Description
This Master's program consists of lectures and seminars on topics regarding industrial mathematics and data analysis. Typically, lectures are accompanied by problem sessions with weekly exercises. For seminars, every participating student works out one theme and presents it to the audience. The specific topics for lectures and seminars vary from semester to semester, the students make their own choices and create individual course plans, according to their personal interests.
The common starting point in the first semester are two lectures (mandatory) on „Mathematical methods for data analysis and image processing“ and on „Numerical methods for PDE“. Based on these each student chooses either data analysis or industrial math for specialization. In the following semesters elective courses, i.e., lectures and seminars, are taken in order to specialize and for broadening regarding the other branch, respectively. Topics may be: Machine Learning, Inverse Problems, Applied Statistics, Parameter Identification (branch data analysis) and Optimal Control, Discrete Optimization, Adaptive FEM (branch industrial math).
In the heart of this master program is the „modeling project“: teams of students are assigned real-world problems – nothing from literature but actual problems from collaborations with engineering institutes or companies. They utilize mathemical modeling, analysis and optimization techniques to tackle their problem in order to find answers for the customer, i.e., the institute or company that has assigned the problem. In particular, the students design, analyze and perform algorithms for numerical simulations and they visualize their results appropriately.
The mathematical part of the program is accompanied by courses from an area of technical applications. Each student chooses either electrical engineering, mechanical engineering, geosciences, applied physics, or computer science as minor subject. You attend master courses on this, offered by the corresponding department. For this, basic knowledge on the chosen subject from bachelor studies is indispensable.
Last but not least, the complete final semester is designated for the master thesis. This is an individual project on a recent research topic, worked out by the student and guided by an expert in this field, i.e., a professor or postdoc.
This is summarized in the following study plans for specialization in:
The given numbers of credit points (CP) describe, more or less, the workload.
In addition, the structure and content of the program is defined in the examination regulations, the application and admission procedure in the admission regulations. Translations of the German versions of the regulations, which are binding, can be found here:
Translations of Regulations:
Modules:
Prerequisites:
Besides the formal prerequisites for application, the following knowledge and skills must be available regarding the subsequent Bachelor studies:
- Experience in programming: python, Matlab, R, or something equivalent
- Sound knowledge in real analysis, multivariate calculus, and linear algebra (matrix theory)
- Ordinary differential equations: Peano’s theorem, Picard-Lindelöf’s theorem
- Lebesgue integration: L_p spaces, Lebesgue's dominated convergence theorem
- Functional analysis: Banach and Hilbert spaces, linear operators, weak convergence
- Probability theory: random variables, probability distributions, law of large numbers
- Numerical mathematics:
- Linear systems: LU decomposition, iterative solvers (conjugate gradients)
- Nonlinear equations and systems: Banach fixed-point theorem, Newton’s method
- Interpolation and extrapolation
- Numerical integration: Newton-Cotes formulas, Gaussian quadrature
- Ordinary differential equations: Runge-Kutta methods
- Approximation of derivatives by finite differences
