# Discrete Mathematics

Lecturer | Univ.-Prof. Dr.-Ing. Ulf Schlichtmann |
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Amount | 3 Lecture + 2 Tutotrial, 11 days |

Cycle | January |

## Objective

At the end of the module students are capable of employing fundamentals of discrete mathematics to design digital systems (circuits as well as more complex systems such as e.g. communication networks or IT-systems). Students are also capable of performing proofs using deduction method, equivalence transformations and resolution method. Student are also familiar with formal descriptions for technical problems and how to employ them e.g. in simulation, synthesis as well as in everyday problems.

## Contents

**Propositional Logic (Boolean Algebra):** propositional forms, truth set, laws of propositional logic, rules of inference, binary decision diagrams;

**Predicate Logic:** predicate logic forms, laws of predicate logic, deduction scheme, induction;

**Sets:** notation, operation, relations between sets, Boolean algebra of subsets;

**Relations:** binary graphs, properties, closures, order relations, equivalence relations;

**Finite State Machines:** description via relations, optimization;

## Material

A formulary, a collection of exercises with solutions and handouts are provided on xSITe.

## Recommended Literature

D.F. Stanat, D.F. McAllister: Discrete Mathematics in Computer Science, Prentice-Hall, Englewood Cliffs, N.J., 1986

## Exam

The examination is in written form with open book policy and takes 90 minutes.