Journal of Online Mathematics and its Applications
Interactive Mathematics on the Web: LiveMath
What is LiveMath?
Have you ever wished you could post interactive mathematics on the web but gave up the idea because you had no time to learn to program in Java? Then LiveMath may be just what you have dreamed about!
LiveMath is a relatively inexpensive computer algebra system that has evolved from the software products previously known as Theorist, MathView, and MathPlus. If any of these names sound familiar, it may be because until 1999 this software was marketed by Waterloo Maple Software, although for a number of years it saw little further development. Its present owner, Theorist Interactive, LLC, is dedicated to continuing to develop and enhance the product.
What is special about LiveMath is not that it can serve as a desktop symbolic manipulator and graphics processor -- every computer algebra system can do that. What makes LiveMath unique is that it is designed to function in a spreadsheet-like fashion, in which a change to a previously written "proposition" causes a cascade of immediate changes to ripple through the resulting "conclusions," thereby allowing the user to interact with the software in a way that is not possible with most other computer algebra systems. [Editor's note: This spreadsheet-like behavior is also available in Mathcad, a more general but more expensive system.] Although this, by itself, would still not be enough to make me interested in dabbling with yet another CAS, the truly unique thing about LiveMath is that its inherent interactivity can be placed on the web without any programming or other specialized skills, and with relatively little cost. Anyone who has ever written a basic web page can learn to create interactive mathematical notebooks with LiveMath, and make them available over the web!
The one hitch is that, in order to interact with a LiveMath notebook on the web, you must first install a free browser plug-in, which can be obtained from the LiveMath download site. After you install the correct plug-in for your operating system, you will be able to interact with the examples listed in the remainder of this review. Please do that now.
Editor's note, 11/04: For purposes of reading this review, you can skip the download step. In the 2.5 years since the review appeared, changes in the LiveMath product have rendered older LiveMath files (including Professor Spitznagel's examples) inoperable. You will still be able to get from this review a sense of how the software works, and you can get current information from the LiveMath site. DAS
Published May, 2002
© 2002 by Carl R. Spitznagel
[See the Editor's Note at the bottom of page 1 -- the examples on this page are no longer "live".]
As a first example, consider the Power Rule web page, which includes a simple LiveMath notebook designed to allow students to make a guided discovery of the formula for the derivative of the function f (x) = xn. In this web page you can change the exponent in the power function and immediately observe the derivative of the new function. When I use this web page with a class, I give the students a worksheet that provides guidance about the kind of experimentation I expect them to do, and that also suggests some values to try for n (positive constants, negative constants, zero, integers and non-integers, and finally non-constant values, such as x). The point of the exercise is to let students discover for themselves not only the form of the Power Rule, but also the fact that it works for all constant powers, but not for non-constant powers.
My parent web page also includes links to discovery learning notebooks for
For an example of the kind of worksheet that I use to guide the students in their interactive discovery process, you can look at a sample Product Rule worksheet. Of course, with any discovery activity, timing is extremely important. There is little point in having students "discover" something after it has already been discussed in class. Also, in certain cases you will need to select very carefully the functions, equations, or expressions that you will ask the students to work with, since LiveMath (or any other CAS) may simplify its results more than you might like, thereby making it difficult for students to make the desired discoveries.
Additional examples of web pages featuring interactive LiveMath notebooks can be found by clicking here. This web page includes
LiveMath on the Web
Once you have figured out how to use LiveMath to create an interactive notebook, posting the notebook on the web is straightforward if you have even rudimentary knowledge of HTML. If you are interested in seeing how easy it is, just go to one of the examples and view the HTML source. A single HTML statement is all that is needed to embed the notebook. In fact, LiveMath can generate this HTML line and can even write a simple web page for you, with the interactive notebook embedded. My own choice for creating interactive web pages for student use is to write most of the instructions in the ordinary HTML portion of the web page, where I have total control over the formatting, and then to embed a relatively short LiveMath notebook, trying whenever possible to limit the LiveMath portion of the web page so that it will fit on a computer screen without scrolling.
Although LiveMath can be used as a standalone CAS on your desktop or in a lab, it is my opinion that its best feature is the ability to embed interactive notebooks in web pages and to have the interactivity inherent in those notebooks accessible over the web at no cost to the user. The total cost to the creator of those notebooks is moderate, as LiveMath Maker -- the software used to create notebooks -- sells for $249 over the web (academic price), with an additional charge for e-mail or telephone support, if desired. The company even offers a free 30-day trial. And remember that the browser plug-in for web interaction is free, so viewers of these interactive pages incur no charge. Although the price for LiveMath Maker is substantially more than its former "bargain-basement" price, it is still well below the cost of using the new client-server systems announced recently by Mathematica and Maple.
Because LiveMath’s "click-and-drag" user interface may at first seem foreign to users of other computer algebra systems, there is an obvious need for documentation. Rather than providing a printed manual, the company maintains an on-line documentation system which, unfortunately, can be frustratingly slow, especially for those whose web access is via dial-up modem. The LiveMath site also provides some tutorial movies and animations to show the user how to get started with the software’s interface.Nonetheless, I have found myself frequently wishing for an updated printed manual. When LiveMath’s predecessor, MathView, was owned by Maple, there was a printed manual that was relatively complete. Since that time, LiveMath has undergone a number of changes, but the printed documentation has not been updated. (You can still download the original MathView manual in pdf format from the LiveMath site -- or, if you want individual chapters, go to the Ask Sally help page and scroll down to near the bottom of the page. A lot of this manual is still relevant.)
The default LiveMath startup screen includes an enormous, intimidating palette of no fewer than 84 icon-labeled buttons, a number of which cause still more choices to pop up. Fortunately, from my point of view, the keyboard and menus can be used to drive LiveMath, and the palette can be ignored or even closed. In future releases of LiveMath, I would like to see the palette reduced to a more manageable size.
LiveMath includes a number of "starter notebooks" that demonstrate some of the software’s potential. Although these notebooks do a great job of showcasing LiveMath’s capabilities, they unfortunately come without instructions for recreating them. And because LiveMath is menu/palette-driven rather than command-driven, it is often difficult to figure out what menu or palette clicks were used to create the notebooks.
In order to function on the web, a LiveMath notebook is embedded in a web page. Although the web page itself can, of course, be written to the author’s specifications, the author has only modest control over the appearance of the embedded LiveMath notebook. In particular, the LiveMath plug-in always causes a small ad banner to be displayed at the top of the notebook, which you have probably noticed if you have looked at any of the examples listed above. While I understand the company’s desire to draw attention to their product, I have frequently wished that I could make the advertising disappear. Also, while font faces, sizes, and colors can be controlled in a notebook, there are a number of other formatting aspects that cannot.
Ironically, the very thing that makes LiveMath so attractive -- the use of a free browser plug-in to support interaction over the web -- has been and may continue to be a source of potential complexities for authors of interactive LiveMath notebooks on the web. As an author, you would like your material to be viewable on a variety of computer systems -- and indeed the company provides free plug-ins for many systems. But maintaining the necessary family of plug-ins for all the browsers and operating systems that LiveMath can interact with is somewhat like shooting at a moving target. For instance, Microsoft's recent decision to discontinue support for Netscape-type plug-ins had the side effect that web pages with LiveMath content would not function in Internet Explorer 6, and so the LiveMath developers were sent scrambling to develop an ActiveX version of the plug-in for use with IE 6. When the ActiveX plug-in became available, it then became necessary for authors of web pages with LiveMath content to perform some maintenance tasks on all of those web pages, in order to allow them to be accessed by Internet Explorer 6.
Moreover, the continual updating of the LiveMath plug-ins for various browsers and operating systems causes LiveMath notebooks to have some small amount of platform dependence. As an example, if you view the LiveMath notebooks that accompany this review using Netscape and again using Internet Explorer 6, you will notice differences in the LiveMath header, as well as in the functionality of the backspace key.
In spite of these shortcomings, however, LiveMath offers something that should be of interest to many mathematicians -- the ability to create and post interactive mathematics on the web quickly and inexpensively, with absolutely no programming! LiveMath truly is the easy way to interactive mathematics on the web -- for the rest of us.