*Please note that not all the courses that can be found in the degree structures mentioned on this page are taught every year. The course selection for a new academic year is usually published each year by the end of June.*

In the study track of Mathematics, you have four specializations: Analysis, Mathematical logic, Geometry, algebra and topology, Mathematical physics and probability.

Hans-Olav Tylli and Xiao Zhong

Complete degree structure: Studies Service page Degree Structure

Specialization-specific structure: Studies Service page advanced studies module - Analysis

Persons responsible for academic mentoring and guiding study plans: Hans-Olav Tylli and Xiao Zhong

Model study plan: General guidance instructions and study plans

Juha Kontinen

Complete degree structure: Studies Service page Degree Structure

Specialization-specific structure: Studies Service page advanced studies module - Mathematical Logic

Persons responsible for academic mentoring and guiding study plans: Juha Kontinen, Åsa Hirvonen and Tapani Hyttinen

Model study plan: General guidance instructions and study plans

Erik Elfving

Complete degree structure: Studies Service page Degree Structure

Specialization-specific structure: Studies Service page advanced studies module - Geometry, Algebra and Topology

Persons responsible for academic mentoring and guiding study plans: Erik Elfving and Pekka Pankka

Model study plan: General guidance instructions and study plans

Year 1 Autumn

- Topology II
- Introduction to Real and Fourier Analysis

Year 1 Spring

- Algebra II
- Introduction to Differential Geometry
**or**Introduction to Algebraic Topology - Introduction to Complex Analysis

Jani Lukkarinen and Konstantin Izyurov

Complete degree structure: Studies Service page Degree Structure

Specialization-specific structure: Studies Service page advanced studies module - Mathematical Physics and Probability

Persons responsible for academic mentoring and guiding study plans: Christian Webb

Model study plan: General guidance instructions and study plans

In the study track of Applied Mathematics, you have three specializations: Inverse Problems and Imaging, Mathematical biology, and Insurance and financial mathematics.

Tapio Helin and Samuli Siltanen

Complete degree structure: Studies Service page Degree Structure

Specialization-specific structure: Studies Service page advanced studies module - Inverse Problems and Imaging

Persons responsible for academic mentoring and guiding study plans: Samuli Siltanen

Model study plan: General guidance instructions and study plans

Mathematical modelling via mathematical biology

Eva Kisdi

Complete degree structure: Studies Service page Degree Structure

Specialization-specific structure: Studies Service page advanced studies module - Mathematical Biology

This information is valid from the academic year 2023-2024 onward. For prior requirements, please check the bottom of the page.

25-85 credits to be chosen from the following courses:

- MAST30157 Case studies in Mathematics and statistics (5 cr)

- MAST30163 Mathematical modelling I (5cr)

- MAST30164 Mathematical modelling II (5 cr)

- LSI33006 Introduction to mathematical biology I (5 cr)

- LSI33007 Introduction to mathematical biology II (5 cr)

- MAST31505 Adaptive dynamics (10 cr)

- MAST30166 Stochastic population models I (5 cr)

- MAST30167 Stochastic population models II (5 cr)

- MAST31503 Spatial models in ecology and evolution (10 cr)

- LSI33002 Evolution and the theory of games I (5 cr)

- LSI33008 Evolution and the theory of games II (5 cr)

- LSI33003 Mathematics of infectious diseases (10 cr)

- MAST30156 Bifurcation theory (5 cr)

0-60 credits of other master courses in MAST;

0-25 credits of other master courses in TCM, LSI or Data Science;

0-35 credits in other sciences (or bachelor level courses agreed with your academic mentor);

5 credits from the Master's seminars I-II;

30 credits from the Master's thesis

Persons responsible for academic mentoring and guiding study plans: Eva Kisdi, Stefanus Geritz

We offer a science-based specialization especially suitable for research-oriented MSc students of applied mathematics and for all students interested in using mathematical models of real-life phenomena. We focus on biological applications, especially on ecology and evolution, because advanced modelling skills can be acquired through this field with little time needed to learn the specifics of the application area. To well-performing and motivated students, we offer publishable projects for the MSc thesis.

(1) The courses of the Mathematical biology specialization are given every second year, so advanced planning is important. We maintain a strict schedule of our regular courses so that students can plan their studies reliably:

Fall of odd years (e.g. fall 2023): Mathematical modelling I-II, Mathematics of infectious diseases

Fall of even years (e.g. fall 2024): Introduction to mathematical biology I-II, Evolution and the theory of games I-II

Spring of odd years (e.g. spring 2025): Stochastic population models I-II, Spatial models in ecology and evolution

Spring of even years (e.g. spring 2024): Adaptive dynamics

(2) Both the Mathematical modelling and the Introduction to mathematical biology courses serve as introductions to this specialization. We recommend these courses to all who are interested in modelling, also to students of other specializations. Parts I of these two courses overlap (no need to take Part I of both) but Parts II are different (you may want to take both).

(3) Some of our specialization courses have LSI codes but all are accepted as part of this specialization.

(4) We encourage learning numerical methods, acquiring basic skills in computer programming, and taking some courses in (bio)statistics during your MSc studies.

Additional courses (e.g. given by guest lecturers) that are not regularly taught are listed on this page.

We expect a background in mathematics that enables learning mathematical concepts and techniques at a certain speed. For specific knowledge, we recommend BSc courses on differential equations, matrix algebra and probability. In more detail:

Differential equations: separable equations (with integration by parts), linear equations, systems of homogeneous linear equations.

Matrix algebra: products of matrices and vectors, rank, inverse, eigenvalue-eigenvector, diagonalisation.

Probability: calculating probabilities, independence, conditional probability, binomial, Poisson and exponential distributions, probability density function.

These study plans are **examples**. You can modify them as you wish, according to the requirements at the top of this page. The model study plans serve to show how you can accommodate many of the specialization courses but the requirement is only 20 credits from these.

**Year 1, autumn** (32 cr):

Mathematical modelling I-II (10 cr)

Mathematics of infectious diseases (10 cr)

Functional analysis (10 cr) OR statistics courses

Master's seminar I (2 cr)

**Year 1, spring **(30 cr):

Adaptive dynamics (10 cr)

Bifurcation theory (independent project, 5cr)

Introduction to programming (5 cr, period III) + Advanced course in programming (5 cr, period IV)

optional studies (5cr)

**Year 2, autumn **(28 cr):

Introduction to mathematical biology II (5cr)

Evolution and the theory of games I-II (10cr)

Master's seminar II (3cr)

thesis work (of 10cr)

**Year 2, spring **(30 cr):

Stochastic population models I-II OR Spatial models in ecology and evolution (10 cr)

thesis work (of 20 cr)

**Time schedule if the student starts in an even year** (e.g. autumn 2024)

**Year 1, autumn **(32 cr):

Introduction to mathematical biology I-II (10 cr)

Evolution and the theory of games I-II (10 cr)

Functional analysis (10 cr) OR statistics courses

Master's seminar I (2 cr)

**Year 1, spring **(30 op):

Stochastic population models I-II (10cr)

Spatial models in ecology and evolution (10 op)

Introduction to programming (5 cr) + Advanced course in programming (5 cr)

**Year 2, autumn** (28 op):

Mathematics of infectious diseases (10 op)

Bifurcation theory (independent project, 5cr)

Master's seminar II (3 cr)

thesis work (of 10 cr)

**Year 2, spring** (30 cr):

Adaptive dynamics (10 cr)

thesis work (of 20 cr)

Prior to curriculum 2023-26, this specialization was called Mathematical modelling. Students enrolled before the fall of 2023 can complete this specialization according to the following requirements:

Mandatory core courses, 10 cr

MAST31501 Mathematical modelling (10 cr) OR LSI33006 Introduction to mathematical biology I (5 cr) and LSI33007 Introduction to mathematical biology II (5 cr)

Specialization courses, at least 15 cr from this list:

MAST31505 Adaptive dynamics (10 cr)

LSI33002 Evolution and the theory of games I (5 cr)

LSI33008 Evolution and the theory of games II (5 cr)

LSI33003 Mathematics of infectious diseases (10 cr)

MAST31503 Spatial models in ecology and evolution (10 cr)

MAST30166 Stochastic population models I (5 cr)

MAST30167 Stochastic population models II (5 cr)

MAST30001 Master´s thesis seminar (5 cr)

MAST31000 Master´s thesis (30 cr) (the link includes grading scale and criteria)

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.

Jaakko Lehtomaa and Dario Gasbarra

Complete degree structure: Studies Service page Degree Structure

Specialization-specific structure: Studies Service page advanced studies module - Insurance and Financial Mathematics

Persons responsible for academic mentoring and guiding study plans: Jaakko Lehtomaa and Dario Gasbarra

At the beginning of your studies, you will create a personal study plan with the help of an academic mentor and model study plans found below.

Apart from the required core and specialization courses, the student can choose any advanced courses from all other specializations in mathematics and statistics. It is possible to include courses from different master’s programs such as economics or computer science if they have sufficient mathematical content.

Some of the courses in insurance mathematics are required for the Finnish actuarial qualification degree. Students who aim for this additional degree after the master’s studies may need to fulfil additional requirements. Requirements for the actuarial qualification degree can be found (in Finnish) from the webpage of The Actuarial Association of Finland.

It is recommended to include courses MAT22001 Todennäköisyyslaskenta IIa and MAT22002 Todennäköisyyslaskenta IIb, MAT22013 Tilastollinen päättely IIa, MAT22014 Tilastollinen päättely IIb and MAT22004 Lineaariset mallit I to bachelor’s studies. These courses are also suitable as optional studies in the master’s degree. In addition, it is recommended to take a course on stochastic processes such as Stochastic methods I (the first 5 cr part of the course) or MAT22015 Stokastiset prosessit during the last year of bachelor’s studies or at the beginning of master’s studies.

Statistics courses support the learning of financial and insurance mathematics. In particular, courses on generalized linear models, time series analysis, econometrics and computational statistics are suitable for a mathematician working in the field of insurance and finance.

Theoretical studies can be complemented by more practical studies. Case studies in insurance mathematics MAST30155 introduces basic concepts of an insurance company by examples. Excel is used to solve problems. Career seminar in insurance mathematics MAST30154 is even closer to insurance business. For example, the students can hear career paths of insurance mathematicians, visit insurance companies and meet interesting persons around the industry. These practical courses are arranged once a year by professor of practice Mikko Kuusela during 2022-2024.

There is a mailing list for students who wish to receive news concerning courses of insurance and financial mathematics. The list also has occasional job announcements. The name of the list is:

finins-students

You can find the instructions on subscribing and unsubscribing a mailing list from Helpdesk.

General guidance instructions and study plans

Most of the courses in insurance and financial mathematics make extensive use of probability theory. This is why the courses on probability theory should be at the beginning of the studies. The mandatory core courses in probability theory are available during the fall semester every year. Students, who begin their master’s studies at a time when probability theory is not available, can start their studies, for example, by completing courses in the other studies module.

The courses in insurance mathematics follow approximately a two-year cycle. All courses are not lectured every year. The courses can be completed in any order after, or at the same time with, probability theory. Courses on mathematical finance and stochastic analysis are lectured every year.

The following schedules give two possible examples for timing the core and specialization courses. The remaining courses needed to fulfil the degree requirements are specified in the personal study plan.

Year 1, Fall semester

Probability Theory I + II 5+5 cr

Risk Theory 10 cr

Stochastic methods I 5 cr

Year 1, Spring semester

Advanced Risk Theory 5 cr

Tariff theory 5 cr

Year 2, Fall semester

Master’s thesis seminar begins

Financial Economics 10 cr

Year 2, Spring semester

Master’s thesis seminar is completed 5 cr

Life insurance mathematics I + II 5+5 cr

Thesis completed 30 cr

Year 1, Fall semester

Probability Theory I + II 5+5 cr

Stochastic analysis I + II 5+5 cr

Year 1, Spring semester

Mathematical Finance I + II 5+5 cr

Year 2, Fall semester

Master’s thesis seminar begins

Malliavin calculus 10 cr

Year 2, Spring semester

Master’s thesis seminar is completed 5 cr

Thesis completed 30 cr

(courses in alphabetical order)

MAST31913 Advanced life insurance mathematics (5 cr)

MAST31806 Advanced risk theory (5 cr)

MAST31910 Financial economics (10 cr)

MAST31911 Life insurance mathematics I (5 cr)

MAST31912 Life insurance mathematics II (5 cr)

MAST31707 Malliavin calculus (10 cr)

MAST31801 Mathematical finance I (5 cr)

MAST31805 Mathematical finance II (5 cr)

MAST31802 Risk theory (10 cr)

MAST31706 Stochastic analysis I (5 cr)

MAST31710 Stochastic analysis II (5 cr)

MAST31804 Tariff theory (5 cr)

In the study track of Statistics you specialize in Statistics.

Petteri Piiroinen, Jarno Vanhatalo and Sangita Kulathinal

Complete degree structure: Studies Service page Degree Structure

Specialization-specific structure: Studies Service page advanced studies module - Statistics

Persons responsible for academic mentoring and guiding study plans: Petteri Piiroinen, Jarno Vanhatalo, Sangita Kulathinal, Jyrki Möttönen, Leena Kalliovirta, Matti Pirinen

Model study plan: General guidance instructions and study plans