing and previewing HTML web pages, you need one of the standard Internet browsers and at least two plug-ins ( IBM techexplorer, MathView) for rendering mathematical formulae and MathView live objects. The valuable advantage of MathView objects is that they do not lose their functionality in the MathView Internet previewer.
On the TCI-web, you have a much easier situation. Editing TCI-LaTeX documents is extremely easy. You don't need to know LaTeX to put a formulae on the page. Editing links and bookmarks is also an easy task. Such web pages are on the whole live documents. You need to save them on a local HD, as a read-write files, to have the opportunity of recalculating each formula, adding your comments, supplementing document or plotting graphs.
Many authors have developed a very complete tutorials for many high school or university subjects. These can be found on the WWW or on the SNB installation disk. SNB resource library enclosed on the installation CD is a good encyclopedia of mathematical terms. All these files you can copy on to your web site and link with your own documents.
TCI-web and SNB 3.5 can significantly improve communication between the teacher and students. Since the time I started publishing my tutorials on my web server, half of my mail are students' works edited in SNB. Very often, they send me new or revised solutions of problems that were done during our classes. Especially some quiet, shy or slower thinking students prefer to use this way of communication. For my students a tutorial or lecture doesn't end when I am leaving the classroom. It continues as long as they have time and access to my web server.
One of the worse drawbacks of SNB 3.5 is lack of animated plots and of the opportunity of using animated GIF files.
In this article I mentioned about two other programs that can be used to publish mathematics on the Internet. here is short information about them.
Techexplorer can be obtained from IBM AlphaWorks: http://www.alphaworks.ibm.com/formula/techexplorer or from techexplorer web site: http://www.ics.raleigh.ibm.com/ics/techexp.htm.
You can find there also a tutorial how to use Techexplorer and a number of interesting examples.
MathView is an interactive computer program that performs numerical and symbolic operations, draws and animates graphs of functions in 2D and 3D. Students using MathView can experiment with mathematical concepts, explore various possibilities, visualize them on the screen using various kinds of graphing tools, finally they can animate graphs, rotate them, cover by various kinds of colors, etc.
Using MathView we can design a teaching example, in official terminology it is called a MathView notebook and embed it in a HTML page using EMBED tag. We can use on such web page all possible HTML design means (colors, graphics, various backgrounds, etc.). Such page can be previewed using any graphics Internet browser with MathView or MathView Internet plug-in.
On the Waterloo Maple web server there is established a very beautiful web site called CyberMath.com ( http://www.cybermath.com/) designated to MathView. We can find there a lot of information about MathView and many interesting examples.
World Wide Web Design Guide, by Stephen Wilson, Hayden Books, 1994.
MathML - working draft of 15 May 97, by W3C - the World Wide Web Consortium, 1997.
How to Integrate Scientific Notebook documents with HTML files on a WWW site, by Mirek Majewski, electronic publication, TCI Resource Center, Brooks & Cole Publishing, 1997.
Building a Web-based Education System, by Colin McCormack and David Jones, John Wiley, 1997.
Added 02/01/98; revised 03/15/00, 1/6/04
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