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The Nature of Mathematical Modeling, by Neil Gershenfeld
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This book first covers exact and approximate analytical techniques (ordinary differential and difference equations, partial differential equations, variational principles, stochastic processes); numerical methods (finite differences for ODE's and PDE's, finite elements, cellular automata); model inference based on observations (function fitting, data transforms, network architectures, search techniques, density estimation); as well as the special role of time in modeling (filtering and state estimation, hidden Markov processes, linear and nonlinear time series). Each of the topics in the book would be the worthy subject of a dedicated text, but only by presenting the material in this way is it possible to make so much material accessible to so many people. Each chapter presents a concise summary of the core results in an area, providing an orientation to what they can (and cannot) do, enough background to use them to solve typical problems, and pointers to access the literature for particular applications.
- Sales Rank: #1292933 in Books
- Brand: Brand: Cambridge University Press
- Published on: 2011-06-23
- Original language: English
- Number of items: 1
- Dimensions: 9.61" h x .75" w x 6.69" l, 1.26 pounds
- Binding: Paperback
- 358 pages
- Used Book in Good Condition
Review
"In a compact but accessible manner, Gershenfeld offers a wide-ranging overview of mathematical ideas and techniques that provide a number of effective approaches to problem solving...a great compendium of techniques. It should be kept within easy reach of anyone who wants to build computer models to help understand the world
Science
"...masterfully written, fun to read, and brimming over with useful information....This text is a marvelous handbook of mathematical modeling."
UMAP Journal
"Gershenfeld's style of giving brief overviews together with a concise summary of key results in the subject area makes [the book] invaluable for mathematical and computational modelers...Highly recommended."
Choice
"...I do not know any other single source of the material presented here."
Michael Marder, Physics Today
"Neil manages to combine new and old flavors like analysis and stochastic modeling, finite element methods and cellular automata, nonlinear function minimization and information-theoretic system identification in a single integrated overview that exposes the purposes and capabilities of each. Any of these areas can be a black hole, capable of swallowing a student in detail, with no observable output. This book performs the valuable service of teaching novice or practitioner of what the methods can offer to the overall purpose of modeling the world around us or before us."
Scott Kirkpatrick, IBM Research, inventor of simulated annealing
"This is a book for anyone who wants to use a computer to build models. The book draws on an enormous variety of sources, but Gershenfeld has seen through to the core ideas and has brought out the key relationships between the various methods. The book is a pleasure to read."
Michael I. Jordan, University of California, Berkeley
"Simulation and mathematical modeling will power the 21st Century the way steam powered the 19th. Gershenfeld masterfully compresses two armloads of dense textbooks into a single clear volume, including both classic and avant garde methods, and with well-selected references for further study. Every student of computing needs this book as the entry ticket into a vital and rapidly changing field."
William H. Press, Harvard University, author of Numerical Recipes
"The sheer breadth of material that this book surveys and unifies in surprising ways is one strong recommendation for including The Nature of Mathematical Modeling in your library. Readers will profit from physicist Neil Gershenfeld's background as he draws connections among the many, often seemingly disparate, facets of mathematical modeling...And, of course, this is a book for practicing mathematicians, computer scientists, physicists, engineers, and any and all others interested in both standard and not so standard techniques viewed in the rich and stimulating context that this book provides."
The American Mathematical Monthly
"This is a well-written and interesting book. It would make an excellent text for a final-year undergraduate course in modeling and a good reference for research students in any situation where data are to be examined."
Computing Reviews
"The exposition of the text is fluent and engrossing...As a mathematician I found many of the topics discussed in the text interesting and worthy of further investigation. I would certainly recommend the text to a colleague interested in understanding the connections that exist among the seemingly unrelated techniques of applied mathematics."
MAA Online
About the Author
Neil Gershenfeld, Ph.D., is an associate professor at MIT, the director of the Media Lab's Physics and Media Group, and codirector of the Things that Think consortium. Gershenfeld has written for "Wired" and for other technology publications, and he lives in Boston. He is the author of several books, including "When Things Start to Think".
Most helpful customer reviews
14 of 15 people found the following review helpful.
Good Book, But Beware of the Reissue Edition
By Romann M. Weber
Please note that this review pertains only to the paperback "reissue edition" and not the 1999 hardcover. The content of the book itself, which deserves its own review, is excellent. I am truly impressed at how much material and insight Gershenfeld has collected in a single slim volume.
When I saw that the book was being reissued as a less-expensive paperback, I assumed that it would have a few minor corrections and a soft cover. Even if it didn't have any corrections (and it appears not to), I'd have been satisfied.
However, the reissue I received, bought as new directly from Amazon, is clearly a print-on-demand (POD) book (indeed, this one was printed in Lexington, KY, the day I ordered it). POD is not always a bad thing, but in this case, images and equations (and sometimes the text itself), all of which look great in the original hardcover edition, have become grainy and look as though they have been printed from a compressed image-based (i.e., scanned) source as opposed to the original files. The effect is more pronounced on some pages than on others, but even a random flipping-through finds plenty of examples.
My book was also damaged during shipment, so the decision to return it was effectively made for me. Had it not been, though, the decision would have been a bit tougher. It's the right book, and a good book, but I can't get over how much it looks like a bootleg. If that doesn't bother you, go for it; it is a good book to have on your shelf. Otherwise, if you're trying to save some money on this title, try to find a used hardcover that's in decent shape.
1 of 1 people found the following review helpful.
OK for a read on a long journey
By Martin A
I bought the book (hard copy form) in a second hand bookshop while on holiday in Ireland. It is well printed on good quality paper and my copy is noted as 'reprinted 2003'.
I have several criticisms:
- It is mistitled. It does not discuss "the *nature* of mathematical modeling" of physical systems. It does give a brief review of numerous mathematical techniques relevant in mathematical modeling of physical systems. It also discusses a few relevant aspects of computer programming.
- The coverage of any individual topic is superficial, covering only a few pages. If you already know about a topic, what the author says makes sense. But if it's new to you, you'll probably only get a general impression of what the topic is all about.
- The book does not touch on large areas of significance in mathematical modeling. For example, although the first page asks "How would you describe ... Highway traffic during a rush hour?", queuing theory and the mathematical analysis of discrete event systems do not seem to be mentioned.
But having said all that, I felt I had my money's worth and enjoyed reading it on a long ferry trip and being reminded of mathematical methods that I had used years ago - a bit of nostalgia.
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