Math 29: Introduction to Computability
What is computability? That is the first question we will try to answer. We'll discuss a few formalizations of computability, two in more depth and the rest just in passing, and the surprising fact that they define the same collection of functions, which we call the computable functions. We'll discuss why this seems like a reasonable title for them, though we could never prove they are the correct collection.
Once that's under our collective belt, we'll see what it leads to. Are there noncomputable functions, and if so, how can we specify them if they're noncomputable? If we assume we magically have the ability to compute one of them, what additional computational power does that give us? We'll finish with a survey of some areas of currently active research, just to get a sense of what the field is about today.
Last modified May 16, 2011