Here are some basic tasks and the EXTREMA commands to perform them.

Create arrays of numerical values
Create and plot an array
Define vectors (1-d arrays)
Define matrices (2-d arrays)
Add and plot vectors
Eigenvalues and eigenvectors
Plot functions
Integrate a function
Solve a matrix equation
Read data from files
Fit a function
Define and plot a function
Analyze data using FFT
Display array data as contours and density plot
Plot parametric functions
Write data to a file