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Read This!
Dongwoo Sheen   2009.04.10   6950

Read This! The MAA Online book review column Introduction to Computational Science: Modeling and Simulation for the Sciences by Angela B. Shiflet and George W. Shiflet Reviewed by William J. Satzer Posted to MAA Reviews July 11, 2006. Posted to Read This! August 29, 2006. My younger son will be applying for college admission this fall and he has suggested that he may be interested in majoring in mathematics. I feel strangely ambivalent about this. It seems to me that the scope of many college and university mathematics programs is still much too narrow. My own experiences suggest that many non-academic employers are reluctant to hire math majors, and their reluctance increases for those with advanced degrees. This is not entirely an irrational prejudice. I have met too many people working in government and industry who have mathematics degrees but are seemingly unable to connect what they had learned to problems in the wide world outside. There are several avenues for broadening the mathematics major. One of the most promising is to introduce computational science early in the undergraduate curriculum. Besides the benefits this offers to the prospective math major, practical knowledge of computational science is increasingly important in the sciences and engineering, and most particularly biology. Introduction to Computational Science is a marvelous introduction to the field, suitable even for beginning undergraduates and full of wonderful examples. The authors are a biologist and a mathematician (who now focuses on computer science). The book truly benefits from their balance of experience. “Computational science” is still somewhat ill-defined. It is situated somewhere between mathematics and computer science, and uses the tools of both fields to investigate problems in the physical and biological sciences, engineering, economics and finance via computational models and simulations. Some years ago (when my job title actually was “computational scientist”) computational science was intimately connected with high performance computing (i.e., supercomputers). Today even the most basic home computer is capable of supporting sophisticated modeling and simulation. The heart of Introduction to Computational Science is a collection of modules. Each module is either a discussion of a general computational issue or an investigation of an application. There are 22 modules of the former kind and 36 of the latter. Each application module provides prerequisite scientific background material and leads the student into the modeling. An early module introduces the modeling process (analyze the problem, formulate a model, solve the model, validate and interpret the solution, and report results). The authors consistently follow this discipline throughout. Two major categories of computational science modeling are considered: system dynamics models and cellular automata simulations. The authors do not assume readers have any computer programming experience. Instead they rely on software tools: for system dynamics models, they suggest Stella, Vensim, and Berkeley Madonna, and for computational tools, there are Maple, Mathematica, MATLAB and Excel. Tutorials for all these software packages are provided on the text’s web site. In addition, models built using these tools are available from the web site for many of the modules. Typically, an instructor would choose one system dynamics tool and one computational tool for use throughout. Application modules draw from biology, physics, chemistry and economics, with biology and physics dominating somewhat. Some of the most interesting applications are models of bungee jumping, malaria, the spread of a forest fire, ideal gas laws and scuba diving, and the movement of ants. The scientific background behind each application is clearly and succinctly described and each topic is well-motivated. Modules typically include “quick review” questions, more or less straightforward exercises, and a collection of more extended “project” problems. All of these are well integrated with the text. This is a visually appealing book that seems to invite browsing. It has been carefully and thoughtfully written with students clearly in mind. I have two concerns about the authors’ approach. First, calculus is not a prerequisite, and that works because it’s possible to do quite a bit of sophisticated modeling without any calculus. However, the authors do include relatively short introductory modules on the derivative and the integral. Then they go on to make pretty free use of differential equations in succeeding modules. (However, they do not require any knowledge of how to differentiate or to solve differential equations.) I wonder how well this works for students who have not seen calculus before. Instead, how about considering an approach based exclusively on difference equations? My other concern is more of a quibble. There is a very good module called “Errors” that includes a range of things from data errors through round-off, underflow, overflow, truncation and implementation mistakes. This is a valuable piece, often omitted from other texts on modeling, but it sits too early in the book. When students have had some experience with modeling and the various ways it can run amuck, this discussion of errors would mean a good deal more to them. Publication Data: Introduction to Computational Science: Modeling and Simulation for the Sciences, by Angela B. Shiflet and George W. Shiflet. Princeton University Press, 2006. Hardcover, 554 pages, $69.50. ISBN 0691125651. Bill Satzer (wjsatzer (at) mmm.com) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics. Go to... * MAA Reviews home page (MAA members and subscribers only) * The main Read This! page * MAA Reviews, Read This... what's the difference? * The index of all Read This! reviews * The MAA front page * MathDL home page Find out... * About the Mathematical Association of America * Why you should be a member of the MAA * How you can help support the activities of the MAA Read This! is the MAA Online book review column. Contributions are welcome; contact the editor if you'd like to be one of our reviewers. Books for review should be sent to the editor: Fernando Gouvêa, Dept. of Mathematics, Colby College, Waterville, ME 04901. Publishers, please check our reviews information page. MAA Online is edited by Fernando Q. Gouvêa (fqgouvea (at) colby.edu). Last modified: Tue Aug 29 11:20:57 Eastern Daylight Time 2006

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