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
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)
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)
Introduction to Neural Networks (MHB: MAT-80-13A-K-4)
Introduction to Systems and Control Theory (MHB: MAT-80-12A-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).
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)
- Economics (in German)
(As soon as the pages are created, we will make the corresponding links available here).
Character Theory of Finite Groups
- Maschke's theorem,
- character table,
- Burnside theorem,
- induced characters,
- Frobenius group.
2 SWS lecture
1 SWS example class
Courses "Algebraische Strukturen" and "Einführung: Algebra".
- stream cipher and block cipher,
- frequency analysis,
- modern ciphers.
- factorization of large numbers, RSA,
- primality tests,
- discrete logarithm, Diffie-Hellman key exchange, El-Gamal encoding, Hash function, signature,
- cryptography on elliptic curves (ECC),
- attacks on the discrete logarithm problem,
- factorization algorithms (e.g. quadratic sieve, Pollard ρ, Lenstra).
4 SWS lecture
2 SWS example class
Courses "Algebraische Strukturen" and "Elementare Zahlentheorie"
- 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)
Monte Carlo Algorithms
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
4 SWS / 60 h Lectures
2 SWS / 30 h Exercise Classes
course „Stochastische Methoden“ and basic knowledge og in numerical methods
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.
Plane Algebraic Curves
- affine and projective spaces, in particular the projective line and the projective plane,
- plane algebraic curves over the complex numbers,
- smooth and singular points,
- Bézout's theorem for plane projective curves,
- the topological genus of a curve,
- rational maps between plane curves and the Riemann-Hurwitz formula.
A selection of the following topics will be covered:
- polars and Hesse curve,
- dual curves and Plücker formula,
- linear systems and divisors on plane curves,
- real projective curves,
- Puiseux parametrization of plane curve singularities,
- invariants of plane curve singularities,
- elliptic curves,
- further aspects of plane algebraic curves.
2 SWS lecture
1 SWS example class
Course "Algebraische Strukturen"; knowledge from the courses "Einführung: Algebra" and "Einführung: Topologie" is beneficial.
Quadratic Number Fields
- structure of imaginary quadratic fields,
- ideals and ideal class group,
- ideals as geometric lattices,
- finiteness of the class group.
2 SWS lecture
1 SWS example class
Course "Algebraische Strukturen"; knowledge from the courses "Elementare Zahlentheorie" and "Einführung: Algebra" are beneficial.
Regression and Time Series Analysis
- Linear regression models
- Parametric curve fitting
- Likelihood ratio tests
- Data adaptive model selection
- Variance Analysis (ANOVA)
- Experimental design
- Stationary stochastic processes
- Autoregressions and ARMA-processes
- Parameter estimation and model selection for time series
- Trend and seasonality
- Forecasting by exponential smoothing and the Box-Jenkins method
- Linear filters