Click Back to return
THE MATHWRIGHT LIBRARY NEWSLETTER, Feb 2004, VOL 5,
#8
A publication of Bluejay Lispware
James E. White, Editor
The official publication of the New Mathwright Library and Café:
In this issue:
Calculus
in Action: A new free
500 Page Calculus Book
1) Calculus in Action: A new free 500 Page Calculus Book
The
entire hypertext version of our new book, Calculus
in Action, is free for all. Why? For two reasons.
First,
it is a new kind of mathematics book. It is dynamic,
written from the point of view of the new dimension of reader interaction.
We make the dynamic version of our book available, online or offline,
only to Library members. The static hypertext version, though, is available
free to any reader. We believe at the Library that this will
be the shape of the teaching and learning environments of the near future.
Books like this one will come to life in the hands of the teacher and student,
full of the rich demonstrations and experiments that will encourage readers
to pursue their own ideas by asking "What if?" questions.
The
500 page book, which consists of 49 lectures and 43 Interactive Explorations,
is presented in 10 Mathwright Microworlds. All of the text is contained within
the Microworlds, just as it is in the text
version here. It may be printed, lecture by lecture, from either place.
Visit our Table of Contents
or the Index to see the range
of topics that we cover. They are nearly all about gravitation. That is the
theme of the story, our main question, for which the Calculus is the language
that provides our best answer.
And
the book is also about a wonderful unification of what had seemed to be two
separate questions. How do objects fall? And how do the Moon and the Planets
move? These are really the same question. And the history of that question
is the subject of our book. We begin to ask the first question in the introductory
Pre-Calculus chapter. The second question will lead the reader, standing
"on the shoulders" of John Kepler and Isaac Newton, to a new understanding
of the Calculus itself, as we follow Newton in the answer that he found.
Second,
this is not a textbook. It is a story of Calculus that will lead the
reader through the equivalent of two or more years of the mathematical foundations
of the subject, but it is not constrained by any curriculum. Rather, it traces
the development of Calculus as a circle of ideas that grew out of the 17th
Century dawning understanding, in the hands of Galileo, Kepler and Newton,
of the nature of Gravity. It refers to original sources, and is generally
written in the spirit of the "Great Books" strategy championed by
such American schools as St. John's University, and widely practiced abroad.
Thus,
it discusses the history and philosophy of these ideas, as well as the mathematics.
The
motivated reader of Calculus in Action will arrive at a mature and
deep understanding of Calculus in the way that it is used today. And, because
of our discursive and problem-oriented approach to the story, the
reader will also appreciate its origins in 17th Century science as well as
its relations to modern areas of mathematics, such as Linear and Abstract
Algebra, Topology and Differential Geometry.
In
fact, this book will likely strike students as a new kind of mathematics book,
unlike one they have ever seen, and certainly not like any Calculus Textbook,
either in content or in form. To that end, each Microworld Section of each
Chapter of the book first discusses a problem that we need to solve to deepen
our understanding of the gravitation theme, and then recruits and explains
the techniques that Calculus can supply to help us solve it. The problems
are not easy ones, but we attempt in the lectures and interactive explorations
to bring them to life, so that readers can experiment, and become familiar
with them. The book is written for readers who enjoy mathematics, and have
the curiosity and the desire to see the small part of it that we develop here,
as a whole: roots, branches, and leaves.
We
give you the text version free in order to encourage you
to explore this new medium with us, and frankly, to join the Mathwright Library.
When we come to discuss the retrograde motion of Mars in the night
sky that so complicated Ptolemy's picture of the motion of the planets, we
show you what the ancients saw, in a 3 dimensional model Solar System. When
we discuss the grand conservation laws: conservation of angular momentum and
conservation of energy, we let you put them to use as you attempt to dock
the Space Shuttle with a Satellite. You will find that this is not easy! But
the main explorations are designed to show you how each new concept: inclined
planes and vectors, center of gravity and radius of curvature, to name a few,
came to be incorporated in the Calculus. Teachers:
Be prepared for a few surprises in the choice and range of topics. Library
and Institutional members are invited to correspond with the author on any
questions about the material or the interactive explorations.
These
Explorations are designed to encourage readers to pursue their own ideas by
asking "What if?" questions. They also play a heuristic role to help the reader
visualize new constructions, techniques and concepts. So
check out the text version of Calculus in Action, then use your Library
membership to bring it to life! Library members may read these 10 Microworlds
(that contain within them the full 500 page text) in their browsers using
MathwrightWeb (or MathwrightNET), but they will probably prefer to download
them to read offline with Mathwright32 Reader (or Mathwright32 Reader NET).
For a beginning student of Calculus, either version will provide years of
enjoyable learning in our alternative to a Calculus Text.