Calca

I found this little gem of a tool called Calca. It is a text editor symbolic calculator.

FRACTRAN

I came across this mathematical programming article on Wikipedia called FRACTRAN.

FRACTRAN is a Turing-complete esoteric programming language invented by the mathematician John Conway.

What an amazing methodology. I decided to buy the referenced book "Nonplussed!: Mathematical Proof of Implausible Ideas". It's easy to read, but the proof is still difficult to follow. I really need to read it again.

J - An Amazing Programming Language

J is a modern, high-level, general-purpose, high-performance programming language. J is portable and runs on Windows, Unix, Mac, and PocketPC handhelds, both as a GUI and in a console.

Quite Basic -- Sieve of Eratosthenes

A BASIC programming website that uses the Sieve of Eratosthenes as an example.

F#

I'm learning F#, Microsoft's latest functional programming language for the .NET family. Very nice and interesting. I recommend buying these books on it: F# for Scientists, Foundations of F#, and Expert F#.

Processing

Processing is an open source programming language and environment for people who want to program images, animation, and interactions. It is used by students, artists, designers, researchers, and hobbyists for learning, prototyping, and production. It is created to teach fundamentals of computer programming within a visual context and to serve as a software sketchbook and professional production tool. Processing is developed by artists and designers as an alternative to proprietary software tools in the same domain.

There's also a Javascript version of the code.

Logo++

Logo++ is an interpreter for drawing graphical figures following very simple instructions. Though it lacks many essential features of programming languages, it remains a funny start for beginners in computer programming, particularly for kids.

Mathematical Illustrations

Mathematical Illustrations is a book on mathematical PostScript programming and geometry. The website contains plenty of examples for downloading.

WIRIS CAS Web Calculator

WIRIS CAS is an on-line platform for mathematical calculations designed for education. It is in fact a CAS that also includes a DGS inside. You can access a powerful calculation toolbar through an HTML page that includes integrals and limits calculation, function graphing in 2D or 3D or symbolic matrices manipulation. It covers all mathematical topics from High School to University level (Calculus, Algebra, …).

Scythe Statistical Library

The Scythe Statistical Library is an open source C++ library for statistical computation, written by Daniel Pemstein (University of Illinois), Kevin M. Quinn (Harvard University), and Andrew D. Martin (Washington University). It includes a suite of matrix manipulation functions, a suite of pseudo-random number generators, and a suite of numerical optimization routines. Programs written using Scythe are generally much faster than those written in commonly used interpreted languages, such as R and MATLAB, and can be compiled on any system with the GNU GCC compiler (and perhaps with other C++ compilers). One of the primary design goals of the Scythe developers has been ease of use for non-expert C++ programmers. We provide ease of use through three primary mechanisms: (1) operator and function over-loading, (2) numerous pre-fabricated utility functions, and (3) clear documentation and example programs. Additionally, Scythe is quite flexible and entirely extensible because the source code is available to all users under the GNU General Public License.

SAGE

Use SAGE for studying a huge range of mathematics, including algebra, calculus, elementary to very advanced number theory, cryptography, numerical computation, commutative algebra, group theory, combinatorics, graph theory, and exact linear algebra.

MPFRCPP

The Multiple Precision Floating-Point Reliable Library C++ Interface (MPFRCPP) is free object oriented interface to the MPFR library. MPFR provides arbitrary precision arithmetic on floating-point numbers. MPFRCPP overloads operators, functions and represents floating point numbers as class objects to make using of MPFR in OO-programs easier.

Distribution package includes Numeric Analysis / Computer Research C++ Classes with implementation of rational numbers, polynomials (including orthogonal polynomials) and complex numbers.

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.

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.

Apfloat for C++

Apfloat is a high performance arbitrary precision package. That means you can do calculations involving millions of digits with it. It uses Number Theoretic Transforms. It's simple to use. It's fast. It's freeware.

Prime Numbers in PostScript

Here's an interesting website that shows you how to use a printer to generate prime numbers. It also has a PostScript file that generates ULAM's Spiral.