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

The degree of Master of Science in 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 are long or compact. The major in Systems and Operations Research is compact. Students taking a compact major must also take a minor. Students taking a long major may include a minor in their 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 an 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 with a broad knowledge of mathematical methods and strong problem solving skills for tackling challenging problems in science, industry, and society.

The students learn to think mathematically. They also learn to build mathematical and statistical models, and to analyze them using advanced 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 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 continue their studies to a doctoral degree. 

Professor in charge: Lasse Leskelä
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 mathematics, statistics, and their applications. It is based on a solid mathematical core that gives the student a broad set of skills for working on diverse mathematical and computational 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 taking this major continue their studies to a doctoral degree.

The importance of mathematical techniques is increasing in science and engineering as new fields employing sophisticated mathematical and statistical 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 and statisticians 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)

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

Probability and statistics

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 below list of recommended courses may also be included with the consent of the professor in charge.

Recommended courses

Professor in charge: Juha Kinnunen 
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, matrix theory, 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

Algebra and discrete mathematics

• MS-E1050 Graph Theory
• MS-E1052 Combinatorial Network Analysis
• MS-E1110 Number Theory
• MS-E1111 Galois Theory
• MS-E1142 Computational Algebraic Geometry
• MS-E1200 Lie Groups and Lie Algebras
• MS-E1370 Analysis, Random Walks and Groups
• other courses, and an optional minor chosen under the guidance of the personal academic advisor.

Analysis and partial differential equations

• MS-E1280 Measure and Integral
• MS-E1281 Real Analysis
• MS-E1370 Analysis, Random Walks and Groups
• MS-E1461 Hilbert Spaces
• MS-E1462 Banach Spaces
• other courses, and an optional minor chosen under the guidance of the personal academic advisor

Mathematical physics

• MS-E1200 Lie Groups and Lie Algebras
• MS-E1370 Analysis, Random Walks and Groups
• MS-E1461 Hilbert Spaces
• MS-E1462 Banach Spaces
• MS-E1531 Differential Geometry
• MS-E1600 Probability Theory
• MS-E1604 Brownian Motion and Stochastic Analysis
• other courses, and an optional minor chosen under the guidance of the personal academic advisor. 

Professors in charge: Fabricio Oliveira
Credits: 40–42 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 and many even during bachelor studies. The recommended years for the core courses are shown below.

Mandatory courses (20 cr)

Select at least one of the following two courses:

Select at least one seminar:

Select further courses from the following list to complete the required  40-42 credits:

^{All other MS-E2XXX courses also qualify.} 

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 academic advisor can provide assistance in selecting a suitable minor. Students can choose a minor from minors offered by Aalto University or, with the consent of the programme director, from other Finnish universities or universities abroad. The minor is confirmed in the Personal Study Plan.

More information on Aalto University’s minors:

• Minors

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, with the consent of the programme director, other Finnish universities through Flexible Study Right (JOO).

Elective studies must be university-level studies that fulfill the degree requirements and, in general, studies that are offered as degree studies at the university in question. Universities also offer courses that are targeted for a larger audience. The suitability of these studies is evaluated taking into consideration the learning outcomes of the degree that the courses are planned to be included in.

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) with the consent of the programme director. 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

Compulsory language studies for students whose language of education is Finnish or Swedish are included as part of the bachelor’s degree. If the language studies have not been completed in the phase preceding master’s studies, they must be taken during the master’s degree studies. In this case, the student must take 2 ECTS in second national language and 3 ECTS in one foreign language (including both oral (o) and written (w) proficiency).

Students who have received their education in a language other than Finnish or Swedish or received their education abroad are required to complete only 3 ECTS in one foreign language. Students with excellent command of English (e.g. English as a first language) may alternatively choose 3 ECTS of Finnish or Swedish 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.

Language studies are included in students’ elective studies and agreed in the personal study plan (HOPS). 

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=41665#section-0