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We’re now twenty years into “calculus reform”, far enough in that the excesses of the early days have been moderated; we’ve achieved a balance between the best of pre1986 calculus teaching and the new ideas of the two decades since then. Indeed, “reform calculus” has in many ways simply become “calculus”, and many people know no other way to approach the subject.
In that light, it’s worth taking a look at an old book through fresh eyes.
On the one hand, we have none of the serious datadriven problems that calculus reform and its parallel reform in statistics teaching have emphasized. In that respect, this book remains a product of its times. On the other hand, though, the basic ideas of calculus and of statistics are here and wellpresented. The foreword makes it clear that this is a specialized calculus text and is thus narrow in its focus–in particular, the trigonometric functions are absent–but that does not detract from its appeal.
The title calls for careful interpretation. “Calculus and Statistics” is very different than “Statistics with Calculus” would be. The text includes more statistics than is common in calculus books and more calculus than in a first statistics text. It successfully resists the temptation to force either subject in where it’s not a good fit — the two topics are used to enhance the other only when appropriate. Both subjects are there, but there are chapters where one predominates — as it should be. Just as calculus has little to tell us about enumerative probability, statistics plays little role in the definition of the derivative. Gemignani’s work reflects that reality while at the same time giving both subjects appropriate treatment.
On balance, then, what we have in this book is a clear introduction to elementary statistics and of those areas of calculus that are useful in that field. Calculus and Statistics also stands as a reminder that good calculus books predate calculus reform.
Mark Bollman (mbollman@albion.edu) is an assistant professor of mathematics at Albion College in Michigan. His mathematical interests include number theory, probability, and geometry. His claim to be the only Project NExT fellow (Forest dot, 2002) who has taught both English composition and organic chemistry to college students has not, to his knowledge, been successfully contradicted.
1.

The Basic Concepts of Function and Probability  
2.  Some Specific Probabilities  
3.  Random Variables. Graphs.  
4.  The Derivative  
5.  Applications of the Derivative  
6.  Sequences and Series  
7.  Integration  
8.  The Integral and Continuous Variates  
9.  Some Basic Discrete Distributions  
10.  Other Important Distributions  
11.  Hypothesis Testing  
12.  Functions of Several Variables  
13.  Regression and Correlation  
Appendix  
Answers to Selected Exercises  
General Index  
Index of Symbols  