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THE MATHWRIGHT LIBRARY NEWSLETTER, June 2003, VOL
5, #4
A publication of Bluejay Lispware
James E. White, Editor
The official publication of the New Mathwright Library and Café:
In this issue:
Artificial
Intelligence goes to School: A new Interactive Web Course in the MATH Cafe
Artificial Intelligence goes to School: A new Interactive Web Course in the MATH Cafe
How
do you think mathematics books may behave in the future? Perhaps
they will act a little like these!
There
are two new Interactive Web Books in the Visualization Studio of the
MATH Cafe. Both tell their stories with Windows compiled HTML Help. They are
the support for a 12-week course in Discrete Mathematics and Computational
Structures. Since they are now in the Cafe, they are freely available (in
the browser) to all visitors to the Library, whether they are Library members
or not. Students may extend their understanding of set theory and propositional
logic at their leisure, and teachers may use the "interactions"
of the Microworlds to support their own lectures on adjacent topics.
The
titles of these Interactive Web Books are:
Discrete Mathematics and Computational Structures Course, Part 1 (Sets, Functions and Relations: Basic Tools) and
Discrete Mathematics and Computational Structures Course, Part 2 (Finite Sets: Counting, Recursion and Logic: Next Steps)
What
makes these Microworlds different from what you might expect to find in Java
Applets is the range of resources available to them, and to every Microworld
that uses the MathwrightWeb Control. The first Microworld is 21 pages in length,
with 11 lectures, and 7 Laboratories, including an interactive Set Theory
Game called Set Safari. It now presents its story (the lectures) in
compiled HTML Help and so these printable pages provide the sophisticated
mathematical formatting that one would find in hardcopy text.
But
there is an important difference from hardcopy texts. The Microworld: Sets,
Functions and Relations contains a Set Theory and Propositional Calculus
Language built into it, that gives the reader the opportunity to experiment
with a variety of elementary discrete structures. Readers may construct colorful
and visual sets of animals and manipulate them with propositions, form unions,
intersections, complements, and construct new sets by applying relations,
functions, and permutations to them. With permutations, the reader can experiment
with a variety of small groups and see the effects in colorful displays.
The
phrase "Artificial Intelligence" is a notorious oxymoron (self-contradictory
expression) that was born in the romantic and youthful days of computer science,
when people waxed lyrical on the idea of building "thinking machines."
What A.I. has come to refer to, however, is the collection of techniques that
facilitate smooth two-way communication between humans and their computing
environments. This is embodied in the increasingly flexible and expressive
environments that are growing up all around us. And object-oriented languages
like Mathscript (which is written in LISP on top of Java, and is the language
that Mathwright uses) can demonstrate this.
Since
the first Microworld contains a Set Theory Language, it makes it possible
for the reader to experiment, and to ask her own questions -- at the level
of her own understanding -- and see the answers to those questions in surprising
new visual ways. The Lectures guide the reader through the interactions, and
suggest in their exercises an increasingly sophisticated series of experiments.
So the book supports a two-way dialog with the reader in a way that textbooks
cannot. In this sense, teaching and learning environments on the web can benefit
from A.I. techniques.
These
"Artificial Intelligence" techniques really come into their own
in the second Microworld: Counting, Recursion and Logic. The Set theory
and propositional calculus language of the first Microworld is now extended
to the more realistic domain of sets of numbers, products of those sets, and
to the user defined relations and functions that manipulate them. In addition
to that, the reader builds short programs that illustrate many basic constructions
in combinatorics, and goes on to study recursion in the construction of Pascal's
Triangle, the Fibonacci Sequence, the Golden mean, and so on.
But
this Microworld contains, in addition to that, a Prolog Interpreter.
Now Prolog is one of the early A.I. Languages whose name means: Programming
in Logic. It is natural in a course on Discrete Computational Structures to
merge Propositional calculus with Prolog. And that is what the Microworld
does. Specifically, it explores strategies of search by allowing the user
to build Relations, represented as Graphs on finite sets, and then to use
Prolog to illustrate Deductive Information Retrieval. The Prolog Interpreter
is written in LISP which is the base language (on top of Java) for both Mathscript
and our Prolog.
If
these topics seem technical, the 20-page Microworld eases the reader into
them with its 9 Lectures (in compiled HTML Help) and its 8 activities. The
last of these activities, the amusing Fly-By-Night Airline is a miniature
but realistic graph-theoretical database on which the reader may apply her
own queries to retrieve information about all the available flights between
cities that satisfy whatever conditions she poses. It illustrates the strategies
of search and deductive information retrieval in a dynamic and colorful way.
We
at the Library invite you to explore these Interactive Web Books. They point
to the way that mathematics books will look and behave in the
future.
James E. White, Ph.D.
Library Director