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 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:

Guidance

Information about personal study planning and guidance in the Master's Programme in Mathematics and Statistics:

Notes and recommendations

(1) The courses of the mathematical biology specialization are offered every second year, so it is important to plan ahead. We maintain a strict schedule of regular courses so that you can plan your studies reliably.

Autumn of even years (e.g. fall 2026): Introduction to mathematical biology I-II, Evolution and the theory of games I-II
Spring of odd years (e.g. spring 2027): Stochastic population models I-II, Spatial models in ecology and evolution
Autumn of odd years (e.g. fall 2027): Mathematical modelling I-II, Mathematics of infectious diseases
Spring of even years (e.g. spring 2028): 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 a neighboring programme, Master's Programme in Life Science Informatics (LSI), but are still accepted as part of this specialization.

Model schedule for mathematical biology

Purpose of the model

Model schedule in table format:

The model has a schedule for a Master of Science degree in its entirety (120 cr) according to the mathematics study track and mathematical biology specialization. There are two models: one for students that start on an even-odd academic year, and one for those that start on an odd-even academic year.            

The model is an example and a tool for selecting and timing studies. When creating a study plan, it is recommended to personalize by consulting an academic mentor and checking course prerequisites in addition to using this model. In case of teaching schedule changes, the study plan can be adjusted accordingly.            

The model focuses on mathematical biology courses, while only selecting courses that are taught regularly. There are some courses that are taught irregularly but are also recommended to students interested in mathematical biology. If such a course is taught, it can be selected instead of a more general course.            

Obligatory studies are courses that must be completed to graduate from this study track and specialization. Obligatory studies are marked with an asterisk (*).  Optional or alternative studies are studies that can be replaced with something else. Alternative studies are not marked with an asterisk.

Selections in the model

MAST300-MATH Mathematics, advanced studies
Under subheading Study track, select Mathematics (MAST-MATH).
Under Specialization, select Mathematical biology (MAST300-MATHBIO).      

MAST300-MATHBIO Mathematical biology
Under Core studies, select Mathematical modelling I and Introduction to Mathematical ecology I.
Under Other core studies in mathematical biology, select Mathematical modelling II, Introduction to mathematical ecology II, Evolution and the theory of games I and II, Stochastic population models I and II, Mathematics of infectious diseases I and II, Bifurcation theory, Adaptive dynamics and Stochastic processes. NOTE! Bifurcation theory is usually organised as a literature-based exam.
Under Additional recommended studies..., select Computational methods I.    

MAST-ADV-MAST Other advanced studies starting with MAST
No selections.

MAST-ADV-EXT Other advanced studies starting with TCM, LSI and/or DATA
No selections.

MAST350 Other studies in mathematics and statistics
No selections.        

MAST340 Other studies
Under Other studies - Optional study units, add Statistical methods in ecology (EEB-003). NOTE! This course is usually organised in Viikki campus.        

Model schedule I (students that start on an even-odd academic year)

Year I (even-odd academic year, such as 2026-2027)          
Teaching period I

LSI33006 Introduction to mathematical ecology I (5 cr)
LSI33002 Evolution and the theory of games I (5 cr)
* MAST30101 Measure and integral (5 cr)
* MAST30011 Master's seminar I (2 cr)

Teaching period II

LSI33007 Introduction to mathematical ecology II (5 cr)
LSI33008 Evolution and the theory of games II (5 cr)

Teaching period III

MAST30166 Stochastic population models I (5 cr)
MAST30146 Computational methods I (5 cr)
EEB-003 Statistical methods in ecology (5 cr)

Teaching period IV

MAST30167 Stochastic population models II (5 cr)
MAST30156 Bifurcation theory (5 cr)

Year II (odd-even academic year, such as 2027-2028)
Teaching period I

MAST30163 Mathematical modelling I (5 cr)
MAST32020 Stochastic processes (5 cr)
MAST31511 Mathematics of infectious diseases I (5 cr)

Teaching period II

MAST30164 Mathematical modelling II (5 cr)
* MAST30000 Master's thesis (30 cr) and MAST30002 Maturity test (0 cr)
MAST31512 Mathematics of infectious diseases II (5 cr)
* MAST30012 Master's seminar II (3 cr)

Teaching period III

MAST31505 Adaptive dynamics (10 cr)
* MAST30000 Master's thesis (30 cr, continues) and MAST30002 Maturity test (0 cr, continues)

Teaching period IV

MAST31505 Adaptive dynamics (10 cr, continues)
* MAST30000 Master's thesis (30 cr, continues) and MAST30002 Maturity test (0 cr, continues)

Model schedule II (students that start on an odd-even academic year)

Year I (odd-even academic year, such as 2027-2028)                   
Teaching period I

MAST30163 Mathematical modelling I (5 cr)
MAST31511 Mathematics of infectious diseases I (5 cr)
* MAST30101 Measure and integral (5 cr)
* MAST30011 Master's seminar I (2 cr)

Teaching period II

MAST30164 Mathematical modelling II (5 cr)
MAST31512 Mathematics of infectious diseases II (5 cr)

Teaching period III

MAST31505 Adaptive dynamics (10 cr)
MAST30146 Computational methods I (5 cr)
EEB-003 Statistical methods in ecology (5 cr)

Teaching period IV

MAST31505 Adaptive dynamics (10 cr, continues)
MAST30156 Bifurcation theory (5 cr)

Year II (even-odd academic year, such as 2028-2029) 
Teaching period I

LSI33006 Introduction to mathematical ecology I (5 cr)
MAST32020 Stochastic processes (5 cr)
LSI33002 Evolution and the theory of games I (5 cr)

Teaching period II

LSI33007 Introduction to mathematical ecology II (5 cr)
* MAST30000 Master's thesis (30 cr) and MAST30002 Maturity test (0 cr)
LSI33008 Evolution and the theory of games II (5 cr)
* MAST30012 Master's seminar II (3 cr)

Teaching period III

MAST30166 Stochastic population models I (5 cr)
* MAST30000 Master's thesis (30 cr, continues) and MAST30002 Maturity test (0 cr, continues)

Teaching period IV

MAST30167 Stochastic population models II (5 cr)
* MAST30000 Master's thesis (30 cr, continues) and MAST30002 Maturity test (0 cr, continues)

 

Meet our student

What's your name, what are you studying and where are you from? 

Hi! I’m Arushi! I’m from New Delhi, India and I study in the Master’s Programme in Mathematics and Statistics, specializing in Mathematical Biology. 

How did you end up studying Mathematical Biology at the University of Helsinki and why? 

I’ve always been fascinated by both numbers and biology. During my bachelor’s degree in India, I double majored in Applied Mathematics and Environmental Studies. I wanted to ensure that I was able to combine both those majors of mine into one, so UH Mathematical Biology programme was perfect for me. It was my top choice, and here I am almost two years later. 

What kind of practical advice you would give to new international students moving to Helsinki soon? 

Explore! Whether it is academically or otherwise, make sure that you do not tie yourselves down to goals you had set before moving to Helsinki. The university offers so much freedom to indulge in one’s other academic interests. Very early on into my degree, I started taking courses from other programmes and that has not only kept me mentally engaged, but has also improved my future job prospects.

What is your favourite thing about summer? 

How incredibly long the days are! For a certain period in June, there was never a time where there was total darkness outside. It felt like I had more time to do all the things I wish I could do in a single day – study, spend time with friends, and cook delicious meals – without feeling like it was time to go to bed already.

What is your favourite place to study in your campus? 

Kumpula campus is great for those studying mathematics. I love to sit and ponder over homework problems at the study spaces on the third floor. There are desks that you can scribble on, take down your work, and then erase! It makes the whole process of finishing homework more interesting.

Mathematical logic

People of the specialization

Director of the specialization:

Academic mentors of the specialization:


Structure

Complete degree structure:

Specialization-specific structure:

Guidance

Information about personal study planning and guidance in the Master's Programme in Mathematics and Statistics:

Model schedule for mathematical logic

Purpose of the model

Model schedule in table format:

The model has a schedule for a Master of Science degree in its entirety (120 cr) according to the mathematics study track and mathematical logic specialization. There are two models: one for students that start on an even-odd academic year, and one for those that start on an odd-even academic year.            

The model is an example and a tool for selecting and timing studies. When creating a study plan, it is recommended to personalize by consulting an academic mentor and checking course prerequisites in addition to using this model. In case of teaching schedule changes, the study plan can be adjusted accordingly.            

The model focuses on mathematical logic courses, while only selecting courses that are taught regularly. There are many more courses that are taught irregularly but are also recommended to students interested in mathematical logic. If such a course is taught, it can be selected instead of a more general course.            

Obligatory studies are courses that must be completed to graduate from this study track and specialization. Obligatory studies are marked with an asterisk (*).  Optional or alternative studies are studies that can be replaced with something else. Alternative studies are not marked with an asterisk.

Selections in the model

MAST300-MATH Mathematics, advanced studies
Under subheading Study track, select Mathematics (MAST-MATH).
Under Optional, select History of mathematics.
Under Specialization, select Mathematical logic (MAST300-MATHLOGIC).        

MAST300-MATHLOGIC Mathematical logic
If starting on an even-odd academic year: under Core studies in mathematical logic, select either Axiomatic set theory I/II or Computability theory I/II, not both, to have time for thesis work on your second year, and then select all other 6 courses in the list.
If starting on an odd-even academic year: under Core studies in mathematical logic, select all 10 courses.
Under Additional recommended studies in mathematical logic, select  Introduction to continuous logic or Introduction to quantum computation. NOTE! These courses are organised as literature-based exams.   

MAST-ADV-MAST Other advanced studies starting with MAST
Under subheading Other advanced studies, select Other advanced studies starting with MAST (MAST-ADV-MAST).
Under Other advanced studies starting with MAST, add Algebra IIa/IIb or Topology IIa/IIb.      

MAST-ADV-EXT Other advanced studies starting with TCM, LSI and/or DATA   
No selections.

MAST350 Other studies in mathematics and statistics
No selections.            

MAST340 Other studies
If starting on an even-odd academic year: under Other studies - Optional study units, add Elements of set theory I and II.        

Model schedule I (students that start on an even-odd academic year)

Year I (even-odd academic year, such as 2026-2027)          
Teaching period I

* MAST30201 Mathematical logic I (5 cr)
MAST30213 Finite model theory I (5 cr)
MAST30301 Algebra IIa (5 cr) / MAST30303 Topology IIa (5 cr)
* MAST30011 Master's seminar I (2 cr)

Teaching period II

* MAST30202 Mathematical logic II (5 cr)
MAST30214 Finite model theory II (5 cr)
MAST30302 Algebra IIb (5 cr) / MAST30304 Topology IIb (5 cr)

Teaching period III

MAST31901 History of mathematics (5 cr)
MAST30211 Model theory I (5 cr)
MAT21031 Elements of set theory I (5 cr)

Teaching period IV

MAST31901 History of mathematics (5 cr, continues)
MAST30212 Model theory II (5 cr)
MAT21030 Elements of set theory II (5 cr)

Year II (odd-even academic year, such as 2027-2028)
Teaching period I

MAST30205 Dependence logic I (5 cr)
MAST31215 Introduction to continuous logic (5 cr) (book exam)
* MAST30101 Measure and integral (5 cr)

Teaching period II

MAST30206 Dependence logic II (5 cr)
* MAST30000 Master's thesis (30 cr) and MAST30002 Maturity test (0 cr)
* MAST30012 Master's seminar II (3 cr)

Teaching period III

MAST30207 Axiomatic set theory I (5 cr) / MAST30203 Computability theory I (5 cr)
* MAST30000 Master's thesis (30 cr, continues) and MAST30002 Maturity test (0 cr, continues)

Teaching period IV

MAST30208 Axiomatic set theory II (5 cr) / MAST30204 Computability theory II (5 cr)
* MAST30000 Master's thesis (30 cr, continues) and MAST30002 Maturity test (0 cr, continues)

Model schedule II (students that start on an odd-even academic year)

Year I (odd-even academic year, such as 2027-2028)                   
Teaching period I

* MAST30201 Mathematical logic I (5 cr)
MAST30205 Dependence logic I (5 cr)
MAST30301 Algebra IIa (5 cr) / MAST30303 Topology IIa (5 cr)
* MAST30011 Master's seminar I (2 cr)

Teaching period II

* MAST30202 Mathematical logic II (5 cr)
MAST30206 Dependence logic II (5 cr)
MAST30302 Algebra IIb (5 cr) / MAST30304 Topology IIb (5 cr)

Teaching period III

MAST30207 Axiomatic set theory I (5 cr)
MAST30203 Computability theory I (5 cr)
MAST31901 History of mathematics (5 cr)

Teaching period IV

MAST30208 Axiomatic set theory II (5 cr)
MAST30204 Computability theory II (5 cr)
MAST31901 History of mathematics (5 cr, continues)

Year II (even-odd academic year, such as 2028-2029) 
Teaching period I

MAST30213 Finite model theory I (5 cr)
MAST31215 Introduction to continuous logic (5 cr) (book exam)
* MAST30101 Measure and integral (5 cr)

Teaching period II

MAST30214 Finite model theory II (5 cr)
* MAST30000 Master's thesis (30 cr) and MAST30002 Maturity test (0 cr)
* MAST30012 Master's seminar II (3 cr)

Teaching period III

MAST30211 Model theory I (5 cr)
* MAST30000 Master's thesis (30 cr, continues) and MAST30002 Maturity test (0 cr, continues)

Teaching period IV

MAST30212 Model theory II (5 cr)
* MAST30000 Master's thesis (30 cr, continues) and MAST30002 Maturity test (0 cr, continues)

Mathematics

People of the specialization

Director of the specialization:

Academic mentor of the specialization:

Structure

Complete degree structure:

Specialization-specific structure:

Guidance

Information about personal study planning and guidance in the Master's Programme in Mathematics and Statistics:

Model schedule for mathematics

Purpose of the model

Model schedule I (focus on analysis, probability, and inverse problems) in table format:
Model schedule II (focus on geometry, algebra and topology) in table format:

The model has a schedule for a Master of Science degree in its entirety (120 cr) according to the mathematics study track and mathematics specialization.            

The model is an example and a tool for selecting and timing studies. When creating a study plan, it is recommended to personalize by consulting an academic mentor and checking course prerequisites in addition to using this model. In case of teaching schedule changes, the study plan can be adjusted accordingly.            

The model focuses on analysis, probability, and inverse problems courses, while only selecting courses that are taught regularly. There are other courses that are taught irregularly but are also recommended to students interested in these topics. If such a course is taught, it can be selected instead of a more general course.            

Obligatory studies are courses that must be completed to graduate from this study track and specialization. Obligatory studies are marked with an asterisk (*).  Optional or alternative studies are studies that can be replaced with something else. Alternative studies are not marked with an asterisk.

Selections in the model schedule I (focus on analysis, probability, and inverse problems)

MAST300-MATH Mathematics, advanced studies
Under subheading Study track, select Mathematics (MAST-MATH).
Under Optional, select Case studies in mathematics and statistics and History of mathematics.
Under Specialization, select Mathematics (MAST300-MATHSPEC).   

MAST300-MATHSPEC Mathematics
Under Core studies: Studies in analysis,  select Functional analysis II, Partial differential equations I and II.
Under Core studies: Studies in mathematical physics and probability, select Probability theory, Stochastic analysis I and II, and Stochastic processes.
Under Core studies: Studies in inverse problems and imaging, select Inverse problems I, Inverse problems II, and Computational methods I.      

MAST-ADV-MAST Other advanced studies starting with MAST
No selections.    

MAST-ADV-EXT Other advanced studies starting with TCM, LSI and/or DATA
No selections.            

MAST350 Other studies in mathematics and statistics
Under Optional, select MAT21043 Introduction to complex analysis. NOTE! The course is taught in Finnish, but it can be completed in English. As this course is optional, it can also be replaced with something taught in English.        

MAST340 Other studies       
No selections.     

Model schedule I (focus on analysis, probability, and inverse problems)

Year I      
Teaching period I

* MAST30011 Master's seminar I (2 cr)
* MAST30101 Measure and integral (5 cr)
* MAST30170 Functional analysis I (5 cr)
MAST30157 Case studies in mathematics and statistics (5 cr)

Teaching period II

* MAST30174 Introduction to Fourier analysis (5 cr)
* MAST31051 Measure, probability, and real analysis (5 cr)
MAST30171 Functional analysis II (5 cr)
MAST30157 Case studies in mathematics and statistics (5 cr, continues)

Teaching period III

MAST30172 Partial differential equations I (5 cr)
MAST30152 Probability theory (5 cr)
MAST31901 History of mathematics (5 cr)    

Teaching period IV

MAST30173 Partial differential equations II (5 cr)
MAT21043 Introduction to complex analysis (5 cr)
MAST31901 History of mathematics (5 cr, continues)

Year II
Teaching period I

MAST32020 Stochastic processes (5 cr)
MAST31706 Stochastic analysis I (5 cr)
MAST31401 Inverse problems I (5 cr)

Teaching period II

* MAST30000 Master's thesis (30 cr) and MAST30002 Maturity test (0 cr)
MAST31710 Stochastic analysis II (5 cr)
MAST31406 Inverse problems II (5 cr)
* MAST30012 Master's seminar II (3 cr)

Teaching period III

* MAST30000 Master's thesis (30 cr, continues) and MAST30002 Maturity test (0 cr, continues)
MAST30146 Computational methods I (5 cr)

Teaching period IV

* MAST30000 Master's thesis (30 cr, continues) and MAST30002 Maturity test (0 cr, continues)

Selections in the model schedule II (focus on geometry, algebra and topology)

MAST300-MATH Mathematics, advanced studies
Under subheading Study track, select Mathematics (MAST-MATH).
Under Optional, select History of mathematics.
Under Specialization, select Mathematics (MAST300-MATHSPEC).       

MAST300-MATHSPEC Mathematics
Under Core studies: Studies in analysis, select Partial differential equations I and II.
Under Core studies: Studies in geometry, algebra and topology, select Algebra IIa and IIb, Topology IIa and IIb, Introduction to differential geometry, Introduction to Riemannian geometry
Under Core studies: Studies in inverse problems and imaging, select Inverse problems I and II. 

MAST-ADV-MAST Other advanced studies starting with MAST
No selections.     

MAST-ADV-EXT Other advanced studies starting with TCM, LSI and/or DATA
No selections.  

MAST350 Other studies in mathematics and statistics
No selections.            

MAST340 Other studies
Under Other studies - Optional study units, add Geometry I and II (MFK-M301 and M302). NOTE! The courses are taught in Finnish, but can be completed in English. As these courses are optional, they can also be replaced with something taught in English.        

Model schedule II (focus on geometry, algebra and topology)

Year I      
Teaching period I

* MAST30170 Functional analysis I (5 cr)
* MAST30101 Measure and integral (5 cr)
MAST30303 Topology IIa (5 cr)
* MAST30011 Master's seminar I (2 cr)

Teaching period II

* MAST30174 Introduction to Fourier analysis (5 cr)
* MAST31051 Measure, probability, and real analysis (5 cr)
MAST30304 Topology IIb (5 cr)

Teaching period III

MFK-M301 Geometry I (5 cr)
MAST30172 Partial differential equations I (5 cr)
MAST30310 Introduction to differential geometry (5 cr)

Teaching period IV

MFK-M302 Geometry II (5 cr)
MAST30173 Partial differential equations II (5 cr)
MAST30310 Introduction to Riemannian geometry (5 cr)

Year II
Teaching period I

MAST30301 Algebra IIa (5 cr)
MAST31401 Inverse problems I: convolution and deconvolution (5 cr)

Teaching period II

MAST30302 Algebra IIb (5 cr)
MAST31406 Inverse problems II: tomography and regularization (5 cr)
* MAST30000 Master's thesis (30 cr) and MAST30002 Maturity test (0 cr)    
* MAST30012 Master's seminar II (3 cr)    

Teaching period III

MAST31901 History of mathematics (5 cr)
* MAST30000 Master's thesis (30 cr, continues) and MAST30002 Maturity test (0 cr, continues)

Teaching period IV

MAST31901 History of mathematics (5 cr, continues)
* MAST30000 Master's thesis (30 cr, continues) and MAST30002 Maturity test (0 cr, continues)

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:

Guidance

Information about personal study planning and guidance in the Master's Programme in Mathematics and Statistics:

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 schedule below.

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

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.

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.

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 the following courses or similar contents into bachelor's studies:
Todennäköisyyslaskenta IIa (Probability IIa)
Todennäköisyyslaskenta IIb (Probability IIb)
Tilastollinen päättely IIa (Statistical inference IIa)
Tilastollinen päättely IIb (Statistical inference IIb)
Lineaariset mallit I (Linear models I).

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 processes 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)

Model schedule for insurance and financial mathematics

Purpose of the model

Model schedule in table format:

The model has a schedule for a Master of Science degree in its entirety (120 cr) according to the insurance and financial mathematics study track. There are two models: one for students that start on an even-odd academic year, and one for those that start on an odd-even academic year.            

The model is an example and a tool for selecting and timing studies. When creating a study plan, it is recommended to personalize by consulting an academic mentor and checking course prerequisites in addition to using this model. In case of teaching schedule changes, the study plan can be adjusted accordingly.            

The model focuses on insurance and financial mathematics courses, while only selecting courses that are taught regularly. There are other courses that are taught irregularly but are also recommended to students interested in these topics. If such a course is taught, it can be selected instead of a more general course.            

Obligatory studies are courses that must be completed to graduate from this study track and specialization. Obligatory studies are marked with an asterisk (*).  Optional or alternative studies are studies that can be replaced with something else. Alternative studies are not marked with an asterisk.  

Selections in the model

MAST310-FIN Insurance and financial mathematics, advanced studies
Under subheading Study track, select Insurance and financial mathematics (MAST-FIN).
Under Core studies - Studies in insurance and financial mathematics, select Measure and integral, Career seminar in insurance mathematics, Case studies in insurance mathematics, Stochastic analysis I and II, Risk theory, Advanced risk theory,
Tariff theory, Financial economics I and II, Life insurance mathematics I and II and Stochastic processes.

MAST-ADV-MAST Other advanced studies starting with MAST
No selections.

MAST-ADV-EXT Other advanced studies starting with TCM, LSI and/or DATA
Under subheading Other advanced studies, select Other advanced studies starting with TCM, LSI and/or DATA (MAST-ADV-EXT)
Under Other advanced studies starting with TCM, LSI and/or DATA, add Data Science (DATA11001).  

MAST350 Other studies in mathematics and statistics
No selections.

MAST340 Other studies
No selections.

Model schedule I (students that start on an even-odd academic year)

Year I (even-odd academic year, such as 2026-2027)          
Teaching period I

MAST30155 Case studies in insurance mathematics (5 cr)
MAST30101 Measure and integral (5 cr)
MAST31807 Financial economics I (5 cr)
MAST32020 Stochastic processes (5 cr)
* MAST30011 Master's seminar I (2 cr)

Teaching period II

MAST30155 Case studies in insurance mathematics (5 cr, continues)
* MAST31051 Measure, probability and real analysis (5 cr)
MAST31808 Financial economics II (5 cr)

Teaching period III

MAST30154 Career seminar in insurance mathematics (5 cr)
* MAST31052 Probability theory (5 cr)
MAST31911 Life insurance mathematics I (5 cr)

Teaching period IV

MAST30154 Career seminar in insurance mathematics (5 cr, continues)
MAST31912 Life insurance mathematics II (5 cr)

Year II (odd-even academic year, such as 2027-2028)
Teaching period I

MAST31802 Risk theory (10 cr)
MAST31706 Stochastic analysis I (5 cr)
DATA11001 Data Science (5 cr)

Teaching period II

MAST31802 Risk theory (10 cr, continues)
MAST31710 Stochastic analysis II (5 cr)
* MAST30000 Master's thesis (30 cr) and MAST30002 Maturity test (0 cr)
* MAST30012 Master's seminar II (3 cr)  

Teaching period III

MAST31806 Advanced risk theory (5 cr)
* MAST30000 Master's thesis (30 cr, continues) and MAST30002 Maturity test (0 cr, continues)

Teaching period IV

MAST31804 Tariff theory (5 cr)
* MAST30000 Master's thesis (30 cr, continues) and MAST30002 Maturity test (0 cr, continues)

Model schedule II (students that start on an odd-even academic year)

Year I (odd-even academic year, such as 2027-2028)                   
Teaching period I

MAST30155 Case studies in insurance mathematics (5 cr)
MAST30101 Measure and integral (5 cr)
MAST31802 Risk theory (10 cr)
MAST32020 Stochastic processes (5 cr)
* MAST30011 Master's seminar I (2 cr)

Teaching period II

MAST30155 Case studies in insurance mathematics (5 cr, continues)
* MAST31051 Measure, probability and real analysis (5 cr)
MAST31802 Risk theory (10 cr, continues)

Teaching period III

MAST30154 Career seminar in insurance mathematics (5 cr)
* MAST31052 Probability theory (5 cr)
MAST31806 Advanced risk theory (5 cr)

Teaching period IV

MAST30154 Career seminar in insurance mathematics (5 cr, continues)
MAST31804 Tariff theory (5 cr)

Year II (even-odd academic year, such as 2028-2029) 
Teaching period I

MAST31807 Financial economics I (5 cr)
MAST31706 Stochastic analysis I (5 cr)
DATA11001 Data Science (5 cr)

Teaching period II

MAST31808 Financial economics II (5 cr)
MAST31710 Stochastic analysis II (5 cr)
* MAST30000 Master's thesis (30 cr) and MAST30002 Maturity test (0 cr)
* MAST30012 Master's seminar II (3 cr)

Teaching period III

MAST31911 Life insurance mathematics I (5 cr)
* MAST30000 Master's thesis (30 cr, continues) and MAST30002 Maturity test (0 cr, continues)

Teaching period IV

 MAST31912 Life insurance mathematics II (5 cr)
* MAST30000 Master's thesis (30 cr, continues) and MAST30002 Maturity test (0 cr, continues)

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 mentor of the specialization:

Structure

Complete degree structure:

Specialization-specific structure:

Guidance

Information about personal study planning and guidance in the Master's Programme in Mathematics and Statistics:

Model schedule for statistics

Purpose of the model

The model has a schedule for a Master of Science degree in its entirety (120 cr) according to the statistics study track. There are two models: one for students that start on an even-odd academic year, and one for those that start on an odd-even academic year.            

The model is an example and a tool for selecting and timing studies. When creating a study plan, it is recommended to personalize by consulting an academic mentor and checking course prerequisites in addition to using this model. In case of teaching schedule changes, the study plan can be adjusted accordingly.            

The model focuses on statistics courses, while only selecting courses that are taught regularly. There are other courses that are taught irregularly but are also recommended to students interested in statistics. If such a course is taught, it can be selected instead of a more general course.            

Obligatory studies are courses that must be completed to graduate from this study track and specialization. Obligatory studies are marked with an asterisk (*).  Optional or alternative studies are studies that can be replaced with something else. Alternative studies are not marked with an asterisk.

Selections in the model

MAST320-STAT Statistics, advanced studies
Under subheading Study track, select Statistics (MAST-STAT).
Under Core studies in statistics, select Measure and integral, Measure, probability and real analysis, Statistical decision theory, Stochastic analysis I, Computational statistics, Advanced Bayesian Inference, Stochastic processes and Robust regression.
Under Core studies in statistics, if starting studies on an even year, also select Nonparametric inference, and also select High-dimensional statistics or Asymptotic statistical inference.
Under Core studies in statistics, if starting studies on an odd year, also select Multivariate statistical analysis, and also select High-dimensional statistics or Asymptotic statistical inference.
Under Additional recommended studies in statistics, select Design and analysis of experiments and surveys, Bayesian inversion, Survival analysis and Multistate models for event history.
Under Additional recommended studies in statistics, if you have not completed Bayesian inference during your bachelor studies, also select Bayesian Data Analysis, to be able to complete Advanced Bayesian inference later.
If you do not have to select Bayesian Data analysis, select any other course. 

MAST-ADV-MAST Other advanced studies starting with MAST
Under subheading Other advanced studies, select Other advanced studies starting with MAST (MAST-ADV-MAST).
Under Other advanced studies starting with MAST, add Computational methods I (MAST30146).

MAST-ADV-EXT Other advanced studies starting with TCM, LSI and/or DATA
Under subheading Other advanced studies, select Other advanced studies starting with TCM, LSI and/or DATA (MAST-ADV-EXT)
Under Other advanced studies starting with TCM, LSI and/or DATA, add Data Science (DATA11001).       

MAST350 Other studies in mathematics and statistics
No selections.       

MAST340 Other studies 
No selections.             

Model schedule I (students that start on an even-odd academic year)

Year I (even-odd academic year, such as 2026-2027)          
Teaching period I

MAST30101 Measure and integral (5 cr)
MAST32001 Computational statistics (5 cr)
MAST32020 Stochastic processes (5 cr)
* MAST30011 Master's seminar I (2 cr)

Teaching period II

MAST31051 Measure, probability and real analysis (5 cr)
LSI35002 Bayesian Data analysis (5 cr) or alternative
MAST32017 Nonparametric inference (5 cr)

Teaching period III

MAST30165 Statistical decision theory (5 cr)
MAST30146 Computational methods I (5 cr)
MAST30210 Design and analysis of experiments and surveys (5 cr) [January intensive, not period 3]

Teaching period IV

MAST31402 Bayesian inversion (5 cr)
MAST32004 Advanced Bayesian inference

Year II (odd-even academic year, such as 2027-2028)
Teaching period I

MAST33004 Robust regression (5 cr)
MAST31706 Stochastic analysis I (5 cr)
DATA11001 Data Science (5 cr)

Teaching period II

MAST32012 Survival analysis (5 cr)
* MAST30000 Master's thesis (30 cr) and MAST30002 Maturity test (0 cr)    
* MAST30012 Master's seminar II (3 cr)

Teaching period III

MAST32006 High-dimensional statistics (5 cr) / MAST30128 Asymptotic statistical inference (5 cr)
* MAST30000 Master's thesis (30 cr, continues) and MAST30002 Maturity test (0 cr, continues)  

Teaching period IV

MAST32013 Multistate models for event history (5 cr)
* MAST30000 Master's thesis (30 cr, continues) and MAST30002 Maturity test (0 cr, continues)  

Model schedule II (students that start on an odd-even academic year)

Year I (odd-even academic year, such as 2027-2028)                   
Teaching period I

MAST30101 Measure and integral (5 cr)
MAST32001 Computational statistics (5 cr)
MAST32020 Stochastic processes (5 cr)
* MAST30011 Master's seminar I (2 cr)

Teaching period II

MAST31051 Measure, probability and real analysis (5 cr)
LSI35002 Bayesian Data analysis (5 cr) or alternative
MAST32012 Survival analysis (5 cr)

Teaching period III

MAST32006 High-dimensional statistics (5 cr) / MAST30128 Asymptotic statistical inference (5 cr)
MAST30146 Computational methods I (5 cr)
MAST30210 Design and analysis of experiments and surveys (5 cr) [January intensive, not period 3]

Teaching period IV

MAST32013 Multistate models for event history (5 cr)
MAST32004 Advanced Bayesian inference

Year II (even-odd academic year, such as 2028-2029) 
Teaching period I

MAST33004 Robust regression (5 cr)
MAST31706 Stochastic analysis I (5 cr)
DATA11001 Data Science (5 cr)

Teaching period II

MAST33021 Multivariate statistical analysis (5 cr)
* MAST30000 Master's thesis (30 cr) and MAST30002 Maturity test (0 cr)   
* MAST30012 Master's seminar II (3 cr) 

Teaching period III

MAST30165 Statistical decision theory (5 cr)
* MAST30000 Master's thesis (30 cr, continues) and MAST30002 Maturity test (0 cr, continues)

Teaching period IV

MAST31402 Bayesian inversion (5 cr)
* MAST30000 Master's thesis (30 cr, continues) and MAST30002 Maturity test (0 cr, continues)

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