Master Scientific Computing Specializations
Within the master program Scientific Computing students can choose from a wide variety of modules and courses. This leads to several possible specializations within the master course. These will finally lead to a master thesis research in one of the groups working in that specialization area.
The following specialization tracks are meant as a guideline for the course selection and the organization of a personal and individual study program.
Data & Text Mining
The objective of the specialization Data and Text Mining in the International Masters Program of Scientific Computing is to study models, techniques, tools, and architectures in support of managing and analyzing large-scale and diverse data sets. The focus is on traditional data mining concepts such as clustering, association rule mining, and classification to more advanced techniques like mining graph data, data/text streams, document collections, and social network data. Techniques such as features extraction approaches and probabilistic data analysis models will be learned, the latter playing an important role in analyzing text data. The applications include traditional frameworks such as scientific data warehouses employed in the natural sciences, the analysis of large-scale social networks, and the exploration of document collections, the latter being a prominent theme in the Digital Humanities.
Simulation & Optimization
The objective of the specialization Simulation and Optimization in the International Masters Program of Scientific Computing is to study techniques, tools, and architectures for the large scale simulation and optimization of discrete and continuous models. The focus is on efficient state-of-the-art methods allowing the solution of large instances such as higher-order finite element methods, a-posteriori error control and adaptive methods, multi-level and domain decomposition methods, all-at-once optimization or mixed-integer optimization. A second focus is placed on the efficient implementation of the above-mentioned methods on modern computer hardware including aspects of parallel high-performance computing, software design and object-oriented programming. Furthermore there is overlap of this specialization with the specializations in "Analysis & Modelling" as well as “Scientific Visualization” and "Statistics". An individual study plan can easily be arranged that combines these fields.
Statistics
The objective of the specialization Statistics in the International Masters Program of Scientific Computing is to study tools and methods of mathematical statistics, probability theory, stochastic modeling, and data analysis, and to apply them to important real world problems.
Modelling & Applied Analysis
The objective of the specialization Modelling and Applied Analysis in the International Masters Program of Scientific Computing is to study analytical methods and tools which are useful in the derivation, analysis, simulation and optimization of complex systems. Our aim ist to understand the spatial and temporal behaviour of these systems in dependence of their intrinsic parameters and initial data. In particular, the focus of this program lies in the investigation of problems arising in the field of Materials Science, Biology and Medicine.
Computational Aspects in Number Theory
The area Computational aspects in Number Theory seeks Master students who on the one hand wish to acquire deep theoretical knowledge in Number Theory and Arithmetic Geometry and on the other hand want to approach the topic from a computational view point. This requires a strong background in the above themes and at the same time interest in computer algebra, computational issues and computer science. Current themes are questions on modular forms (classical or Drinfeldian), the computation of Heegner points over function fields, and explicit equations of certain deformation rings that occur in number theory.
Imaging Science
The specialization Imaging Science within the International Masters Program of Scientific Computing covers all aspects of visual data analysis ranging from low-level image processing to high-level computer vision and it has deep foundations in applied mathematics (statistics, variational analysis, optimization), machine learning, and artificial intelligence. Besides covering the state-of-the-art of the field, there is also a strong focus on applying this basic level research to challenging applications in diverse areas ranging from industry to research in the life sciences and humanities.
Scientific Visualization
The objective of the specialization “Scientific Visualization” is to generate meaningful visualizations for the exploration of the acquired data. These visualizations have to be fast and interactive in order to give feedback to the user which enables self exploration. The tools to be developped have to find the most significant critical changes or hot spots in high dimensional spaces and condense these features in projections dealing with colors, space and time. Therefore the training involves mathematical skills in dynamical systems, curvature analysis, graph theory, topological invariants and abstract thinking. On the other hand the focus is on good programming skills regarding parallel multicore programming, the use of graphical embedded systems, sorting strategies, image analysis and image processing.