meta numerics

The following texts have proved very useful in my own education. I heartily recommend them to others.

Basic Library
Numerical Recipes Numerical Recipes: The Art of Scientific Computing
W. Press, S. A. Teukolsky, et al.

The first numerical programming text for any practicioner's shelf. It covers scores of areas, contains scads of code, and is chock full of useful practical advice, delivered in a friendly tone.

Acton's Numerical Methods Numerical Methods That (Usually) Work
F. S. Acton

An overview of the field by an early practioner. The algorithms profiled aren't the latest and greatest, but the mode of approach to numerical problems outlined here shouldn't be missed.

Cartoon Guide to Statistics The Cartoon Guide to Statistics
L. Gonick and W. Smith

A fun, helpful, and graphic introduction to mathematical statistics. No, this book won't let you turn off your brain and ignore the math. But it will ease you in to thinking like a statistician.

Advanced Library
Abramowitz and Stegun Handbook of Mathematical Functions
M. Abramowitz and I. A. Stegun

The classic reference on special functions. You won't find any code here, but you will find nearly every known mathematical property of your favorite function from grad school.

Golub and van Loan Matrix Computations
G. Goulb and C. van Loan

A standard reference on matrix decompositions and eigenvalue problems.

Cramer's Mathematical Statistics Mathematical Method of Statistics
H. Cramer

A classic, in-depth treatment by one of the pioneers in the field. Don't use this as an introduction, but when you are ready for the big league, this is a good book to have handy.

Brent Algorithms for Minimization Without Derivatives
R. P. Brent

A careful exposition of still state-of-the-art algorithms for root-finding in one dimension, and extrema-finding in one and multiple dimensions. Contains (ALGOL) code and rigorous algorithmic analysis.