- Membership
- Publications
- Meetings
- Competitions
- Community
- Programs
- Students
- High School Teachers
- Faculty and Departments
- Underrepresented Groups
- MAA Awards
- MAA Grants

- News
- About MAA

Publisher:

Chapman & Hall/CRC

Publication Date:

2003

Number of Pages:

910

Format:

Hardcover

Edition:

31

Price:

62.95

ISBN:

9781584882916

Category:

Handbook

[Reviewed by , on ]

Allen Stenger

05/27/2010

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+x
^{4})? - 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 MathNerds.com, a math help site that fosters inquiry learning.

Analysis

Constants

Special numbers

Series and products

Fourier series

Complex analysis

Interval analysis

Real analysis

Generalized Functions

Algebra

Proofs without words

Elementary algebra

Polynomials

Number theory

Vector algebra

Linear and matrix algebra

Abstract algebra

Discrete Mathematics

Symbolic logic

Set theory

Combinatorics

Graphs

Combinatorial design theory

Communication theory

Difference equations

Discrete Dynamical Systems and Chaos

Game theory

Operations research

Geometry

Coordinate systems in the plane

Plane symmetries or isometries

Other transformations of the plane

Lines

Polygons

Conics

Special plane curves

Coordinate systems in space

Space symmetries or isometries

Other transformations of space

Direction Angles and Direction Cosines

Planes

Lines in space

Polyhedra

Cylinders

Cones

Surfaces of revolution: the torus

Quadrics

Spherical geometry & trigonometry

Differential geometry

Knots up to eight crossings

Angle conversion

Continuous Mathematics

Differential calculus

Differential forms

Integration

Table of Indefinite Integrals

Table of definite integrals

Ordinary differential equations

Partial differential equations

Eigenvalues

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

Polylogarithms

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

Z-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

Statistics

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

Miscellaneous

Units

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

Index

- Log in to post comments