A highly informative and interesting site
If this column is vaguely reminiscent of my last column and seems a bit like shameless pandering to Wolfram Research, well…it is! Whether finding a site on my own or being pointed in that direction by others, upon see-ing something that is not only informative, non-trivial and interesting, but also easy-to-grasp, colorful and fun, there is a compulsion to share with colleagues.
The Wolfram Demonstrations Project (http://demonstrations.wolfram.com/) met and exceeded most of the above quali-fications, as it simplifies some of the more complex features of many areas of mathematics and graphics. The site bills itself as “An open resource of interactive Mathematica visualizations…” andthat actually sells the product a bit short. Yes, the demos are interactive slider-driven graphics, but there is more to it than that. These visualizations are only the starting point, as each graphic is supplemented with information on the underlying mathematics (or chemistry or engineering or law or economics or… well, you get the picture!). In addition, there is information on related demos by the same author, details of the process and background material, links to sites with related material, and instructions on how to cite the demo. Further material may be found to the right of every interactive graphic in ‘Related Topics’ and ‘Some Related Demonstrations’ boxes. Thus, there is not only support for the learning experience but an inducement to follow the links and learn even more.
The home page is adequately arranged; it not only has enough teasers to cover most of the subject matter, but a brief menu bar to quickly get you where you want to go. The ‘Topics’ choice is highly recommended to the first-time user, as it allows you to easily drill down thru the subtopics to any particular demo. The most recently added demos may be accessed from the ‘Latest’ tab, although I’m not quite sure what this adds, i.e., why not just add the demo to its appropriate area and skip the redundant section? The ‘Random’ tab may serve two functions: recreational, for those who just need the entertainment, and instructional for those who can find new and exciting subject matter. ‘About’ tells us that these wonderful demo graphics are created with brief snippets of Mathematica code and run freely on Windows, Mac, Linux or Unix. In addition, a Mathematica player is available (for free!) that allows playing the demos without having the actual program on your machine.
For the terminally curious, a FAQ tab provides background information on why the site was developed (ostensibly educational, but it’s also a great promotional tool), how new demos can be developed and modified, and how to find demos on particular topics. The extensive questions on how to use these tools seem almost superfluous, as they are so intuitive that even your editor could answer most of them after a few minutes working at the site. I also found it humorous that these devices could be counted as an academic publication (or so says the site!). This tab does clarify two very important points: 1) The user does not actually have to download anything to see a demo work, since there are Web previews, and 2) you do not need to own a copy of Mathematica to download and play the visualizations, as the free player is available. I should warn readers that the Web preview moves awfully fast.
To whet the appetite, I’ll describe the Demo for one of my favorite series approximations topics: ‘Accuracy.’ The graphic shows how the approximation for sinc(x) changes as the range of the function and number of terms in the approximation changes. Even at Web preview speed, we can see accuracy increasing as both changeable factors increase. Below the graph-ic, we get some mathematical motivation for using approxima-tions followed by more details of their uses in physics, other examples and related links. To the right, is the box listing similar demos, such as Taylor Series and Taylor Polynomials.
This is basically a new slant on supplementary mathematics instruction. Try it, you might even like it.
John Wass is a statistician based in Chicago, IL. He may be reached at editor@ScientificComputing.com.