I will talk about the problem of separating multiple signals from each other when we only have access to a few linear (or non-linear) combinations of them. An example of this type of problem is at a cocktail party when you are trying to have a conversation with a friend but there are several conversations happening around you. Your ears provide you with a superposition of all the voices, and your brain does remarkably well at focusing on your friend's voice and drowning out all the others. We will talk about one computer algorithm (or time permitting, more) that does such a task (reasonably) successfully. Along the way, we will talk about important tools in mathematical signal processing, including the Fourier transform and sparsity.