Study tracks and specializations

The Master's Programme in Mathematics and Statistics offers three study tracks: Mathematics, Insurance and Financial Mathematics and Statistics. As a student in this Master’s Programme, you will select a preliminary study track at the start of your studies. However, you may freely switch between the three study tracks later in your studies.

Please note that not all courses found in the degree structure are taught every year. The list of available courses for a new academic year is generally published by the end of June each year.

Study track: Mathematics

In the study track of Mathematics, you will choose from three specializations: Mathematical logic, Mathematical biology, and Mathematics, under which you can delve into various subfields.

Specializations
Mathematical logic

People of the specialization

Director of the specialization:

Academic mentors of the specialization:


Structure

Complete degree structure:

Specialization-specific structure:

Model schedule and instructions

Mathematical biology

Aims of the stud­ies

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 required to learn the specifics of the application area. To accomplished and motivated students, we offer publishable projects for the MSc thesis.

Prerequisites

We expect a background in mathematics that enables learning mathematical concepts and techniques at a certain rate. 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.

People of the specialization

Director of the specialization:

Academic mentors of the specialization:

Structure

Complete degree structure:

Specialization-specific structure:

Structure in text format

This information is valid for academic years 2023-2026. The structure for academic years from 2026 onward will be added later.

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

Model schedule and instructions

This information is valid for academic years 2023-2026. The model schedule for academic years from 2026 onward will be added later.

These study plans are examples. You can modify them as you wish, according to the degree requirements. The model study plans serve to show how you can accommodate many of the specialization courses.

Time schedule if student starts in an odd year (e.g. autumn 2023)

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)

Important to note

(1) The courses of the Mathematical biology specialization are given every second year, so advanced planning ahead 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 partially overlap but Parts II do not and you may want to take both.

(3) We encourage learning numerical methods and (bio)statistics, as well as acquiring basic skills in computer programming during your MSc studies.

(4) Some of our specialization courses are organised by neighboring programme, Master's Programme in Life Science Informatics (LSI), but are still accepted as part of this specialization.

Mathematics

People of the specialization

Director of the specialization:

Academic mentors of the specialization:
(analysis)
(geometry, algebra and topology)
(mathematical physics and probability)
(inverse problems and imaging)

Structure

Complete degree structure:

Specialization-specific structure:

Model schedule and instructions


 

What do the teachers of mathematics say about their fields?
Study track: Insurance and financial mathematics

In this study track, you will learn about insurance, finance, risk management, and related topics.

Specializations
Insurance and financial mathematics

People of the specialization

Director of the specialization:

Academic mentors of the specialization:

Structure

Complete degree structure:

Specialization-specific structure:
Studies Service page

Model schedule and instructions

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 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.

Over­view of the stud­ies

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 .

Re­com­men­ded or suit­able courses

It is recommended to include courses Todennäköisyyslaskenta IIa and Todennäköisyyslaskenta IIb, Tilastollinen päättely IIa,  Tilastollinen päättely IIb  and 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 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.

Practical courses 

Theoretical studies can be complemented by more practical studies. Case studies in insurance mathematics introduces basic concepts of an insurance company by examples. Excel is used to solve problems. Career seminar in insurance mathematics 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 2022-2027.

RiskEd network

Master’s students of mathematics and statistics can take selected courses from Aalto University in mathematical risk management via RiskEd network. The available courses are:

TU-E2211 Financial Risk Management with Derivatives 1 (5 cr)
TU-E2221 Financial Risk Management with Derivatives 2 (5 cr)
TU-E2231 Machine Learning in Financial Risk Management (5 cr)
MS-E2114 Investment Science (5 cr)

Additional information about the courses is available on , on , and from Eljas Toepfer ().

It is possible to register for the courses in the Sisu system. Instructions for self-registration can be found on .

Mailing list

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 .

List of in­sur­ance and fin­an­cial mathematics courses

University of Helsinki courses

Career seminar in insurance mathematics
Case studies in insurance mathematics
Stochastic analysis I (5 cr)
Stochastic analysis II (5 cr)
Mathematical finance I (5 cr)
Mathematical finance II (5 cr)
Risk theory (10 cr)
Tariff theory (5 cr)
Advanced risk theory (5 cr)
Financial economics (10 cr)
Life insurance mathematics I (5 cr)
Life insurance mathematics II (5 cr)

Aalto university courses via RiskEd network

TU-E2211 Financial Risk Management with Derivatives 1 (5 cr)
TU-E2221 Financial Risk Management with Derivatives 2 (5 cr)
TU-E2231 Machine Learning in Financial Risk Management (5 cr)
MS-E2114 Investment Science (5 cr)

What does the Director of the Specialization say about the field?

"The focus is on problems motivated by real life, rather than theoretical questions", says the Director of the Specialization, Jaakko Lehtomaa.

Study track: Statistics

In this study track, you will delve deeper into various topics in statistics and understand its relevance to society.

Specializations
Statistics

People of the specialization

Director of the specialization:


Academic mentors of the specialization:





Structure

Complete degree structure:

Specialization-specific structure:
Studies Service page

Model schedule and instructions

What does the Director of the Specialization say about the field?

Statistics goes through all parts of science, culture, and nature. The deeper you go, the more complex and interesting problems you encounter, says the Director of the Specialization, Petteri Piiroinen.

More about the programme