Have computers and the web made books of math tables obsolete? To test this, I devised a list of ten math questions that you might expect to find answered in a book like this, and compared the book’s coverage against that of various free online sources. I also checked against the 27th edition of this book. The results are in the middle of this review.
This is definitely not the same book we knew in college. It was completely rewritten in the 30th edition (published in 1996). This 31st edition (published in 2003) is a big improvement over my 27th edition, in selection of material, in organization, and in appearance. The index is very thorough, and I was able to find the answers to my test questions almost immediately through the index.
There are a few infelicities. There’s a nine-page section on Signal Processing within the Probability and Statistics chapter. About half of this material really is signal processing, but should have been in the Analysis chapter. The other half is optimal filtering and really does belong in this chapter, but is not signal processing. The amount of context and background information vary a lot; at the low end, there is a page on interval analysis (p. 65) that gives you all its properties, but doesn’t tell you where the subject came from or why it is useful.
Now for the test! The questions:
- What’s the area of an ellipse?
- What’s the sum of the first n squares?
- What’s the biggest known prime?
- Is there a neat formula for the sum of the first n harmonic numbers?
- What’s Newton’s formula for the sum of the squares of the roots of a polynomial?
- What statistical test do you use to test whether two distributions have the same mean?
- What’s the indefinite integral of 1/(1+x4)?
- There’s a formula that relates Γ(z) and Γ(1-z). What is it?
- Are there any formulas for products of Fibonacci numbers?
- What’s the continued fraction for π/2?
And the results (number of questions answered):
Wolfram MathWorld: 7
CRC 31: 6
Wolfram Alpha: 5
Planet Math: 5
CRC 27: 4
Google and Wikipedia answered all the questions that CRC did, and then some. Google was especially impressive because it took almost no effort: just type in the question exactly as it is shown here, and the answer (except the indefinite integral) appeared in one of the three top-ranked results.
Although it only made a middling showing in my web test, this book has an edge over the web in a couple of areas. One is statistics: unlike math, statistics does not have a large presence on the web, and it’s hard to find answers to statistical methods questions there. The present book has 100 pages of useful statistical methods. The other area is for browsing for a useful result. When working on a math problem, it’s often valuable to look through handbooks for results or formulas that resemble the result you need and that you may be able to adapt to your needs. It’s very hard to do a web search for this purpose.
Allen Stenger is a math hobbyist and retired software developer. He is webmaster and newsletter editor for the MAA Southwestern Section and is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis. He volunteers in his spare time at MathNerds.com, a math help site that fosters inquiry learning.