The student’s curriculum consists of a major (40–65 ECTS), an option for a minor (20–25 ECTS), elective studies (25–30 ECTS) and a Master’s thesis (30 ECTS), total 120 ECTS.

Following the degree requirements the Master’s student has two possibilities to structure his/her studies:

1) Long major (55–65 ECTS) plus elective studies (25–35 ECTS) and Master’s Thesis (30 ECTS) (not possible in Systems and Operations Research major).

2) Compact major (40–45 ECTS), minor (20–25 ECTS) plus elective studies (25–35 ECTS) and Master’s Thesis (30 ECTS).

The extent of a major may not exceed 65 ECTS. Thus, the students will always have a choice of completely elective studies at minimum 25 ECTS.

The objective of the Master's Programme in Mathematics and Operations Research is to train experts who have broad knowledge of mathematical methods and tools as well as strong problem solving skills so that they can successfully tackle challenging scientific, industrial, economic, and environmental problems.

The students learn to think mathematically. They also learn to build mathematical models and to analyze them by developing and deploying state-of-the-art methods and algorithms. Through their choice of major, the students can focus on mathematical theory, computational methods, or modelling and problem solving skills that are needed in practice.

Professors in charge: Nuutti Hyvönen, Antti Hannukainen, Camilla Hollanti, Pauliina Ilmonen, Lasse Leskelä, Rolf Stenberg
Credits: 40–65
Abbreviation: AM
Code: SCI3053

The major in Applied Mathematics is designed for students interested in mathematical sciences and their application to other disciplines. It is based on a solid mathematical core that gives the student a broad set of skills for working on diverse mathematical problems. The major also includes an elective part that provides flexibility to orientate toward a master's thesis project in a chosen application area. A high proportion of students majoring in applied mathematics will continue their studies to a doctoral degree.

The importance of mathematical techniques is increasing in science and engineering as new fields employing sophisticated mathematical models are constantly emerging. The driving forces for such development are the ever-increasing computational resources, which should be used wisely and to their full power. This requires education of mathematicians who are able to interact and collaborate with experts in application areas. The major in Applied Mathematics responds to this need.

Each student choosing Applied Mathematics as major is assigned a mentor among the faculty of the Department of Mathematics and Systems Analysis.

Mathematical core (35 cr)

The student learns core skills in applied mathematics by taking seven courses in the following key areas: numerical analysis and computational methods, probability and statistics, discrete mathematics, and optimization.

Choose seven of the following ten courses.

Specialization area (30 cr)

A personalized collection of mathematical courses and studies in a selected application area. The student is required to include some courses from an applied discipline, for example one related to engineering, computer science, or natural sciences. This part of the studies is designed under the guidance of the mentor. All specialization area studies can be chosen on an individual basis, or they can be composed of a minor and 5–10 credits of supporting mathematical courses.

Examples of possible course contents

I Mathematical core (“Numerical analysis”)

MS-E1050 Graph theory, MS-E1461 Hilbert spaces, MS-E1651 Numerical matrix computations, MS-E1652 Computational methods for differential equations, MS-E1653 Finite element method, MS-E1654Computational inverse problems, MS-E2139 Nonlinear programming.

Possible specialization areas: 

1. MS-E1740 Continuum mechanics 1, MS-E1741 Continuum mechanics 2, MS-E1742 Computational mechanics 1, MS-E1743 Computational mechanics 2, two courses in Structural Mechanics.

2. MS-E1740 Continuum mechanics 1, PHYS-E0413 Theoretical mechanics, a minor or a selection of courses in Applied Physics and/or Structural Mechanics.

3. MS-E1600 Probability theory, MS-E1602 Large random systems, a minor or a selection of courses in Applied Physics and/or Computer Science.

II Mathematical core (“Discrete mathematics and probability”)

MS-E1050 Graph theory, MS-E1110 Number theory, MS-E1600 Probability theory, MS-E1651 Matrix computations, MS-E1654 Computational inverse problems, MS-E2112 Multivariate statistical analysis, MS-E2139 Nonlinear programming.

Possible specialization areas:

1. MS-E1111 Galois theory, MS-E2146 Integer programming, a minor or a selection of courses in Computer Science.

2. MS-E1602 Large random systems, a minor or a selection of courses in Computer Science and/or Applied Physics.

3. MS-E1601 Brownian motion and stochastic analysis, MS-E1602 Large random systems, a selection of courses in Systems and Operations Research and/or Computer Science.

Professors in charge: Juha Kinnunen, Alexander Engström, Kalle Kytölä, Riikka Korte, Kaie Kubjas
Credits: 40–65
Abbreviation: MA
Code: SCI3054

The major in Mathematics helps students develop their mathematical thinking so that they understand how mathematical theories are constructed and how mathematical problems are formulated and solved. The education is research-based with all courses taught by mathematicians who lead active research projects related to the course topics. This major is partly intended as a preparation for students who plan to become researchers or university teachers in mathematics or related sciences. A master’s degree in mathematics also provides the student with a broad range of skills in problem solving, logical reasoning, and flexible thinking, which are attributes valued throughout the society. The covered mathematical areas include abstract and commutative algebra, algebraic geometry, complex analysis, differential geometry, graph theory, mathematical physics, partial differential equations, probability theory, and real analysis.

Each student choosing Mathematics as major is assigned a mentor among the faculty of the Department of Mathematics and Systems Analysis.

Mathematics is a versatile major: the student has the opportunity to choose her/his field of mathematics with no pre-assigned restrictions. The course content of the major is planned under the supervision of the mentor, with emphasis on the mathematics courses lectured at the Department of Mathematics and Systems Analysis. You have the opportunity to include a minor in your studies. Depending on whether a minor is included or not, the extent of the major is 40–45 credits or 55–65 credits.

The recommended courses include:

In addition, you can take courses in applied mathematics, operations research, or other mathematical sciences.

Examples of possible orientations

I Analysis

MS-E1280 Measure and integral
MS-E1281 Real analysis
MS-E1461 Hilbert spaces
MS-E1462 Banach spaces
MS-E1531 Differential geometry
Other courses and a minor chosen under the guidance of the mentor.

II Discrete Mathematics

MS-E1050 Graph theory
MS-E1110 Number theory
MS-E1111 Galois theory
MS-E1140 Algebraic geometry 1
MS-E1141 Algebraic geometry 2
Other courses and a minor chosen under the guidance of the mentor.

III Stochastics and Statistics

MS-E1600 Probability theory
MS-E1601 Brownian motion and stochastic analysis
MS-E1602  Large random systems
MS-E2112 Multivariate statistical analysis
Other courses and a minor chosen under the guidance of the mentor.

Professors in charge: Harri Ehtamo, Ahti Salo, Kai Virtanen
Credits: 41
Abbreviation: OR
Code: SCI3055

The goal of the major in Systems and Operations Research is to teach the students modelling methods and practical skills for problem solving and decision making in complex industrial, managerial, economic, and environmental problems. The core is an engineering-economic systems approach, which is based on systems thinking and mathematical modelling. The field of Operations Research (OR) is generally called “the Science of Better”. OR people can work to improve the efficiency of processes or logistics, to optimize the use of limited resources, or to make better decisions under multiple criteria and risks. An important sub-area of OR called Analytics uses OR methods on large data sets to make better data-based decisions. Systems analysis and OR are needed everywhere in the modern society. Modelling and decision support are essential in energy markets and environmental management as well as in understanding the complex dynamics of climate change.

The core topics in the major include optimization, simulation, dynamic systems, decision modelling, statistics, forecasting, risk analysis, as well as hands on laboratory modelling and project case studies on real industrial problems. The major also provides an excellent basis for doctoral studies and many students do continue their studies to a doctoral degree. The graduates in Systems and Operations Research are in high demand in many areas ranging from the financial sector to industry, energy, and environment.

All courses can be taken in the first or second year of studies. The recommended years for the core courses are shown below.

Mandatory courses (31 cr)

Select one seminar:

Select one additional MS-E2 course (5 cr). 

Recommended courses

All students in the Master’s Programme in Mathematics and Operations Research are recommended to include a minor as a part of their studies. For the students having Systems and Operations Research as their major, including a minor is compulsory.

There are no restrictions on the content of the minor. For instance, all minors in Aalto University are admissible. The minor is confirmed in the Personal Study Plan. The mentor can provide assistance in selecting a suitable minor.

More information on Aalto University’s minor subjects:

• Minors 2017-2018.

Students are required to select 25-35 credits of elective studies. The student can complete a minor and/or take individual courses lectured at Aalto University or the other universities in Finland. The student can also participate in an international student exchange programme or do an internship (max. 10 credits) in Finland or abroad. The mentor can provide assistance in selecting the elective studies.

For more information on internationalisation or Aalto University’s minor subjects:

• Minors 2017-2018
• Internationalisation and studies abroad
• Internship.

In Aalto School of Science, students have compulsory language studies as a part of the bachelor’s degree. If these language studies have not been completed before entering the master’s programme, they must be included in the master’s degree as explained in the following:

A student whose language of school education is Finnish or Swedish must take 2 credits in the other national language. In addition, all students must demonstrate both oral (o) and written (w) proficiency in one foreign language (3 credits).

Students with excellent command of English (e.g. English as a first language) may apply for the exemption from the compulsory foreign language requirement and take 3 ECTS of Finnish courses instead. In this case, according to the Degree Regulations, the student has not demonstrated the requisite written and oral language requirement in a foreign language, which is reflected in the appendix of the degree certificate. Students may apply for an exemption in the beginning of each term (deadlines 15 September and 15 January) with an application form.

The language studies are included in the elective studies.

More information about language courses can be found on the Language Centre’s website.

All students are required to write a master's thesis, which is an individual research project with a workload of 30 credits. The topic of the thesis is usually related to the student’s major, or in some special cases to the minor. The details of the thesis project are agreed upon with the supervisor who must be a professor in the Aalto University. The advisor(s) of the thesis must have at least a master’s degree.

Master’s thesis work includes a seminar presentation or equivalent presentation. The student is also required to write a maturity essay related to the master’s thesis.

The master’s thesis is a public document and cannot be concealed.

For more information, please see https://mycourses.aalto.fi/course/view.php?id=19277.