# Discrete Mathematics (dt. Diskrete Mathematik und Analyse von Algorithmen)

 Level, degree of commitment Advanced module, depends on importing study program Forms of teaching and learning,workload Lecture (4 SWS), recitation class (2 SWS), 270 hours (90 h attendance, 180 h private study) Credit points,formal requirements 9 CP Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises. Examination type: Written or oral examination (individual examination) Language,Grading German,The grading is done with 0 to 15 points according to the examination regulations for the degree program B.Sc. Mathematics. Origin B.Sc. Mathematics Duration,frequency One semester, irregular Person in charge of the module's outline Prof. Dr. Volkmar Welker

## Contents

Introduction to elementary objects of discrete mathematics, such as permutations, partitions, graphs. Treatment of basic methods of enumeration. Generating functions and solving recursions. Elementary concepts of graph theory. Application to complexity analysis of algorithms and word-count generating functions of regular and context-free languages, types of trees, their counting and complexity of tree algorithms.

## Qualification Goals

Students will

• understand basic principles of elementary structures of discrete mathematics,
• recognize how these principles can be applied in the analysis of simple algorithms.
• Have practiced mathematical ways of working (developing mathematical intuition and its formal justification, abstraction, proof),
• have developed algorithmic thinking (understanding the influence of combinatorial properties of objects on the complexity of algorithms manipulating the objects)
• Have improved oral communication skills in exercises through discussion and free speech in front of an audience.

## Prerequisites

None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis.

## Applicability

The module can be attended at FB12 in study program(s)

• B.Sc. Data Science
• B.Sc. Mathematics
• M.Sc. Computer Science
• M.Sc. Mathematics
• LAaG Mathematics
• BA Minor Mathematics

When studying B.Sc. Mathematics, this module can be attended in the study area Compulsory Elective Modules in Mathematics.

The module can also be used in other study programs (export module).

• Aigner, Martin: Diskrete Mathematik, Vieweg. 2004
• Matousek, Jiri: Diskrete Mathematik, Springer 2002

This page describes a module according to the latest valid module guide in Winter semester 2023/24. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

• Winter 2016/17 (no corresponding element)
• Summer 2018 (no corresponding element)
• Winter 2018/19 (no corresponding element)
• Winter 2019/20 (no corresponding element)
• Winter 2020/21 (no corresponding element)
• Summer 2021 (no corresponding element)
• Winter 2021/22 (no corresponding element)
• Winter 2022/23 (no corresponding element)
• Winter 2023/24

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.