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 is 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 is an enabling technology for scientific discovery and engineering design. It involves mathematical modelling, numerical analysis, computer science, high-performance computing and visualization. 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 is mainly concerned with the mathematical foundations of computational science and engineering. However, in this track we will also discuss issues of high-performance computing. Given the interdisciplinarity, the final curriculum may vary greatly depending on your interests. The Computational Mathematics track contains courses providing knowledge of design, analysis and application of numerical methods for mathematical modelling, usable in computer simulations catering to both research and prototyping.

Financial mathematics track

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 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 opinions of future market prices and combine their views with current market prices to take steps to manage 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 much attention from academics and practitioners over recent decades, and mathematical sophistication has risen substantially. However, a mathematical model is, at best, a simplification of the real-world phenomenon being modelled, and mathematical sophistication can never replace common sense and knowledge of the limitations of mathematical modelling.

Optimization and Systems Theory track

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. 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 optimization problems (both linear and nonlinear), build up and analyze mathematical models for multiple engineering systems, and design optimal algorithms, feedback control, filters and estimators for such systems.

Optimization 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 optimization and system integration.

Mathematics of Data Science track

Statistics is the science of learning from data. Classical statistics is trying to understand data by determining a plausible model and testing whether the data fits the model. Modern learning is concerned with computational statistics and automated data extraction methods. Technological progress and the increased availability of information contribute to the emergence of massive and complex data sets. Various scientific fields are contributing to the analysis of such data at the interface of mathematics, statistics, optimization and computational learning methods. Optimal decision-making under uncertainty based on 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.

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).

KTH Royal Institute of Technology in Stockholm is one of Europe’s leading technical universities, as well as a key centre of intellectual talent and innovation. We are Sweden’s largest technical research and learning institution and home to students, researchers, and faculty from around the world dedicated to advancing knowledge.

History

KTH is a university with a rich history of pioneering ideas and innovation that dates back to 1827. For nearly 200 years KTH has educated students who have gone on to influence our present and make the technological advances that define modern society. Still today, KTH shapes the talents that will find the solutions for tomorrow’s challenges.

Research

KTH is working with industry and society in the pursuit of sustainable solutions to some of humanity’s most significant challenges: climate change, future energy supply, urbanisation, and quality of life for the rapidly-growing elderly population. We are addressing these with world-leading, high-impact research and education in natural sciences and all branches of engineering, as well as in architecture, industrial management, urban planning, history, and philosophy. Almost two-thirds of the SEK 4 billion turnovers are related to research.

Basic and applied research is performed side-by-side at KTH and interdisciplinary research is conducted in parallel with work in specific fields.

Career

KTH maintains close relationships with an expanding network of international companies and the industrial community in a number of fields, and working and studying here provides access to this network.

The latest career report shows that 94 percent of those who graduated from KTH 2010-2012 have been employed since they finished their degree and a remaining 6 percent have gone on to Ph.D. studies. Of the international student population, 30 percent go on to Ph.D. studies at KTH or other renowned universities. 32 percent of KTH Alumni leave Sweden for work or studies abroad. 13 percent lead others in their work, and 13 percent have already received their first managerial position.