KTH Royal Institute of Technology

MSc Applied and Computational Mathematics

The master’s programme in Applied and Computational Mathematics fosters skilled applied mathematicians, well-prepared for advanced industrial positions or PhD studies. The programme offers four tracks: Computational Mathematics, Financial Mathematics, Optimisation and Systems Theory, and Mathematics of Data Science. Graduates acquire skills in advanced mathematics and computer simulation that are in demand in several important fields.

Applied and Computational Mathematics at KTH

Computer simulations are of great importance for the high-tech industry and scientific and engineering research, for example, virtual processing, climate studies, fluid dynamics and advanced materials. Thus, computational science and engineering are enabling technologies for scientific discovery and engineering design. It involves mathematical modelling, numerical analysis, computer science, high-performance computing and visualisation. The remarkable development of large-scale computing in the last decades has turned computational science and engineering into the "third pillar" of science, complementing theory and experiment.

Computational Mathematics Track

The Computational Mathematics track focuses on the mathematical foundations of computational science and engineering, with an emphasis on three core areas: numerical methods for partial differential equations, high-performance computing, and inverse problems. In addition, the track addresses broader topics in high-performance computing and its role in large-scale simulations.

Given its interdisciplinary nature, the curriculum can be tailored to your individual interests, allowing flexibility in specialisation. The courses offered provide a strong background in the design, analysis, and application of numerical methods for mathematical modelling, equipping you with the tools needed for advanced computer simulations in both research and prototyping.

Financial Mathematics Track

Financial mathematics is a branch of applied mathematics devoted to analysing and solving problems related to financial markets. A central principle is that any informed market participant would exploit an opportunity to make a profit without risk of loss—this is the foundation of the theory of arbitrage-free pricing of derivative instruments. While arbitrage opportunities do exist, they are rare; in practice, both potential gains and losses must be carefully considered. Tools such as hedging and diversification are used to reduce risk, while speculative strategies aim to maximise profits. Market participants form different expectations about future price movements and combine these with current market information to manage risk while seeking opportunities for return.

The field encompasses portfolio theory and quantitative risk management, which provide the theoretical and methodological basis for decision-making in modern financial markets. Over the past decades, financial mathematics has attracted significant attention from both academics and practitioners, with mathematical sophistication in the field growing substantially.

Within this landscape, the financial mathematician plays a key role: designing and analysing mathematical models of financial instruments, developing pricing techniques, assessing and managing risk, and translating complex market dynamics into quantitative strategies. While such models are powerful tools, it remains essential to recognise that they are simplifications of reality—mathematical sophistication can inform and guide decision-making, but it cannot replace common sense or a clear understanding of the limitations of modelling.

Optimisation and Systems Theory track

Optimisation and Systems Theory is a discipline in applied mathematics primarily devoted to optimisation methods, including mathematical programming and optimal control, and systems theoretic aspects of control and signal processing. The field is also closely related to mathematical economics and applied problems in operations research, systems engineering and control engineering. The track provides knowledge and competence to handle various optimisation problems (both linear and nonlinear), build up and analyse mathematical models for multiple engineering systems, and design optimal algorithms, feedback control, filters and estimators for such systems.

Optimisation and Systems Theory have broad applications in both industry and research. Examples of applications include aerospace, engineering, radiation therapy, robotics, telecommunications, and vehicles. Furthermore, many new areas in biology, medicine, energy and environment, and information and communications technology require an understanding of both optimisation and system integration.

Mathematics of Data Science track

Statistics is the science of learning from data. In classical statistics, the goal is to explain data by proposing a plausible model and testing whether the data support it. In contrast, modern approaches focus more on computational statistics and automated methods for extracting information.

Advances in technology and the vast growth of available information have led to the rise of massive, complex data sets. Analysing such data requires tools that combine mathematics, statistics, optimisation, and computational learning methods.

Making good decisions under uncertainty in these settings involves modelling and identifying the most relevant features in the data, optimising decision policies and model parameters, reducing complexity through dimension reduction, and performing large-scale computations.

As a result, data science grounded in applied mathematics has enormous potential to transform fields ranging from the natural sciences to business and the social sciences.

This is a two-year programme (120 ECTS credits) given in English. Graduates are awarded the degree of Master of Science. The programme is given mainly at the KTH Campus in Stockholm by the School of Engineering Sciences (at KTH).