Appendix 2: Specialisations
Master's Programme, Applied and Computational Mathematics, 120 credits (TTMAM), Programme syllabus for studies starting in autumn 2019
Track, Computational Mathematics (COMA)
The field of computer simulations is of great importance for high-tech industry and scientific/engineering research, e.g. virtual processing, climate studies, fluid dynamics, advanced materials, etc. Thus, Computational Science and Engineering (CSE) is an enabling technology for scientific discovery and engineering design. CSE involves mathematical modeling, numerical analysis, computer science, high-performance computing and visualization. The remarkable development of large scale computing in the last decades has turned CSE into the "third pillar" of science, complementing theory and experiment.
The track Computational Mathematics (COMA) is mainly concerned with the mathematical foundations of CSE. However, in this track we will also discuss issues of high-performance computing. Given the interdisciplinarity, your final curriculum may vary greatly depending on your interests.
Track, Mathematics of Data Science (DAVE)
The technological progress and the increased availability of information contributes to the emergence of massive and complex data sets. A variety of scientific fields are contributing to the analysis of such data at the interface of mathematics, statistics, optimization and computational methods for learning. Optimal decision making under uncertainty based in such circumstances require modelling and discovering relevant features in data, optimization of decision policies and model parameters, dimension reduction and large scale computations. Data science based on applied mathematics has the potential for transformative impact on natural sciences, business and social sciences.
Track, Financial Mathematics (FMIA)
Financial mathematics is applied mathematics used to analyze and solve problems related to financial markets. Any informed market participant would exploit an opportunity to make a profit without any risk of loss. This fact is the basis of the theory of arbitrage-free pricing of derivative instruments. Arbitrage opportunities exist but are rare. Typically both potential losses and gains need to be considered. Hedging and diversification aim at reducing risk. Speculative actions on financial markets aim at making profits. Market participants have different views of the future market prices and combine their views with current market prices to take actions that aim at managing risk while creating opportunities for profits. Portfolio theory and quantitative risk management present theory and methods that form the theoretical basis of market participants’ decision making.
Financial mathematics has received lots of attention from academics and practitioners over the last decades and the level of mathematical sophistication has risen substantially. However, a mathematical model is at best a simplification of the real world phenomenon that is being modeled, and mathematical sophistication can never replace common sense and knowledge of the limitations of mathematical modeling.
Track, Optimization and Systems Theory (OPST)
Optimization and Systems Theory is a discipline in applied mathematics primarily devoted to methods of optimization, including mathematical programming and optimal control, and systems theoretic aspects of control and signal processing. The discipline is also closely related to mathematical economics and applied problems in operations research, systems engineering and control engineering.
Master’s education in Optimization and Systems Theory provides knowledge and competence to handle various optimization problems, both linear and nonlinear, to build up and analyze mathematical models for various engineering systems, and to design optimal algorithms, feedback control, and filters and estimators for such systems.
Optimization and Systems Theory has wide applications in both industry and research. Examples of applications include aerospace industry, engineering industry, radiation therapy, robotics, telecommunications, and vehicles. Furthermore, many new areas in biology, medicine, energy and environment, and information and communications technology require understanding of both optimization and system integration.