Chapter 1
ALGEBRAIC FUNDAMENTALS
Algebra, at its core, is a compendium of mathematical concepts, axioms,
theorems, and algorithms rooted in abstraction. Mathematics is most pow-
erful when it is not fettered by the limitations of the concrete, and the first
step toward shedding those restrictions is the introduction of the variable,
a structure into which any number of values may be substituted. However,
algebra students must first possess considerable knowledge of numbers be-
fore they can make the next logical step, representing concrete values with
abstract notation.
This chapter ensures that you are thoroughly familiar with the most com-
mon classifications used to describe numbers, provides an opportunity to
manipulate signed numbers arithmetically, and investigates the founda-
tional mathematical principles that govern algebra.
You might be anxious to dive into the nuts and bolts of algebra, but
don’t skip over the stuff in this chapter. It’s full of key vocabulary words,
such as “rational number” and “commutative property.” You also learn things
like the difference between real and complex numbers and whether 0
is odd or even. Some of the problems might be easy, but you might be
surprised to learn something new.
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