Advanced Mathematics
A few examples of what you can ask Wolfram|Alpha about:
compute properties of a function of a complex variable (use the variable z)
locate poles of a complex function
compute the residue of a function at a point
compute the gradient of a function
compute the divergence of a vector field
calculate alternate forms of a vector analysis expression
compute properties of a knot
specify a knot using Alexander–Briggs notation
compare several knots
compute a Fourier transform
compute a Laplace transform