Thirty years ago mathematical, as opposed to
applied numerical, computation was difficult to perform and so
relatively little used. Three threads changed that: the emergence of the
personal computer; the discovery of fiber-optics and the consequent
development of the modern internet; and the building of the Three “M’s”
Maple, Mathematica and Matlab. We intend to persuade that
Maple and other like tools are worth knowing assuming only that one
wishes to be a mathematician, a mathematics educator, a computer
scientist, an engineer or scientist, or anyone else who wishes/needs to
use mathematics better. We also hope to explain how to become an
`experimental mathematician' while learning to be better at proving
things. To accomplish this our material is divided into three main
chapters followed by a postscript. These cover elementary number theory,
calculus of one and several variables, introductory linear algebra, and
visualization and interactive geometric computation.