General Information
This page provides an overview of the courses offered by our working group:
Under Lectures you will find the lectures for mathematics students offered by our working group in the current or upcoming semester. If you would like to participate in a seminar, proseminar or reading course during the semester, please register with the respective supervisor or in the URM. Dates will then be set in consultation with the participants. Additionally, we offer introductory courses for new students and math lectures designed for students from other disciplines.
Several times a semester, the working group meets for the Oberseminar. All interested people are invited to attend the talks, students in particular.
If you are interested in doing your bachelor's or master's thesis in optimization, please contact Prof. Schöbel, Prof. Krumke or Prof. Ruzika.
Near the end of each semester, you can also find the dates for oral examinations with members of the working group on this page.
Introductory course to mathematics for students of mathematics and computer science
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
Linear and network optimization
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. Sven Krumke
Prof. Dr. Stefan Ruzika
Daniel Eichhorn, M.Sc.
Shai Dimant, M.Sc.
Dates
Tuesday, 8:15-9:45 (48-208)
Thursday, 13:45-15:15 (48-208)
Tutorials
Registration and group assignments for the tutorials are handled by the URM.
Materials
Further Information
This course is only offered in German.
Nonlinear Optimization
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
Prof. Dr. Sven Krumke
Fabian Chlumsky-Harttmann, M.Sc.
Date
Monday, 08:15-09:45 (48-208)
Wednesday, 10:00-11:30 (48-208)
Tutorials
Registration and group assignments for the tutorials are handled by the URM.
Materials
OpenOLAT (standard access code)
Multicriteria Optimization
Lecturer and staff
Prof. Dr. Stefan Ruzika
Nils Hausbrandt, M.Sc.
Kathrin Prinz, M.Sc.
Dates
Monday, 10:00 - 11:30 (48-210)
Thursday, 11:45 - 13:15 (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
Introduction to Didactics of Mathematics
for Students of Teacher Training Programs
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
Date
Monday, 8:15 - 9:45 (48-582)
Materials
Further Information
Registration is handled by the URM.
Geometry
for Students of Teacher Training Programs
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
Date
Friday, 10:00-11:30 (46-268)
Tutorials
Registration and group assignments for the tutorials are handled by the URM
Materials
Further Information
This course is only offered in German.
Modern Mathematics
for Students of Teacher Training Programs
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 Busam, M.Sc.
Dates
Monday, 15:30 - 17:00 (48-208)
Tuesday, 15:30 - 17:00 (11-205)
Wednesday, 15:30-17:00 (48-208)
Materialien
Further Information
Registration is handled by the URM.
Reading Course (Prof. Krumke)
Lecturer
Date
By arrangement.
If you are interested please send an e-mail to sven.krumke(at)math.rptu.de.
Reading Course (Prof. Ruzika)
Lecturer
Date
By arrangement.
If you are interested please send an e-mail to stefan.ruzika(at)math.rptu.de.
Proseminar Elementary Mathematics from a Higher Perspective
for Students of Teacher Training Programs
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
Date
Wednesday, 11:45-13:15 (48-538)
Material
Further Information
Registration is handled by the URM.
Advanced Seminar
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)