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CRC Standard Mathematical Tables and Formulae

Daniel Zwillinger
Chapman & Hall/CRC
Publication Date: 
Number of Pages: 
[Reviewed by
Allen Stenger
, on

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):

Google: 8
Wikipedia: 8
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, a math help site that fosters inquiry learning.

Special numbers
Series and products
Fourier series
Complex analysis
Interval analysis
Real analysis
Generalized Functions

Proofs without words
Elementary algebra
Number theory
Vector algebra
Linear and matrix algebra
Abstract algebra

Discrete Mathematics
Symbolic logic
Set theory
Combinatorial design theory
Communication theory
Difference equations
Discrete Dynamical Systems and Chaos
Game theory
Operations research

Coordinate systems in the plane
Plane symmetries or isometries
Other transformations of the plane
Special plane curves
Coordinate systems in space
Space symmetries or isometries
Other transformations of space
Direction Angles and Direction Cosines
Lines in space
Surfaces of revolution: the torus
Spherical geometry & trigonometry
Differential geometry
Knots up to eight crossings
Angle conversion

Continuous Mathematics
Differential calculus
Differential forms
Table of Indefinite Integrals
Table of definite integrals
Ordinary differential equations
Partial differential equations
Integral equations
Tensor analysis
Orthogonal coordinate systems
Control theory

Special Functions
Trigonometric or circular functions
Circular functions and planar triangles
Inverse circular functions
Ceiling and floor functions
Exponential function
Logarithmic functions
Hyperbolic functions
Inverse hyperbolic functions
Gudermannian Function
Orthogonal polynomials
Gamma function
Beta function
Error functions
Fresnel integrals
Sine, cosine, and exponential integrals
Hypergeometric functions
Legendre functions
Bessel functions
Elliptic integrals
Jacobian elliptic functions
Clebsch-Gordan coefficients
Integral transforms: Preliminaries
Fourier integral transform
Discrete Fourier transform (DFT)
Fast Fourier transform (FFT)
Multidimensional Fourier transforms
Laplace transform
Hankel transform
Hartley transform
Hilbert transform
Tables of transforms

Probability and Statistics
Probability theory
Classic probability problems
Probability distributions
Queuing theory
Markov chains
Random number generation
Control charts and reliability
Risk analysis and decision rules
Confidence intervals
Tests of hypotheses
Linear regression
Analysis of variance (ANOVA)
Probability tables
Signal processing

Scientific Computing
Basic numerical analysis
Numerical linear algebra
Numerical integration and differentiation
Programming techniques

Financial Analysis
Financial formulae
Financial tables

Interpretations of powers of 10
Calendar computations
AMS classification scheme
Fields medals
Greek alphabet
Computer languages
Professional Mathematical Organizations
Electronic mathematical resources
Biographies of mathematicians

List of references
List of figures
List of notation