After successful completion of the course, students are able to...

• explain the concept of proofs and their purpose.
• apply fundamental proof techniques.
• explain the relation to the proof calculus of natural deduction

• What is a proof? What are the porpuses of proofs?
• Fundamental proof techniques
  
• Proofs for universal and existential statements, conjunctions, discjunctions, implications, equivalences
• Applying these proof techniques in a proof
• Connection to the calculus of natural inference 
• What is a proof by induction? What is it needed for?
  
• Different types of induction (mathematical, strong, structural, Noetherian), each with a discussion of the corresponding induction scheme and application cases (demonstrated in detail with examples) 
• How to write a proof by induction proof?

In the practice part, the more complex proofs are considered, including application cases from computer science (e.g. induction proofs for the termination of recursive programs).

The course consists of a lecture part and an exercise part. In the lecture part, proof techniques are discussed, which can then be applied independently to exercises in the exercise part.

ECTS breakdown:

VLecture part (ca 2.5 ECTS):

24h in class  and 36h preparation (before and after the lecture).

Exercise part  (ca 3.5 ECTS):

90h Development of proofs  including the  documentation, presentation in exercise groups and review of  proofs developed by other students.

Elaboration of proofs including their documentation, presentation in exercise groups and peer review of proofs from other students.

Kursunterlagen (Folien, Aufgabensammlung,...) werden im tuwel-Kurs bereitgestellt

First experiences with definitions, predicate logic, formalization and proofs.

Mathematics knowledge from algebra and discrete mathematics,

Recursion as a programming technique (e.g. from algorithms and data structures).