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Mathematics (Master level) (minor)
Basic information
Code:
SCI3076
Extent:
20–25
ECTS
Curriculum:
2024–2026
2022–2024
2020–2022
Previous curricula
Level:
Advanced studies
Language of learning:
English
Theme:
Mathematics and research methods
Target group:
All Aalto students
Teacher in charge:
Antti Hannukainen
Administrative contact:
Susanna Ylhävuori
Organising department:
Department of Mathematics and Systems Analysis
School:
School of Science
Prerequisites:
BSc minor in Mathematics or equivalent knowledge. Please check the course prerequisites before signing up.
Quotas and restrictions:
-
Application process:
-
Content and structure of the minor
About the minor
Target group: All MSc students with sufficient prerequisite knowledge. The minor is intended for students who do not have Applied Mathematics or Mathematics as their master’s level major.
This minor is designed for students willing to develop their general mathematical thinking and problem solving skills, and to learn mathematical and statistical methods that can be applied in science, technology, arts, and business.
Structure
Select 20–25 credits including 15–25 credits of MS-E***** courses and 0–5 credits of MS-C**** courses. Other courses can be included with the approval of the professor in charge. Suitable courses are listed below.
Content
| Code | Course name | ECTS | Period |
|---|---|---|---|
General mathematics |
|||
| MS-E1000 | Crystal Flowers in Halls of Mirrors: Mathematics Meets Art and Architecture D | 5–15 | III–IV (2024-2025) |
Algebra and discrete mathematics |
|||
| MS-C1081 | Abstract Algebra | 5 | III |
| MS-E1050 | Graph Theory D | 5 | I |
| MS-E1052 | Combinatorial Network Analysis D | 5 | II (2025-2026) |
| MS-E1082 | Special course: Advanced Topics in Algebra D | 5 | IV (2024-2025) |
| MS-E1110 | Number Theory D | 5 | II |
| MS-E1111 | Galois Theory D | 5 | IV (2024-2025) |
| MS-E1142 | Computational Algebraic Geometry D | 5 | V (2025-2026) |
| MS-E1145 | Algebraic Geometry D | 5 | I-II (2025-2026) |
| MS-E1200 | Lie Groups and Lie Algebras D | 5 | IV (2025-2026) |
| MS-E1688 | Special course: Advanced Cryptography D | 5 | I-II (2025-2026) |
Analysis |
|||
| MS-C1350 | Partial Differential Equations | 5 | I–II |
| MS-E1210 | Sobolev Spaces D | 5-10 | I-V |
| MS-E1215 | Elliptic Partial Differential Equations D | 5-10 | I-V |
| MS-E1280 | Measure and Integral D | 5 | II |
| MS-E1281 | Real Analysis D | 5 | IV (2025-2026) |
| MS-E1423 | Fourier Theory D | 5 | III |
| MS-E1426 | Harmonic Analysis D | 5 | II (2024-2025) |
| MS-E1461 | Hilbert Spaces D | 5 | I |
| MS-E1462 | Banach Spaces D | 5 | II (2024-2025) |
| MS-E1531 | Differential Geometry D | 5 | III (2025-2026) |
Computational mathematics |
|||
| MS-C1342 | Linear Algebra | 5 | V |
| MS-E1142 | Computational Algebraic Geometry D | 5 | V (2025-2026) |
| MS-E1150 | Matrix Theory D | 5 | II (2024-2025) |
| MS-E1651 | Numerical Matrix Computations D | 5 | I |
| MS-E1652 | Computational Methods for Differential Equations D | 5 | II (2025-2026) |
| MS-E1653 | Finite Element Method D | 5 | III–IV |
| MS-E1654 | Computational Inverse Problems D | 5 | IV |
Optimization |
|||
| MS-E2121 | Linear Optimization D | 5 | III-IV |
| MS-E2122 | Nonlinear Optimization D | 5 | I–II |
| MS-E2145 | Combinatorial Optimization D | 5 | III-IV |
| MS-E2148 | Dynamic Optimization D | 5 | III |
Probability and statistics |
|||
| MS-C2111 | Stochastic processes | 5 | II |
| MS-E1600 | Probability Theory D | 5 | I |
| MS-E1603 | Random Graphs and Network Statistics D | 5 | V (2025-2026) |
| MS-E1604 | Brownian motion and stochastic analysis D | 5 | IV (2024-2025) |
| MS-E1622 | Algebraic Methods in Data Science D | 5 | III-IV (2024-2025) |
| MS-E1623 | How to lie with statistics? D | 5 | II |
| MS-E1624 | High-Dimensional Statistics D | 5 | IV |
| MS-E2112 | Multivariate Statistical Analysis D | 5 | III–IV |
Previous curricula
Basic information
Code: SCI3076
Extent: 20–25 ECTS
Language of instruction: English
Level: Masters
Theme: Mathematics and research methods
Curriculum: 2022–2024
Target group: All Aalto students
Teacher in charge: Antti Hannukainen
Administrative contact: Emma Perilä
Organising department: Department of Mathematics and Systems Analysis
Prerequisites: BSc minor in Mathematics or equivalent knowledge. Please check the course prerequisites before signing up.
Quotas and restrictions: No quotas
Application process: Open to all students of Aalto University
Target group: All MSc students with sufficient prerequisite knowledge. The minor is intended for students who do not have Applied Mathematics or Mathematics as their master’s level major.
Objectives
This minor is designed for students willing to develop their general mathematical thinking and problem solving skills, and to learn mathematical and statistical methods that can be applied in science, technology, arts, and business.
Structure
Select 20–25 credits including 15–25 credits of MS-E***** courses and 0–5 credits of MS-C**** courses. Other courses can be included with the approval of the professor in charge. Suitable courses are listed below.
| Code | Course name | ECTS credits | Period |
|---|---|---|---|
| General mathematics | |||
| MS-E1000 | Crystal Flowers in Halls of Mirrors: Mathematics Meets Art and Architecture D | 5–15 | III–IV |
| Algebra and discrete mathematics | |||
| MS-C1081 | Abstract Algebra | 5 | III |
| MS-E1050 | Graph Theory D | 5 | I |
| MS-E1052 | Combinatorial Network Analysis D | 5 | II (2023-2024) |
| MS-E1110 | Number Theory D | 5 | II |
| MS-E1111 | Galois Theory D | 5 | IV (2022-2023) |
| MS-E1142 | Computational Algebraic Geometry D | 5 | III (2023-2024) |
| MS-E1200 | Lie Groups and Lie Algebras D | 5 | IV (2023-2024) |
| MS-E1687 | Advanced Topics in Cryptography V D | 5 | III-IV |
| Analysis | |||
| MS-C1350 | Partial Differential Equations | 5 | I–II |
| MS-E1280 | Measure and Integral D | 5 | II |
| MS-E1281 | Real Analysis D | 5 | IV (2023-2024) |
| MS-E1370 | Analysis, Random Walks and Groups | 5 | III (2022-2023) |
| MS-E1461 | Hilbert Spaces D | 5 | I |
| MS-E1462 | Banach Spaces D | 5 | II (2022-2023) |
| MS-E1531 | Differential Geometry D | 5 | III (2023-2024) |
| Computational mathematics | |||
| MS-C1342 | Linear Algebra | 5 | V |
| MS-E1142 | Computational Algebraic Geometry D | 5 | III (2023-2024) |
| MS-E1150 | Matrix Theory D | 5 | II (2022-2023) |
| MS-E1651 | Numerical Matrix Computations D | 5 | I |
| MS-E1652 | Computational Methods for Differential Equations D | 5 | II (2023-2024) |
| MS-E1653 | Finite Element Method D | 5 | III–IV |
| MS-E1654 | Computational Inverse Problems D | 5 | IV |
| Optimization | |||
| MS-E2121 | Linear Optimization D | 5 | III-IV |
| MS-E2122 | Nonlinear Optimization D | 5 | I–II |
| Probability and statistics | |||
| MS-C2111 | Stochastic processes | 5 | II |
| MS-E1600 | Probability Theory D | 5 | III |
| MS-E1603 | Random Graphs and Network Statistics D | 5 | I |
| MS-E1604 | Brownian motion and stochastic analysis | 5 | IV (2022-2023) |
| MS-E1622 | Algebraic Methods in Data Science | 5 | III-IV (2022-2023) |
| MS-E1623 | How to lie with statistics? | 5 | II |
| MS-E2112 | Multivariate Statistical Analysis D | 5 | III–IV |
Basic information
Code: SCI3076
Extent: 20–25 cr
Language: English
Professor in charge: Antti Hannukainen
Administrative contact: Emma Perilä
Target group: All MSc students with sufficient prerequisite knowledge
Application procedure: Open to all students of Aalto University
Quotas and restrictions: No quotas
Prerequisites: BSc minor in Mathematics or equivalent knowledge. Please check the course prerequisites before signing up.
Objectives
This minor is designed for students willing to develop their general mathematical thinking and problem solving skills, and to learn mathematical and statistical methods that can be applied in science, technology, arts, and business.
Structure
Select 20–25 credits including 15–25 credits of MS-E***** courses and 0–5 credits of MS-C**** courses. Other courses can be included with the consent of the professor in charge. Suitable courses are listed below.
| Code | Course name | ECTS credits | Period |
|---|---|---|---|
| General mathematics | |||
| MS-E1000 | Crystal flowers in halls of mirrors: Mathematics meets art and architecture | 5–15 | III–IV |
| Algebra and discrete mathematics | |||
| MS-C1081 | Abstract algebra | 5 | III |
| MS-E1050 | Graph theory | 5 | I |
| MS-E1051 | Combinatorial network analysis | 5 | II (2021-2022) |
| MS-E1110 | Number theory | 5 | II |
| MS-E1111 | Galois theory | 5 | IV (2020-2021) |
| MS-E1142 | Computational algebraic geometry | 5 | III (2020-2021), V (2021-2022) |
| MS-E1200 | Lie groups and Lie algebras | 5 | IV (2021-2022) |
| Analysis | |||
| MS-C1350 | Partial differential equations | 5 | I–II |
| MS-E1280 | Measure and integral | 5 | II |
| MS-E1281 | Real analysis | 5 | IV (2021-2022) |
| MS-E1461 | Hilbert spaces | 5 | I |
| MS-E1462 | Banach spaces | 5 | II (2020-2021) |
| MS-E1531 | Differential geometry | 5 | III (2021-2022) |
| Computational mathematics | |||
| MS-C1342 | Linear algebra | 5 | V |
| MS-E1142 | Computational algebraic geometry | 5 | III (2020-2021), V (2021-2022) |
| MS-E1150 | Matrix theory | 5 | II (2020-2021) |
| MS-E1651 | Numerical matrix computations | 5 | I |
| MS-E1652 | Computational methods for differential equations | 5 | II |
| MS-E1653 | Finite element method | 5 | III–IV |
| MS-E1654 | Computational inverse problems | 5 | IV |
| Optimization | |||
| MS-E2121 | Linear optimization | 5 | III-IV |
| MS-E2122 | Nonlinear optimization | 5 | I–II |
| Probability and statistics | |||
| MS-C2111 | Stochastic processes | 5 | II |
| MS-E1600 | Probability theory | 5 | III |
| MS-E1603 | Random graphs and network statistics | 5 | I |
| MS-E1621 | Algebraic statistics | 5 | I–II (2020-2021) |
| MS-E2112 | Multivariate statistical analysis | 5 | III–IV |
Basic information
Code: SCI3076
Extent: 20-25 cr
Language: English
Teacher in charge: Lasse Leskelä
Administrative contact: Emma Perilä
Target group: All master's students with sufficient prerequisite knowledge.
Application procedure: Open for all students of Aalto University
Quotas and restrictions: No quotas.
Prerequisites: Bachelor-level minor in Mathematics or equivalent knowledge. Please check the course prerequisites before signing up.
Content and structure of the minor
This minor is designed for students willing to develop their general mathematical thinking and problem solving skills, and interested in learning mathematical and statistical methods that can be applied in science, technology, arts, and business. The student selects 20-25 credits of MS-E**** courses. Other courses can also be included with the consent of the professor in charge. A nonexhaustive list of suitable courses is given below.
| Code | Course name | ECTS credits | Period |
|---|---|---|---|
| General mathematics | |||
| MS-E1000 | Crystal Flowers in Halls of Mirrors: Mathematics meets Art and Architecture | 5-15 | III-IV |
| Algebra and discrete mathematics | |||
| MS-E1050 | Graph theory | 5 | I (2018-2019) II (2019-2020) |
| MS-E1110 | Number Theory | 5 | II (2018-2019) I (2019-2020) |
| MS-E1111 | Galois Theory | 5 | IV |
| MS-E1200 | Lie groups and Lie algebras | 5 | II |
| MS-E1687 | Advanced topics in cryptography | 5 | III-IV |
| Analysis | |||
| MS-E1280 | Measure and Integral | 5 | II |
| MS-E1281 | Real Analysis | 5 | IV |
| MS-E1461 | Hilbert spaces | 5 | I |
| MS-E1462 | Banach spaces | 5 | II |
| MS-E1531 | Differential Geometry | 5 | III |
| Computational mathematics | |||
| MS-E1142 | Computational algebraic geometry | 5 | I |
| MS-E1651 | Numerical Matrix Computations | 5 | II |
| MS-E1652 | Computational Methods for Differential Equations | 5 | I |
| MS-E1653 | Finite Element Method | 5 | III-IV |
| MS-E1654 | Computational Inverse Problems | 5 | IV |
| Mechanics | |||
| MS-E1742 | Computational Mechanics 1 | 5 | I |
| MS-E1743 | Computational Mechanics 2 | 5 | II |
| Optimization | |||
| MS-E2121 | Linear optimization | 5 | I-II |
| MS-E2122 | Nonlinear optimization | 5 | I-II |
| MS-E2123 | Integer optimization | 5 | III-IV |
| Statistics and probability | |||
| MS-E1600 | Probability Theory | 5 | III |
| MS-E1602 | Large Random Systems | 5 | IV |
| MS-E1603 | Random graphs and network statistics | 5 | I |
| MS-E2112 | Multivariate Statistical Analysis | 5 | III-IV |
| MS-E2115 | Experimental and statistical methods in biological sciences | 5 | I-II |
Code: SCI3076
Extent: 20-25 cr
Language: English
Teacher in charge: Nuutti Hyvönen, Alexander Engström, Antti Hannukainen, Camilla Hollanti, Pauliina Ilmonen, Juha Kinnunen, Riikka Korte, Kaie Kubjas, Kalle Kytölä, Lasse Leskelä, Rolf Stenberg
Target group: All master's students with sufficient prerequisite knowledge.
Application procedure: Open for all students of Aalto University
Quotas and restrictions: No quotas.
Prerequisites: Bachelor-level minor in Mathematics or equivalent knowledge.
Content and structure of the minor
Objectives
The minor in Mathematics is designed for students interested in mathematical sciences and their application to other disciplines. The minor is motivated by the increase in the importance of mathematical and computational techniques in science and engineering as new fields employing sophisticated mathematical models are constantly emerging.
Mathematics is a flexible minor: The student chooses 20-25 credits of courses in mathematics, mechanics and statistics. It is recommended that the student discusses the choice of courses with one of the professors in charge. The courses, as well as the supervising professor, are to be chosen so that they support the interests and other studies of the student.
Structure of the minor
The student selects 20-25 credits of MS-E courses under the supervision of a professor in charge. A non-exhaustive list of accepted courses is as follows:
| Code | Course name | ECTS credits | Period |
|---|---|---|---|
| MS-E1000 | Crystal Flowers in Halls of Mirrors: Mathematics meets Art and Architecture | 5-15 | III-IV |
| MS-E1050 | Graph theory | 5 | I |
| MS-E1110 | Number Theory | 5 | II |
| MS-E1111 | Galois Theory | 5 | IV |
| MS-E1140 | Algebraic geometry 1 | 5 | IV |
| MS-E1141 | Algebraic geometry 2 | 5 | V |
| MS-E1280 | Measure and Integral | 5 | II |
| MS-E1281 | Real Analysis | 5 | IV |
| MS-E1461 | Hilbert spaces | 5 | I |
| MS-E1462 | Banach spaces | 5 | II |
| MS-E1531 | Differential Geometry | 5 | III |
| MS-E1600 | Probability Theory | 5 | III |
| MS-E1601 | Brownian Motion and Stochastic Analysis | 5 | IV |
| MS-E1602 | Large Random Systems | 5 | IV |
| MS-E1651 | Numerical Matrix Computations | 5 | I |
| MS-E1652 | Computational Methods for Differential Equations | 5 | II |
| MS-E1653 | Finite Element Method | 5 | III-IV |
| MS-E1654 | Computational Inverse Problems | 5 | IV |
| MS-E1740 | Continuum Mechanics 1 | 5 | I |
| MS-E1741 | Continuum Mechanics 2 | 5 | II |
| MS-E1742 | Computational Mechanics 1 | 5 | IV |
| MS-E1743 | Computational Mechanics 2 | 5 | V |
| MS-E2112 | Multivariate Statistical Analysis | 5 | III-IV |
| MS-E2139 | Nonlinear Programming | 5 | II |
Sample combinations of the minor
Analysis 20-25 cr (Prof. Juha Kinnunen)
MS-E1280 Measure and Integral (5 cr), MS-E1281 Real Analysis (5 cr), MS-E1461 Hilbert spaces (5 cr), MS-E1531 Differential Geometry (5 cr). In addition, e.g.,a course of varying content can be included in the minor.
Discrete Mathematics 20-25 cr (Profs. Alexander Engström and Camilla Hollanti)
MS-E1050 Graph Theory (5 cr), MS-E1110 Number Theory (5 cr), MS-E1111 Galois Theory (5 cr), MS-E1140 Alebraic geometry 1. In addition, e.g., a course of varying content can be included in the minor.
Mechanics 25 cr (Prof. Rolf Stenberg)
MS-E1653 Finite Element Method (5 cr), MS-E1740 Continuum Mechanics 1 (5 cr), MS-E1741 Continuum Mechanics 2 (5 cr), MS-E1742 Computational Mechanics 1 (5 cr), MS-E1743 Computational Mechanics 2 (5 cr).
Numerical analysis 25 cr (Profs. Antti Hannukainen and Nuutti Hyvönen)
MS-E1651 Numerical Matrix Computations (5 cr), MS-E1652 Computational Methods for Differential Equations (5 cr), MS-E1653 Finite Element Method (5 cr), MS-E1654 Computational Inverse Problems (5 cr), MS-E2139 Nonlinear Programming (5 cr).
Stochastics and statistics 20-25 cr (Profs. Pauliina Ilmonen, Kalle Kytölä, Lasse Leskelä)
MS-E1600 Probability Theory, MS-E1601 Brownian Motion and Stochastic analysis, MS-E1602 Large Random Systems, MS-E2112 Multivariate Statistical Analysis. In addition, a course of varying content can be included in the minor.
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