The author of this wonderful text delivers a brief, easy-to-absorb, yet very comprehensive text on modeling real-world data with Maple. As readers of these reviews know, Maple is software for performing mathematics, with a none-too-steep learning curve. In the introduction, the author is quick to point out that this is neither a detailed textbook of mathematical modeling, nor Maple. It is, however, a very well-written manual of introductory modeling and use of Maple. It may be very profitably used by undergraduates, especially in statistics and the life sciences.
The math used is simple extrapolation of those techniques used in high-school and freshman college statistics. As the language of statistical computation is matrix algebra, these are very valuable techniques to learn. The other technique used in this volume are called difference (NOT differential) equations, calculations of iterative processes by simple arithmetic and algebra that are far easier to master than differential equations. As we will learn later on, if we chose to pursue modeling, the mathematics can be as complicated as the analyst wishes to attempt.
Often times in the real world, complex computation is necessary. Now for more details…
The following is a brief chapter listing. It simply breaks up the subject matter by modeling types and is useful if the reader is only interested in a single type.
- Overview of Discrete Dynamical Modeling and Maple
- Modeling with First-Order Difference Equations
- Modeling with Matrices
- Modeling with Systems of Linear Difference Equations
- Modeling with Nonlinear Systems of Difference Equations
What I really appreciated was the stress put on integrating as much math as possible with life sciences as we have been undergoing a huge shift in biology from a predominantly descriptive science to an analytic science. This shift requires a tweak in the education of undergraduate life science majors to include any remedial high-school math, as well as statistics and matrix algebra. A beginning course in calculus (useful in just about anything) and differential equations (especially useful for modeling how things enter and leave cells) would be a good idea at the freshman/sophomore level.
Chapter 1 gives a brief introduction to modeling with difference equations. I found the math sections, while for the most part easy, were still more challenging than the Maple sections. The programs used were simple and introduced much of the code used in a variety of problems. And, although Maple is capable of generating a variety of sophisticated graphics, the book keeps them at simple dot- and line-plots.
The next four chapters follow the same sequence, i.e., introduction, fairly simple math, simple Maple Code for a given real-world problem, and a few simple graphics. And most of the code can be found at the Web site (but see the problem below).
If there are any shortcomings to the book they are rare. Among them are the missing supplementary materials at the Web site mentioned in the preface (although this is probably due to my receiving a free review copy). As these materials also contain answers to some of the problems, it is vital to be sure that students have access. An even better idea than just answers would be the solutions for each problem, i.e., “how did we get the answer?”
Although the area of genomics is growing by leaps and bounds, only 1-1/2 pages have a genetic example, and even that merely addresses a classic Mendalian gene cross. Instead, the author chooses to rely on the old tried and true growth/decay curves as well as models from quantitative ecology (although there are some interesting departures, such as a section on “Forensic Application of Newton’s Law of Cooling,” i.e. the calculation of body temperature at n hours after a murder! And of course there is my standing gripe of far too brief an index. Perhaps my biggest gripe concerns the lack of simple, straight-forward definitions of words, such as closed-form and analytic solutions. As most mathematical textbooks do, the author gives examples of each, shows the student how to verify the solutions, and describes what they are good for, but will not come forth with a simple definition.
Despite these few shortcomings, this book is highly recommended, especially to those in biology and data analysis. As both an introduction to Maple and modeling biological systems, it is highly desirable from a standpoint of not only readability, but relevance.
Explorations of Mathematical Models in Biology with Maple. Mazin Shahin. John Wiley & Sons, Inc., Hoboken, NJ (2015). Pp 292+X, $ 115
John Wass is a statistician based in Chicago, IL. He may be reached at editor@ScientificComputing.com.