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Mathematics and Operations Research, Master of Science (Technology)
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Webinar | Mathematics and Operations Research
Learn more about Master's programme in Mathematics and Operations Research. Watch the Webinar recording where programme representatives and students tell more about the studies, career possibilities and answer some other questions you might have.
It is hard to think of another field with such a predictive capability and problem-solving power as mathematics. Climate action, sustainable energy transition management, and resilience to pandemics are timely examples of application areas which can be addressed with systematic problem structuring and mathematical modelling. The Master's Programme in Mathematics and Operations Research educates top mathematical thinkers with strong analytical and logical reasoning skills. The demand for experts with these mathematical and problem-solving skills continues to grow rapidly in many areas of society, offering graduates a large variety of career opportunities in companies, research institutes, and universities.
Mathematics and Operations Research graduates will have:
- Strong problem solving skills that are needed to address some of the most complex and interesting challenges in society. Graduates possess a broad set of skills to work on a broad array of problems and answer some of humankind's greatest questions.
- Extensive analytical toolbox to choose the most appropriate techniques from. Graduates understand how different mathematical tools and statistical methods work and how they can best be implemented to achieve desired goals.
- Ability to think mathematically. Graduates can generate mathematical ideas, test and refine conjectures, and make connections to fully understand how mathematical ideas interconnect.
- Expertise to build mathematical models and create new tools for unexpected demands. Graduates can adapt and stay ahead of the rapidly changing nature of the modern world by creating new tools for unexpected demands.
- Mastery of the art of scientific thinking. Graduates understand the principles of theory generation, hypothesis testing and data interpretation, and have the competencies needed to come up with scientific discoveries. This provides an excellent basis to continue studies further towards a doctoral degree in mathematics, statistics, and other mathematical sciences.
Tuition fees and scholarships
Aalto University’s tuition fee for master’s programmes taught in English is 15 000 euros per academic year. Tuition fees apply to citizens of countries other than those of the European Union (EU), the European Economic Area (EEA) or Switzerland.
Aalto University has a scholarship programme to support non-EU/EEA citizens who study in a fee-charging degree programme. The scholarship may cover 100% or 50% of the tuition fee.
More information on tuition fees and scholarships at Aalto University is available at the Scholarships and Tuition Fees webpage.
Structure of studies
Master’s Programme in Mathematics and Operations Research comprises a total of 120 ECTS credits. The two-year programme consists of:
- Major studies (40-65 ECTS)
- Possible minor studies (20-25 ECTS)
- Elective studies (25-35 ECTS)
- Master’s thesis (30 ECTS)
The studies are flexible and can be completed at the student's own convenience. Basic core courses provide a strong foundation before further study in specific sub-areas. By selecting modules that fit with the student’s particular interests, the student will develop a wide palette of skills and creativity to tackle problems of significant importance. The programme has three majors: Mathematics, Applied Mathematics, and Systems and Operations Research. The major is chosenupon entering the programme. In addition to the major, students may select a minor from any discipline that suits their preferences.
Mathematics embraces mathematical thinking and educates students on how mathematical theories are constructed and how mathematical problems are formulated and solved. Education is research-oriented with all courses taught by mathematicians who lead active research projects related to the course topics.
This major is well suited 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 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. A high proportion of students majoring in mathematics will continue their studies to a doctoral degree.
Applied Mathematics is designed for students who are interested in applying mathematical sciences to other disciplines and learning to connect mathematical models and theories to real-world data via advanced statistical methods. It is based on a solid mathematical core that gives the student a broad set of skills in computational methods, statistics, and optimisation needed for working on challenging mathematical problems. The major also includes an elective part that provides flexibility to focus on a master's thesis project in a chosen area of interest. A high proportion of students majoring in applied mathematics will continue their studies to a doctoral degree.
The importance of mathematical and statistical 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 educating mathematicians who are able to interact and collaborate with experts in application areas. The major in Applied Mathematics responds to this need.
The Systems and Operations Research major educates experts who master quantitative methods and can tackle decision problems in the planning and management of complex systems. Core topics in the major are optimisation, statistics, forecasting, dynamic systems, simulation, and decision and risk analysis. The major includes hands-on laboratory assignments exercises and team-based projects assignments on real problems posed by external organisations.
Overall, the major is founded on a balanced engineering-economic approach which builds on structured problem solving, systems thinking, and mathematical modeling. This approach allows operations research (OR) professionals to optimise the use of limited resources, to improve the efficiency of production and services, and to support decisions in recognition of risks and multiple objectives.
Examples of possible topics covered in the programme include:
- Computational Algebraic Geometry (5 ECTS)
- Decision Analysis (5 ECTS)
- Lie Groups and Lie Algebras (5 ECTS)
- Numerical Matrix Computations (5 ECTS)
- Random Graphs and Network Statistics (5 ECTS)
More information on the programme content and curriculum can be found in the Student guide. There may be some changes to the courses for the academic years 2024–2026 — the new curricula will be published in April 2024, when they will also be visible in the Student guide.
The Master’s Programme in Mathematics and Operations Research is international by definition. Education is acknowledged globally and – as mathematics is a universal language – graduates can take their skills to any country in the world. The Department of Mathematics and Systems Analysis that offers the programme co-operates closely with high-quality international universities, research institutes and companies in the field.
Aalto University is international by nature, welcoming thousands of degree and exchange students from abroad every year. These students join the diverse Aalto community not only through their studies, but also through multiple free time events, celebrations and extracurricular activities around the campus. Active tutoring programs and support services work hard to help international students integrate to the Nordic culture and feel at home in Finland.
Further study opportunities
The programme qualifies for doctoral studies (Doctor of Science in an applicable field).
Mathematics and operations research are among the fastest growing fields in which the demand for highly skilled experts continues to increase rapidly. Throughout the programme, students get a good grasp of their strengths and career aspirations by participating in various projects together with research teams, companies, and organisations.
The Master's Programme in Mathematics and Operations Research has a strong reputation in educating top-level experts with strong analytical skills and the ability to think two steps ahead. Such skills are in high demand in various specialist and management positions in the industry and the public sector, and thus students can use their expertise in a number of ways after graduation. Examples of career paths our graduates have taken include:
- Academic career in mathematics, operations research, statistics, data science, machine learning, and quantitative finance, and engineering
- Specialist and management roles in leading international companies
- Research scientist in academia or industry, e.g., government laboratories, environmental organisations, specialist research organisations or universities
Many of our recent graduates choose to pursue doctoral studies at Aalto University or at another top-ranking school for science.
Aalto University has well-established career services to support students’ employment in Finland and abroad. Thanks to the flexible curriculum, many Aalto students work already during their studies and guarantee themselves entry positions before graduation. There is also a very active entrepreneurship community at Aalto, working as a springboard for founding a company.
Co-operation with other parties
Aalto University embraces collaboration, creativity, and the sharing of knowledge, and thus the Master’s Programme in Mathematics and Operations Research strongly fosters cross-departmental interaction. The primary focus of the programme is on teaching the universal language of science. Students learn to apply mathematical models and theories, advanced statistical methods, and computational optimisation skills to any discipline where such knowledge is needed. Some of the cutting-edge topics revolve around climate action, sustainable energy transition, modelling of pandemics, large-scale inverse problems in medical imaging, privacy-enabled cloud computing, unsupervised statistical learning, and network analytics for next-generation AI solutions.
Aalto University is well-known for bridging disciplines of business, arts, technology and science. The lively campus and freedom of choosing elective courses across the University bring students from different fields under one roof. This spontaneous multidisciplinary environment sparks new ideas, gathers enthusiasts around them and gives birth to friendships, networks, and every so often, startups.
Programme-specific admission requirements
Mathematics and Operations Research applicants meeting the general eligibility criteria for master's studies are evaluated according to the below Evaluation criteria. The evaluation process is described under Applicant evaluation process. In addition to the obligatory application documents, this study option asks the applicants to submit also the documents listed under Requested documents.
The applications to Mathematics and Operations Research are evaluated based on the following criteria:
|What is evaluated?||Grades of the previous degree(s), and possible other university studies, pace of studies|
|What we look for in an applicant?||The applicant’s study success will be evaluated based on the grade point average (GPA) and results in key courses. Excellent previous academic performance is expected.|
|Method of demonstrating competence||Transcript(s) of records, degree certificate(s)|
Relevance of previous studies
|What is evaluated?||Contents and scope of previous studies|
|What we look for in an applicant?||
Applicants are expected to have a relevant Bachelor’s degree that contains solid mathematical foundation in differential and integral calculus, linear algebra, and probability and statistics.
The contents of the applicant’s previous degree(s) are evaluated based on the courses available on the official transcript of records and the course descriptions submitted.
Relevant professional certificates and/or online courses are judged case-by-case, but they do not, in general, compensate for the university level studies that include also the theoretical foundations of the required subjects.
|Method of demonstrating competence||Transcript(s) of records, degree certificate(s)|
|What is evaluated?||Applicant’s further applicability to the study option, motivation, commitment for studies, and professional written communication skills|
|What we look for in an applicant?||
Applicant’s motivation and commitment for studies is evaluated based on the motivation letter.
Studies in the Master’s programme should provide genuinely new knowledge for the applicant. If the applicant already has a Master’s degree (in any subject) or is studying towards one, the motivation letter must clearly address the additional benefits that he or she seeks to gain by studying in the Master’s Programme in Mathematics and Operations Research. We may not consider for further evaluation applicants that already have a master’s degree in mathematics, operations research, or overlapping previous studies in the field. To be considered for acceptance in the programme, the additional benefits must be indisputably substantial. In most cases, non-degree studies are recommended to complement a previous Master’s degree.
|Method of demonstrating competence||Motivation letter|
Recognition and quality of institution
|What is evaluated?||Recognition and quality of the applicant's previous institution|
|What we look for in an applicant?||The recognition of the applicant’s home university affects the final interpretation of the academic performance.|
|Method of demonstrating competence||International and national rankings of higher education institutions|
Other areas of competence
|What is evaluated?||Other acquired knowledge/achievements e.g. publications, non-formal education, competitions|
|What we look for in an applicant?||
Applicants will benefit of the following:
|Method of demonstrating competence||Curriculum vitae (CV), letters of recommendation, publications, recognitions and awards|
During the evaluation of eligible applications, applications to Mathematics and Operations Research are first evaluated based on the following criteria:
- Academic performance
- Relevance of previous studies
Only the applications who fulfill the requirements for these criteria will be evaluated against the full set of evaluation criteria.
After the evaluation of the remaining criteria below, the best applicants will be selected based on the joint evaluation of all criteria.
- Recognition and quality of institution
- Other areas of competence
The admission process is very competitive and only the best applicants are selected yearly. Not all applicants fulfilling the requirements can be admitted.
In addition to obligatory application documents, applicants to Mathematics and Operations Research are requested to provide the following programme-specific documents.
- Motivation letter*
- The motivation letter should be written in English. The recommended length is one page.
- Curriculum Vitae (CV)*
- Degree certificate and the official transcript of records for possible other university-level studies that are not included in the Bachelor's degree transcript
- Letters of recommendation and list of publications
*) The lack of these documents will adversely affect the evaluation of your application.
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Our main research areas are algebra and discrete mathematics, analysis, applied mathematics and mechanics, stochastics and statistics, and systems analysis and operations research.
The Guild of Physics is the association for the Engineering Physics and Mathematics students at the Aalto University, although everyone else is welcome too. The Guild was founded in 1947 and currently has about 550 members.
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Learning Services of Aalto University School of Science
For enquiries regarding the programme-specific application documents or studies in the programme, please contact Learning Services of Aalto University School of Science
For enquiries regarding the application process, obligatory application documents or English language proficiency, please contact Admission Services