Director of degree programme: Professor Lasse Leskelä
Degree: Master of Science (Technology)
Extent: 120 ECTS
Abbreviation: MathOR

The degree of Master of Science (Technology) consists of a major, an optional minor, master's thesis, and elective studies. The Master's Programme in Mathematics and Operations Research offers the following majors:

• Applied Mathematics
• Mathematics
• Systems and Operations Research

The majors in Applied Mathematics and Mathematics offer long and compact options. The major in Systems and Operations Research is compact. Students taking a compact major take also a minor. Students taking a long major may include an optional minor in their elective studies. The extent of a major may not exceed 65 ECTS. Thus the students always have a choice of a minimum of 25 ECTS completely elective studies.

Long major

Major (55–65 ECTS)
Master's thesis (30 ECTS)
Elective studies (25–35 ECTS)

Compact major

Major (40–45 ECTS)
Master's thesis (30 ECTS)
Minor (20–25 ECTS)
Elective studies (25–30 ECTS)

Each student is assigned a personal academic advisor who guides the student through the programme. The advisor helps the student in writing a personal study plan, and can be consulted in various types of study-related matters, such as selecting a master's thesis supervisor.

The objective of the Master's Programme in Mathematics and Operations Research is to train experts who have a broad knowledge of mathematical methods and strong problem solving skills so that they can successfully tackle challenging problems in science, industry, and society.

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 and statistical methods, or modelling and problem solving skills that are needed in practice.

Graduates from the Master's Programme in Mathematics and Operations Research are in growing demand in many industries and in the public sector. This growth is partly driven by the ability to collect more data about a great variety of phenomena, which together with advances in mathematical methods and greater computational power makes it possible to apply mathematical skills ever more extensively.

All three majors provide an excellent basis for building a career in scientific research. Thus, a large share of the students will continue their studies and obtain a doctoral degree.

Professor in charge: Nuutti Hyvönen
Other professors: Chris Brzuska, Antti Hannukainen, Camilla Hollanti, Pauliina Ilmonen, Kaie Kubjas, Lasse Leskelä, Rolf Stenberg
Extent: 55–65 ECTS (long major) or 40–45 ECTS (compact major)
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 the education of mathematicians who are able to interact and collaborate with experts in application areas. The major in Applied Mathematics responds to this need.

The major in Applied Mathematics can be taken either as a long major (55–65 ECTS) or a compact major (40–45 ECTS). The student's personal academic advisor provides assistance in planning the curriculum details.

Mandatory studies (15 ECTS)

Core studies (25–45 ECTS) 

Select 25–45 credits for a long major or 25–30 credits for a compact major. In both cases, select at least one course from each of the three categories below.

Computational mathematics

Optimization 

Statistics and probability

Students taking a long major select in addition sufficiently many courses in mathematics or other mathematical sciences to obtain a total of 55–65 credits. Courses not in the list below of recommended courses may also be included with the consent of the professor in charge.

Recommended courses

Professor in charge: Juha Kinnunen 
Other professors: Chris Brzuska, Alexander Engström, Camilla Hollanti, Riikka Korte, Kaie Kubjas, Kalle Kytölä, Lasse Leskelä
Credits: 55–65 ECTS (long major) or 40–45 ECTS (compact major)
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.

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 student's personal academic advisor, 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.

Recommended courses include:

In addition, the student 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 an optional minor chosen under the guidance of the personal academic advisor.

II Discrete Mathematics

MS-E1050 Graph theory
MS-E1110 Number theory
MS-E1111 Galois theory
MS-E1200 Lie groups and Lie algebras
Other courses, and an optional minor chosen under the guidance of the personal academic advisor.

III Stochastics and Statistics

MS-E1600 Probability theory
MS-E1602  Large random systems
MS-E1461 Hilbert spaces
Other courses, and an optional minor chosen under the guidance of the personal academic advisor.

Professors in charge: Ahti Salo
Other professors: Pauliina Ilmonen, Risto Lahdelma, Fabricio Oliveira, Antti Punkka, Kai Virtanen, Harri Ehtamo
Credits: 40–43 ECTS (compact major)
Abbreviation: OR
Code: SCI3055

The objective of the major in Systems and Operations Research is to educate experts who master quantitative methods and have professional skills for solving decision problems arising in the planning and management of complex systems. Core topics in the major are optimization, statistics, forecasting, dynamic systems, simulation, and decision and risk analysis. The major includes hands-on laboratory exercises and project assignments on real problems posed by external organizations.

Overall, the major is founded on a balanced engineering-economic approach which builds on structured problem solving, systems thinking and mathematical modelling. This approach allows operations research (OR) professionals to optimize the use of limited resources, to improve the efficiency of production and services, and to support decisions in recognition of risks and multiple objectives, for instance.

Methods of systems and operations research are used extensively in application areas such as finance, logistics, manufacturing, services, defence, energy, environment and healthcare. OR is widely known as “the Science of Better”. The rapidly expanding field of analytics employs OR methods to provide data-driven decision support.

Graduates in Systems and Operations Research are in growing demand by firms, consultancies, research institutes and the public sector. Many start their careers as analysts and then advance to more senior positions and even to top management. The major provides an excellent basis for continued studies and graduates often choose to pursue a doctoral degree.

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 (30 ECTS)

Select one seminar (5–7 cr):

Select one additional course (5–6 ECTS), for example:

Students taking a compact major must also take a minor (20–25 ECTS). Students taking a long major are encouraged to include a minor in their elective studies. The student's personal academic advisor can provide assistance in selecting a suitable minor. The selection of a minor is confirmed in the personal study plan after approval by a professor in charge.

More information on Aalto University’s minors:

• Minors 2018-2020

Students choose 25–35 credits of elective studies. As elective studies, students can complete a minor and/or take individual courses. Individual elective courses can also be taken from other programmes at Aalto University, or other Finnish universities through Flexible Study Right (JOO).

Also studies completed abroad during student exchange can be included in the elective studies (exchange studies can also form an international minor or be included in the major). Work experience (at most 10 credits) completed during an internship in Finland or abroad can also be included in the elective studies.

More information about studies abroad and internships:

• Exchange studies
• Practical training
• Minors 2018-2020

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 below:

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.

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 a minor. The thesis work must have one supervisor and may have one or two advisors. The supervisor is a professor at Aalto University who ensures that the thesis meets all aims and requirements set by the School of Science. The advisor is usually from an organization for which the thesis is written. The thesis advisor shall hold at least a master’s degree. The advisor is an expert in the field of the thesis, who can give advice on content and writing of a thesis. The duties of the advisor are agreed on by the student, supervisor and advisor.

Master’s thesis work also includes a maturity essay, and a seminar presentation or an equivalent presentation.

More information about the aims and requirements of the master's thesis project:

• https://mycourses.aalto.fi/course/view.php?id=19277