id: 06048640
dt: b
an: 2013b.00794
au: Adam, John A.
ti: X and the city. Modeling aspects of urban life.
so: Princeton, NJ: Princeton University Press (ISBN 978-0-691-15464-0/hbk;
978-1-4008-4169-1/ebook). xviii, 319~p. (2012).
py: 2012
pu: Princeton, NJ: Princeton University Press
la: EN
cc: M10 A80
ut: mathematical modeling; applied mathematics; urban life
ci: Zbl 1181.00024; Zbl 1102.00004; ME 2010b.00063; ME 2013b.00070
li:
ab: The new book by Professor Adam is an excellent companion to his award
winning titles [A mathematical nature walk. Princeton, NJ: Princeton
University Press (2009; Zbl 1181.00024; ME 2010b.00063)] and
[Mathematics in nature. Modeling patterns in the natural world.
Princeton, NJ: Princeton University Press (2006; Zbl 1102.00004; ME
2013b.00070)]. This time the reader is invited to take an urban walk
exploring no less intriguing problems that arise in mathematical
modeling of daily city life. According to the author’s description,
“this book is an eclectic collection of topics ranging across
city-related material, from day-to-day living in a city, traveling in a
city by rail, bus, and car (the latter two with their concomitant
traffic flow problems), population growth in cities, pollution and its
consequences, to unusual night time optical effects in the presence of
artificial sources of light, among many other topics.” In a very
enjoyable manner, a variety of simple and not-so-simple routine daily
situations are first set into the mathematical frame and then
skillfully analyzed using arguments ranging from straightforward
“quick and dirty” computations to delicate combinations of
estimations, probability, geometry, discrete and continuous modeling.
Using thoroughly selected real problems, John Adam nicely illustrates
the three fundamental steps of mathematical modeling ‒ model’s
mathematical formulation, problem’s analysis and solution, and
solution’s interpretation in the original setting. Practical
questions answered in the book include, for instance, the following.
What is the average distance traveled in a city/town center? How does
gasoline consumption vary with speed? How long does it take to cook a
turkey (without solving an equation)? What is the optimal distance from
which to view a painting/sculpture/display? On the list of less
standard problems, one can find estimates for the number of doctor’s
offices in one’s town, evaluation of the number of squirrels in
Central Park, computation of the likelihood of a city/town being hit by
an asteroid, and many other curious questions provided with elegant and
instructive explanations. Some questions are left without answers as
exercises for an interested reader. The knowledge of mathematics
required from the reader varies from arithmetic and single-variable
calculus to ordinary and, on times, partial differential equations. The
book has an extensive bibliography; numerous helpful diagrams and
illustrations are spread throughout the text. There is also a concise
but useful index in the end. It goes without saying that the exposition
is very friendly and lucid: this makes the vast majority of material
accessible to a general audience interested in mathematical modeling
and real life applications. This excellent book may well complement
standard texts on engineering mathematics, mathematical modeling,
applied mathematics, differential equations; it is a delightful and
entertaining reading itself. Thank you, Vickie Kern, the editor of {\it
A mathematical nature walk}, for suggesting the idea of this book to
Professor Adam ‒ your idea has been delightfully implemented!
rv: Svitlana P. Rogovchenko (Kristiansand)