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THE MATHWRIGHT LIBRARY NEWSLETTER, Aug 2003, VOL 5, #5
A publication of Bluejay Lispware
James E. White, Editor

The official publication of the New Mathwright Library and Café:

In this issue:

Featured this month: Vectors in the Plane

Interactive Web Books

Featured this Month: Vectors in the Plane

Vectors in the Plane by Mike Pepe (Seattle Central Community College) is an 8 page Mathwright Microworld that is a visual introduction to the basic algebra and geometry associated with plane vectors. You may use it to experiment with vector addition and subtraction, vector spans and coordinate systems. It also includes interactive demonstrations of the vector representation of a line and of vector projections.

 

Interactive Web Books

In our previous Newsletter, we described two new Interactive Web Books that are available as a demonstration of our new web technology in the MATH Cafe. Presently, we offer 7 Interactive Web Books at the Cafe. These are:

  1. Exploring Quadratic Functions (9 pages)
  2. Interactive Web Course: Discrete Mathematics and Computational Structures, Part 1 (21 pages)
  3. Interactive Web Course: Discrete Mathematics and Computational Structures, Part 2 (19 pages)
  4. Heron's Formula (10 pages)
  5. Dynamical Systems Primer (23 pages)
  6. Odds and Integrals (7 pages)
  7. Cardano (12 pages)

We would like to invite you to download the free MathwrightWeb Control (Version 2.10, May, 2003 or later, if you do not already have it) and view any of these free books in your browser. Library members may download and view them offline with Mathwright32 Reader whenever they like.

All of the Interactive Web Books in the Cafe tell their stories using page-by-page HTML Help. Most pages are dynamic interaction pages, where you experiment with the ideas of the story as it unfolds. They offer simulations, command lines, and sometimes their own built-in command languages, and range through topics in geometry, algebra, calculus, dynamical systems, set theory and logic. As you come to each page, push the Instructions Button to read (or print) the story, then roll up your sleeves and ... play!

The mathematical documentation for these stories was created fairly easily using Design Science MathPage™ technology with Microsoft Word 2000™ and Microsoft Help Compiler. And the mathematical interactions were created with Mathwright32 Author™. These books may be read in Microsoft Windows™ (95, 98, Me, 2000, or XP) using Internet Explorer Browser 5.0 or later. In order to read them, as we mentioned above, you should sure you have MathwrightWeb Version 2.10 (after May 12, 2003, or later).

It may appear that the interactions that one finds on the exploration pages of an Interactive Web Book are simply Java applets. While they behave like applets, they are different from them for several reasons. Perhaps the most important from the viewpoint of authorship and web design is that (while they run in Microsoft Java) they were not written in Java, but were created in a high level, object-oriented, mathematics scripting language called MathScript (which is written on top of LISP). Further the visual design was graphical "point-and-click" or "What you see is what you get." This combination, using our new Mathwright32 Author™ program, produces efficient Java code, but does not require any knowledge of Java itself. It is much simpler to write books using MathScript than with Java.

Another important difference is that each multi-page document is integrated into a coherent whole that "remembers" what happens on other pages (for example, students' answers to questions) and that generates appropriate material as the reader moves through the book. The engine that generates this content is (ultimately) LISP, which has long been the language of choice for artificial intelligence design. What this means, practically speaking, is that Interactive Web Books such as these can point the way to content-rich and versatile mathematical stories that move far beyond what it is possible to do in static text, or even in dedicated applets. For a simple example, please browse our "Discrete Mathematics and Computational Structures" Course.

One might also point to the range of resources available to these books, and to every Microworld that uses the MathwrightWeb Control. They may use a symbolic Expert System, computer algebra, sprite animation, 2D and OpenGL 3D graphics, command-line tools, spreadsheets, and special-purpose command languages to represent and manipulate such things as ring-theoretic objects (Cardano), or logical propositions and sets (Discrete Mathematics and Computational Structures). All of these are immediately available to the web book after a one-time download. Future visits to the book would require no further downloads of resources. An applet would, in principle, have to download these resources each time this book (or a similar book) was read. And of course, these books may be read off-line in the Mathwright32 Reader.

Another difference is this. An Interactive Web Book is a multi-page mathematically savvy interactive story that invites you to ask questions, and (usually) gives you answers. You read it with page-by-page HTML Help that provides sophisticated navigation, attractive and colorful mathematical formulas, charts, illustrations and text. It is a new medium, whose purpose is not simply to calculate, but to tell mathematical stories in the heuristical, dialectical and dynamic way that computers have always promised to do. Welcome to the future!

We at the Library invite you to explore these Interactive Web Books. They point to the way that mathematics books will both look and behave in the future. If you are a teacher and would like to be part of that future, please write to us to learn how you may build (or use) our Microworlds on your own website.

James E. White, Ph.D.
Library Director