Author’s Note

The physicist, in explaining projectile motion to the novice, as a first step, ignores air resistance (or friction) because it makes the analysis easier for beginners to digest—focusing on some of the crucial fundamentals without overly complicating things.

I fully concur with this plan of attack as well as with the thoughts of Renaissance educator Wolfgang Ratke when he states: “Before the learner has a notion of the thing itself, it is folly to worry him about its accidents.”1

In this text, I have taken a similar tack and have, for the purposes of exposition, chosen to view the elementary operations of arithmetic as they look through the lens of whole numbers only, ignoring the details of how they look when negatives, fractions, and irrational numbers enter the arena. I make no apology for this approach.

For readers who would like to see more examples of some of the conceptual procedures involved in the next five chapters please visit: www.howmathworks.com.