Offered courses

Content

• Support of new students of mathematics and computer science within the transition from school to university
• Matching different educational backgrounds and refreshing some of the important fundamentals of the school subject
• Introduction to the initially unfamiliar mathematical thinking and working methods as well as the abstract language and form of presentation of mathematics lectures at the university
• Familiarization with the usual form of lecture and group exercise

Lecturer

Dr. Florentine Kämmerer

Dates

April 8th - April 19th, 2024

Materials

OpenOLAT

Further Information

You can find the latest information regarding the course, in particular concerning the registration, on its website.

This course is only offered in German.

Content

In this lecture we introduce the basic terminology used in analysis. We construct, amongst other things, the field of the real numbers and deduce important consequences of the so-called supremum property. Topics covered here are:

• the real and complex numbers
• sequences and series
• limits and continuity
• sequences and series of functions
• the Riemann integral on R

Lecturer and staff

Prof. Dr. Sven O. Krumke

Dates

Tuesday, 12:15 - 13:45 (48-210)
Thursday, 10:15 - 11:45 (48-210)

Tutorials

Registration and group assignments for the tutorials are handled by the URM.

Materials

OpenOLAT

Further Information

This course is only offered in German.

Content

Problems in linear optimisation deal with the optimisation of linear objective functions in a polyhedral set. The methods make it possible to model and solve a large number of practical problems (e.g. in production planning or telecommunications). In particular, this part of the lecture delves into the following topics:

• modelling with linear programs,
• the fundamental theorem of linear programming,
• duality, and
• solving linear programs using the simplex and interior point methods.

Questions in the area of network optimisation work with a network or graph. An abundance of real-world problems (like route planning) can be modelled with the help of graphs. In this part of the lecture, classical questions on graphs will be introduced and theoretical concepts and algorithms for their resolution will be presented. In particular, the following topics shall be discussed:

• spanning tree problems,
• shortest path problems,
• maximum flow problems, and
• minimum cost flow problems.

Lecturers and staff

Prof. Dr. Anita Schöbel
Dr. Oliver Bachtler

Dates

Tuesday, 8:15-9:45 (48-208)
Thursday, 14:00-15:30 (48-208)

Tutorials

Registration and group assignments for the tutorials are handled by the URM.

Materials

OpenOLAT

Further Information

This course is only offered in German.

Content

Nonlinear optimization problems are optimization problems where the objective function and / or constraints are nonlinear. Such problems that arise in a variety of applications can not be solved by methods known from linear optimization. This lecture covers theoretical background and algorithmic approaches to solve nonlinear optimization problems, both with and without constraints.
Among other things, the following topics are covered:

• one-dimensional and multi-dimensional search,
• Newton and Quasi-Newton procedures,
• convex analysis and separation theorems,
• optimality conditions for convex problems,
• optimality conditions for general problems,
• penalty- and barrier-methods, and
• the SQP-method.

Lecturer and staff

Dr. Tobias Seidel
Daniel Eichhorn, M.Sc.

Date

Monday, 08:15-09:45 (48-208)
Wednesday, 10:15-11:45 (48-208)

Tutorials

Registration and group assignments for the tutorials are handled by the URM.

Materials

OpenOLAT

Content

• Mathematical Modelling with several objective functions
• Orderings and notations of optimality
• Characterization of efficient solutions and nondominated points
• Scalarization methods and approximation algorithms
• Multicriteria linear programs
• Multicriteria combinatorial optimization problems

Lecturer and staff

Prof. Dr. Stefan Ruzika
Levin Nemesch, MSc

Dates

Monday, 10:15 - 11:45 (48-538)
Thursday, 08:15 - 09:45 (48-208)

Content requirements

Students should have knowledge of

• linear and network optimization
• integer optimization (offered in the winter term)

Tutorials

Registration and group assignments for the tutorials are handled by the URM.

Materials

OpenOLAT

Content

The course "Introduction to the Didactics of Mathematics" is the first course in the field of didactics of mathematics and forms the basis for all further mathematics didactics courses. Among other things, the following topics are covered: Curriculum and educational standards, lesson planning, mathematical learning objectives, didactic analysis, teaching methods, learning phases and motivation, teaching and learning concepts and rules, practicing in mathematics lessons, open forms of teaching, problem solving in mathematics lessons, reasoning and proving, modeling, computer use.

Lecturer

Dr. Florentine Kämmerer

Date

Monday, 8:15 - 9:45 (48-582)

Materials

OpenOLAT

Further Information

Registration is handled by the URM.

Content

In this course, which is specific to the teaching profession, a deeper understanding of geometric content that goes beyond school education is to be developed. The relevance to school mathematics should be recognisable, but we want to approach the various topics from a slightly different perspective.

We will deal with different subject areas and selected questions from the large field of geometry. Key points on the contents: Euclid and the "elements", axiomatic structure of geometry according to Hilbert, axiom systems and models, finite incidence geometries, symmetry, congruence maps, geometric aspects of linear maps (rotations, reflections, ... ), polyhedra, Platonic solids, Euler's polyhedron formula, geometry in linear and integer optimisation, Voronoi diagrams, location problems, special points and lines in triangles (Fermat point, nine-point circle, ...), Pythagorean triples, conic sections, insights into basic ideas and overview of other sub-areas of geometry (projective geometry, algebraic geometry, non-Euclidean geometries).

Lecturer

Dr. Florentine Kämmerer

Date

Friday, 10:15-11:45 (46-268)

Tutorials

Registration and group assignments for the tutorials are handled by the URM

Materials

OpenOLAT

Further Information

This course is only offered in German.

Content

Student should gain insights into current mathematical areas from applied and pure mathematics and become familiar with their practical relevance as well as current developments and applications. The aim is to establish links to their future work as teachers.
With this semester's chosen topic of "Artificial Intelligence", we cover a highly topical subject that is also being discussed in schools, the media and the general public.
We will shed light on the mathematical foundations of algorithms in the field of artificial intelligence, show the wide range of applications of such algorithms and discuss how the topic can be addressed in the classroom on the one hand and how the broad access to intelligent systems and their ease of use will change teaching in the future on the other.

Lecturer and staff

Prof. Dr. Stefan Ruzika
Simon Wirschem, M.Sc.

Dates

Monday, 15:45 - 17:15 (48-562)
Tuesday, 12:15 - 13:45 (48-562)
Wednesday, 15:45-17:15 (48-562)

Materialien

OpenOLAT

Further Information

Registration is handled by the URM.

Inhalt

• Erarbeitung eines vertieften, über die Schulbildung hinaus gehenden Verständnisses elementarmathematischer, teils schulmathematischer, Inhalte als solides Fundament für das weitere Lehramtsstudium
• Behandlung unterschiedlicher Fragestellungen aus den Bereichen Zahlen, Kombinatorik, Wahrscheinlichkeitstheorie, Graphentheorie, lineare Algebra und Analysis

Lecturer

Dr. Florentine Kämmerer

Dates

Wednesday, 11:45-13:15 (48-538)

Materials

OpenOLAT

Registration

Registration via Email to florentine.kaemmerer(at)math.rptu.de.

Content

The aim is to gain a basic overview of current research topics. In this respect, the Reading Course prepares for a master's thesis in these subject areas.

Lecturer

Prof. Dr. Sven O. Krumke

Date

By arrangement.

If you are interested please send an e-mail to sven.krumke(at)math.rptu.de.

Content

The aim is to gain a basic overview of current research topics. In this respect, the Reading Course prepares for a master's thesis in these subject areas.

Lecturer

Prof. Dr. Stefan Ruzika

Date

By arrangement.

If you are interested please send an e-mail to stefan.ruzika(at)math.rptu.de.

Content

We want to deal with current research topics in the field of Mathematics and Mobility.

Lecturer and staff

Prof. Dr. Anita Schöbel
Sarah Roth
Reena Urban
Lena Dittrich

Dates

The seminar is planned as a compact event on the weekend of January 24/25. Depending on the number of presentations, it may only take place on Saturday. A preliminary meeting for the seminar will be held on October 23 at 12:00 in 14-420.

Further Information

KIS
URM

Content

• Development of a deeper understanding of elementary mathematics, partly school mathematics, beyond school education, as a solid foundation for further teacher training studies.
• Independent development and preparation of a mathematical topic given by the respective literature and turning it into a presentation.
• Addressing of different questions from the areas of geometry, numbers, combinatorics, probability theory, graph theory, linear algebra and analysis.

Lecturer

Dr. Florentine Kämmerer

Date

Wednesday, 12:15-13:45 (48-538)

Material

OpenOlat

Further Information

Registration is handled by the URM.

Inhalt

Im Proseminar „Modellierung in der Wirtschaftsmathematik“ werden wirtschaftsmathematische Themen erarbeitet. Die Themen kommen aus verschiedenen Bereichen und haben jeweils einen realen Anwendungshintergrund. Man lernt im Proseminar die Grundprinzipien der mathematischen Modellierung und erarbeitet in Teamarbeit erste Lösungsansätze für Anwendungsprobleme aus Industrie und Wirtschaft.

Lecturer and staff

Prof. Dr. Sven Krumke

Materialien

 OpenOLAT

Further information

Please register via the URM and OpenOLAT.

This course is usually in German.

Content

In the Oberseminar (advanced seminar), members and guests of the working group will give talks on various topics of mathematical optimization. Guests are welcome at any time - even without prior registration. An announcement of each talk will be made in the news section of the website. (Look for entries starting with "Oberseminar".)

Lecturers

Prof. Dr. Sven Krumke
Prof. Dr. Stefan Ruzika
Prof. Dr. Anita Schöbel
and all members of the optimization research group

Date

irregularly, Tuesdays, 17:15-18:45 (48-208)