Content

In this education-specific lecture, which builds upon the material covered in the lecture "Fundamentals of Mathematics I", further fundamental concepts of (multivariate) analysis and linear algebra are presented. This lecture serves as a foundation for the subsequent mathematical studies. The tutorials serve to develop a safe and precise understanding of the definitions, results, and methods covered in the lecture.

We discuss topics in analysis and linear algebra and find connections between the two. Amongst the topics discussed are:

• metric spaces
• differentiation and integration in more than one variable
• the geometry of Euclidian space
• diagonalisability
• the principle axis theorem
• computing the Jordan normal form

Lecturer and Staff

Prof. Dr. Stefan Ruzika
Meiko Volz

Dates

Tuesday, 11:45-13:15 (48-562)
Friday, 10:00-11:30 (48-210)

Tutorials

tba.

Materials

OpenOLAT

Content

• Modelling with integer programming,
• Polyhedra and polytopes,
• Complexity,
• Formulations,
• Connections between integer programming and polyhedral theory,
• Integerity of polyhedra: unimodularity, total dual integrality,
• Matchings,
• Dynamic programming,
• Relaxations,
• Branch-and-Bound methods,
• Cutting planes,
• Column generation

Lecturer and staff

Prof. Dr. Stefan Ruzika

Prof. Dr. Anita Schöbel

N.N.

Dates

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

Tutorials

tba.

Materials

OpenOLAT

Contents

This lecture introduces advanced concepts and algorithmic techniques for graph theoretic problems. Among the topics studied are:

• graph colorings and coverings,
• transitive hulls and irredundant kernels,
• graph search techniques,
• treewidth with algorithmic consequences, and
• matchings.

Lecturer and staff

Prof. Dr. Sven O. Krumke

N.N.

Dates

Monday, 8:15-9:45 (48-208)
Wednesday, 10:00-11:30 (48-208)

Tutorials

tba.

Materials

OpenOLAT

Inhalt

In this lecture we will discuss the basics of mathematical public transport planning. The goal is to construct a public transport plan that is attractive for both passengers and operators. We will discuss and model the corresponding problems as well as specific solution methods. The covered topics may include:

• network design
• line planning
• timetabling
• vehicle scheduling
• disposition management

Lecturer and staff

Prof. Dr. Anita Schöbel

N.N.

Dates

Wednesday, 08:15-09:45 (48-582)

Tutorials

tba.

Materials

OpenOLAT

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. Anita Schöbel

Date

By arrangement.

If you are interested please send an e-mail to schoebel(at)mathematik.uni-kl.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 ruzika(at)mathematik.uni-kl.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 krumke(at)mathematik.uni-kl.de.

Content

Many problems on graphs are in general hard to solve (e.g. NP-hard), but become easy or more manageable when the underlying graphs are restricted or the problem is decomposed into smaller subproblems on subgraphs.

In the seminar we deal on the one hand with different so-called width parameters for graphs, first of all the so-called tree width. This measures how far a graph moves away from being a tree. The concept of treewidth has turned out to be one of the most important approaches to find polynomial algorithms for NP-hard graph problems. Other width parameters include clique width and band width.  We study how these parameters affect the complexity of particular problems.

A second aspect of the seminar is the decomposition of a graph into suitable subgraphs.  Here we cover concrete decomposition-based solution methods for combinatorial optimization problems.

Lecturer

Prof. Dr. Sven O. Krumke

Material

OpenOLAT

Content

Data Science is an interdisciplinary scientific field and deals with the extraction of knowledge, patterns and structures from data in order to answer questions, make decisions and solve problems. Mathematical methods are used to analyze available data and extract information from it.

The goal of the proseminar is to work together on the basics of data analysis. The book by Shikhman and Müller "Mathematical Foundations of Big Data Analysis" will serve as a literature resource. The participants will be asked to work on a chapter of about 20 pages and to give a presentation of about one hour. Afterwards we will discuss the contents and give feedback on the presentation.

After successful participation we will have an overview of different techniques of data analysis, in-depth knowledge of a selected topic (the one we have prepared and presented), understand the mathematical background of the techniques, and are able to apply the methods. In addition, we have learned to present mathematical topics appropriately and to lead a mathematical discourse.

Lecturer

Prof. Dr. Stefan Ruzika

Material

OpenOLAT

Registration

If you are interested in participating, please contact Prof. Dr. Stefan Ruzika by email.

Content

• Development of basic mathematical knowledge for students of civil engineering
• Topics covered: Vector space Rⁿ, matrices, determinants, linear systems of equations, eigenvalue problems, vector calculus and analytic geometry, probability calculus
• Application of the treated mathematical tools to concrete subject-specific problems from various disciplines of civil engineering

Lecturer and adjunct

Dr. Florentine Kämmerer

Date

Monday, 08:15 - 09:45 (24-102)
Thursday, 10:00 - 11:30 (46-220)

Tutorials

tba.

Materials

OpenOLAT