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X and the City: Modeling Aspects of Urban Life [Hardcover]

John A. Adam
4.0 out of 5 stars  See all reviews (1 customer review)
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Book Description

27 May 2012

X and the City, a book of diverse and accessible math-based topics, uses basic modeling to explore a wide range of entertaining questions about urban life. How do you estimate the number of dental or doctor's offices, gas stations, restaurants, or movie theaters in a city of a given size? How can mathematics be used to maximize traffic flow through tunnels? Can you predict whether a traffic light will stay green long enough for you to cross the intersection? And what is the likelihood that your city will be hit by an asteroid?

Every math problem and equation in this book tells a story and examples are explained throughout in an informal and witty style. The level of mathematics ranges from precalculus through calculus to some differential equations, and any reader with knowledge of elementary calculus will be able to follow the materials with ease. There are also some more challenging problems sprinkled in for the more advanced reader.

Filled with interesting and unusual observations about how cities work, X and the City shows how mathematics undergirds and plays an important part in the metropolitan landscape.


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Product details

  • Hardcover: 336 pages
  • Publisher: Princeton University Press (27 May 2012)
  • Language: English
  • ISBN-10: 0691154643
  • ISBN-13: 978-0691154640
  • Product Dimensions: 2.8 x 16.5 x 24.1 cm
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Bestsellers Rank: 566,305 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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Review

"[Adam's] writing is fun and accessible. . . . College or even advanced high school mathematics instructors will find plenty of great examples here to supplement the standard calculus problem sets."--Library Journal

"For mathematics professionals, especially those engaged in teaching, this book does contain some novel examples that illustrate topics such as probability and analysis."--Choice

"Read this book and come away with a fresh view of how cities work. Enjoy it for the connections between mathematics and the real world. Share it with your friends, family, and maybe even a municipal planning commissioner or two!"--Sandra L. Arlinghaus, Mathematical Reviews Clippings

"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 Kearn, the editor of A Mathematical Nature Walk, for suggesting the idea of this book to Professor Adam--your idea has been delightfully implemented!"--Svitlana P. Rogovchenko, Zentralblatt MATH

"[Y]ou'll find this book quite extensive in how many different areas you can apply mathematics in the city and just how revealing even a simple model can be. . . . A Mathematical Nature Walk opened my eyes to nature and now Adam has done the same for cities."--David S. Mazel, MAA Reviews

"The author has an entertaining style, interweaving clever stories with the process of mathematical modeling. This book is not designed as a textbook, although it could certainly be used as an interesting source of real-world problems and examples for advanced high school mathematics courses."--Theresa Jorgensen, Mathematics Teacher

From the Inside Flap

"In X and the City, John Adam proves himself to be a genial and endlessly curious companion as he takes us on a stroll through that fascinating place where reality meets the mathematical imagination. How many squirrels live in Central Park? Should you walk or run in the rain? Anyone who's ever pondered puzzles like these will find this book to be a treat."--Steven Strogatz, Cornell University

"Why did the chicken cross the road? Because the Jaywalker Equation said it had enough time between cars. How does the Ambler Gambler Graph tell if you can blast through a yellow traffic light before it turns red? And why are taxicabs slower than Euclid? These and many other mathematical conundrums are answered in John Adam's admirable new collection."--Neil A. Downie, author of The Ultimate Book of Saturday Science and Vacuum Bazookas, Electric Rainbow Jelly, and 27 Other Saturday Science Projects (both Princeton)

"This is a nice introduction to modeling that draws from questions arising naturally to people who are curious about how cities work. It will certainly interest readers of pop math books and will be useful to teachers of calculus and differential equations who are looking for good examples for their classes."--Anna Pierrehumbert, Community Charter School of Cambridge, Massachusetts


Inside This Book (Learn More)
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Front Cover | Copyright | Table of Contents | Excerpt | Index
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1 of 1 people found the following review helpful
4.0 out of 5 stars Modeling the Mudane 13 Oct 2012
By Reader
Format:Hardcover|Verified Purchase
If you're interested in math modeling and want some interesting examples of how it can be applied to life around you, then this is the book for you. At times the maths can be a little daunting for a non-mathematician, such as myself, but the concepts can be followed fairly readily for most readers who have done a higher maths course at some point in their education. Each 'case study' is short enough to engage the reader and the explanations and illustrations are clear.
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Amazon.com: 4.0 out of 5 stars  5 reviews
5 of 5 people found the following review helpful
5.0 out of 5 stars A great intro to Mathematical Modeling 27 July 2012
By Ed Pegg Jr - Published on Amazon.com
Format:Hardcover
Of the classes I had in college, mathematical modeling was the smallest class I had, but many times over the most valuable. Basically, the lesson is Use What You Know! After learning many other classes, this was the class that answered "What do we need this for?" Calculus, programming, linear algebra -- these are all good to know. Better is to know how to apply them. Even if you don't know the math, knowing that a particular type of problem can be solved with a particular type of math can often be 90% of solving the problem. Math modeling turns your knowledge into a toolbox. Once you get there, you don't even need to really understand some of the tools available in your toolbox -- if you need a particular math tool, you can look at the reference manual for it when you need to.

For X and the City, the author applies many aspects of math modeling to urban living. He looks at Traffic congestion, for example, and asks for the percentage of (waking) time people spend driving. Average commute time in Chicago was 34 minute. He gives the formula for the carrying capacity of a road network. Then he models the effect of adding one more car to a roadway at capacity.

One benefit of a book about modeling -- everything starts in the real world. Every single chapter and section, the first few paragraphs will be completely understandable by everybody, presenting an urban problem (visibility in smog). The next few paragraphs, he explains equations (x^2 = 4a+c) that can solve the problem.

There are hundreds of great little math-related stories in this book, many that I did not know. Also, I didn't know some of this math. All in all, this book added quite a bit to my math modeling toolbox, all in an entertaining, well-written style.

Highly recommended for everybody.
1 of 1 people found the following review helpful
5.0 out of 5 stars X and the City 16 Sep 2012
By Dottie - Published on Amazon.com
Format:Hardcover|Verified Purchase
Bought this for my daughter for Christmas. He was one of her favorite professors, & she enjoys anything he writes. He is good at making math easy to understand for laymen as well, and not only demonstrates why math is important but why it is FUN.
5.0 out of 5 stars Excellent food for mathematically inquisitive minds 16 Aug 2014
By Elmar Schmidt - Published on Amazon.com
Format:Hardcover
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.
0 of 1 people found the following review helpful
2.0 out of 5 stars This is a strange relic of old school engineering. 15 Mar 2014
By Jeffrey L. Beddow - Published on Amazon.com
Format:Hardcover|Verified Purchase
It might be my prejudice against tech education practices, but this is too much like listening to a good engineer make a bad presentation.

I bought it thinking it might be something to refer to the new generation of visualization practitioners who wanted to understand civic issues and social policy models. Instead it seems to be a "creative" approach to teaching hard core engineering concepts using "friendly" examples drawn from living in the city.

If they revisited this concept and packed Adam's stuff down smaller in an anthology of more relevant materials I could recommend it. He is a good guy and a good engineer. But his approach would tend to leave non-engineers in the dust.
0 of 3 people found the following review helpful
3.0 out of 5 stars Life in the Mathematical City 19 Aug 2012
By ubpdqn - Published on Amazon.com
Format:Hardcover|Verified Purchase
This book takes the 'city' as the landscape to explore Mathematical Modeling. The author covers a number of interesting areas. Some of the exercises are 'back of envelope' calculations. The use of geometric mean ("Goldilocks principle") for calculations using objects the extreme ranges, harmonic mean for average speeds to highlight common misconceptions is similar to other books.

The book presents these explorations a sequence of questions and answers. It starts with simple models (with declared assumptions) and explores where these lead. The model is then modified to include some other real world features. The appendices at the end of the book amplify the discussion in the various chapters.

The chapters on traffic and public transport were interesting. I enjoyed the exploration of atmospheric phenomena at the end of the book.

I did not enjoy this book as much as I anticipated. It is, however, an engaging way to think about city life.
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