Introduction:
This
Interactive Web Book is a demonstration of a possible shape for mathematics
books of the future. It presents its story in the familiar way that a static
text might present it, but with the exception that the pages of the story
"come to life" and offer the reader the opportunity to make and
test hypotheses, to experiment and explore in a visual and interactive way
many of its main constructions and concepts. For many readers, this active
participation in the story can add a dynamic dimension that will help them
visualize certain of its ideas for the first time. Of course, you
may download and extract the Word 2000 version here in order to print
and read it in the traditional way as static text off-line, but these interactions
are not ancillary; they are from the beginning an essential part of the narrative.
Cardano
is not actually intended to teach the mathematical topics it develops
to any particular student target audience. It covers a range of topics from
high school to graduate-level mathematics. It moves at warp speed across several
centuries of mathematics, beginning perhaps in the 16th Century, and ending
with some results obtained by the authors, and published in the November 2001
issue of The American Mathematical Monthly. But it was written so that almost
anyone who has studied a little algebra can "jump in" and play with
it. Some topics that it covers are accessible to high school students, others
to university students of Modern Algebra and Theory of Equations, and others
may be of interest to graduate students, teachers, and professional mathematicians.
So the aim is not to teach the mathematics but to demonstrate the range and
the efficacy of a new style of web pedagogy and of authorship.
It
may appear that the interactions that one finds on the eight exploration pages
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 they were not written in Java, but were
created in a high level object-oriented mathematics scripting language called
MathScript. 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 with than
Java.
One
might also point to the range of resources available to this book, and to
every interactive web book that uses the MathwrightWeb Control. It
uses a symbolic Expert System, computer algebra, sprite animation and graphics,
command-line tools, and a special-purpose command language to represent and
manipulate ring-theoretic objects. All of this is immediately available to
the book. A Java applet would, in principle, have to download these resources
each time this book (or a similar book) was read.
The
mathematical documentation for this story was created fairly easily using
Design Science MathPage™ technology with Microsoft Word 2000™. And
the mathematical interactions were created with Mathwright32 Author™.
The Cardano Book may be read in Microsoft Windows™ (95, 98, Me, 2000,
or XP) using Internet Explorer Browser 5.0 or later. In order to read it,
you must download and install the free Personal
MathwrightWeb Control. Once you install the control, please check that
the browser is prepared to read the books. Be sure to download Version 1.004
(after Feb. 22, 2002 or later).
Your
browser must be able to use ActiveX controls. Microsoft Internet Explorer
5.0 Browser (or later) is so equipped. You should check that the Security
Settings under Tools, Internet Options, Security for the Internet,
Custom Level has:
- "Run ActiveX Controls and Plugins" set either to enable or prompt.
- "Initialize and Script ActiveX Controls not marked as safe" set either to enable or prompt.
The Interactive Web Book: Cardano
