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 in the high-tech industry and in scientific and engineering research, for example, in 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 over the last few decades has made computational science and engineering the "third pillar" of science, complementing theory and experiment. The programme offers four tracks: Computational Mathematics, Financial Mathematics, Optimisation and Systems Theory, and Mathematics of Data Science.
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. The field encompasses portfolio theory, derivative pricing and quantitative risk management, providing the theoretical and methodological basis for decision-making under uncertainty. A central part of the discipline is developing mathematical models that help analyse markets, price financial instruments, and manage financial risk.
You develop the skills to design and analyse mathematical models of financial instruments, develop pricing techniques, assess and manage risk, and translate complex market dynamics into quantitative strategies Such skills are increasingly important as financial markets have grown in complexity. While mathematical models are powerful tools for understanding and supporting decision-making, you also learn to recognise their assumptions, limitations and appropriate use in practice.
Optimization and Systems Theory track
The Optimisation and Systems Theory track focuses on optimisation methods, mathematical modelling and systems theory, with applications in control, signal processing and engineering. The field is also closely related to mathematical economics and applied problems in operations research, systems engineering and control engineering. The track provides the knowledge and skills needed to handle various optimisation problems (both linear and nonlinear), build and analyse mathematical models for a wide range of engineering systems, and design optimal algorithms, feedback control systems, filters, and estimators for such systems.
Optimisation and Systems Theory have broad applications in both industry and research. Examples of applications include aerospace, 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
The Mathematics of Data Science track focuses on mathematical, statistical and computational methods for analysing complex data and supporting decision-making under uncertainty. While classical statistics aims to explain data through mathematical models, modern data science also relies on computational methods to analyse increasingly large and complex data sets.
You develop the skills to model data, identify relevant features, optimise decision models, reduce complexity through dimensionality reduction, and perform large-scale computations. By combining mathematics, statistics, optimisation and computational learning, the track prepares you to solve data-driven problems in fields ranging from the natural sciences and engineering 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 KTH Campus in Stockholm by the School of Engineering Sciences (at KTH).
Programme structure and progression
During primarily the first semester, all students build a common foundation through mandatory courses in probability theory, scientific methodology and sustainable development, numerical analysis, and optimization and systems theory. During primarily the second and third semesters, you specialise within one of four tracks: Computational Mathematics, Financial Mathematics, Optimisation and Systems Theory, or Mathematics of Data Science. Each track offers a broad selection of elective courses that allow you to tailor your studies to your interests and career goals. During the final semester, you complete a degree project within your chosen specialisation in an academic or industrial environment.
Courses in the programme
The courses in the programme cover topics such as optimisation, mathematical systems theory, systems engineering, modelling and simulation, numerical methods and applications, parallel and high-performance computations, big data, machine learning, arbitrage pricing, portfolio theory and risk management.
Courses in the master's programme Applied and Computational Mathematics
Future and career
Advanced mathematics and computer simulations are present in several important fields; their use has increased dramatically with the rapid development of computer software and hardware. Financial mathematics, medicine, and biology are prevalent areas, but you will be able to apply mathematics and simulations to a multitude of applications.
The graduates of this programme are in high demand in the labour market as well as in academia. Graduates work in companies like Ericsson, ABB, Comsol, SAAB, RaySearch Labs, Modelon, If, Citibank, Brainlab, ÅF, Atlas Copco, Elekta, Process Systems Enterprise, Goldman Sachs, and many others. You can expect to take on roles such as technology manager, deep learning software engineer, team leader, professor, credit risk analyst, CEO, marketing and sales manager, technical director and development engineer.
Graduates from the programme also go on to academic careers with doctoral studies at KTH, other Swedish universities, or other leading European and US universities.
Sustainable development
Graduates from KTH have the knowledge and tools for moving society in a more sustainable direction. The particular strength of mathematics is its high degree of abstraction, with the same mathematical model used to describe very different features in many different areas of application. This versatility leads to the effect that once you can quantify phenomena, you will be able to investigate them independently of their source, for example, in science, engineering, society and the economy.
Many of the UN goals of sustainable development are accordingly linked to Applied Mathematics, to name just a few: Good health and well-being, Affordable and clean energy, Decent work and economic growth, Industry, innovation and infrastructure, Sustainable cities and communities, Climate action, Life below water, Reduced inequality and others.
The master’s programme in Applied and Computational Mathematics provides the student with the knowledge and tools applicable for their successful treatment. You will see examples of how to do this in different courses. It is not uncommon for the final master’s degree project to be devoted to questions related to sustainable development and its various goals. The examples of sustainable development goals addressed by the programme are:
Examples of master's degree projects related to Climate Action include: Efficient computational methods for climate models (in collaboration with SMHI), Consequences of climate change for the electric power supply (in collaboration with SWECO), and Polynomial chaos expansion for climate-economy assessment (in collaboration with Karlsruhe Institute of Technology).
Examples of master's degree projects related to Good Health and Well-Being include: Optimal design of medical equipment for cancer treatment (in collaboration with RaySearch Labs), Simulation of suturing for surgeon training (in collaboration with SenseGraphics), and Proton arc therapy optimisation (in collaboration with RaySearch Labs).
Examples of master's degree projects relating to Industry, Innovation and Infrastructure are: Optimal traffic planning for autonomous vehicles (in collaboration with Volvo Construction Equipment), Optimal energy management for parallel hybrid electric vehicles (in collaboration with Scania), and Optimal driving decision based on energy and time costs (in collaboration with Volvo).
Faculty and research
The programme is run by the Department of Mathematics at KTH, which hosts some of the strongest Swedish research groups in mathematics. It comprises four units: Mathematics, Mathematical Statistics, Optimisation and Systems Theory, and Numerical Analysis. Together, these units conduct research across a broad spectrum of mathematical disciplines, ranging from pure to applied mathematics. Some of the current larger research centres hosted at the department are:
- Random matrices, sponsored by the Wallenberg Foundation
- Image processing, sponsored by SSF
- PDE, sponsored by the ERC/VR/Gustafsson's foundation
- MathDataLab, sponsored by Brummer & Partners
Research carried out at the Division of Optimization and Systems Theory includes various topics in mathematical systems theory (Xiaoming Hu, Per Enqvist and Johan Karlsson), with particular emphasis on stochastic systems, filtering, identification and robust and nonlinear control; mathematical programming (Anders Forsgren, Per Enqvist and Jan Kronqvist), with large-scale nonlinear programming, structural optimization, mixed-integer optimization; and a wide range of applications. Examples of applications include radiation therapy (Forsgren), robotics (Hu), and telecommunications (Karlsson).
The research in the Division of Numerical Analysis includes:
- numerical methods for stochastic and deterministic differential equations (Anders Szepessy, member of the Royal Swedish Academy of Sciences, and Mattias Sandberg),
- numerical methods for micro and complex flow (Anna-Karin Tornberg, member of the Royal Swedish Academy of Sciences and the Royal Swedish Academy of Engineering Sciences, and Katarina Gustavsson),
- multiscale methods (Olof Runborg),
- numerical linear algebra (Elias Jarlebring)
- inverse problems (Ozan Öktem),
- and finite element methods for multiphase flow (Sara Zahedi, Jennifer Ryan).
The researchers are actively engaged in many interdisciplinary cooperative ventures, including the Swedish e-Science Research Centre (SeRC), the Linné FLOW Centre, and Karolinska Institutet. You will also have access to Sweden's fastest supercomputers via the PDC Centre for High-Performance Computing.
The Division of Mathematical Statistics hosts active groups in probability theory and statistical theory with applications to finance and risk management (Boualem Djehiche, Henrik Hult, Sigrid Källblad and Camilla Landen), statistical learning (Henrik Hult, Jimmy Olsson, Pierre Nyquist, Joacim Anden and Nacira Agram), Monte Carlo methods (Henrik Hult, Jimmy Olsson and Pierre Nyquist), computational statistics (Jimmy Olsson and Pierre Nyquist), and high-dimensional models (Kevin Schnelli).
