John A. Adam is an experienced mathematician with a recognized track record of technical papers and reviews, but also very much committed to teaching his field to students and educated laypersons alike. This book is one in a small but very worthwhile series of popular works by Adam. In 25 chapters it comprises not less than about 75 studies, projects, and morsels, all bound together by their potential appearance or relevance in life in a city, something, which obviously will not decrease in the world of the future.
For this reviewer the dust cover could be a bit more elaborate or artistic, but other than this, and as usual for Princeton University Press hardcovers, the format, haptic quality, choice of paper, and layout are all excellent. The book's graphs and graphics refrain of color, but are always inviting and enlightening. The typography of the very many equations is outstanding. It is calculations and equations, which set the tone and pace for most of this tome.
Here, Adam excels with lucid explanations and proofs throughout, which sometimes does not im- or explicitly spare his reader a few additional steps by paper and pen. So, this is obviously not your coffee table math book to be perused in a few days. When grading the subjects into three stages from easy to difficult, the material falls into these brackets with percentages of about 30:40:30. Whereas the easy and intermediate problems are accessible to anyone with a good command of arithmetics, geometry, trigonometry, basic probability, and real functions, the advanced topics would cater to a typical science major with a good footing in calculus and the beginnings of differential equations.
It should be noted that some 20% of the problems and projects involve "guesstimation" with occasional glimpses on dimensional analysis. This is the art of approximately solving so called Fermi problems by educated guesses, and has been the subject and title of a pocket book, coauthored by Adam.
The individual topics selected by the author are neither arranged by difficulty, nor can they always be grouped together by a certain field of science or math. The many traffic and transportation studies in Chapters 7 to 14 are a notable exception, and actually worth buying the book alone, although some related models, drawn from the literature, leave the reader a bit clueless on which is the prevailing one. For other subjects like those on outdoor optics in Chapters 20 to 23, a field in which the author is well-known by his technical contributions, the "City" theme comes across a bit forced.
The ensuing mix of sorts will not be everybody's favorite, as might be the case for some of the reserved "English" jokes, which this reviewer certainly took delight in. All these minor quibbles would only take half a star away from this one-of-a-kind book, so it got rounded-off to five.
It should be noted, that the book comes with extensive lists of both references and suggestions for further reading.
So, anyone looking for something both enlightening and challenging in the mathematics of everyday life should get a copy. John's other books, as well as all those authored by Paul J. Nahin, also with Princeton University Press, would be recommended too.
Addendum: this reviewer has compiled a cross-reference in MS Excel for this book's content and will be glad to provide it to anyone who can reach him through a message here or at SRH University of Applied Sciences, Heidelberg, Germany.