Mathematical Fundamentals of Computer Science

level of course unit

Bachelor

Learning outcomes of course unit

The students know and master those mathematical structures and methods
used in the fields of basic information technology, software development, data engineering, computer networks and IT security. In particular, they master the handling and application of logical operators, set operators, properties of relations and place value systems (in particular binary and decimal systems). They understand basic concepts and properties of number sequences, as well as the O-notation used in algorithms.

prerequisites and co-requisites

Successfully completed courses of the previous semester.

course contents

Propositional logic and logical operators, predicate logic, calculation laws of propositional and predicate logic;
Set theory: Basic concepts, set operators, calculation rules for sets;
Relations: Basic concepts, properties of relations, equivalence and order relations
Numeric terms: Number sets, sum and product characters, place value systems, binary and hexadecimal system
Sequences: term of the sequence, some essential properties, convergence, O-notation
Modular arithmetic: Concept and calculation rules, applications

recommended or required reading

- Brill, Manfred: Mathematik für Informatiker: Einführung an praktischen Beispielen aus der Welt der Computer. 2. Auflage, München, Wien, Carl Hanser Verlag, 2005.
- Nehrlich, Werner: Diskrete Mathematik: Basiswissen für Informatiker. München, Wien, Carl Hanser Verlag, 2003.
- Schwarze, Jochen. Mathematik für Wirtschaftswissenschaftler: Band 1: Grundlagen. 14. Auflage, Herne, NWB Verlag, 2015.
- Teschl, Gerald; Teschl, Susanne: Mathematik für Informatiker: Band 1: Diskrete Mathematik und Lineare Algebra. 4. Auflage, Berlin, Heidelberg, Springer Vieweg, 2013.