People have been doing mathematics with pen or pencil and paper for more than two thousand years. People have been doing mathematics with computers, and doing it widely, for no more than two or three decades. The methods and notation of paper-based mathematics are mature and universal. Likewise, the teaching of mathematics using lectures, blackboard, and books has had the advantage of time-tested trial and error to mature. With maturity comes a ready recognition of excellence when we see it. Most of us have little trouble recognizing an excellent teacher or an excellent book. We also know in short order when we are looking at something short of excellence.
The situation concerning computer-based mathematics is not so clear. Anyone who has used a symbolic manipulation system recognizes the enormous challenge that went into creating it, making it work correctly, and making it reasonably intuitive and easy to use. Yes, we have to allow for the shortcomings of the machinery available to tell the computer the mathematical stuff we want to communicate to it. And we recognize the need for some sort of mechanism to tell the computer, concisely and unambiguously, that part of mathematics that we normally communicate with a combination of notation and plain English. Here, at last, we come to the point of this short essay. The technology is so new that two things become obvious. First, there is no universal notation or mechanism. Second, since teaching these systems is a product-specific affair, about which we have relatively limited experience, there is great variety in the methods and in the quality of teaching and of available textbooks.
This volume falls well short of my expectations. I want to think there is no such thing as a bad technical book. I want to make allowances: the need is great; the audience is eager. If a book is based on classroom experience, as this book is, and if the renown of the universities at which the authors teach and by which the book is published is high, as it is in this case, I tend to believe that some sort of winnowing process has taken place and that I am reading what experience has shown works best. I expect a great book, or at least a good book.
But I do have my personal biases, and I have seen plenty of great technical books. When a book does not measure up, I feel it within the first few pages. When shortcomings occur throughout the book, I cannot endorse it with any enthusiasm. At best, I recommend that you look at this book yourself, and I leave it up to you to decide whether you want to teach with it, or, if you are not a teacher, whether you want to have it by your side as you work with Maple.
I will provide a minimum sketch of the things that bother me: haphazard and unclear descriptions; excessive computerese left to stand on its own; no demarcation between topics and subsections; unimaginative organization and page layout; shallow editing; and ubiquitous use of the phrase “there is,” or a variant of it, to begin sentences and even paragraphs. If these things do not bother you, so be it.
The book has 12 chapters that cover introduction, numbers, functions, basic algebra, calculus and differential equations, matrices and linear algebra, numerical methods, graphs and graphics, computational algebra, utilities, packages, data structures, Maple programming, and programming examples. Chapters end with bare-bones reference sections; the first five chapters have exercises. There is no bibliography. The table of contents is broken down by chapters, sections, and subsections. The 13-page index is incomplete and, on occasion, erroneous.
Learning Maple and working with Maple can be great fun. Reading this book is not.
