Factorization Using the Elliptic Curve Method

Click here for a Java implementation of integer factorization using the elliptic curve method (ECM). Source code included.

Prime Number Spiral

The Prime Number Spiral software is a tool for exploring the Ulam spiral.

Gnuplot

Gnuplot is a portable command-line driven interactive data and function plotting utility for UNIX, IBM OS/2, MS Windows, DOS, Macintosh, VMS, Atari and many other platforms. The software is copyrighted but freely distributed (i.e., you don't have to pay for it). It was originally intended as to allow scientists and students to visualize mathematical functions and data. It does this job pretty well, but has grown to support many non-interactive uses, including web scripting and integration as a plotting engine for third-party applications like Octave. Gnuplot has been supported and under development since 1986.

Project Euler

Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems.

The motivation for starting Project Euler, and its continuation, is to provide a platform for the inquiring mind to delve into unfamiliar areas and learn new concepts in a fun and recreational context.

uCalc

UCALC Windows Graphing Calculator comes with the following features: Expression Evaluator, Unit Converter, User Solution Modules, Graphing, Equation Solver, User Functions & Variables, Summation Tables, Integrator, and General Ledger.

UCalc Fast Math Parser allows programs to evaluate math expressions that are defined at run time. Ease of implementation, flexibility, sturdiness and speed are at the core of the product's design. It includes direct support for Visual Basic, C++ (Microsoft and Borland), PowerBASIC (PB/DLL and PB/CC), and Delphi.

Euler Angles

A good read on three-dimensional space and how to rotate the orthogonal coordinate system.

Command Line Quaternions

Quaternions are numbers with 4 parts: one for time, three for space. This project hopes to create command line functions that generate thousands of points of quaternions, to be fed into animation software. Think: analytical animation!

Wolfram Web Resources

In addition to Mathworld, Wolfram Web Resources hosts an extensive list of other sites, including: Demonstrations, Functions, Gallery, Integrals, and Tones,

Mathematica 6

Mathematica 6 has been released and you can see some nice demonstration over at the Wolfram Demonstration Project.

Calculus Videos

The Department of Mathematics at University of Houston has created this library of calculus videos viewable using Apple's QuickTime. They also have a list of shorter videos for some calculus concepts.

Gnofract 4D

Gnofract 4D is a free, open source program which allows anyone to create beautiful images called fractals. The images are automatically created by the computer based on mathematical principles. These include the Mandelbrot and Julia sets and many more. You don't need to do any math: you can explore a universe of images just using a mouse. It runs on Unix-based systems such as Linux and FreeBSD.

SpeQ Mathematics

SpeQ is a small, extensive mathematics program with a simple, intuitive interface. All calculations are entered in a sheet. In there you can freely add, edit and execute all calculations. You can define variables and functions, and plot graphs of your functions. You can save your calculations for later re-use.

Maths Films

The aim of this website is to provide a source of animated mathematical films, images and text to support the teaching of mathematics in ways that build on the intuitions and powers we have all possessed all our lives.

What is the 4th Dimension?

Four-dimensional geometry is Euclidean geometry extended into one additional dimension. The prefix "hyper-" is usually used to refer to the four- (and higher-) dimensional analogs of three-dimensional objects, e.g. hypercube, hyperplane, hypersphere. n-dimensional polyhedra are called polytopes.

Here are some interesting notes, images and movies for understanding what the fourth dimension would look like.

Mesecina

Mesecina is a software to visualize and study the medial axis and related computational geometry structures in the plane.

Cornell University Library Historical Mathematics Monographs

The Cornell University Library Historical Mathematics Monographs is a collection of selected monographs with expired copyrights chosen from the mathematics field. These were monographs that were brittle and decaying and in need of rescue. These monographs were digitally scanned and facsimile editions on acid free paper were created.

FreeTechBooks.com

FreeTechBooks.com has a large number of free mathematics books.

yEd - Java Graph Editor

yEd is a very powerful graph editor that is written entirely in the Java programming language. It can be used to quickly and effectively generate drawings and to apply automatic layouts to a range of different diagrams and networks.

What Do Numbers Sound Like?

This website contains a list of math songs. The numbers assigned are actually the major scale degrees that correlate. If you don't know basic music theory, think "Do = 1, Re = 2, Mi = 3, Fa = 4, So = 5, La = 6, Ti = 7, Do + Octave = 8, Re + Octave = 9, and 0 = Quarter Rest." Listen to $\pi$ up to 1,000 digits on the piano alone or on the piano, bass & flute together.

Open (to interpretation) question: Which number sounds the best? Which transcendental constant sounds the best?

BBP-Type Formulas

The BBP (named after Bailey-Borwein-Plouffe) is a formula for calculating `\pi` discovered by Simon Plouffe in 1995,
`\pi = \sum_(n=0)^\infty(\frac{4}{8n+1}-\frac{2}{8n+4}-\frac{1}{8n+5}-\frac{1}{8n+6})(1/(16))^n`.

Amazingly, this formula is a digit-extraction algorithm for `\pi` in base 16.

Following the discovery of this and related formulas, similar formulas in other bases were investigated. This class of formulas are now known as BBP-type formulas.