StudyQA — Master: Applied and Computational Mathematics — Royal Institute of Technology (Page 2)

Description Contents Requirements Funding

Students from the Master’s programme in Applied and Computational Mathematics will become skilled applied mathematicians, well-prepared for advanced industrial positions or continued graduate studies. The programme contains three tracks: Mathematical Statistics and Financial Mathematics, Computational Mathematics and Optimisation and Systems Theory.

The programme consists of foundation courses that are mandatory for all students, and once the individual specialisation track is chosen, there are relevant required courses within that area as well.

Within the Mathematical Statistics and Financial Mathematics track students are provided with the ability to analyse and model situations where randomness and uncertainty are common and applicable in several areas.

The Computational Mathematics track contains courses providing knowledge of design, analysis and application of numerical methods for mathematical modeling, usable in computer simulations catering to both research and prototyping.
Finally, the Optimisation and Systems Theory track focuses on the ability to provide optimal solutions within certain restraints, applicable in areas such as economics, operation analysis, biology and robotics, where these dynamic systems are modeled and controlled with assets gained from the systems theory area.

Courses for all specialisations

Year 1

The tracks of the Master’s program Applied and Computational Mathematics are closely connected and a skilled applied mathematician has knowledge and skills from several of the fields of applied mathematics presented below.

Mandatory courses

Theory and Methodology of Science with Applications (Natural and Technological Science) 7.5 credits
Applied Numerical Methods 7.5 credits
Probability Theory 7.5 credits

Conditionally elective courses

Applied Linear Optimization 7.5 credits
Mathematical Systems Theory 7.5 credits
Systems Engineering 7.5 credits

Optional courses

Molecular Modeling 7.5 credits
Computational Chemistry 7.5 credits
Bioinformatics and Biostatistics 7.0 credits
Visualization 7.5 credits
Advanced Computation in Fluid Mechanics 7.5 credits
Machine Learning 6.0 credits
Mathematical Modelling of Biological Systems 9.0 credits
Introduction to High Performance Computing 7.5 credits
Optimization 6.0 credits
Computational Methods for Stochastic Differential Equations 7.5 credits
Topics in Scientific Computings 3.0 credits
Program Construction in C++ for Scientific Computing 7.5 credits
Advanced Individual Course in Scientific Computing 6.0 credits
Project Course in Scientific Computing 7.5 credits
Financial Mathematics, Basic Course 7.5 credits
Applied Nonlinear Optimization 7.5 credits
Geometric Control Theory 7.5 credits
Optimal Control Theory 7.5 credits
Applied Systems Engineering 7.5 credits
Regression Analysis 7.5 credits
Modern Methods of Statistical Learning 7.5 credits
Portfolio Theory and Risk Management 7.5 credits
Time Series Analysis 7.5 credits
Computer Intensive Methods in Mathematical Statistics 7.5 credits
Martingales and Stochastic Integrals 6.0 credits
Game Theory 7.5 credits
Financial Derivatives 7.5 credits
Risk Management 7.5 credits
Computational Fluid Dynamics 7.5 credits
Applied Computational Fluid Dynamics 5.0 credits

Year 2

Conditionally elective courses

Mathematical Systems Theory 7.5 credits
Systems Engineering 7.5 credits

Optional courses

Molecular Modeling 7.5 credits
Computational Chemistry 7.5 credits
Bioinformatics and Biostatistics 7.0 credits
Machine Learning 6.0 credits
Mathematical Modelling of Biological Systems 9.0 credits
Introduction to High Performance Computing 7.5 credits
Optimization 6.0 credits
Applied Systems Engineering 7.5 credits
Modern Methods of Statistical Learning 7.5 credits
Portfolio Theory and Risk Management 7.5 credits
Risk Management 7.5 credits

Track; Computational Mathematics (COMA)

The field of computer simulations is of great importance for high-tech industry and scientific/engineering research, e.g. virtual processing, climate studies, fluid dynamics, advanced materials, etc. Thus, Computational Science and Engineering (CSE) is an enabling technology for scientific discovery and engineering design. CSE involves mathematical modeling, numerical analysis, computer science, high-performance computing and visualization. The remarkable development of large scale computing in the last decades has turned CSE into the "third pillar" of science, complementing theory and experiment.

The track Computational Mathematics (COMA) is mainly concerned with the mathematical foundations of CSE. However, in this track we will also discuss issues of high-performance computing. Given the interdisciplinarity, your final curriculum may vary greatly depending on your interests.

Year 1

Mandatory courses

Numerical Solutions of Differential Equations 7.5 credits
Parallel Computations for Large- Scale Problems 7.5 credits

Year 2

Mandatory courses

Matrix Computations for Large-scale Systems 7.5 credits
The Finite Element Method 7.5 credits

Track; Financial Mathematics (FMIA)

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 any 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 views of the future market prices and combine their views with current market prices to take actions that aim at managing 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 lots of attention from academics and practitioners over the last decades and the level of mathematical sophistication has risen substantially. However, a mathematical model is at best a simplification of the real world phenomenon that is being modeled, and mathematical sophistication can never replace common sense and knowledge of the limitations of mathematical modeling.

Year 1

Mandatory courses

Financial Mathematics, Basic Course 7.5 credits

Conditionally elective courses

Regression Analysis 7.5 credits
Time Series Analysis 7.5 credits

Year 2

Mandatory courses

Portfolio Theory and Risk Management 7.5 credits

Conditionally elective courses

Financial Derivatives 7.5 credits
Risk Management 7.5 credits

Track; Mathematical Statistics (MASA)

Statistics is the science of learning from data. Decision making based on only partial information and incomplete data is a necessity and statistics is an essential tool in such circumstances. The world is full of stochastic phenomena and randomness appear in many ways. Probability theory is the framework for describing stochastic phenomena.

Mathematical statistics is a structured approach to statistics based on probability theory. Mathematical statistics typically aims at determining a plausible model for a stochastic phenomenon or a set of observations, and to use this model to make predictions about the future or to design optimal strategies for decision making. Computational statistics is a rapidly developing field of mathematical statistics that includes theory and methods for efficient stochastic simulation. Computational statistics have become indispensable in a variety of applications.

Year 1

Conditionally elective courses

Regression Analysis 7.5 credits
Modern Methods of Statistical Learning 7.5 credits
Time Series Analysis 7.5 credits
Computer Intensive Methods in Mathematical Statistics 7.5 credits
Martingales and Stochastic Integrals 6.0 credits

Year 2

Conditionally elective courses

Modern Methods of Statistical Learning 7.5 credits
Risk Management 7.5 credits

Track; Optimization and Systems Theory (OPSA)

Optimization and Systems Theory is a discipline in applied mathematics primarily devoted to methods of optimization, including mathematical programming and optimal control, and systems theoretic aspects of control and signal processing. The discipline is also closely related to mathematical economics and applied problems in operations research, systems engineering and control engineering.

Master’s education in Optimization and Systems Theory provides knowledge and competence to handle various optimization problems, both linear and nonlinear, to build up and analyze mathematical models for various engineering systems, and to design optimal algorithms, feedback control, and filters and estimators for such systems.

Optimization and Systems Theory has wide applications in both industry and research. Examples of applications include aerospace industry, engineering industry, radiation therapy, robotics, telecommunications, and vehicles. Furthermore, many new areas in biology, medicine, energy and environment, and information and communications technology require understanding of both optimization and system integration.

Year 1

Conditionally elective courses

Applied Linear Optimization 7.5 credits
Applied Nonlinear Optimization 7.5 credits
Mathematical Systems Theory 7.5 credits
Geometric Control Theory 7.5 credits
Optimal Control Theory 7.5 credits
Systems Engineering 7.5 credits
Applied Systems Engineering 7.5 credits

Year 2

Conditionally elective courses

Mathematical Systems Theory 7.5 credits
Systems Engineering 7.5 credits
Applied Systems Engineering 7.5 credits

Degree project and thesis

The project may be carried out in an academic or industrial environment in Sweden or abroad. Students are welcome to discuss project ideas with the staff at the mathematics department, but are also encouraged to seek other contacts, in the academic world and in industry, to identify suitable projects. The result of this thesis work is provided as a written report and as a presentation at a seminar.

Requirements

A completed Bachelor's degree, corresponding to a Swedish Bachelor's degree (180 ECTS credits), or equivalent academic qualifications from an internationally recognised university.
Students in their final year of undergraduate education may apply to KTH and, if qualified, receive conditional acceptance. If you have not yet completed your studies, please include a written statement issued by the degree awarding university. This statement must be certified and stamped by the Academic Registrar's Office, the Examinations Office or equivalent of the institution. Statements from other staff members, such as faculty members, will not be accepted.
Students who are following longer technical programmes, and have completed courses equivalent to a Bachelor´s degree (180 ECTS credits), will be considered on a case-by-case basis.
Cover sheet (generated from the web-based application). However, if you have a Swedish personal ID number or if you choose to upload your documents, the cover sheet is not required.
Certificates and diplomas from previous education at an internationally recognised university.
Transcripts of records (including course list). All courses taken and grades must be included. Sort them in reverse chronological order, i.e. put the last received document on top.
Proof of English proficiency.
A copy of your passport or some other document of identification. If you are from an EU/EEA country or Switzerland and are required to document your citizenship status in order to be considered exempt from paying application and tuition fees, your passport copy must be certified. If you are not a citizen of an EU/EEA country or Switzerland, certification of your passport copy is not required.
Completed summary sheet
IELTS A minimum overall mark of 6.5, with no section lower than 5.5 (only Academic Training accepted).
TOEFL Paper-based test: total result of 575 (written test, minimum grade 4.5)
TOEFL Internet-based test: total result of 90 (written test, minimum grade 20)

A Bachelor of Science corresponding to 180 ECTS, or equivalent, with at least 45 ECTS credits in mathematics. The students are required to have documented knowledge corresponding to basic university courses in analysis in one and several variables, linear algebra, numerical analysis, differential equations and transforms, mathematical statistics, and basics of programming in a higher programming language.

The specific requirements may be assessed as not fulfilled if
the grade point average below 75% of the scale maximum
the degree awarding institution is not considered to meet acceptable quality standards by the authorities of the country in which the institution is located
the degree does not qualify for admission to equivalent Master’s level in the country where the degree is awarded