Master's Degree Programme in Mathematics
Kuvaus
The aim of the programme is a research-oriented master’s 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.
Osaamistavoitteet
The graduate has received a general training in Mathematics on a Master’s 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’s 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
Tutkintorakenne
- Sisällön valinnaisuus
- Vähintään 90 opintopistettä
- Sisällön valinnaisuuden lisätiedot
- 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’s thesis is 30 cr.
- Arvosteluasteikko
-
- 0-5
- Esitietovaatimukset
- Bachelor's Degree in Mathematics
- MATS111 Mitta- ja integraaliteoria 1 (5 op)
- MATS112 Mitta- ja integraaliteoria 2 (4 op)
- MATS121 Kompleksianalyysi 1 (5 op)
- MATS900 Pro gradu -tutkielma (20 - 30 op)
- MATS901 Kypsyysnäyte (0 op)
- MATS122 Kompleksianalyysi 2 (5 op)
- MATS213 Metriset avaruudet (5 op)
- MATS214 Topologia (4 op)
- MATS220 Funktionaalianalyysi (10 op)
- Sisällön valinnaisuus
- Vähintään 22 opintopistettä
- MATS230 Osittaisdifferentiaaliyhtälöt (7 - 9 op)
- MATS340 Osittaisdifferentiaaliyhtälöt 2 (5 - 9 op)
- MATS235 Sobolev-avaruudet (9 op)
- MATS311 Reaalianalyysi (9 op)
- MATS348 Inversio-ongelmat (4 - 9 op)
- MATS104 Differentiaaliyhtälöiden jatkokurssi 2 (4 op)
- MATS132 Lineaariset Lien ryhmät (4 op)
- MATS195 Pintojen differentiaaligeometria (4 op)
- MATS196 Differentiaaligeometrian perusteet (4 op)
- MATS197 Differentiaaligeometria (4 op)
- MATS198 Riemannin geometriaa (4 op)
- MATS199 Valittuja kohtia differentiaaligeometriaa (4 op)
- MATS215 Algebrallinen topologia (9 op)
- MATS225 Kvasikonformikuvaukset (5 - 9 op)
- MATS227 Funktionaalianalyysin jatkokurssi (5 op)
- MATS254 Stokastiset prosessit (4 op)
- MATS256 Markov-prosessien jatkokurssi (5 op)
- MATS352 Stokastinen analyysi (5 op)
- MATS260 Todennäköisyysteoria 1 (5 op)
- MATS262 Todennäköisyysteoria 2 (5 op)
- MATS315 Fourier-analyysi (4 - 9 op)
- MATS353 Stokastiset differentiaaliyhtälöt (4 - 5 op)
- MATS423 Optimaalinen massansiirto (4 - 9 op)
- MATS424 Viskositeettiteoria (4 - 9 op)
- MATS2110 Geometric Measure Theory (5 op)
- MATS4100 Introduction to Geometric Group Theory (3 op)
- MATS4200 Alexandrov-avaruudet (5 op)
- MATS4300 Analyysiä ja Röntgen-tomografiaa (4 op)
- MATS4400 Density Functional Theory for Strong Correlated Systems and Optimal Transport (5 op)
- MATS4110 Metrics with non-positive curvature (4 op)
- MATS0900 Matematiikan syventävien opintojen harjoitustyö (1 - 3 op)
- MATS4310 Geometriset inversio-ongelmat (5 op)
- MATS4120 Geodeesien geometria (5 op)
- MATS4320 Johdatus tietokonetomografian matematiikkaan (4 op)
- MATA271 Stokastiset mallit (4 op)
- MATS260 Todennäköisyysteoria 1 (5 op)
- MATS262 Todennäköisyysteoria 2 (5 op)
- MATS352 Stokastinen analyysi (5 op)
- Sisällön valinnaisuus
- Vähintään 27 opintopistettä
- MATS254 Stokastiset prosessit (4 op)
- MATS256 Markov-prosessien jatkokurssi (5 op)
- MATS280 Riskiteoria (5 op)
- MATS2300 Rahoitusteorian stokastisia malleja (5 op)
- MATS353 Stokastiset differentiaaliyhtälöt (4 - 5 op)
- MATS442 Stokastinen simulointi (4 op)
- MATS122 Kompleksianalyysi 2 (5 op)
- MATS311 Reaalianalyysi (9 op)
- MATS220 Funktionaalianalyysi (10 op)
- MATS230 Osittaisdifferentiaaliyhtälöt (7 - 9 op)
- MATS340 Osittaisdifferentiaaliyhtälöt 2 (5 - 9 op)
- MATS235 Sobolev-avaruudet (9 op)
- MATS348 Inversio-ongelmat (4 - 9 op)
- MATS195 Pintojen differentiaaligeometria (4 op)
- MATS196 Differentiaaligeometrian perusteet (4 op)
- MATS198 Riemannin geometriaa (4 op)
- MATS225 Kvasikonformikuvaukset (5 - 9 op)
Advanced Studies in Mathematics (vähintään 90 op)
Line 1: Analysis and Geometry, Optional Studies (vähintään 22 op)
Optional advanced studies (MATSxxx) at least 22 cr. Advanced MATA-courses are allowed (not MATA1xx/MATA2xx).
Line 2: Probability and Stochastics, Optional Studies (vähintään 27 op)
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.