Bests & Worsts Reviews from Amazon

Despite its billing as a history of science book, I would really categorize "An Imaginary Tale" as a supplemental math text with occasional historical color, much as you'll find, for example, in offset boxes of "friendly" freshman calculus treatments. The author largely concedes this in the preface. Granted, the first couple of chapters have a more historical emphasis, but by the end of chapter 3 we've largely left behind the etiology of complex analysis. However, as long as you are aware of this going in, you'll be treated to an absolutely first-rate trip through the motivation, development and application of complex function theory, including several thoroughly worked out real-world examples. I was delighted by Nahin's painstaking efforts to build intuition about the meaning of complex algebra. If nothing else, drilling in the idea that i is a pi/2 rotation operator in the complex plane would give a conceptual toehold to thousands of high school students who never learn anything about complex algebra beyond formal symbol manipulation. One can easily imagine "An Imaginary Tale" as recommended reading for interested high school seniors, or for undergraduates looking for some background and motivation of ideas they are required to understand. Make no mistake, when the author says he will not "fall to his knees in dumbstruck horror" at the sight of an integral, you should take him at his word --- this book is packed with integral calculus equations, and you're not going to get much out of it if you're not prepared to follow along with them. But I think Nahin has achieved the right blend of explaining each step versus leaving algebra to the reader (here I disagree somewhat with smlauer@mindspring.com, though I am sympathetic to his point). I have deducted a star for exactly the reasons Duwayne Anderson and others complained about: (1) we need to have *many* of the results numbered, but unfortunately we only get a box or two in the entire text, and (2) who proofed this thing? I mean, honestly, stating Green's theorem correctly twice and then misprinting it in the section where it's proved? Randomly leaving the circle off of contour integrals? (sqrt(15)i)^2 = 15? It's fun to work the algebra that's left to the reader, but it's *tedious* to work out which results are misprinted and which aren't. Despite these typographical problems, I can enthusiastically recommend "An Imaginary Tale" to all readers at a moderate level of mathematical sophistication who are curious about the origins, theory and application of complex analysis.