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

Name

Credits

Period                   

MS-E1000Crystal Flowers in Halls of Mirrors: Mathematics meets Art and Architecture5-15III-IV
MS-E1050Graph theory5I

MS-E1110

Number Theory5II
MS-E1111Galois Theory5IV
MS-E1140Algebraic geometry 15IV
MS-E1141Algebraic geometry 25V
MS-E1280Measure and Integral5II
MS-E1281Real Analysis5IV
MS-E1461Hilbert spaces5I
MS-E1462Banach spaces5II
MS-E1531Differential Geometry5III
MS-E1600Probability Theory5III
MS-E1601Brownian Motion and Stochastic Analysis5IV
MS-E1602Large Random Systems5IV
MS-E1651Numerical Matrix Computations5I
MS-E1652Computational Methods for Differential Equations5II
MS-E1653Finite Element Method5III-IV
MS-E1654Computational Inverse Problems5IV
MS-E1740Continuum Mechanics 15I
MS-E1741Continuum Mechanics 25II
MS-E1742Computational Mechanics 15IV
MS-E1743Computational Mechanics 25V
MS-E2112Multivariate Statistical Analysis5III-IV
MS-E2139Nonlinear Programming5II


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.