Teaching
Der Schwerpunkt der Lehre im Fachgebiet Diskrete Mathematik liegt auf der Kombinatorik und Graphentheorie. Unsere Lehre umfasst ein breites Spektrum, beginnend mit Grundlagenmodulen wie Lineare Algebra und Grundlagen der Informatik, über weiterführende Veranstaltungen wie diskreter Mathematik, bis hin zum Oberseminar Algorithmische Algebra und Diskrete Mathematik, das in Zusammenarbeit mit der gleichnamigen Arbeitsgruppe durchgeführt wird.
Lehrveranstaltungen im Wintersemester 2026 / 2027
This lecture provides a comprehensive introduction to the fundamental concepts and techniques of graph theory, a central area of discrete mathematics with far-ranging applications in combinatorics, computer science, and network analysis. This lecture covers fundamental notions and results in graph theory: trees, matchings, connectivity, cycles, planarity and coloring. Further subjects covered are graph coloring, extremal graph theory, Ramsey theory, and the theory of random graphs. Emphasis is placed on both classical results and modern methods, with a focus on mathematical rigor and proof techniques.
This required elective module is suitable for Bachelor and Master students of Mathematics and Computer Science. It assumes basic knowledge in linear algebra and discrete mathematics, and it is very suitable to be followed up by the required elective modules Discrete Mathematics II+III.
A link to the respective moodle page will be provided before the start of the semester.
Mehr Informationen folgen.
Mehr Informationen folgen.
Lehrveranstaltungen im Sommersemester 2026
This lecture offers a comprehensive introduction to selected topics in discrete and computational geometry, emphasizing the interplay between their geometric structure and combinatorial properties. Central topics include convexity and its manifestations in convex hulls and polytopes as well as the theory of regular subdivisions and triangulations, and their associated flip graphs. Core geometric constructions, most notably Delaunay triangulations and Voronoi diagrams, are studied in connection with proximity structures and geometric graphs, including visibility and intersection graphs. Within this framework, we examine algorithmic and structural questions such as existence of Hamiltonian cycles, as well as classical optimization and coverage problems exemplified by the art gallery problem. Further topics address graph-theoretic aspects arising from geometric settings, including graph recognition, alongside planar structure theory via Schnyder woods.
This required elective module is suitable for Bachelor and Master students of Mathematics and Computer Science. Familiarity with linear algebra and basic concepts from discrete mathematics is expected. It is advantageous if students have previously attended Discrete Mathematics I, but this is not a strict requirement. The module is also very suitable to be followed up by the required elective module Discrete Mathematics III.
Link to the moodle-page
Lehrveranstaltungen im Wintersemester 2025 / 2026
This lecture provides a comprehensive introduction to the fundamental concepts and techniques of graph theory, a central area of discrete mathematics with far-ranging applications in combinatorics, computer science, and network analysis. This lecture covers fundamental notions and results in graph theory: trees, matchings, connectivity, cycles, planarity and coloring. Further subjects covered are graph coloring, extremal graph theory, Ramsey theory, and the theory of random graphs. Emphasis is placed on both classical results and modern methods, with a focus on mathematical rigor and proof techniques.
This required elective module is suitable for Bachelor and Master students of Mathematics and Computer Science. It assumes basic knowledge in linear algebra and discrete mathematics, and it is very suitable to be followed up by the required elective modules Discrete Mathematics II+III.
Link to the moodle-page
In dieser Veranstaltung werden grundlegende mathematische Begriffe, Konzepte, Beweistechniken und Arbeitsweisen eingeführt. Diese erlauben es Informatikern, mathematische Sachverhalte und formale Argumentationen im Bereich der Informatik und ihrer Anwendungen zu verstehen und selbstständig zu formulieren.
Dieses Modul ist Pflichtmodul im Rahmen des Bachelorstudiums Informatik.
Im Rahmen dieses Seminars setzen sich die Studierenden eigenständig mit verschiedenen Knobel- und Rätselaufgaben auseinander und erarbeiten deren mathematische Hintergründe. Ziel ist es, scheinbar einfache Probleme unter mathematischen Gesichtspunkten zu analysieren, zu strukturieren und anschaulich zu erklären.
Nähere Informationen zu den genauen Inhalten, Anforderungen und Zielen folgen vor Semesterstart.
Lehrveranstaltungen im Sommersemester 2025
In der Vorlesung werden grundlegende Fragestellungen der diskreten Mathematik behandelt. Themen sind u.a. das Abzählen diskreter Mengen und Strukturen mittels verschiedener Techniken, das Auflösen von Rekursionen, asymptotische Abschätzungen, Kombinatorik, sowie eine Einführung in die Graphentheorie.
Die Vorlesung ist für Bachelor- und Lehramtstudenten als Vertiefung im Bereich diskrete Mathematik bzw. angewandte Mathematik geeignet. Voraussetzung ist Vertrautheit mit grundlegenden mathematischen Konzepten.
Aufbauend auf den Inhalten der Veranstaltung Elementare Lineare Algebra werden weiterführende Konzepte der linearen Algebra wie beispielsweise Eigenwerte und Eigenvektoren, Diagonalisierung von Matrizen, und Bilinearformen behandelt.
This seminar covers various topics in discrete mathematics such as graph theory, discrete geometry, and related topics. We will provide scientific articles from which the students should choose one, read and understand it, and then present the content in a seminar talk. You also attend the seminar talks of the other participants.
The talks should be given in English (if this is a problem, we can discuss individual exceptions). You also have to submit a report on your topic, which will then be graded.