Publisher: John Wiley (2008)Details: 599 pages, Hardcover
Price: $96.95
ISBN: 9780470416747
Category: Textbook
Topics: Pre-Calculus
Sheldon Axler
Publisher: John Wiley (2008)
Details: 599 pages, Hardcover
Price: $96.95
ISBN: 9780470416747
Category: Textbook
Topics: Pre-Calculus
[Reviewed by Allen Stenger, on 04/22/2009]
This is a competent but not very innovative precalculus text. It has a fairly conventional coverage of high school algebra, functions, and trigonometry, and an unusual amount on area.
It does have some unusual approaches to particular topics. These are often improvements over the usual approach, but they don't reach very far. The most interesting innovation is to express exponential decay in terms of powers of 2 instead of powers of e, because that makes the half-life very obvious. One reason for the emphasis on area is to define the constant e in terms of an area under the curve y = 1/x; I wasn't convinced that this was an improvement over more traditional approaches, although it does give a glimpse into what's coming in calculus.
The book includes complete solutions for all the odd-numbered exercises, and each even-numbered exercise is constructed to use the same techniques as the immediately-preceding odd-numbered exercise. The solutions are well-written and easy to follow.
The existence of precalculus texts and courses raises the question: Is precalculus a real subject? The present book answers in the negative, saying in the Preface, "This book seeks to prepare students to succeed in calculus". The book takes this to its logical conclusion by omitting those portions of algebra and trigonometry that are not useful in calculus.
I think on the whole this streamlined approach is unsuccessful. It does not really cut out that much, and by cutting it gives the impression that no part of precalculus is interesting in itself: it's just something you have to suffer through so you can enjoy the good stuff later.
In particular motivations are weak. For example, on p. 147 we launch into an investigation of how to define exponentiation by positive integers, which is explained clearly but is explained without any hints about whether this operation, if we could figure out how to do it, would be interesting or useful. This approach is used throughout the book and could be thought of as an axiomatic approach to precalculus: define everything first, ensure that everything is consistent, but don't worry about where the subject came from or where it's going
Allen Stenger is a math hobbyist, library propagandist, and retired computer programmer. He volunteers in his spare time at MathNerds.com, a math help site that fosters inquiry learning. His mathematical interests are number theory and classical analysis.