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Ants, bikes and clocks : problem solving for undergraduates
Briggs W., Society for Industrial and Applied Mathematics, Philadelphia, PA, 2004. 168 pp. Type: Book (9780898715743)
Date Reviewed: Feb 22 2006

I assume that most students who take undergraduate courses in science or engineering are at some point in time unable to solve some of the proposed problems or exercises, despite having a good theoretical knowledge of the topic. They may know the equations, understand the mathematical passages, and have a grasp of the physical meaning of the equations, and yet sometimes they are unable to solve the problem. Unfortunately, this inability to solve problems often leads to frustration, and this starts a vicious circle, as the incapability of solving some problems results in diminished motivation to study and, as a consequence, more difficulty in solving future problems. Surely, problem solving is an important and complex aspect of our education; however, it is frequently overlooked by teachers. For this reason, a book aimed at the development of problem solving skills should be welcomed by students and teachers.

About 50 years ago, Polya wrote a book on problem solving strategies, which became very popular [1]. Briggs’ book is not intended to replace Polya’s classic book, but rather to complement it. For example, Polya’s principles of analytical problem solving are cited and discussed, and are adapted to computational problems. In fact, the interplay between the analytical and computational approaches to problem solving is very useful.

Throughout the book, the reader is encouraged to focus as much on the process of problem solving as on the final answer. A lone answer, which is typically a numerical result, is not acceptable, says the author. It must always be accompanied by a full account of how one arrives at the answer. One goal of the book is to improve mathematical communication, both written and verbal. With mathematical proofs, the standards of exposition are fairly clear. With the more open-ended story problems that appear in this book, the rules may not be so evident. Here, the book gives many guidelines.

One of the best qualities of this book is that it is pleasant to read. It is well written, and comprehension of the text is aided by numerous tables, graphs, charts, and figures. This is especially important, considering the main target of the book--undergraduate students. Everyone will certainly enjoy browsing the chapters, reading the small notes in the margins, and going through the various and inventive examples. Another interesting aspect of Briggs’ book is how the exercises are organized. At the end of the chapters, each exercise is followed by hints and respective answers. In addition, full solutions for all exercises can be found at the end of the book.

In summary, this is an excellent and timely book about problem solving, not only for undergraduates, but for everyone interested in problem solving strategies.

Reviewer:  Klaus Galensa Review #: CR132463 (0701-0052)
1) Polya, G. How to solve it. Princeton University Press, Princeton, NJ, 1957.
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