MAT4630 – Computability Theory
Course description
Course content
Introduction to classical computability theory with emphasis on relative computability, degrees of unsolvability and on applications to computable analysis and theoretical computer science.
Learning outcome
Based on the primitive recursive functions and the ?-operator, the computable functions and relations over the natural numbers are introduced. The basic theorems concerning the partial computable functions and the computable and semicomputable sets are proved.
Various classical approaches to degrees of non-computable functions and sets are studied. Towards the end we will see how classical computability is used for investigating computability phenomena in analysis and topology and how alternative approaches to computability have applications in theoretical computer science.
Admission
Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.
If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.
Overlapping courses
*The information about overlaps for discontinued courses may not be complete. If you have questions, please contact the Department.
Teaching
3 hours per week throughout the semester.
Upon the attendance of three or fewer students, the lecturer may, in conjunction with the Head of Teaching, change the course to self-study with supervision.
Examination
Final oral examination.
Examination support material
No examination support material is allowed.
Language of examination
Subjects taught in English will only offer the exam paper in English.
You may write your examination paper in Norwegian, Swedish, Danish or English.
Grading scale
Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.
Explanations and appeals
Resit an examination
Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.
Re-scheduled examinations are not offered to students who withdraw during, or did not pass the original examination.
Withdrawal from an examination
It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.
Special examination arrangements
Application form, deadline and requirements for special examination arrangements.
Evaluation
The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.