Master's Degree Programme in Mathematics
Description
The aim of the programme is a research-oriented master鈥檚 degree in Mathematics giving the student expertise of the subject and ability to apply scientific knowledge and methods in practice. The programme is divided in two lines of specialization: analysis and geometry (line 1), and probability and stochastics (line 2). All students have general mandatory courses in Mathematics and mandatory studies of chosen line 1 or 2. The curriculum allows students to include freely chosen studies to their degree to strengthen their skills and knowledge according to their interests.
Learning outcomes
The graduate has received a general training in Mathematics on a Master鈥檚 degree level and deepened knowledge in one of the core fields of research carried out within the department. The graduate has learned modern methods in these fields and is prepared to apply them in practise (as for example in Economics, in the Finance and Insurance sector, in Natural Sciences, and Industrial Research and Production) or to continue with postgraduate studies in Mathematics, in particular in the areas analysis, geometry, probability, and stochastics.
A Master of Science in Mathematics
- masters one鈥檚 own field of specialization and knows the essential concepts and theories of related fields of Mathematics
- can solve mathematical problems independently
- is interested and is able to follow scientific publications of the field of specialization
- is able to work as a specialist or a manager
- is able to organize and conduct work assignments
- is able to work and make decisions independently and responsibly
- has a wide understanding how mathematics is involved in everyday life and can justify the social impact of mathematics
- is cooperative and ready to take responsibility
- takes ethical questions seriously, follows ethical principles and tries to develop them further
Degree structure
- Optionality
- Minimum of 90 credits
- Optionality description
- The programme is divided in two lines of specialization: analysis and geometry (line 1), and probability and stochastics (line 2). All students have general mandatory courses in Mathematics and mandatory studies of chosen line 1 or 2. Master鈥檚 thesis is 30 cr.
- Grading scale
-
- 0-5
- Prerequisites
- Bachelor's Degree in Mathematics
- MATS111 Measure and Integration Theory 1 (5听肠谤)
- MATS112 Measure and Integration Theory 2 (4听肠谤)
- MATS121 Complex Analysis 1 (5听肠谤)
- MATS900 Master's Thesis (20 - 30聽cr)
- MATS901 Maturity Examination (0听肠谤)
- MATS122 Complex Analysis 2 (5听肠谤)
- MATS213 Metric Spaces (5听肠谤)
- MATS214 Topology (4听肠谤)
- MATS220 Functional Analysis (10听肠谤)
- Optionality
- Minimum of 22 credits
- MATS230 Partial Differential Equations (7 - 9聽cr)
- MATS340 Partial Differential Equations 2 (5 - 9聽cr)
- MATS235 Sobolev Spaces (9听肠谤)
- MATS311 Real Analysis (9听肠谤)
- MATS348 Inverse Problems (4 - 9聽cr)
- MATS104 Advanced Differential Equations 2 (4听肠谤)
- MATS132 Linear Lie Groups (4听肠谤)
- MATS195 Differential Geometry of Surfaces (4听肠谤)
- MATS196 Elements of Differential Geometry (4听肠谤)
- MATS197 Differential Geometry (4听肠谤)
- MATS198 Riemannian Geometry (4听肠谤)
- MATS199 Advanced Differential Geometry (4听肠谤)
- MATS215 Algebraic Topology (9听肠谤)
- MATS225 Quasiconformal Mappings (5 - 9聽cr)
- MATS227 Advanced Functional Analysis (5听肠谤)
- MATS254 Stochastic processes (4听肠谤)
- MATS256 Advanced Markov Processes (5听肠谤)
- MATS352 Stochastic Analysis (5听肠谤)
- MATS260 Probability Theory 1 (5听肠谤)
- MATS262 Probability Theory 2 (5听肠谤)
- MATS315 Fourier Analysis (4 - 9聽cr)
- MATS353 Stochastic Differential Equations (4 - 5聽cr)
- MATS423 Optimal Mass Transportation (4 - 9聽cr)
- MATS424 Viscosity Theory (4 - 9聽cr)
- MATS2110 Geometric Measure Theory (5听肠谤)
- MATS4100 Introduction to Geometric Group Theory (3听肠谤)
- MATS4200 Alexandrov spaces (5听肠谤)
- MATS4300 Analysis and X-ray tomography (4听肠谤)
- MATS4400 Density Functional Theory for Strong Correlated Systems and Optimal Transport (5听肠谤)
- MATS4110 Metrics with non-positive curvature (4听肠谤)
- MATS0900 (1 - 3聽cr)
- MATS4310 Geometric inverse problems (5听肠谤)
- MATS4120 Geometry of geodesics (5听肠谤)
- MATS4320 Introduction to Computational X-ray Tomography (4听肠谤)
- MATA271 Stochastic Models (4听肠谤)
- MATS260 Probability Theory 1 (5听肠谤)
- MATS262 Probability Theory 2 (5听肠谤)
- MATS352 Stochastic Analysis (5听肠谤)
- Optionality
- Minimum of 27 credits
- MATS254 Stochastic processes (4听肠谤)
- MATS256 Advanced Markov Processes (5听肠谤)
- MATS280 Risk Theory (5听肠谤)
- MATS2300 Models in Financial Mathematics (5听肠谤)
- MATS353 Stochastic Differential Equations (4 - 5聽cr)
- MATS442 Stochastic Simulation (4听肠谤)
- MATS122 Complex Analysis 2 (5听肠谤)
- MATS311 Real Analysis (9听肠谤)
- MATS220 Functional Analysis (10听肠谤)
- MATS230 Partial Differential Equations (7 - 9聽cr)
- MATS340 Partial Differential Equations 2 (5 - 9聽cr)
- MATS235 Sobolev Spaces (9听肠谤)
- MATS348 Inverse Problems (4 - 9聽cr)
- MATS195 Differential Geometry of Surfaces (4听肠谤)
- MATS196 Elements of Differential Geometry (4听肠谤)
- MATS198 Riemannian Geometry (4听肠谤)
- MATS225 Quasiconformal Mappings (5 - 9聽cr)
Advanced Studies in Mathematics (Minimum of 90聽cr)
Optional courses in Line 1: analysis and geometry (Minimum of 22聽cr)
Line 2: Probability and Stochastics, Optional Studies (Minimum of 27聽cr)
Elective Studies
Optional courses within the faculty, in information technology, in numerics, language courses as for example Basics in Finnish and courses to support the writing process of the thesis so that the extent of the degree is at least 120 ECTS. Also courses completed during an international exchange period and career courses (URAXXX) can be included in the optional courses.