Preface for Teachers

Precalculus Made Difficult is a straightforward text that guides students from the Plains of Mathematical Nowhere (I presuppose only arithmetic and a hazily-recalled encounter with the rudiments of algebra) to the base of Mt. Calculus in just 200 pages. I achieve this concision largely by treating my readers as literate, interested, capable people – people who just happen not to know much mathematics yet.

My choice of topics is mainly conventional, but I’ve squirreled novelties away in nooks and crannies. A few examples: an honest discussion of why we have an arithmetic of negative numbers (it’s not for debts and subzero temperatures); a unit-circle definition of the tangent function (in lieu of the logically equivalent but aesthetically unsatisfying sine-over-cosine definition); a clean, symmetric substitution-based exposition of transformations in analytic geometry (which holds for graphs of all equations, unlike the usual asymmetric treatment, which applies only to graphs of functions); a proof Heron’s formula (supplemented by a meditation on Heron’s name); a rare excerpt from the Annals of Long Shu; dozens of delightful epigraphs; occasional dry humor flying low under the radar; and several story problems of questionable taste.

I am sufficiently immodest to assert that this book will be something of a connoisseur’s choice. If you are a teacher who can appreciate the fine-wine qualities of G.F. Simmons’ Precalculus in a Nutshell or Gelfand and Shen’s Algebra (while recognizing that neither would work as an actual classroom text), then Precalculus Made Difficult may be the right text for you and your students. Unlike Simmons, which is addressed to calculus students in need of a quick refresher, or Gelfand and Shen, which is addressed to isolated Russian prodigies in correspondence school, this is an honest-to-God textbook, accessible to the average student who is meeting this material for the first time. I and a few others have used it in classes of perfectly ordinary community college students. Students who take their studies seriously handle it well. Students who do not do not. Such is life. $ ^{*} $

My website, BraverNewMath.com, contains information about my other books and an email address for those with a burning desire to contact me.

Changes in the $ 2^{nd} $ Edition

The changes are small and unobtrusive. I’ve tidied the book up, quietly improving its exposition in places as I did so, and I have corrected some typos sent to me by sharp-eyed readers of the $ 1^{st} $ edition. The only substantial change – the true occasion for issuing this $ 2^{nd} $ Edition – is the change of publisher.

I am honored to have been invited to publish PMD with the highly exclusive (and notoriously secretive) Vector Vectorum Books. They gambled by publishing my most recent book, The Dark Art of Linear Algebra, and pleased with the results, they then expressed interest in my back catalog. Here’s to a long and fruitful relationship.