Starting with Matlab/Octave

Matlab (MATrix LABoratory) and Octave are program designed mainly for numerical computations, and producing graphs with the results.

For simplicity, we refer to Matlab when we mean both Matlab and Octave.
It supports matrix operations, offers easy graphing commands, knows how to solve (numerically) algebraic and differential equations, computes Fourier and wavelet transforms, as well as many other things.

You can find a few resources on the web (including a manual by its producers) under Help on the left.