Cactus is a general, modular, parallel environment for solving systems of partial differential equations. The code has been developed over many years by a large international collaboration of numerical relativity and computational science research groups and can be used to provide a portable platform for solving any system of partial differential equations.
Calc is arbitrary precision arithmetic system that uses a C-like language. It's useful as a calculator, an algorithm prototype, and as a mathematical research tool. More importantly, calc provides a machine-independent means of computation. Calc comes with a rich set of builtin mathematical and programmatic functions.
distributed.net is a loosely knit group of computer users from all of the world that is taking up challenges requiring lots of computing power (most notably the RC5, DES, and OGR cracking contests). It is simple to participate in the challenges by downloading and running their client software (which uses idle CPU time to complete its tasks).
GNU TeXmacs is a free wysiwyw (what you see is what you want) editing platform with special features for scientists. The software aims to provide a unified and user friendly framework for editing structured documents with different types of content: text, mathematics, graphics, interactive content. TeXmacs can also be used as an interface to many external systems for computer algebra, numerical analysis, and statistics. New presentation styles can be written by the user and new features can be added to the editor using Scheme.
Isabelle is a popular generic theorem prover developed at Cambridge University and TU Munich. Existing logics like Isabelle/HOL provide a theorem proving environment ready to use for sizable applications. Isabelle may also serve as framework for rapid prototyping of deductive systems. It comes with a large library including Isabelle/HOL (classical higher-order logic), Isabelle/HOLCF (Scott's Logic for Computable Functions with HOL), Isabelle/FOL (classical and intuitionistic first-order logic), and Isabelle/ZF (Zermelo-Fraenkel set theory on top of FOL).
GTL can be seen as an extension of the Standard Template Library STL to graphs and fundamental graph algorithms. It is a platform independent and extendible C++ library, and is a useful aid to any software designer. It contains the classes needed to work with graphs, nodes, and edges, and some fundamental algorithms as building blocks for more complex graph algorithms. Customized algorithms can be developed by experienced programmers.
Botan is a crypto library written in C++. It provides a variety of cryptographic algorithms, including common ones such as AES, MD5, SHA, HMAC, RSA, Diffie-Hellman, DSA, and ECDSA, as well as many others that are more obscure or specialized. It also offers SSL/TLS (client and server), X.509v3 certificates and CRLs, and PKCS #10 certificate requests. A message processing system that uses a filter/pipeline metaphor allows for many common cryptographic tasks to be completed with just a few lines of code. Assembly and SIMD optimizations for common CPUs offers speedups for critical algorithms like AES and SHA-1.
Torch is a machine learning library written in C++ that works on most Unix/Linux platforms. It can be used to train MLPs, RBFs, HMMs, Gaussian Mixtures, Kmeans, Mixtures of experts, Parzen Windows, KNN, and can be easily extended so that you can add your own machine learning algorithms.
DigitizeIt digitizes scanned graphs and charts. Graphs can be loaded in nearly all common image formats (including gif, tiff, jpeg, bmp, png, psd, pcx, xbm, xpm, tga, pct), pasted from the clipboard, or imported via a screenshot. Digitizing of line and scatter plots occurs automatically, and manual digitizing via mouse clicks is also possible. Data values are transformed to a specified axes system and can be saved in ASCII format, ready to use in many other applications such as Microcal Origin or Excel. Axes can be linear, logarithmic, or reciprocal scale. Multiple data sets can be defined and edited. Tilted and distorted graphs can be handled. Comprehensive online help is included. Java 1.4 is required.