Master's Programme in Mathematics and Operations Research
This page summarizes the 2024-2026 curriculum structure for the Master’s Programme in Mathematics and Operations Research. Official source: Aalto University curriculum 2024-2026.
Degree Structure
| Module | Credits |
|---|---|
| Major | 40-65 cr |
| Master’s thesis | 30 cr |
| Minor for compact major | 20-25 cr |
| Elective studies | 25-30 cr |
| Total | 120 cr |
The programme has three majors: Mathematics, Applied Mathematics, and Systems and Operations Research. Mathematics and Applied Mathematics can be compact or long majors; Systems and Operations Research is offered as a compact major.
Major: Mathematics
Code: SCI3054
Extent: 40-45 cr or 60-65 cr
Mathematics has no fixed compulsory course list in the curriculum. Students choose courses from mathematical sciences according to their orientation.
Recommended Courses
| Code | Course | cr | Timing |
|---|---|---|---|
| MS-E1050 | Graph Theory | 5 | I/1 |
| MS-E1052 | Combinatorial Network Analysis | 5 | II (2025-2026)/1 or 2 |
| MS-E1082 | Special course: Advanced Topics in Algebra | 5 | IV (2024-2025)/1 or 2 |
| MS-E1110 | Number Theory | 5 | II/1 |
| MS-E1111 | Galois Theory | 5 | IV (2024-2025)/1 or 2 |
| MS-E1142 | Computational Algebraic Geometry | 5 | V (2025-2026)/1 or 2 |
| MS-E1145 | Algebraic Geometry | 5 | I-II (2025-2026)/1 or 2 |
| MS-E1150 | Matrix Theory | 5 | II (2024-2025)/1 or 2 |
| MS-E1200 | Lie Groups and Lie Algebras | 5 | IV (2025-2026)/1 or 2 |
| MS-E1210 | Sobolev Spaces | 5-10 | I-V/1 or 2 |
| MS-E1215 | Elliptic Partial Differential Equations | 5-10 | I-V/1 or 2 |
| MS-E1280 | Measure and Integral | 5 | II/1 or during BSc |
| MS-E1281 | Real Analysis | 5 | IV (2025-2026)/1 or 2 |
| MS-E1423 | Fourier Theory | 5 | III/1 |
| MS-E1426 | Harmonic Analysis | 5 | II (2024-2025)/1 or 2 |
| MS-E1461 | Hilbert Spaces | 5 | I/1 or during BSc |
| MS-E1462 | Banach Spaces | 5 | II (2024-2025)/1 or 2 |
| MS-E1531 | Differential Geometry | 5 | III (2025-2026)/1 or 2 |
| MS-E1542 | General Topology | 5 | IV/1 or 2 |
| MS-E1600 | Probability Theory | 5 | I/1 |
| MS-E1604 | Brownian Motion and Stochastic Analysis | 5 | IV (2024-2025)/1 or 2 |
| MS-E1688 | Special Course: Advanced Cryptography | 5 | I-II (2025-2026)/1 or 2 |
| CS-E4340 | Cryptography | 5 | I-II/1 |
| CS-E4370 | Applied Cryptography | 5 | III-IV/1 |
| CS-E4380 | Special Course: Advanced Cryptography | 5 | I-II (2024-2025)/1 or 2 |
| CS-E4700 | Logic and Hard Computational Problems | 5 | I-II/1 or 2 |
Major: Applied Mathematics
Code: SCI3053
Extent: 40-45 cr or 60-65 cr
Compulsory Studies 20 cr
These core courses are compulsory unless similar content has already been included in previous studies.
| Code | Course | cr | Timing |
|---|---|---|---|
| MS-E1600 | Probability Theory | 5 | I/1 |
| MS-E1651 | Numerical Matrix Computations | 5 | I/1 |
| MS-E2112 | Multivariate Statistical Analysis | 5 | III-IV/1 |
| MS-E2122 | Nonlinear Optimization | 5 | I-II/2 |
Optional Studies 20-45 cr
Choose enough courses from the following categories to complete either a compact or long major.
Computational Mathematics
| Code | Course | cr | Timing |
|---|---|---|---|
| MS-E1423 | Fourier Theory | 5 | III/1 or 2 |
| MS-E1461 | Hilbert Spaces | 5 | I/1 or during BSc |
| MS-E1652 | Computational Methods for Differential Equations | 5 | II (2025-2026)/1 or 2 |
| MS-E1653 | Finite Element Method | 5 | III-IV/1 |
| MS-E1654 | Computational Inverse Problems | 5 | IV/1 |
| MS-E2121 | Linear Optimization | 5 | III-IV/1 |
| MS-E2148 | Dynamic Optimization | 5 | III/1 |
| CS-E5755 | Nonlinear Dynamics and Chaos | 5 | III-IV/1 |
| CS-E5795 | Computational Methods in Stochastics | 5 | I-II/2 |
Statistics and Probability
| Code | Course | cr | Timing |
|---|---|---|---|
| MS-C2128 | Prediction and Time Series Analysis | 5 | II/1 or during BSc |
| MS-E1603 | Random Graphs and Network Statistics | 5 | V (2025-2026)/1 or 2 |
| MS-E1604 | Brownian Motion and Stochastic Analysis | 5 | IV (2024-2025)/1 or 2 |
| MS-E1623 | How to Lie with Statistics? | 5 | II/1 or 2 |
| MS-E1624 | High-Dimensional Statistics | 5 | IV/1 |
| MS-E1622 | Algebraic Methods in Data Science | 5 | III-IV (2024-2025)/1 or 2 |
| MS-E1280 | Measure and Integral | 5 | II/1 or during BSc |
| CS-E5710 | Bayesian Data Analysis | 5 | I-II/2 |
| CS-E4825 | Probabilistic Machine Learning | 5 | III-IV/1 |
| CS-E5745 | Mathematical Methods for Network Science | 5 | III/1 or 2 |
Discrete Applied Mathematics
| Code | Course | cr | Timing |
|---|---|---|---|
| MS-E1050 | Graph Theory | 5 | I/1 or 2 |
| MS-E1052 | Combinatorial Network Analysis | 5 | II (2025-2026)/1 or 2 |
| MS-E1142 | Computational Algebraic Geometry | 5 | V (2025-2026)/1 or 2 |
| MS-E1150 | Matrix Theory | 5 | II (2024-2025)/1 or 2 |
| MS-E2145 | Combinatorial Optimization | 5 | III-IV/1 |
| CS-E4565 | Combinatorics of Computation | 5 | V/1 |
| CS-E4720 | Computational Geometry | 5 | III-IV/1 |
Major: Systems and Operations Research
Code: SCI3055
Extent: 40-45 cr
Mandatory Courses 20 cr
| Code | Course | cr | Timing |
|---|---|---|---|
| MS-E2112 | Multivariate Statistical Analysis | 5 | III-IV/1 or during BSc |
| MS-E2121 | Linear Optimization | 5 | III-IV/1 or during BSc |
| MS-E2132 | Laboratory Assignments in Operations Research II | 5 | I-II/2 |
| MS-E2135 | Decision Analysis | 5 | I-II/1 |
Seminars 5-12 cr
Include at least one of the seminars in the major.
| Code | Course | cr | Timing |
|---|---|---|---|
| MS-E2177 | Seminar on Case Studies in Operations Research | 5-7 | III-V/1 or 2 |
| MS-E2191 | Graduate Seminar on Operations Research | 5 | I-II/2 |
Specialization Studies
| Code | Course | cr | Timing |
|---|---|---|---|
| MS-E2122 | Nonlinear Optimization | 5 | I-II/1 or 2 |
| MS-E2145 | Combinatorial Optimization | 5 | III-IV/1 or 2 |
| MS-E2148 | Dynamic Optimization | 5 | III/1 or 2 |
| MS-E2114 | Investment Science | 5 | I-II/1 or 2, or during BSc |
| MS-E2117 | Riskianalyysi | 5 | III-IV/1 or during BSc |
| MS-E2130 | Mathematical Modelling | 5 | I-II/1 or 2 |
| MS-E2150 | Discrete Event Simulation | 5 | IV (2025-2026)/1 or during BSc |
| MS-E2155 | System Dynamics Simulation | 5 | IV (2024-2025)/1 or during BSc |
| MS-E2107 | Independent Research Projects in Systems and Operations Research Analysis | 5-8 | I-V/1 or 2 |
| CS-E4715 | Supervised Machine Learning | 5 | I-II/1 or 2 |
Courses on Special Topics
| Code | Course | cr | Timing |
|---|---|---|---|
| MS-E2120 | Suomalaisen yhteiskunnan resilienssi | 1-5 | I-II/1 or 2 |
| MS-E2147 | Optimization in Public Transport | 5 | I-II/2 |
| MS-E2160 | Stochastic Programming and Robust Optimization | 5 | I-II (2024-2025)/2 |
Master’s Thesis 30 cr
The master’s thesis is a 30-credit individual research project. The topic is usually related to the student’s major, and the thesis has a supervisor and may have one or two advisors. Thesis work also includes a maturity essay and a seminar presentation or an equivalent presentation.
Minor 20-25 cr
Students taking a compact major must also take a minor. Students taking a long major may include a minor in their elective studies.
Elective Studies 25-30 cr
Elective studies can include a minor, individual courses, exchange studies, or 1-10 credits of practical training. Any compulsory language studies in the master’s degree are included in elective studies.