Department of Mathematics

Courses in Summer Semester 2022

We are pleased that, as things stand at present, we will be able to return to face-to-face teaching for almost all courses in the summer semester 2022 - while, of course, complying with the safety and hygiene requirements that will then be in place.

 

On the current page we present the course offerings of the Department of Mathematics for the summer semester 2022 with links to the respective courses in the handbook of modules (MHB) and continuously updated information (in particular: links to the courses in the online teaching platform OLAT - as soon as they are available).

 

The lecture period begins on 25.04.2022 and ends on 30.07.2022.


Registration for the exercise classses and other courses (requiring registration) will (usually) be possible until 29.04.2022, 12:00 noon in URM (https://urm.mathematik.uni-kl.de). We ask you to register there as early as possible.
 

The allocation to the (small group) exercise classes is planned to take place (as usual) on Friday of the first week of lecture period (29.04.2022)!

Courses for Undergraduate Students and Students of Teacher Training Programmes

Fundamentals:

Grundlagen der Mathematik I: Analysis (MHB: MAT-10-11A-K-2)

Grundlagen der Mathematik I: Lineare Algebra (MHB: MAT-10-11B-K-2)

Grundlagen der Mathematik II (MHB: MAT-10-12-K-2)

Pure Mathematics:

Algebraische Strukturen (MHB: MAT-12-11-K-2)

Einführung: Gewöhnliche Differentialgleichungen (MHB: MAT-12-25-K-3)

Einführung: Topologie (MHB: MAT-12-26-K-3)

Elementare Zahlentheorie (MHB: MAT-12-21-K-3)

Maß- und Integrationstheorie (MHB: MAT-12-28-K-3)

Vektoranalysis (MHB: MAT-12-27-K-3)

Applied Mathematics / Modelling:

Einführung in das Wissenschaftliche Programmieren (MHB: MAT-14-00-K-2)

Einführung in das Symbolische Rechnen (MHB: MAT-14-12-K-3)

Grundlagen der Finanzmathematik (MHB: MAT-60-15-K-4)

Lineare und Netzwerkoptimierung (MHB: MAT-14-13-K-3)

Mathematische Modellierung (MHB: MAT-14-01-K-3)

Specialisation Bachelor:

Character Theory of Finite Groups (MHB: MAT-40-25-K-4)

Cryptography (MHB: MAT-40-14-K-4)

Functional Analysis (MHB: MAT-70-11-K-4)

Introduction to Neural Networks (MHB: MAT-80-13A-K-4)

Introduction to Systems and Control Theory (MHB: MAT-80-12A-K-4)

Monte Carlo Algorithms (MHB: MAT-60-14-K-6)

Nonlinear Optimization (MHB: MAT-50-12-K-4)

Plane Algebraic Curves (MHB: MAT-40-28-K-4)

Quadratic Number Fields (MHB: MAT-40-29-K-4)

Regression and Time Series Analysis (MHB: MAT-60-12-K-4)

Special Courses for Students of Teachers Training Programmes:

Didaktik der elementaren Algebra und der Zahlbereichserweiterungen (MHB: MAT-20-11-K-3)

Didaktik der Linearen Algebra und der Analytischen Geometrie (MHB: MAT-20-22-K-5)

Geometrie (für Studierende des Lehramts) (MHB: MAT-18-03-K-3)

Moderne Mathematik (MHB: MAT-22-01-K-6)

Proseminar Elementarmathematik vom höheren Standpunkt (MHB: MAT-20-02-K-3)

 

For Information on the courses in German language, please switch to the German version of this page.

Courses for Graduate Students (Master)

Here you can find information about advanced master's courses (lectures, seminars, reading courses).

Read more

Mathematikvorlesung an der TUK: Bild aus Hörsaal

Courses for Students of other Departments

Please switch to the German version of the current page to find information on courses for students of other departments (in German language).

Information on courses offered by other departments

Information on the courses offered for the subsidiary subjects can be found on the respective information pages of the departments:

 

  • Biology (in German)
  • Chemistry (in German)
  • Electrical Engineering
  • Computer Science
  • Mechanical and process engineering (in German)
  • Physics
  • Economics (in German)

 (As soon as the pages are created, we will make the corresponding links available here).

Functional Analysis

Content

  • Hahn-Banach theorem and its applications
  • Baire category theorem and its applications (uniform boundedness principle, Banach-Steinhaus theorem, open mapping theorem, inverse mapping theorem, closed graph theorem)
  • weak convergence (Banach-Alaoglu theorem, reflexive Banach spaces, lemma of Mazur and its applications)
  • projections (closed complement theorem)
  • bounded operators (adjoint operators, spectrum, resolvent, normal operators)
  • compact operators (Fredholm operators, Fredholm alternative and its applications, spectral theorem (Riesz-Schauder) and applications to normal operators)

contact time

4 SWS lecture
2 SWS exercise classes

substantive prerequisites

content of the introductory lecture "Einführung in die Funktionalanalysis" as well as concepts from "Maß- und Integrationstheorie"

Monte Carlo Algorithms

Content

Monte Carlo algorithms are the algorithms which use randomness. The course gives an introduction to this important basic algorithmic technique in mathematics and computer science.

It discusses the topics

  • Direct Simulation
  • Simulation of distributions
  • Variance reduction
  • Markov Chain Monte Carlo algorithms
  • High-dimensional integration

and applications in physics as well as in financial and actuarial mathematics

Contact Time

4 SWS / 60 h Lectures
2 SWS / 30 h Exercise Classes

Prerequisites

course „Stochastische Methoden“ and basic knowledge og in numerical methods

Frequency

The lecture is offered irregularly (in summer semester)

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