This is an intimidatingly-thorough reference work on how to survive and prosper in college mathematics courses. The book is well-crafted and really does cover everything you need to know to succeed, and it only occasionally drifts into platitudes and verbosity. It is especially strong in explaining the structure and reward systems of college departments and how math curricula are organized. Most of the book is not math-specific, and except for some examples it does not attempt to teach math itself.

The book suffers from being too predictable: it emphasizes the traditional academic values of self-discipline, being prepared, paying attention, and knowing your place. It assumes you will be taught strictly by lecture, which although probably accurate for most students (especially those not majoring in mathematics) overlooks the exciting things that are being done with inquiry-based learning today. It is also weak on technology (or maybe just realistic about what non-majors will find), and focuses more on the dangers of technology than its benefits. To a large extent the technology discussion is limited to calculators (and not even graphing calculators), with no mention of mathematical software, and web site use being limited to visiting the instructor's and the publisher's sites.

I compared the book to another, very different one: Adams & Hass & Thompson's How to Ace Calculus: The Streetwise Guide (Freeman, 1998). This is obviously a more specialized book, and comparatively lightweight. But it too is a reference book, and includes the most important points in Dahlke's much longer work, along with a lot of calculus. The tone is completely different: "Ace" is a very funny book and is a quick read (if you skip the calculus parts). I think "Ace", although not necessarily a better book, has a big competitive advantage for these books' intended market of college undergraduates because it is cheaper, shorter, and funnier.

Is anything missing from Dahlke's very long and detailed book? The joy is missing. The author gives the impression that college mathematics is something to be endured and overcome on your way to your goal, and doesn't hint that it might be possible to enjoy your mathematics courses.

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.