Preface
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. Prof. Fred E. Szabo |