The difference between a clear and lucid math book and one that is, to coin a politically correct phrase, organizationally challenged can be the difference between success and failure for the math student. I can't tell you that I have read through even a sizeable fraction of the calculus texts and study guides that are on the market, but I have looked at a bunch of them. If you are taking a college calculus course, you probably have already been assigned a required text. You will, of course, have to buy that text, whether it is any good or not, just so that you can do the homework assignments. But it doesn't hurt anything besides your pocket book to have other references at your fingertips. So here I shall make my recommendations from among the books I am familiar with that are still in print. If you click on a book, it will take you to the page of where you can order that title. The prices listed here are those posted by Amazon.com at the time I prepared this page.

Here is a book I highly recommend for anybody who tends to fall
asleep while reading math books. The style in *How to Ace Calculus: The
Streetwise Guide*
by Joel Hass, Abigail Thompson, Colin Conrad Adams
is so lively that I had to put it down in order
avoid succumbing to the urge to plagiarize it. In the actual calculus
material, you don't have to wade through a lot of stuff to get to the
critical points. This book specializes in critical points -- that is
the stuff you must know to pull down a good grade. And it describes
them language so plain it will have you chuckling from time to time.
It also has some
great practical advice on how to select a good teacher, how to
ask questions, how to study, etc. The examples worked in the text
are not the really difficult ones that sometimes might
show up on an exam, but you have to learn the not-so-hard ones before you
can do the hard ones. To those of you who thought you could never
understand math, this book is worth many times its price.

- How to Ace Calculus: The Streetwise Guide by Hass, Thompson, and Adams, Paperback: $11.96

An outfit called **Schaum's Outline Series** has been publishing study aids
in a wide variety of subjects for decades now. I once had a coworker who was
fond of saying that he got his degree from Schaum's Institute of Technology.
There are several calculus volumes that they publish. One of them I am
quite familiar with, and that is the one by Frank Ayres and Elliot Mendelson.
There are brief, clear explanations of the concepts and methods. But the
emphasis is upon worked examples. There are over 1000 of them. For what
it's worth, this book has sold over a million copies in the 30 years it's
been in print.

- Theory and Problems of Differential and Integral Calculus by Ayres and Mendelson, 3rd ed., Paperback: $11.96

Here's another from the **Schaum's** series. It has fewer worked problems,
covers fewer topics, but has much more explanatory text. And the explanations are
organized in a consistent way. Each section is divided into the concepts
of Approximation, Refinement, and Limit. The author, Eli Passow, shows how
these three stages are effective at attacking a wide variety of problems.

- Understanding Calculus Concepts by Eli Passow, Paperback: $11.16

Having a different viewpoint of a topic always helps.
Silvanus P. Thompson believed that calculus did not have to
be difficult. In the first decade of the 20th century, he
wrote a little book called *Calculus Made Easy* in which
he appealed to concepts that most of us already have to
explain how calculus works. His approach is different from
the one commonly used in college calculus courses today
(no epsilons and no deltas).
He uses a concept he calls "orders of smallness." But when
married to elementary algebra it
leads to the very same conclusions you would learn in any
calculus course. More recently Martin Gardner (author of
*Scientific American's* Mathematical Games column) has annotated
Thompson's work, and this edition is now available from
St. Martin's Press. Some of Gardner's comments explain
how Thompson's approach to a topic differs from the
approaches that are popular today. The important point,
though, is that Thompson's methods and his elegantly simple
explanations lead you to an understanding that is every
bit as useful and valid as the one you will get in
class. And once you have traveled Thompson's road,
your instructor's road won't seem nearly as rocky.

- Calculus Made Easy by Sylvanus P. Thompson and Martin Gardner, Hardcover: $15.37

Of all the beginning calculus texts that have been foist onto students,
there is one that, in my opinion, stands head and shoulders above the rest.
Apparently I am not the only one to think so. Enough others feel
this way to have kept this book in print for nearly 40 years.
This is *Calculus and Analytic Geometry* by George B. Thomas Jr.
at M.I.T. It is now in its 9th edition. Later editions have
some contributions from Thomas' associate, Ross L. Finney.
The development is logical, there are loads of worked examples,
the explanations are clear, and the authors have had 9 editions
and several decades to bring this work very near perfection.

- Calculus and Analytic Geometry by Thomas & Finney, 9th ed., Hardcover: $93.75
- Calculus and Analytic Geometry by Thomas & Finney, 9th ed., Paperback Vol 1: $22.50
- Calculus and Analytic Geometry by Thomas & Finney, 9th ed., Paperback Vol 2: $22.50

For anyone planning a career in science or engineering, I recommend that you
**eventually** get *Mathematical Methods in the Physical Sciences* by
Mary Boas. It is a broad survey of theory and methods that you will be
using to solve problems that involve physics or engineering. It is
quite accessible to anybody who has had two semesters of calculus, and
the explanations of the methods are clear and concise. When you take
your advanced undergrad courses, this book may prove to be invaluable.

- Mathematical Methods in the Physical Sciences by Mary L. Boas, 2nd ed. $92.95

If your second or third semester calculus course covers differential equations, you will want this book. It begins by explaining concepts in linear algebra, which is a skill you will need if you plan to continue your math education. It then goes on to the basics of differential equations, with emphasis on linear differential equations. There is plenty of explanatory text and worked examples.

- Introduction to Linear Algebra and Differential Equations by John W. Dettman, Paperback: $9.56

Here are two very useful reference books for those of you who will be using math in your future studies or careers:

- CRC Standard Math Tables and Formulae 30th ed. Hardcover $44.95
- Handbook of Mathematical Functions by Milton Abramowitz and Irene Stegun Paperback: $26.93

- 1 2 3 Infinity by George Gamow, Paperback: $7.16
- The Mathematical Tourist by Ivars Peterson, Paperback: $11.96

More books will be appearing on this list soon, including titles that I recommend for those of you who plan to continue your math studies beyond first year calculus.

email me at *hahn@netsrq.com*