Preface by Prof. Fred Szabo
Concordia University, Montreal , Canada
The selection of topics making up mainstream mathematics has always been in a state of flux, depending on the state of 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.
An additional force is about to make inroads into determining our choice of topics: the personal computer and the computer algebra systems created for it. 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.
The book MuPAD Pro Computing Essentials does not pretend to be all things to all people. It is a very personal account of one new perspective of how mathematics can be taught and studied with the help of computer algebra. The selection of topics in this book is broad enough to satisfy the needs of most college and undergraduate university mathematics majors programs.
Teachers of mathematics are currently 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 book is an excellent example of what is needed.
Let us consider the range of topics covered in the text.
The first five chapters deal with the mechanics of using MuPAD. In doing so, they provide a quick introduction to basic principles of mathematical programming. 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 student who hope to use their knowledge in the workplace. Today and in the years to come, 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.
The real contribution of the computer algebra approach to teaching and learning begins with Chapter 6. The study of graphs and surfaces has been revolutionized with help of computers. It is generally agreed that today’s students are visually than verbally oriented. What better way to begin their mathematical career than to build on this skill.
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, the book is in many ways a launching 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 the project well beyond the practical limits set for this book.
I am looking forward to introducing my students to new ways of thinking about mathematics using the MuPAD Pro Computing Essentials.
Prof. Fred Szabo