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German original

Computability and Provability
(dt. Berechenbarkeit und Beweisbarkeit)

Level, degree of commitment in original study programme Advanced module, compulsory elective module
Forms of teaching and learning,
workload
Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements
9 CP
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises as well as at least 2 presentations of the tasks.
Examination type: Oral or written examination
Language,
Grading
German,
The grading is done with 0 to 15 points according to the examination regulations for study course M.Sc. Computer Sciences.
Original study programme M.Sc. Informatik / Vertiefungsbereich Informatik
Duration,
frequency
One semester,
irregular
Person in charge of the module's outline Prof. Dr. H.-Peter Gumm

Contents

  • Concepts of computability
  • Definability, provability
  • proofs of impossibility
  • Gödel's incompleteness theorem
  • Lambda Calculus, Combinatorial Logic
  • Object Calculi (Featherweight Java)
  • Intuitionistic Logic

Qualification Goals

  • Deepening the knowledge of the calculability theory,
  • Discovering and applying these principles in
  • - Programming languages,
  • - Logic,
  • - Algebra,
  • Practice of scientific working methods (recognition, formulation, problem solving, training of abstraction skills),
  • Training of oral communication skills in the exercises by practicing free speech in front of an audience

Prerequisites

None. The competences taught in the following modules are recommended: Logic, Theoretical Computer Science, either Algorithms and Data Structures or Practical Informatics II: Data Structures and Algorithms for Pre-Service-Teachers.


Recommended Reading

  • P.Smith: An Introduction to Gödel’s Theorems. Cambridge Univ. Press
  • M. Abadi, L. Cardelli: A Theory of Objects. Springer.
  • M.H. Sørensen, P. Urzyczyn, 2006, Lectures on the Curry-Howard Isomorphism
  • G. Mints: A short introduction to Intuitionistic Logics. Springer.



Please note:

This page describes a module according to the latest valid module guide in Wintersemester 2022/23. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.