Scheinerman Remodeled Math Course, Then Wrote Book For It


Ken Keatley
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Homewood News and Information


     Ed Scheinerman says the tasks of writing a textbook and
remodeling a basement have a lot in common. He should know--he's
doing both.

     "There's always something to do, even now when it's
virtually finished," said Scheinerman, professor in the De-
partment of Mathematical Sciences. "There are still some more
little details and things to take care of." 

     Now that the carpeting's in, Scheinerman's basement in
Columbia is just about ready for use. The same can be said for
his first book, "Invitation to Dynamical Systems," now that he
and publisher Prentice-Hall have finalized drawings and the cover
image.

     The book, intended for sophomore-junior level college
students who are beyond linear algebra but not quite ready for
such highly abstract mathematical material as topology, grew out
of department chair John Wierman's "invitation" to Scheinerman
that he teach a course in dynamical systems.

     "I protested. It's outside my area of interest [discrete
mathematics], and besides I'd taught it once before and found it
to be very dull," said Scheinerman. "But [Wierman] said I could
completely redesign the course the way I think it should be done.
And that sounded interesting."

     Scheinerman felt that the course he had originally taught
had failed to include some of the more interesting concepts and
methods for describing and analyzing systems that evolve over
time, such as fractals and chaos theory. But, when he searched
for an intermediate text that would include those topics, none
was to be found.

     "Graduate level textbooks were incredibly difficult, and
introductory texts were too elementary," Scheinerman explained.
"Since I couldn't find appropriate material, I decided to write
one."

     The resultant text, gleaned primarily from his lecture
notes, has been completed--much as his basement work--over the
last 18 months in between Scheinerman's regular teaching and
research projects. In it, he aims to present the underlying
mathematical concepts on a pictorial and intuitive level, since
many of its readers will be non-mathematicians (i.e., computer
scientists, engineers and economists).

     "It's a serious mathematical book, but one which doesn't
emphasize theorem proving," he said, adding that the book is
richly illustrated with over 200 figures. "The underlying
concepts are very hard, and I believe you must see the examples
before you see the theory."

     Scheinerman used the term invitation, rather than 
introduction, in order to emphasize the multidisciplinary 
nature of the material, which can be applied to fields outside
mathematics.

     "A lot of people who are not mathematicians would profit
from learning this material. But if you write it purely from a
mathematical point of view, you cut out a large segment of the
population. A lot of people can enjoy this beyond the arcane
folks like me."