INTRODUCTION
The mathematics that we teach and learn today includes concepts and
ideas that once were pondered only by the most brilliant men and
women of ancient, and not so ancient, times. Numbers such as 1,000, for
example, or two, or zero, were at one time considered very abstract
ideas. There was a time when a quantity more than two or three was
simply called “many.” Yet we have grown up learning all about
quantities and how to manipulate them. We teach even young children
the concept of fractions as we ask them to share, or divide, their candy
between them. Today, in many ways, what used to be stimulating
thought for only the privileged few is now considered child’s play.
Yet scholars, philosophers, scientists, and writers of the past have spent
lifetimes devising ways to explain these concepts to benefit merchants,
kings, and countries. The idea that two items of different weight could
fall to the Earth at the same rate was, in its time, controversial. Creating
calculations that pointed to the fact that the Earth revolved around the
Sun was heresy. Mathematicians have, in fact, been beheaded by kings,
imprisoned by churches, and murdered by angry mobs for their
knowledge. Times have changed, thankfully. It is fair to say we have
come a long way.
This book is designed to help you come even further in your
understanding of algebra. To start with, there is a lot of algebra that
you already know. The Additive Identity Property, the Commutative
Property of Multiplication, the MultiplicativeProperty of Equality,
and the Zero Product Theorem are already concepts that, while you
might not knowthem by name, are in your personal database of
mathematical knowledge. This book will help you identify, and make
a connection with, the algebra that you already do know, and it will
give you the opportunity to discover new ideas and concepts that you
are about to learn.
This book is designed to give you a good broad base of understanding of
the basics of algebra. Since algebra plays such an integral role in the
understanding of other parts of mathematics, for example, algebraic
geometry, there is naturally some crossover of terms. As you become
interested in other fields of mathematics, whether on your own or
ix