How to sum a large array of floats while keeping errors in check

Books on J

Nice way of deriving the sum and diff identities for sine and cosine based on Euler's Formula (exp(alpha*i) = cos(alpha) + i sin(alpha))

Cool math-oriented pics of nature

A classic

Describes a simple method for generating an endless succession of beautiful fractal patterns by iterating simple maps and ordinary differential equations with coefficients chosen automatically by the computer. It contains over 350 examples of such patterns. Each pattern produces a corresponding piece of fractal music.

This book collects in the same document all state-of-the-art algorithms in multiple precision arithmetic (integers, integers modulo n, floating-point numbers). The best current reference on that topic is volume 2 from Knuth's The art of computer programming, which misses some new important algorithms (divide and conquer division, other variants of FFT multiplication, floating-point algorithms, ...)

A Brilliant Madness is the story of a mathematical genius whose career was cut short by a descent into madness. At the age of 30, John Nash, a stunningly original and famously eccentric MIT mathematician, suddenly began claiming that aliens were communicating with him and that he was a special messenger.

A formula that "renders" itself

Why is e^(pi i) = -1?

The BaileyBorweinPlouffe formula (BBP formula) provides a spigot algorithm for the computation of the nth binary digit of À.

"The intent of this project is to compile information about ALL the mathematicians of the world."

Just awesome...

Published in 1991 and still in print from Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. There is also an online Instructor's Manual and a student Study Guide.

Statistics 202: Statistical Aspects of Data Mining, Summer 2007

Computing reciprocal square roots is necessary in many
applications, such as vector normalization in video games. Often,
some loss of precision is acceptable for a large increase in speed.
This note examines and improves a fast method found in source-
code for several online libraries, and provides the ideas to derive
similar methods for other functions

CORDIC (digit-by-digit method, Volder's algorithm) (for COordinate Rotation DIgital Computer) is a simple and efficient algorithm to calculate hyperbolic and trigonometric functions.

The wonders of base-3

contours gnuplot demo

The "dude" from the Game of Life! Math's Prof. at Princeton

Looks like a quite serious book on Graph Theory... Springer!

The "evolution" of bit-twiddling: awesome book with tons of hackerish routines

In this book, Eli Maor draws on his remarkable talents as a guide to the world of numbers to dispel that view. Rejecting the usual arid descriptions of sine, cosine, and their trigonometric relatives, he brings the subject to life in a compelling blend of history, biography, and mathematics. He presents both a survey of the main elements of trigonometry and a unique account of its vital contribution to science and social development. Woven together in a tapestry of entertaining stories, scientific curiosities, and educational insights, the book more than lives up to the title Trigonometric Delights.

Vectorized trigonometric unit circle

The Stanford Center for Professional Development has digitized more than one hundred tapes of Knuth's musings, lectures, and selected classes and posted them online. These archived tapes resonate with not only his thoughts, but with insights from students, audience members, and other luminaries in mathematics and computer science.

Compilation of free online lectures from several universities.

The Online Encyclopaedia of Mathematics is the most up-to-date and comprehensive English-language graduate-level reference work in the field of mathematics today. This online edition comprises more than 8,000 entries and illuminates nearly 50,000 notions in mathematics. The Encyclopaedia of Mathematics is updated on a regular basis to remain a quick, precise source of reference to mathematical definitions, concepts, explanations, surveys, examples, terminology and methods, which will prove useful for all mathematicians and other scientists who encounter mathematics in their work.

G.H. Hardy's A Mathematician’s Apology

Factorization using the Elliptic Curve Method Java Applet

Issues of technical writing and the effective presentation of mathematics and computer science. Preparation of theses, papers, books, and literate computer programs.

Mathematica's Google Aptitude

Attacking Hash Functions by Poisoned Messages. With an actual example of a _meaningful_ collision.

Detailed technical description of MD5 collisions

Things you might not know about Bruce Schneier

The Science of Programming Matrix Computations

DETECTING PERFECT POWERS IN ESSENTIALLY LINEAR TIME

Why we should have considered 2*pi as pi instead of pi.

Using DeBruijn Sequences to Index a 1 in a Computer Word

FLATLAND A Romance of Many Dimensions

Cheat sheets and notes

Funny math tests "results".