This page is under construction and is best viewed with Netscape 3.0 or higher.MathML consists of a number of XML tags which can be used to mark up an equation in terms of its presentation and also its semantics. MathML attempts to capture something of the meaning behind equations rather than concentrating entirely on how they are going to be formatted out on the screen. This is on the basis that mathematical equations and are meaningful to many applications without regard as to how they are rendered aurally or visually.
XML is closely related to HTML and assumes a very similar, but not identical syntax. One distinction is that in XML you cannot omit end tags. Furthermore, tags for elements which don't have any content are specially marked by a slash before the closing angle bracket.
MathML is a low-level format for describing mathematics as a basis for machine to machine communication. MathML is not intended for editing by hand, but is for handling by specialized authoring tools such as equation editors, or for export to and from other math packages.
MathML is intended to facilitate the use and re-use of mathematical and scientific content on the Web, and for other applications such as computer algebra systems, print typesetters, and voice synthesizers. MathML can be used to encode both mathematical notation, for high-quality visual display, and mathematical content, for more semantic applications like scientific software, or voice synthesis. MathML is a low-level format for describing mathematics as a basis for machine to machine communication. It will provide a much needed solution to including mathematical expressions in Web pages.
This page is under construction and is best viewed with Netscape 3.0 or higher.For those of you that may want to develop mathematical pages on the
Web that include mathematical expressions, graphic images, and movies here is
a very brief tutorial based on my limited experience on a Windows based PC using Matlab 
for the computations and graphics. I'm quite sure that Mathematica or Maple can also be used for this purpose.
At this time the HTML language does not provide for mathematical symbols, such as integral or summation signs, on Web pages. Although draft standards for mathematics have been proposed, neither of the dominant webrowsers, Netscape or Internet explorer, have adopted them. There are a couple of ways to overcome this shortcoming. One is to display mathematical symbols and expressions as graphic images.
Perhaps the most successful method of this type is provided by a program that converts LaTeX to HTML. This program was developed by Nikos Drakos at the University of Leeds. For further information on this program or to download the source visit the website: latex2html info page. We have this program running on our server, renamed to l2h, and can be run (by locals only) using telnet. Presuming that your latex file compiles without errors, you should copy your latex document, call it mymath.tex, to your pub_html directory on the server. Now telnet to the server and change directory to your pub_html directory. Issue the command:
If all goes well you will find that a new subdirectory, called mymath, has been created and contains the desired html documents and several *.gif files that are used to display the mathematics.
The program enables the display of mathematical expressions using graphical images, instead of text, by first converting the expression to a postscript file and then converting the postscript file to a gif file that is inserted in the page at the correct location and with the correct size. Unfortunately, the images are of generally low resolution and there are difficulties with alignment and sizing of the equations. Its main advantage is that no additional software installation is required of the browser (i.e. no plugin is needed).
Caution: If you have a large document with lots of math symbols, the download time for the resulting webpage may be quite lengthy.
Here is a sample:
For simplicity and reasonably good accuracy one can use Simpson's rule for adaptive quadrature. In this case we have
and the error formula is valid for p=4. The criterion for acceptance is
end of sample.
Look at the source code corresponding to the sample! Notice that the mathematics is displayed by reference to two images in gif format.
TTH: a TEX to HTML translatorTTH translates TEX, the predominant mark-up language for expressing mathematics, into a near equivalent in HTML. In this approach graphics files are not used for mathematical symbols/expressions and hence it produces more compact, faster viewing, web documents than other converters. TTH actually translates the equations, instead of converting them to images. For information on this approach check the web site for TTH.
Here is a sample produced by TTH:
It can be shown [1] from basic
electromagnetic theory that this electron produces a scattered field
at a distant point x whose Fourier spectral component a
scattered frequency ws is
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For comparison the same formula is displayed by using the latex2html program as follows:
Techexplorer-an IBM pluginThere is another approach whereby a LaTeX document can be viewed directly. There is a plug-in for Netscape and Internet explorer, development by IBM, called Techexplorer. Techexplorer comes in two flavors--an introductory version (free) and a professional version ($29.95 as of 9/30/99). This plug-in is known to work with Microsoft Windows 32 bit versions of the Netscape Navigator version 4. It may not work with pre-release (e.g., "beta" or "preview release") versions of the Netscape Navigator. Many of the features of this plug-in are also available when used with the Microsoft Internet Explorer 4.0. One major exception is the scripting interface where Netscape LiveConnect is used. This plug-in further requires Microsoft Windows 9x or Windows NT 4.0 with Service Pack 3 (or greater).
Linux comes to IBM techexplorer!
For the first time, the new Preview
version PR1 of techexplorer Hypermedia Browser 2.5--now available for
download--supports Linux . Other features include support for MathML
content tags and additional formatting abilities, such as the LaTeX picture
environment. Try it today.
techexplorer is a plug-in for Netscape Navigator and Microsoft Internet
Explorer, enabling the display of TeX, LaTeX, and MathML documents and
the publishing of interactive mathematical and scientific material on the
Web.
To learn more about Techexplorer and to ensure that you always have the newest version, please visit the official IBM Techexplorer web site.
Scientific NotebookA somewhat similar product, not a plug-in, that can be used to view and create LaTeX files on the Web is called Scientific Notebook . The following is a list of features that I lifted from the Scientific Notebook web site:
< img src="icons/mathpic.gif">When used as source code there results the display:
The following "movie" illustrates the convergence of Fourier series. This movie is actually an animated gif file that was constructed using Matlab to generate each frame. These frames are loaded, using the animation wizard feature of the program Gif Construction Set by Alchemy Mindworks, to form the following:
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To summarize, the process used to create graphically intensive mathematical Web pages consists in the following steps:
For the novice this may appear to be a daunting task. However, I assure you that it is not so difficult. The best way to learn this process is to "borrow" the source code from a Web page (view source in Netscape) that you like. Good luck!
MathML Related Software:
Other Related Software:
tth TeX to
HTML converter