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Mathematics

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-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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