by Prof Fred Szabo
Concordia University, Montreal, Canada
The second edition of this wonderful book promises to have a significant impact on how college-level mathematics is taught and learned. While the first edition was mainly addressed to mathematics teachers, its audience turned out to be significantly wider than intended. In fact, user reaction to the first edition suggests that the book has already changed the way certain aspects of undergraduate mathematics are viewed and understood.
Apart from the breadth of topics covered in this book, three features make this book a must-read for most mathematics and many science students. The book shows how the use of a computer-algebra system can enhance, facilitate and accelerate the learning of mathematics. This is particularly true for MuPAD, given its flexible pedagogical strengths and focus. The book also shows how structural programming encourages, motivates, and justifies mathematical rigor. The third and perhaps most striking feature of the book is its emphasis on visualization. This book takes its readers gently by the hand and helps them explore the visual properties of a large collection of basic mathematical objects in a way that is simply superb. The conversational style adopted by the author builds confidence, creates excitement, and may even have an influence on the content of the undergraduate mathematics curriculum in the years to come.
The selection of topics making up mainstream mathematics has always been in a state of flux, depending on existing mathematical knowledge and discovery, our changing understanding and interpretation of basic mathematical theorems and concepts, newly-found solutions to important mathematical problems, the interests of young researchers, and the computational needs of users of mathematics. This book adds new dimensions to this dynamic by helping to shape the view of mathematics of a new generation and by stimulating their visual imagination. This book is one of the first to provide us with an exciting glimpse into the vast range of possibilities for rethinking what and how we teach in our mathematics courses.
As mentioned by the author, neither the first edition, nor this new addition of MuPAD Pro Computing Essentials pretends to be all things to all people. They represent a very personal account of a new perspective of how mathematics can be taught and studied with the help of computer algebra. The selection of topics in these books is broad enough to satisfy the needs of most college and undergraduate university mathematics majors programs. However, user feedback has already resulted in significant changes and improvements to the first addition. While reader influence is apparent in almost all chapters of this second edition, the author also takes full advantage of advances in the development of the MuPAD computer algebra system. This particularly apparent in Chapter 7, which is completely new, and precedes the descriptive exploration of curves and surfaces in Chapter 8 with a fascinating and manageable introduction the dynamic world of interactive graphics and computer animation.
Teachers of mathematics are currently still locked in vigorous debate about the virtues of computer-assisted teaching and learning. Opponents of the use of this technology argue that student fails to learn the basics. All they manage to acquire is a facility for pressing appropriate buttons to achieve mathematical output that they fail to understand. This is precisely why it is essential that the proponents of computer-assisted teaching and learning write good books that illustrate the pedagogical and mathematical benefits of technology. The present text is an excellent example of what is needed. It shows clearly the pedagogical value of a modest form of structural programming, and explains in motivational detail the basic steps and structure of many of the algorithms usually studied by mathematics undergraduates.
Let us briefly consider the range of topics covered in the text. It illustrates the comprehensive nature and extent of possible use of this book as a stand-alone textbook for college-level mathematics major programs.
The first five chapters still deal with the mechanics of using MuPAD, but in much greater detail and with more mathematical emphasis than the corresponding chapters in the first edition. They provide a careful introduction to basic principles of mathematical programming and algorithmic thinking. This is appropriate for several reasons. First of all, it is required reading for those interested in using MuPAD. But it is also indispensable for all mathematics students who hope to use their knowledge in the workplace. Today, and in the years to come, most mathematics graduates worth their salt are expected to be able to program in much the same way as they were expected to be able to use logarithm tables, slide rules and other gadgets in the past.
Chapters 9 to 13 provide an excursion into the more traditional topics of college mathematics: the language of sets, number systems, and some algebra, trigonometry, calculus and linear algebra. As such, MuPAD Pro Computing Essentials represents, in a real sense, a launch pad for the study of deeper mathematics with the help of MuPAD. The rapid development of specialized and advanced MuPAD libraries makes it possible to advance this project well beyond the practical limits set for this book.
I am looking forward to introducing my students to this new edition of MuPAD Pro Computing Essentials.