MSc Applied and Computational Mathematics
KTH Royal Institute of Technology
Key Information
Campus location
Stockholm, Sweden
Languages
English
Study format
On-Campus
Duration
2 years
Pace
Full time
Tuition fees
SEK 342,000 / per year *
Application deadline
Request info
Earliest start date
Aug 2024
* non-EU/EEA/Swiss is 342,000 SEK.
Introduction
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).
Admissions
Curriculum
Year 1
At least one of the conditionally elective courses among the general courses has to be studied during the first or second year.
Mandatory courses for all tracks
- Theory and Methodology of Science (Natural and Technological Science) (AK2030) 4.5 credits
- Sustainable development and research methodology in mathematics (SA2001) 3.0 credits
- Applied Numerical Methods (SF2520) 7.5 credits
- Probability Theory (SF2940) 7.5 credits
Conditionally elective courses for all tracks
- Applied Linear Optimization (SF2812) 7.5 credits
- Mathematical Systems Theory (SF2832) 7.5 credits
- Systems Engineering (SF2863) 7.5 credits
Year 2
At least one of the conditionally elective courses among the general courses has to be studied during the first or second year.
Conditionally elective courses for all tracks
- Mathematical Systems Theory (SF2832) 7.5 credits
- Systems Engineering (SF2863) 7.5 credits
Program Outcome
Sustainable development
Graduates from KTH have the knowledge and tools for moving society in a more sustainable direction, as sustainable development is an integral part of all programmes. The particular strength of mathematics is its high degree of abstraction, with one and 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 these phenomena 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:
- 13 Climate Action
- 3 Good Health and Well-Being
- 9 Industry, Innovation, and Infrastructure
Examples of master's degree projects relating to Climate Action are Efficient computational methods for climate models (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 relating to Good Health and Well-Being are Optimal construction 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 optimization (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 decisions based-on energy and time costs (in collaboration with Volvo).
Sustainable development
Graduates from KTH have the knowledge and tools for moving society in a more sustainable direction, as sustainable development is an integral part of all programmes. The particular strength of mathematics is its high degree of abstraction, with one and 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 these phenomena 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:
- 13 Climate Action
- 3 Good Health and Well-Being
- 9 Industry, Innovation, and Infrastructure
Examples of master's degree projects relating to Climate Action are Efficient computational methods for climate models (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 relating to Good Health and Well-Being are Optimal construction 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 optimization (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 decisions based-on energy and time costs (in collaboration with Volvo).
- Technology manager
- Deep learning software engineer
- Team leader
- Professor
- PhD student
- Credit risk analyst
- CEO
- Head of marketing and sales
- Technical director
- Development engineer.
Scholarships and Funding
KTH offers four different scholarship opportunities for master's studies. The KTH Scholarship covers the tuition fee of a one or two year master’s programme. The KTH One-Year Scholarship is aimed at current KTH master's programme students and covers the tuition fee of the second year of studies. The KTH Joint Programme Scholarship is aimed at students in certain joint programmes and covers the tuition fee for the study period spent at KTH. The KTH India Scholarship is aimed specifically at students from India.
- KTH Scholarship
- KTH One-Year Scholarship
- KTH Joint Programme Scholarship
- KTH India Scholarship
Swedish Institute
The Swedish Institute (SI) offers a number of scholarships for students from targeted countries coming to Sweden.
KTH associated scholarship organisations
KTH cooperates with the following organisations providing scholarship opportunities for prospective KTH students.
- COLFUTURO (Programa Crédito Beca) for students from Colombia
- LPDP (Indonesia Endowment Fund for Education) for students from Indonesia
- FUNED for students from Mexico
Scholarship portals
IEFA database
The IEFA database offer a comprehensive scholarships search, grant listing and international student loan programmes.
Studyportals
The Studyportals scholarship database lists over 1,000 scholarship and grants for students worldwide applying for studies in the EU.
Scholars4dev
Scholarships for Development is a database of scholarships open to students from developing countries.
WeMakeScholars
WeMakeScholars helps students from India secure education loans from banks and NBFCs. They also lists more than 26,000 international scholarships from different trusts, foundations and govt. bodies.
Deferment of student loans in the United States
KTH is an accredited institution at the US Department of Education and holds a Title IV 'Deferment Only' status (OPE ID 03274300). US students may defer payments on existing federal student loan accounts while enrolled in a master’s programme at KTH. The 'Deferment Only' status does not allow students to take out federal student loans for enrolment at KTH. However, the accreditation facilitates grant and loan opportunities for US students as many private student loan institutions in the US use this designation as a requirement to grant new loans. Students who wish to defer payments must contact their lending institution in the US.
Several scholarship options are available. Please check the institute website for more information.
Gallery
Career Opportunities
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 bring the usage of mathematics and simulations into 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. 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.
After graduation
Technology manager, deep learning software engineer, team leader, professor, PhD student, credit risk analyst, CEO, head of marketing and sales, technical director, and development engineer.