Note: This review is by my husband Jim.
This is a VERY interesting book. Ever wonder why we had to learn so much trigonometry before trying calculus? Jason Wilkes shows that it may make more sense to learn calculus first! In fact, he argues that most of what passes as pre-calculus doesn’t make much sense until we have a basic understanding of limits and derivatives. He even show how calculus can be “invented,” beginning with only the tools of addition and multiplication.
Wilkes creates a whole new vocabulary that substitutes common English words for abstract mathematical concepts. For example, he writes about “machines” that turn out to be what mathematicians call “functions.” They “eat” numbers and spit out other numbers. For the mathematicians’ universal symbol for unknowns, ‘x’, he substitutes “stuff.” Polynomials are “plus-times machines” because they can be described using only addition and multiplication. He pretends to examine his “machines” so microscopically so that their curved lines become straight, and produces the concept of a derivative. From there, the author builds a complete calculus of infinite dimensions, along the way showing (by Taylor expansion, which he labels a “nostalgia machine”) how to calculate the value of ∏, (Euler’s) ℮, and all the trigonometric functions.
Evaluation: Despite the fact that the author argues that his approach will penetrate some of the mystery associated with learning higher math, this is not an easy book. For someone with an interest in math, however, it is an enlightening approach that is bound to help the reader appreciate the intrinsic beauty of the concepts dealt with. One carping criticism I have of the book is that the final two chapters, dealing with the idea of “metaconcepts,” seem a bit kooky. Otherwise, a terrific read, and his dedication in the form of mathematical equations is terrifically clever.
Rating: 4/5 stars
Published by Basic Books, a member of the Perseus Books Group, 2016