**MA29: Introduction to Recursion Theory
Spring 2003**

**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). The class 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. 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 relating to relative computability and degrees
of unsolvability, as time permits. This schedule corresponds to covering chapters
1-7 of the text, with selections from the remaining chapters or supplementary
material.

**Class meetings**: MWF 12:30- 1:35 in Bradley 13, x-hours T 1-1:50. We
will make intermittent use of the x-hours.

PLEASE NOTE CHANGE: No X-hour on Tuesday, April 8.

There will be no class on Wednesday, April 30, and Friday, May 16. The special class meetings, below, will replace the missed classes.

**Special Class Meetings**: There will be two class meetings outside the
regular schedule; one on May 1 at 4pm in Bradley 102, and the other TBA.

**Text**: *Computability, An Introduction to Recursive Function Theory*,
by Nigel Cutland, available at Wheelock Books.

Note: This book is now in stock.

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

**Office Hours**: TBA

**Grading**: The course grade is based on homework (30%), a mid term (30%),
and a final(40%). The mid-term will be on Monday, April 28, from 5:30-7:30 pm.
The final will be scheduled by the Registrar.

**Homework**: Homework is due in class, the second class meeting after it
is assigned. The assignments will be posted regularly on the homework
site.

**Honor Principle:** Every student who matriculates at Dartmouth agrees
to abide by the academic honor principle. You have an obligation to act with
integrity in your own academic work, and to take action if you observe honor
code violations by others.

In Math 29 you are encouraged to work together on homework problems, and to
use professors, tutors, other students, other textbooks, and generally any resource
you can find that will help you understand and work the problems. You should
write up the homework solutions by yourself in your own words.

You must do all work on exams independently, without giving or receiving assistance
of any kind.

**Disabilities:** If you have a disability of any sort that may affect your
participation in the course or require accommodations, please speak to me at
the beginning of the term. These conversations will be completely confidential,
with the single exception that I may contact the Student Disabilities Coordinator
at the Academic Skills Center to discuss appropriate accommodations. Students
with disabilities that may need classroom accommodations should also talk to
the Student Disabilities Coordinator directly.

**Special Concerns:** Please talk to me as soon as possible, or whenever
something comes up, about any special concerns you have about the class. If
you have athletic or other extracurricular commitments and hope to accommodate
them (for example, by taking the midterm at an alternative time), talk to me.
If you are in any way concerned about the course or your performance in it,
talk to me. If you can't do the homework, talk to me. Please make an appointment
if you cannot come to regular office hours.

last updated 24 March, 2003