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Mathematical Modelling

Seppo Pohjolainen, editor
Publication Date: 
Number of Pages: 
[Reviewed by
Tom Schulte
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According to the preface, “This book is the result of seven Finnish universities joining their efforts to teach mathematical modelling with the help of the World Wide Web.” As a survey of modelling approaches, techniques, and examples this work is a good introduction for the advanced undergraduate or early graduate level in either a brick-and-mortar or virtual classroom. The preface also states that “The authors would like to thank … MSc Tuomas Myllykoski for the initial translation and … Tobias Schwaibold for his careful and professional proofreading of the English language.” I, too, thank the gentlemen as this reads as naturally and fluently as if it were written by a native speaker.

What is lacking in depth and rigor here is made up for breadth and variety. The authors seek to inspire readers and to detail departure points as well as frameworks for use as assignments or lectures. Networks, trees, and other graphs, along with computational complexity, such basics as interpolation/extrapolation, probabilistic models such as Markov chains, and ODEs are discussed in the the ample if brief introductory material. “Soft computing” comes in via an overview of fuzzy logic, neural networks, evolutionary algorithms, the theoretical underpinnings of machine learning, etc.

This book provides some material that stands out, ready-made for lectures. Examples are chapters on dimensional analysis around Bridgman, a Bayesian approach to forestry data (see the cover image), and an extensive study of balloon motion in the context of conservation laws for mass, energy, momentum, etc.

The book concludes with over thirty paragraph-length project ideas. For example, “A common spring mass combination makes up an oscillator with the well-known physical model. Now assume that the spring constant as well as the matter that causes the dampening are known only vaguely, i.e. as fuzzy numbers. What can be said about the oscillator’s movement?”

Tom Schulte is a software architect as SaaS ERP provider Plex Systems based in Troy, Michigan.

See the table of contents in the publisher's webpage.