# General Information

The Chair offers the following courses included in the degree program “Business Mathematics” (BSc & MSc) on a regular basis. You can find more detailed information in the respective module catalogues.

**Numerical Mathematics (4+2+2 SWS / 9 ECTS) **(BSc):

Numerical mathematics is of crucial relevance in numerous fields of mathematical applications. This course focuses on the following basic problems in numerical mathematics:

- solutions to systems of linear and nonlinear equations
- interpolation and approximation
- numerical quadrature

Related mathematical concepts such as the condition number of a numerical problem as well as accuracy and error, computational cost and stability of algorithms will be introduced.

The course is composed of a four-hour lecture, a two-hour exercise offering theoretical exercises and a two-hour exercise with programming tasks.

**Functional Analysis (4+2 SWS / 8 ECTS) **(BSc):

This lecture will take a particularly close look at functions as elements of adequate normed vector spaces, thus providing new tools of linear algebra for problem-solving in mathematical analysis. Thus, functional analysis creates a general approach to dealing with (partial) differential equations, optimization problems and approximations and, being the basis of advanced stochastics and numerical mathematics, constitutes the core of mathematics.

This introduction will address classical results and methods. Main topics are: metric and normed spaces, linear operators, dual spaces, Hilbert spaces, Hahn-Banach theorems, compact operators, theorems for operators (principle of uniform boundedness, open mapping theorem, closed graph theorem), adjoint and compact operators, spectral theory (Riesz-Schauder theorem).

The course consists of a two-hour lecture and a one-hour exercise and the prerequisities are Analysis I, II and Linear Algebra.

**Computational SDEs (2+2 SWS / 6 ECTS)** (MSc)

This lecture addresses numerical methods for stochastic differential equations (SDEs). In particular, it focuses on the calculation of the expected values of functionals of the solution, which is of interest for applications from mathematical finance. The lecture consists of four thematic units:

- Brownian Motion and Multilevel Monte Carlo method for Brownian functionals
- SDEs with additive noise and discretization of the Wong-Zakai approximation
- Itô-theory of SDEs
- Numerical methods for general stochastic differential equations

The course is composed of a two-hour lecture and a two-hour exercise including theoretical and programming tasks.

Knowledge in the field of stochastic processes as well as of theory and numerics of ordinary differential equations is desirable.

**Computational Finance (2+1 SWS / 5 ECTS) **(MSc)

This course provides a problem-oriented overview on numerical methods for valuation of options in standard models (binominal model, Black-Scholes model, Heston model). The main focus is on the characteristic properties as well as on the implementation of the presented methods, which include the following:

- tree models
- Finite Difference Method
- (Quasi-) Monte Carlo methods
- Fourier methods

The course consists of a two-hour lecture and a one-hour exercise with theoretical and practical tasks.

Knowledge of mathematical finance is a __prerequisite__.

**Seminar “Selected Topics in Numerical Analysis” (2 SWS / 3 ECTS) **(BSc & MSc)

This seminar is offered every semester and, on an alternating semester basis, addresses selected topics in numerical analysis.

Successful participation in one of the Chair’s seminars is a prerequisite for writing your final thesis at the Chair.