Elementary Numerical Mathematics for Programmers and Engineers

It is well-known that many mathematical problems that arise as part of the mathematical modeling of scientific and engineering phenomenon are often so complex that the use of computational or numerical techniques is the best, if not only, approach to obtaining useful solutions. This is highlighted, for example, by the cameo appearance of Euler’s method in the recent film Hidden Figures. That is why there exist programming languages and software that cleverly implement many of the most common numerical routines for solving, at least approximately, many types of problems in applied mathematics. For better or worse, however, numerical methods are never one-size-fits-all and numerical software/programs are never simply black boxes for problem solving. Therefore, it is often reckless to naively use numerical software without a reasonable understanding of what is going on “under the hood.’ Hence, the need for courses and texts in numerical mathematics.

The recent offering by Gisbert Stoyan and Agnes Baran provides nice coverage of the most prominent numerical mathematics in a way that is accessible to a relatively wide audience, but without resorting to a mathematically superficial treatment. At around two hundred pages, the book is also refreshingly concise. In fact, Elementary Numerical Mathematics for Programmers and Engineers is part of the Compact Textbooks in Mathematics series by Birkhäuser. I have been really impressed with the books in this series; Elementary Numerical Mathematics for Programmers and Engineers shows why.

The book is well-written and the typesetting is attractive. The book, as with several others in the series, contains professionally produced graphics and the most important concepts/results are well-highlighted with boxing or bold-face. One complaint I have is that the index is rather sparse. On the other hand, the table of contents is very thorough.

Elementary Numerical Mathematics for Programmers and Engineers covers the standard topics well. Results are never simply stated and the main ideas are always fleshed out either through derivations or highly insightful examples. The authors also use clear and consistent notation throughout the book. I would particularly recommend this book to someone who is trying to learn numerical mathematics independently without the help of an instructor.

Some may consider this book to have the following pitfalls as a sole textbook for a course in numerical analysis. For one, there are very few exercises, though the one that are included are of high quality. In addition, there is not as much on computer implementation, as is currently fashionable to include in numerical analysis textbooks. Some of the exercises do introduce short MATLAB commands for solving certain types of problems. For example, exercise 6 in Chapter 3 gives the command for LU factorization in MATLAB. Nevertheless, Elementary Numerical Mathematics for Programmers and Engineers is a very nice book and pleasant to read.

Jason M. Graham is an assistant professor in the department of mathematics at the University of Scranton, Scranton, Pennsylvania. His current professional interests are in teaching applied mathematics and mathematical biology, and collaborating with biologists specializing in the collective behavior of groups of organisms.