Mathematics and Statistics Master's Programme has four study tracks: mathematics, applied mathematics, statistics and social statistics. Mathematics study track includes specializations analysis, geometry, algebra and topology, mathematical logic and mathematical physics. Applied mathematics study track includes specializations applied analysis, mathematical modelling, mathematics of imaging, stochastics, insurance and financial mathematics and probabilistic modelling. Statistics and social statistics are both study tracks and specializations.

# Study tracks, specializations, courses

**Core courses**

MAST31001 Real analysis I (5 cr)

MAST31002 Functional analysis (10 cr)

MAST31003 Topology II (10 cr)

MAST31201 Mathematical logic (10 cr)

MAST31701 Probability theory I (5 cr)

MAST31702 Probability theory II (5 cr)

MAST31501 Mathematical modelling (10 cr) or LSI33001 Introduction to mathematical biology (10 cr)

**Specializations in mathematics study track**

MAST310 Analysis

MAST311 Geometry, Algebra and Topology

MAST312 Mathematical logic

MAST313 Mathematical Physics**Specializations in applied mathematics study track**

MAST314 Applied analysis

MAST315 Mathematical modelling

MAST316 Mathematics of Imaging

MAST317 Stochastics

MAST318 Insurance and Financial Mathematics

MAST319 Probability modelling

Personal study plan form for Mathematics and Applied Mathematics

**Directors of the specialization:**Hans-Olav Tylli and Xiao Zhong**Mandatory core courses**

MAST31001 Real analysis I (5 cr)

MAST31002 Functional analysis (10 cr)**Specialization courses**, at least 10 cr from this list

MAST31006 Complex analysis I (5 cr)

MAST31008 Fourier analysis ( (5 cr)

MAST31010 Partial differential equations I (10 cr)- Other advanced courses from the list of core courses, mathematics, applied mathematics, statistics courses and/or courses from other programmes as approved in personal study plan.
- MAST30001 Master´s thesis seminar (5 cr)
- MAST30000 Master´s thesis (30 cr) (the link includes grading scale and criteria)
- Other requirements, such as possibly required bachelor´s level mathematics courses (the module 0-35 cr other studies) are explained here:
**Schedule and instructions of Analysis studies**

**Director of the specialization**: Pekka Pankka**Mandatory core course**

MAST31003 Topology II (10 cr)**Specialization courses**, at least 10 cr from this listMAST31005 Algebra II (10 cr)

MAST31023 Introduction algebraic topology (10 cr)

MAST31017 Introduction to differential geometry (10 cr)

MAST31026 Riemannian geometry (10 cr)- Other advanced courses from the list of core courses, mathematics, applied mathematics, statistics courses and/or courses from other programmes as approved in personal study plan,
- MAST30001 Master´s thesis seminar (5 cr)
- MAST30000 Master´s thesis (30 cr) (the link includes grading scale and criteria)
- Other requirements, such as possibly required bachelor´s level mathematics courses (the module 0-35 cr other studies) are explained here:
**Schedule and instructions of geometry, algebra and topology studies**

**Director of the specialization**: Juha Kontinen**Mandatory core course**10 cr

MAST31201 Mathematical logic (10 cr)**Specialization courses**, at least (10 cr)-
MAST31202 Axiomatic set theory (10 cr)

MAST31314 Computability theory (10 cr)

MAST31203 Model theory (10 cr) - Other advanced courses from the list of core courses, mathematics, applied mathematics, statistics courses and/or courses from other programmes as approved in personal study plans.
- MAST30001 Master´s thesis seminar (5 cr)
- MAST30000 Master´s thesis (30 cr) (the link includes grading scale and criteria)
- Other requirements, such as possibly required bachelor´s level mathematics courses (the module 0-35 cr other studies) are explained here:
**Schedule and instructions of mathematical logic studies**

**Directors of the specialization**: Antti Kupiainen and Jani Lukkarinen**Mandatory core courses**, at least 15 crMAST31001 Real analysis I (5 cr)

MAST31002 Functional analysis (10 cr)

MAST31701 Probability theory I (5 cr)

MAST31702 Probability theory II (5 cr)**Specialization courses**, at least xx cr from the following list

MAST31302 Hamiltonian dynamics (10 cr)

TCM309 Kinetic theory (10 cr)

MAST31303 Quantum dynamics (10 cr)

MAST31301 Specialization course in mathematical physics (10 cr)

TCM310 Stochastic methods (10 cr)- Other advanced courses from the list of core courses, mathematics, applied mathematics, statistic courses and/or courses from other programmes as approved in personal study plan.
- MAST30001 Master´s thesis seminar (5 cr)
- MAST30000 Master´s thesis (30 cr) (the link includes grading scale and criteria)
**Schedule and instructions of mathematic physics studies**

**Directors of the specialization**: Matti Lassas and Petri Ola**Core courses**, recommended

MAST31002 Functional analysis (10 cr)

MAST31001 Real analysis I (5 cr)**Specialization courses**, at least 10 cr from this list- MAST31402 Bayesian inversion (10 cr)

MAST31403 Integral equations (10 cr)

MAST31401 Inverse problems 1: convolution and deconvolution (5 cr)

MAST31010 Partial differential equations I (10 cr)

MAST31404 Introduction to wavelets (5cr)

MAST31036 Convex analysis and optimization I (5 cr)

MAST31041 Convex analysis and optimization II (5 cr) - Other advanced courses from the list of core courses, mathematics and applied mathematics. statistics courses and/or courses from other programmes as approved in personal study plan.
- MAST30001 Master´s thesis seminar (5 cr)
- MAST31000 Master´s thesis (30 cr) (the link includes grading scale and criteria)
**Schedule and instructions of applied analysis studies**

**Directors of the specialization**: Tapio Helin and Samuli Siltanen**Mandatory core course**

MAST31002 Functional analysis (10 cr)**Specialization courses**, at least 10 cr from this list

MAST31402 Bayesian inversion (10 cr)MAST31401 Inverse problems 1: convolution and deconvolution (5 cr)

MAST31405 Inverse problems project work (5 cr)- Other advanced courses from the list of core courses, mathematics, applied mathematics, statistics courses and/or courses from other programmes as approved in personal study plan.
- MAST30001 Master´s thesis seminar (5 cr)
- MAST31000 Master´s thesis (30 cr) (the link includes grading scale and criteria)
**Schedule and instructions of mathematics of imaging studies**

**Directors of the specialization**: Mats Gyllenberg and Eva Kisdi**Mandatory core courses,**10 cr

MAST31501 Mathematical modelling (10 cr) OR

LSI33001 Introduction to mathematical biology (10 cr)**Specialization courses,**at least 15 cr from this list:

MAST31505 Adaptive dynamics (10 cr)

LSI33002 Evolution and the theory of games (5 cr)

LSI33003 Mathematics of infectious diseases (10 cr)

MAST31503 Spatial models in ecology and evolution (10 cr)

MAST31504 Stochastic population models (10 cr)- Other advanced courses from the list of core courses, mathematics, applied mathematics, statistics courses and/or courses from other programmes as approved in personal study plan.
- MAST30001 Master´s thesis seminar (5 cr)
- MAST31000 Master´s thesis (30 cr) (the link includes grading scale and criteria)
**Schedule and instructions of mathematical modelling studies**

**Director of the specialization**: Konstantin Izyurov**Mandatory core courses**, 10-25 cr

MAST31701 Probability theory I (5 cr)

MAST31702 Probability theory II (5 cr)

MAST31001 Real analysis I (5 cr) recommended

MAST31002 Functional analysis (10 cr) recommended**Specialization courses**, at least 10 cr from this list:MAST31707 Malliavin calculus (10 cr)

MAST31706 Stochastic analysis I (5 cr)

MAST31710 Stochastic analysis II (5 cr)

TCM310 Stochastic methods (10 cr)

MAST31704 Topics in probability I (5 cr)

MAST31705 Topics in probability II (5 cr)- MAST30001 Master´s thesis seminar (5 cr)
- MAST31000 Master´s thesis (30 cr) (the link includes grading scale and criteria)
**Schedule and instructions of stochastic studies**

**Directors of the specialization**: Jaakko Lehtomaa and Dario Gasbarra**Mandatory core courses,**at least 10 cr

MAST31701 Probability theory I (5 cr)

MAST31702 Probability theory II (5 cr)**Specialization courses**, at least 10 cr

MAST31911 Life insurance mathematics I (5 cr)

MAST31912 Life insurance mathematics II (5 cr)

MAST31801 Mathematical finance I (5 cr)

MAST31805 Mathematical finance II (5 cr)

MAST31802 Risk theory (10 cr)

MAST31804 Tariff theory (5 cr)- MAST30001 Master´s thesis seminar (5 cr)
- MAST31000 Master´s thesis (30 cr) (the link includes grading scale and criteria)
- Other requirements, such as possibly required bachelor´s level mathematics and statistics courses (the module 0-35 cr other studies) are explained here:
**Schedule and instructions of financial and insurance mathematics studies**

**Director of the specialization**: Jarno Vanhatalo**Mandatory core courses**, at least 10 cr

MAST31701 Probability theory I (5 cr)

MAST31702 Probability theory II (5 cr)**Specialization courses**, at least 10 cr from this list

MAST32004 Advanced course in Bayesian statistics (5 cr)

DATA12001 Advanced Course in Machine Learning (5 cr)MAST32001 Computational statistics I (5 cr)

MAST32002 Computational statistics II (5 cr)

MAST32006 High dimensional statistics (5 cr)

DATA11002 Introduction to Machine Learning (5 cr)

DATA12002 Probabilistic Graphical Models (5 cr)

MAST32005 Spatial modelling and Bayesian inference (5 cr)- MAST30001 Master´s thesis seminar (5 cr)
- MAST31000 Master´s thesis (30 cr) (the link includes grading scale and criteria)
- Other requirements, such as possibly required bachelor´s level mathematics and statistics courses (the module 0-35 cr other studies) are explained here:
**Schedule and instructions of probabilistic modelling studies**

**Directors of the statistics study track**: Petteri Piiroinen, Jarno Vanhatalo and Sangita Kulathinal**The advanced module 85-120 cr**

MAST32001 Computational statistics I (5 cr), mandatory course**Optional courses 45-80 cr**

MAST32004 Advanced course in Bayesian statistics (5 cr)

MAST32002 Computational statistics II (5 cr)

MAST33001 Generalized linear models II (5 cr)

MAST32006 High dimensional statistics (5 cr)

MAST33003 Nonparametric and robust methods (5 cr)

MAST32014 Regression and regularisation (5 cr)

MAST33004 Robust regression (5 cr)

MAST32005 Spatial modelling and Bayesian inference (5 cr)

MAST32012 Survival and event history analysis I (5 cr)

MAST32013 Survival and event history analysis II (5 cr)

MAST32007 Time series analysis I (5 cr)

MAST32008 Time series analysis II (5 cr)

Courses from social statistics, mathematics, applied mathematics study tracks. See the list of all courses.- Courses from Life Science Informatics, Computer science, Datascience and Economics

master´s programmes, as approved in personal study plan.

- Courses from Life Science Informatics, Computer science, Datascience and Economics
- MAST30001 Master´s thesis seminar (5 cr), mandatory
- MAST32000 Master´s thesis (30 cr) (the link includes grading scale and criteria), mandatory
**Other studies 0-35 cr**

This module can include, for example, bachelor´s level statistics and/or mathematics, or other discipline courses.**Schedule and instructions of statistics studies**

**Directors of the social statistics study track**: Mikko Myrskylä and Kimmo Vehkalahti

**The advanced module module 85-120 cr**

MAST33001 Generalized linear models II (5 cr), mandatory course**Optional courses 45-80 cr**

MAST33015 Analysis of complex surveys (5 cr)

MAST33011 Data-analysis with SAS (5 cr)

MAST33012 Demographic analysis (5 cr)

MAST33010 Introduction to register-based research (5 cr)

MAST33013 Register-based data analysis (5 cr)

MAST33014 Small area estimation (5 cr)

MAST33009 Structural equation models (5 cr)

MAST33018 Survey sampling (5 cr)

MAST33019 Survey-methodology and European statistical system (5 cr)

MAST33017 Topics in social statistics (5 cr)- Courses from statistics, mathematics and applied mathematics study tacks

Courses from other Master´s programmes as approved in personal study plan

Students can specialize in official statistics and receive the European Master in Official Statistics (EMOS) certificate. - MAST30001 Master´s thesis seminar (5 cr), mandatory
- MAST33000 Master´s thesis (30 cr) (the link includes grading scale and criteria), mandatory

- Courses from statistics, mathematics and applied mathematics study tacks
**Other studies 0-35 cr**

This module can include, for example, bachelor´s level statistics and/or mathematics or other discipline courses.**Schedule and instructions of social statistics studies**