Program Overview

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.

Introduction to the Programme

The programme 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).

Tracks in the Programme

• Computational Mathematics: 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.
• Financial Mathematics: Financial mathematics is a branch of applied mathematics devoted to analyzing 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 lossthis is the foundation of the theory of arbitrage-free pricing of derivative instruments.
• Optimisation and Systems Theory: Optimization and Systems Theory is a discipline in applied mathematics primarily devoted to optimization methods, including mathematical programming and optimal control, and systems theoretic aspects of control and signal processing.
• Mathematics of Data Science: 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 supports it. In contrast, modern approaches focus more on computational statistics and automated methods for extracting information.

Courses in the Programme

The courses in the programme cover topics such as:

• Optimization
• 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

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 graduates will be able to bring the usage of mathematics and simulations into a multitude of applications.

Research Areas

The programme is run by the Department of Mathematics at KTH, which hosts some of the strongest Swedish research groups in mathematics. Research areas include:

• Random matrices
• Image processing
• PDE
• MathDataLab
• Mathematical systems theory
• Mathematical programming
• Numerical methods for stochastic and deterministic differential equations
• Numerical methods for micro and complex flow
• Multiscale methods
• Numerical linear algebra
• Inverse problems
• Finite element methods for multiphase flow
• Probability theory and statistical theory with applications to finance and risk management
• Statistical learning
• Monte Carlo methods
• Computational statistics
• High-dimensional models

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. Many of the UN goals of sustainable development are accordingly linked to Applied Mathematics, including:

• 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

Application Deadlines

• 16 October: Application opens
• 15 January: Last day to apply
• 2 February: Submit documents and, if required, pay application fee
• 26 March: Admission results announced

Faculty and Research

The researchers are working actively in many interdisciplinary cooperative ventures, for example, the Swedish e-Science Research Centre (SeRC), the Linné FLOW Centre, and Karolinska Institutet. Students will also have access to Sweden's fastest supercomputers via the PDC Centre for High-Performance Computing.