Biomathematics / mathematical modelling Curriculum

We teach biomathematics and mathematical modelling via applications in biomathematics (mathematical ecology and evolution). The best entry point is either the course "Mathematical modelling" or "Introduction to mathematical biology", both offered in the fall semester but in alternate years. However, each biomathematics course can be taken also independently of the others (the course descriptions specify the mathematics pre-requisites, usually BSc-level matrix algebra, differential equations and/or probability calculus).

Most of our courses assume some knowledge of ordinary differential equations. If you are interested in applied mathematics in general or in biomathematics in particular, we recommend that you take a course on differential equations during your BSc studies. We also encourage learning numerical methods and acquiring basic skills in computer programming.

All courses are in English.

Why study modelling and biomathematics? Why employ biomathematicians? 

Note that our courses are part of two MSc programs, Mathematics and Statistics (MAST) and Life Science Informatics (LSI). All of our regular courses can be taken as part of the Mathematical modelling specialization of MAST as well as the Biomathematics study track of LSI, irrespective of whether the course has a course code in MAST or in LSI.

Regular courses

These courses are given regularly in a 2-year cycle.

• Mathematical modelling, 10 credits (MAST 31501, Stefan Geritz): Fall 2013, Fall 2015, Fall 2017, Fall 2019, Fall 2021
  Mathematical modelling I and II, 5+5 credits (MAST 30163 and MAST 30164, Stefan Geritz): Fall 2023 Part I, Fall 2023 Part II; Fall 2025; next time Fall 2027
• Introduction to mathematical biology, 10 credits (LSI33001, Eva Kisdi): Fall 2012, Fall 2014, Fall 2016, Fall 2018, Fall 2020
  Introduction to mathematical biology I and II, 5+5 credits (LSI 33006 and LSI33007, Eva Kisdi): Fall 2022 Part I, Fall 2022 Part II; Fall 2024; next time Fall 2026
• Adaptive dynamics, 10 credits (MAST 31505, Stefan Geritz): Spring 2014, Spring 2016, Spring 2018, Spring 2020, Spring 2022; Spring 2024; next time Spring 2026
• Evolution and the theory of games, 5 credits (LSI33002, Stefan Geritz): Fall 2014, Fall 2016, Fall 2018, Fall 2020
  Evolution and the theory of games I and II, 5+5 credits (LSI33002 and LSI33008, Stefan Geritz): Fall 2022 Part I, Fall 2022 Part II; Fall 2024; next time Fall 2026
• Stochastic population models, 10 credits (MAST31504, Stefan Geritz): Spring 2013, Spring 2015, Spring 2017, Spring 2019, Spring 2021, Spring 2023
  Stochastic population models I and II, 5+5 credits (MAST 30166 and MAST 30167, Stefan Geritz): Spring 2025; next time Spring 2027
• Spatial models in ecology and evolution, 10 credits (MAST31503, Eva Kisdi): Spring 2013, Spring 2015, Spring 2017, Spring 2019, Spring 2021, Spring 2023 (self-study supported with weekly exercise classes); Spring 2025; next time Spring 2027
• Mathematics of infectious diseases, 10 credits, book reading course (LSI33003, Eva Kisdi): Fall 2013, Fall 2015, Fall 2017, Fall 2019, Fall 2021, Fall 2023; Fall 2025; next time Fall 2027
• Bifurcation theory, 5 credits, independent study (MAST30156, Eva Kisdi): Spring 2022 and thereafter every year

Master thesis topics: see a few ideas under Mathematical modelling in the department's collection of proposed thesis topics. In most cases, we find a topic through personal discussions with students. We offer publishable topics to students who want to do original research.

What other courses should you take? To cover biomathematics at large, one needs to be a jack of all trades; and this is reflected in our courses as well. We recommend that next to biomathematics courses, you include in your studies also some advanced courses in pure mathematics. Be it functional analysis or probability theory, you'll find parts of biomathematics to apply to; and you may want to expand towards other fields later. It is however important to learn early the way how to learn one area of mathematics deeper than the level of typical applied courses.

Other courses for students of biomathematics (LSI) / mathematical modelling (MAST)

• Stochastic differential equations with applications to biology and finance, 5 credits (Fall 2022)
• The mathematics of infectious diseases: Spread, vaccination, elimination, 5 credits (Mats Gyllenberg, Spring 2021)
• Semigroups of operators, 5 credits (Mats Gyllenberg, Fall 2021)
• Operator semigroups with applications in biology (Barbara Boldin, Spring 2020)
• Stochastic differential equations with biological applications (Carlos Braumann, Fall 2018)
• Dynamics of Lotka-Volterra systems (Ping Yan; Fall 2014, Fall 2017)
• Introduction to bifurcation theory: Differential equations, dynamical systems and applications I (Ping Yan, Fall 2016, Fall 2018)
• Introduction to bifurcation theory: Differential equations, dynamical systems and applications II (Ping Yan, Spring 2017)
• Monotone dynamical systems (Ping Yan; Spring 2015)
• Qualitative theory of ordinary differential equations (Ping Yan; Fall 2014)

For students of biology

These courses are given in Viikki and targeted to students of biology with no background in mathematics. These courses are therefore not intended for students of LSI and MAST.

• Speciation theory (Eva Kisdi; Fall 2008, Fall 2010, Fall 2012, Fall 2014, Fall 2018, Fall 2020, Fall 2022)
• Mathematical methods in biology Parts 1, 2, 3, 4 (link to a former page with overview of all parts) (Eva Kisdi; full academic years 2005-2006, 2007-2008, 2009-2010, 2011-2012, 2013-2014, 2015-2016, 2017-2018, 2019-2020, 2021-2022, 2023-2024)

Past courses

• Modelling health care interventions (Simopekka Vänskä, THL; spring 2017, intensive course)
• Introduction to dynamical systems (Paolo Muratore-Ginanneschi, Fall 2015)
• Nonlinear diffusion problems (Odo Diekmann; Fall 2014)
• Introduction to bifurcation theory: Differential equations, dynamical systems and applications (Tadeas Priklopil; Fall 2013)
• Mathematical theory of population genetics (Tadeas Priklopil; Fall 2012)
• Stochastic methods in physics and biology (Stefan Geritz and Paolo Muratore-Ginanneschi, Spring 2010)
• Monotone competitive dynamical systems (Yi Wang; Fall 2009)
• Operator semigroups (Mats Gyllenberg; Spring 2005; Spring 2009)
• Modelling fluctuating populations (Stefan Geritz; Fall 2006)
• Dynamics of structured populations (Mats Gyllenberg; Spring 2006)
• The qualitative theory of ordinary differential equations (Mats Gyllenberg; Fall 2005)
• Mathematical population dynamics (Mats Gyllenberg; Fall 2004, in Finnish)
• The mathematics of contagious diseases (Mats Gyllenberg)
• Mathematical models of biological adaptation (Eva Kisdi)

Regular courses given in the past

This list is for our records.

• Mathematical modelling (Stefan Geritz; Fall 2005, Fall 2007, Fall 2009, Spring 2012)
• Evolution and the theory of games (Stefan Geritz; Spring 2005, Spring 2007, Spring 2009, Fall 2011)
• Adaptive dynamics (Stefan Geritz; Spring 2006, Spring 2008, Fall 2010, Fall 2012)
• Stochastic population models (Stefan Geritz; Fall 2008, Spring 2011, Spring 2013)
• Introduction to mathematical biology (Eva Kisdi; Spring 2011, Fall 2012)
• Spatial models in ecology and evolution (Eva Kisdi; Fall 2006, Spring 2009, Spring 2013)
• Mathematics of infectious diseases (Barbara Boldin; Fall 2009)
• Mathematics of infectious diseases (Thanate Dhirasakdanon, Fall 2011)
• Evolution and the theory of games (Tadeas Priklopil; Spring 2013)

Book-reading seminars

• Sean H. Rice (2004): Evolutionary Theory (Spring 2006, in English)
• Mathematical population genetics (Stefan Geritz / Mats Gyllenberg; Spring 2005, in English)