It has long been recognized that the development of technology should effect the curriculum of mathematics [3] [2]. A key point of Young's book is that these effects should not be merely pedagogical, but substantive. The speed of computers has fundamentally changed the kinds of computations that are possible and this changes the kinds of mathematics people do. Since the advent of computers, the ability to do numerical calculations has increased astronomically. In response, fields of numerical mathematics have blossomed in recent years and the use of numerical methods in the sciences and engineering has become ubiquitous.

The invention of symbolic manipulators in the mid 1980's added a whole new dimension to the interaction between mathematics and computers. For example, students can now find the integral of a function without learning lots of ``tricks", which were a big part of traditional calculus courses. This example only scratches the surface; both students and researchers can now do many abstract operations on the computer, something that a generation ago was only a dream of a handful of people.

Precisely because the new **CS** is so remarkable,
to use it properly requires training. Consider the now familiar
example of a calculator.
Even though a calculator alleviates the need for most
people to do long division, a calculator is
useless to the person who does not understand when
to add and when to divide. Take this example and
multiply its complexity be several thousand.
**CS** is to a calculator
as chess is to tic-tac-toe.^{4}
The user of **CS** must understand
a number of things to take advantage of it.
First, since both numerical and symbolic
operations are possible, the user must understand the
advantages and disadvantages of each. Not only must the user
understand what she wants to calculate, but she must also have
some understanding of how the computer is going
about it's work. Moreover, with the new software
it is quite possible to
believe that the computer is doing what is desired, but
in fact it is doing something completely different.
This is because the new software does things for which
fail-safe algorithms do not exist. Results of these computations can be
misleading or even wrong. Fortunately, most problems
of this nature can be avoided if students master
a few basic mathematical principals about the software.
To not make use of the software as an educational
tool is bad enough in itself. However, it would be an even
more serious problem if our graduates
are ill-prepared to use computational software when
they inevitably encounter it in the workplace.