**MA29: Introduction to Recursion Theory
**

**Course Description**: This course is an introduction to recursion theory,
also known as computability theory, a dynamic area of contemporary research
with consequences for the foundations of mathematics, and for theoretical computer
science.

Recursion theory is concerned with the nature and structure of computable functions,
i.e. those functions whose output can be determined by a finitary program. (A
program taking finitely more machine space than we currently command is computable,
while a program that requires infinite capacity is not). In class, we will formalize
several notions of computability, and consider their relationship to each other.
We will discuss Church's Thesis, which equates these formalizations with intuitive
notions of computability. Then we will examine functions which are, and are
not, computable. Some functions are not computable by any means whatsoever;
this is linked to incompleteness phenomena via the Halting Problem.

We will then study selected topics from among: relative computability, degrees
of unsolvability, and recursive sets, as time permits.This schedule corresponds
to covering chapters 1-7 of the text, with selections from the remaining chapters,
as time and class interest mandate.

**Class meetings**: MWF 1:45-2:50 in Bradley 104.

**Text**: *Computability, An Introduction to Recursive Function Theory,*
by Nigel Cutland.

**Instructor**: E.T. Brown;
e-mail: elizabeth.t.brown@dartmouth.edu;
office: 412 Bradley Hall; phone: (603) 646 1720.

**Office Hours**: MWF 8-8:30 am, TTH 12:45-1:45pm, in Bradley 412.