INF5840 - Computability theory

Schedule, syllabus and examination date

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Course content

Computability theory can be regarded as a systematic mathematical theory of algorithms and computations. The successful development of this theory in the 1930s preceded and inspired the engineering of modern programmable computers.

This course gives an introduction to basic computability theory, and should be of interest to a broad range of students and researchers.

The course covers the following topics:
primitive recursion,  computable functions and computable indices, semi-computable and computably enumerable sets and undecidability.

We will use the computability theory we develop to prove

- Undecidability of the halting problem

- Undecidability of the Entscheidungsproblem

- Godel's First Incompleteness Theorem

We will also discuss the negative solution of Hilbert's 10th problem.

Learning outcome

Basic skills in theoretical computer science and in-depth skills in computability theory.


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.

Students enrolled in other Master's Degree Programmes can, on application, be admitted to the course if this is cleared by their own study programme.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.

Overlapping courses

10 credits overlap with INF9840 - Computability theory


Two lectures a week.


Written or oral exam. No mandatory assignments prior to the exam.

Examination support material

No examination support material is allowed.

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.

Facts about this course






Spring 2016

Spring 2015


When the course is given

Teaching language