Approaching
Precalculus Mathematics Discretely introduces concepts of discrete mathematics
through the computer, making them easier to teach and more fun to learn. Philip
Lewis shows how this can be accomplished using the Logo language to apply and
explore much of the material in standard high school advanced algebra and
precalculus programs. He develops sophisticated programming techniques in
conjunction with mathematical concepts that make the book a model for teachers
looking for ways to integrate computers into the mathematics curriculum. The
opening chapter introduces the use of Logo to express a variety of basic
mathematical functions. The next four chapters broaden the discussion to
include elementary vector operations, in the plane and linear transformations
and matrix operations defined as vector-valid functions. Chapter 4 applies the
theory of linear transformations to the mapping of two dimensional geometric
objects drawn on the computer screen. Chapter 5 takes up mathematical induction
and recursion. This allows the transformation theory of chapter 4 to be
extended to wire frame objects in space that are projected on the computer
screen. Chapter 7 constructs a graphing utility that is used in subsequent
chapters to examine the graphs of a variety of functions and to introduce the
concept of a limit. This extends to an intuitive introduction to slope and the
derivative in order to establish a territory for the calculus. The two chapters
that follow examine the traditional cyclic functions from a graphic and
transformational point of view. The book concludes by outlining explorations of
topics from earlier chapters. Philip G. Lewis teaches mathematics and computer
science atLincoln Sudbury Regional High School in Sudbury Massachusetts.
“Approaching Precalculus Mathematics Discretely” is included in the series
Exploring with Logo, edited by E. Paul Goldenberg.