Maple (Maple 9 is the premium software system for any activity that involves mathematics. Whether you do mathematical research, teach mathematics, publish, or connect to other technical software, Maple 9 will amplify your efforts. Maple 9 provides the most robust and complete symbolic math engine in the software industry, a reputation we work tirelessly to uphold. We are continually enhancing the algorithms in Maple through our partnerships with research institutes from all over the world and the expertise of our team of Ph.D. mathematicians.)
Mathematica (From simple calculator operations to large-scale programming and interactive document preparation, Mathematica is the tool of choice at the frontiers of scientific research, in engineering analysis and modelling, in technical education from high school to graduate school, and wherever quantitative methods are used.)
MuPad (Open computer algebra systems which can handle mathematical expressions symbolically rather than numerically. You gain insight by getting expressions as results instead of drowning in endless columns of numbers. View a short demo about MuPAD's astonishing capabilities or try it online.)
Maxima for Symbolic Computation Program, released under the GNU Public License. Maxima is a descendant of DOE Macsyma, which had its origins in the late 1960s at MIT. It is the only system based on that effort still publicly available and with an active user community, thanks to its open source nature. Macsyma was the first of a new breed of computer algebra systems, leading the way for programs such as Maple and Mathematica.
MatLab (MATLAB is an integrated technical computing environment that combines numeric computation, advanced graphics and visualization, and a high-level programming language.)
Geometer's Sketchpad (The Geometer's Sketchpad is an exciting software program that has revolutionized the teaching and study of geometry.)
Cabri (Cabri-geometry is used for teaching secondary school geometry, but, equally important, is its use for university level instruction and as a tool by mathematicians in their research work.)
Cinderella (Cinderella is a new tool for doing geometry on the computer. It replaces pencil, ruler, compass and paper and enables you to do exact geometric drawings with the mouse. Although the software is easy enough to use to make it the perfect tool in K-12 geometry education, its mathematical foundation is powerful enough to serve college and highschool students as well as advanced geometry researchers.
(Groups, Algorithms, and Programming)
Magma Computational Algebra System for Algebra, Number Theory and Geometry
Singular (A computer algebra system for algebraic geometry and singularity theory)
Macaulay (A computer algebra system for algebraic geometry)
Macaulay2 (A software system for algebraic geometry research)
CoCoA (Computing in Commutative Algebra)
Fermat - Fermat is a computer algebra system for Macintosh and Windows by me, Robert H. Lewis of Fordham University, that does arithmetic of arbitrarily long integers and fractions, symbolic calculations, matrices over polynomial rings, graphics, and other numerical calculations. It is extremely fast and extremely economical of space.
Qhull (Qhull computes convex hulls, Delaunay triangulations, halfspace intersections about a point, Voronoi diagrams, furthest-site Delaunay triangulations, and furthest-site Voronoi diagrams.)
NTL (A Library for doing Number Theory)
LiDIA (A C++ library for Computational Number Theory)
Schubert (Schubert is a Maple package for Intersection Theory)
GrafEq (GRAFEQ (pronounced "graphic") is an intuitive, flexible, precise and robust program for producing graphs of implicit relations.)
NuCalc (Graphing Calculator is a tool for quickly visualizing math. Just type an equation and it is drawn for you without complicated dialogs or commands.)
Peanut Software for Windows; Wingeom, Windisc (Free Mathematical Softwares)
Dr Geo (Dr Geo is an interactive geometry program and a piece of GNU free software.)
Compass and Ruler - a program, that simulates school geometry constructions with a pair of compasses and a straightedge (ruler). The program uses Java, and runs on almost any modern platform. Moreover, constructions and assignments can be published in the Net. The program is freeware, and the source is available and free by the GNU General Public License.
EUKLID DynaGeo - a Windows program about geometry. It lets you create dynamic drawings i.e. drawings that allow to move (some) objects without losing the interdependences of the geometrical objects established during the preceeding construction
GRACE - Graphical Ruler and Compass Editor, an interactive ruler and compass construction editor for use in teaching the fundamental concepts of geometry to high school students.
Geometric Supposer (An interactive geometry program, not free, but there is a demo version)
NonEuclid - NonEuclid is Java Software for Interactively Creating Ruler and Compass Constructions in both the Poincaré Disk and the Upper Half-Plane Models of Hyperbolic Geometry for use in High School and Undergraduate Education.
JavaView (3D geometry viewer and a mathematical visualization software. The web-integration allows display of 3D geometries and interactive geometry experiments in any HTML document on the internet. JavaView also runs as application on local computers from a Unix or Dos command prompt. The open API of JavaView enables a smooth integration as 3D viewer and advanced visualization toolkit into commercial software like Mathematica and Maple)
Logo Foundation A place to find information and resources for learning and teaching Logo.
Softronics (An Educational Software Company, MMLogic and MSWLogo; MSWLogo is free.)
DC Proof 1.0 (A new software learning aid to teach the fundamentals of logic and proof..., free)
InterSys (IDL - Data Analysis Software)
Kali (Kali lets you draw symmetrical patterns based on any of the 17 tiling groups.)