Objective
competence
Taxonomy level
Students understand the basic terminology of mathematics. Students meet the field’s standards in preciseness and rigor in expressing mathematical statements.
F,M
K2, K3
Students are able to prove simple mathematical statements and evaluate proofs for their level of correctness and rigor.
M
K3, K4
Students understand the difference between syntax and semantics of a formal system. They know the syntax and semantics of propositional logic.
F
K1, K2
Students are able to formalize colloquial mathematical statements in terms of first order logic. Students understand statements denoted in first order logic
Students understand the basics of set theory (union, intersection, relative complements and power set). Students know the sets ℕ, ℤ, ℚ and ℝ.
K1, K2, K3
Students know how sets are compared in terms of cardinalities and they know the notion of (un-) countability. Students are able to prove that the sets ℤ and ℚ are countable and that ℝ is uncountable.
K2, K3, K4
Students know the notions of equivalence- and ordering relations and their basic properties and notations.
Students are able to apply the principle of mathematical induction and they understand the relationship between induction and recursion.
Students apply the Euclidean algorithm to compute gcd and lcm as well as to solve systems of linear congruencies.
Students are familiar with the basics of modular arithmetic. Students know the Chinese remainder Theorem.
title = "Diskrete Strukturen -- kurz gefasst" series = "Spektrum--Hochschultaschenbuch" author = "Ulrich Knauer" year = "2011" publisher = "Spektrum Akademischer Verlag"
title = "Mathematik für Informatiker -- ein praxisbezogenes Lehrbuch" series = "Mathematik/Informatik" author = "Peter Hartmann" year = "2004" publisher = "Vieweg" edition = "3"
title = "Diskrete Mathematik für Informatiker" author = "Rod Haggarty" year = "2007" publisher = "Pearson Studium"