UCLAMathnet has several mathematical software packages installed for both Windows and Linux hosts. Most of these are licensed; the Mathematics Department has purchased licenses for a certain number of simultaneous users. When you have finished working on your project and will be away from it for several hours or overnight, please close the program, so others can use the license. (And log out from your computer at the end of the day, for security.)
The best way to use mathematical software is to use the subroutines it provides, rather than implementing complex algorithms using their scripting language. For example, if you compute a Fourier transform or find the eigenvectors of a matrix, the package can do this for you with one subroutine call, whereas if you write the algorithm yourself you could put a lot more effort into a possibly inferior implementation, and give a lot more work to the computer too.
If you have your own desktop workstation, Mathnet recommends that you use the software packages there, because the workstations are generally faster than the servers, you don't have to share with other users, and users without their own workstations need server resources.
The licensed packages may be used only at Mathnet.
 Maple

Maple by Waterloo Maple Inc. is for symbolic mathematics. In other words, you give it formulae and it can substitute one into another, solve for one of the variables, solve a differential equation symbolically, and numerous other activities. It can then go on to evaluate the resulting formulae including numerical solution of differential equations. Follow this link to an index of Maple's features.
We have the 2015 x86_64 version. This software is licensed.
To start it, type maple at the command prompt. This gives you a textmode interface. If you give the x option or use the command xmaple, you will get an XWindows interface. Alternatively find it in your desktop environment's software menu in the Mathematics category. (If we or they had set that up…)
 Mathematica

Mathematica by Wolfram Research is another symbolic mathematics package with a similar function as Maple but quite a contrasting style. Particularly see the reference document on the Wolfram Language.
We have the latest version 10. OK on both x86_64 and i686. This software is licensed. Wolfram has a cloud service, which is not cheap.
To start Mathematica, type mathematica at the command prompt. Alternatively find it in your desktop environment's software menu in the Mathematics category. (If we or they had set that up…) You get an XWindows interface.
 Matlab

Matlab by Mathworks is mainly intended for numerical and matrix computations, and data visualization. See this link for a summary of key features of Matlab.
We have version R2016a. OK on both x86_64 and i686. Available for Linux and Windows. This software is licensed. We also have licenses for a number of Matlab toolboxes.
To start Matlab, type matlab at the command prompt. Alternatively find it in your desktop environment's software menu in the Mathematics category. (If we or they had set that up…)
 Octave

Octave from GNU is intended for numerical computations and data visualization. It has been described as a free Matlab; the programming language is very similar and programs are easily ported from one to the other.
We have version 3.6.4; the latest is 3.8.2. OK on both x86_64 and i686. Octave is free software under GPL; client licenses are not required.
To start it, type octave at the command prompt. This is a text interface (not a GUI); however, graphs are plotted using XWindows (OpenGL).
 To see the online documentation do tkinfo octave
 The reference manual is available online.
 The support page has links to the FAQ, wiki, and other resources.
 Sage

Sage is a free opensource mathematics software framework that incorporates many other opensource packages, including:
 GAP (computational discrete algebra, computational group theory)
 PARI/GP (number theory)
 Maxima (symbolic mathematics, descendant of Macsyma)
 mwrank (elliptic curves)
 R (statistics)
 singular (polynomial rings and noncommutative algebras)
 KANT/Kash (algebraic number theory)
 Macaulay2 (algebraic geometry and commutative algebras)
 And quite a number of others, plus infrastructure
 The framework language is Python.
We have version 4.7; latest is 6.5. OK for x86_64 and i686. Sage and its components are free software; client licenses are not required.
To start Sage, just type sage at the command line. It takes a while to start up. When you get its command prompt (sage:), you can enter commands or type notebook() for a GUI. It will open an instance of Firefox on the local machine and you can use Sage from the web form.
An alternate way to use Sage is via the SageMathCloud. This is a free service hosted at the University of Washington.
 Math Libraries

Mathnet hosts have a range of mathematical software and libraries installed in addition to the major packages listed above.
 liblapack3: Simultaneous linear equations, least squares, eigenvalues, singular value problems. We have version 3.4.2, latest is 3.5.0. The man pages are also installed; see also the Users Guide.
 libfftw33, libfftw3_threads3: Discrete Fourier transform. We have version 3.3.3; latest is 3.3.4. See the project page for links to the documentation.
 gsl: Gnu Scientific Library, for linear algebra, roots of polynomials, Fourier transform, wavelet transformations, differential equations, and many more areas.
 singular: Polynomial rings and noncommutative algebras