Robert Browning,

**Math 29: Introduction to Computability**

- Instructor: Rebecca Weber
- Office hours Tu 12:45-1:45, We 2-3, Th 2:30-3:30 and by appointment in Kemeny 317
- Class meets MWF 12:30-1:35, X-hour (to be used rarely) Tu 1:00-1:50; Kemeny 004
**Syllabus** - Course notes are available electronically and through the Copy Center.

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.

General Resources:

- Slides from an introductory computability talk I gave to an undergraduate audience at MIT, March 2009

- My LaTeX page, in particular the template file, examples one and two, and symbols useful for your term papers in pdf or tex.

Last modified May 16, 2011