This course is an introduction to formal mathematical reasoning and to some fundamental concepts of algebra and logic that are crucial for computer science (and computer scientists). This course is mandatory for first-semester students in the CS Bachelor's program, in the IIW Bachelor's program, and in the Data Science Bachelor's program.

• Lecturer: Prof. Dr. Antoine Wiehe
• Language: English
• Winter semesters
• 6 ECTS
• 2 meetings per week (1.5 hour lectures, 1.5 hour tutorials)

• Elementary set theory: sets, functions, cardinals
• Propositional logic and proofs (contraposition, contradiction, induction)
• Counting and counting principles (pigeonhole principle, double counting, Ramsey's theorem)
• Arithmetic: integers, greatest common divisor, Euclid's algorithm, prime numbers, prime factor decomposition, decomposition in a base, application to RSA
• Algebraic structures: groups, Lagrange's theorem, rings, fields, classification of finite fields, polynomials over a ring, application to the Reed-Solomon error-correcting codes, Boolean algebras, classification of finite Boolean algebras