# Master's Programme, Applied and Computational Mathematics, 120 credits

## A place to communicate

Here you will get reminders on important deadlines and other information from the Programme Director Michael Hanke or from Master Coordinator My Delby. You can ask questions that might be of interest for several students.

## About the programme

Applied and Computational Mathematics is a two-year (120 university credits) Master’s program on the advanced level (second cycle). The instruction language is entirely English. The program consists of a basic curriculum followed by four tracks: (i) statistical learning and data analytics, (ii) financial mathematics, (iii) computational mathematics, and (iv) optimization and systems theory. The courses in the basic curriculum are compulsory and worth 30 university credits. To obtain sufficient depth in a track, a student is required to complete courses worth approximately 30 university credits among the profile courses for the track in question. More details are found in the study program.

The detailed study plan can be found here.

Statistics is the science of learning from data. Classical statistics is trying to understand data by determining a plausible model for data, and testing whether the data fits the model. Modern learning is concerned with computational statistics and automated methods for extracting information from data.

As a result of technological progress and the emergence of massive data sets, a variety of scientific fields and their approaches to data analysis are converging at the interface of statistics and machine learning. This new field of “data analytics” focuses on modeling and knowledge extraction for predictive purposes. In **statistical learning and data analytics**, focus is on discovering new features in the data and on confirming or falsifying existing hypotheses. Predictive data analytics applies statistical models for predictive forecasting or classification. Data analytics, when it includes at its core mathematical statistics and computational learning, has the potential for transformative impact on science, business, and social sciences.

**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.

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 "Scientific Computing" 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.

**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.

The tracks of the **Master’s program Applied and Computational Mathematics** are closely connected and a skilled applied mathematician has knowledge and skills from several of the fields of applied mathematics presented above.

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