### Directors of the specialization

Mats Gyllenberg and Eva Kisdi

### Persons responsible for discussing the study plans

Eva Kisdi

### General instructions and aims of the studies

We offer a strongly 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.

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.

The courses of the Mathematical modelling 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 2019): Mathematical modelling, Mathematics of infectious diseases

Fall of even years (e.g. fall 2020): Introduction to mathematical biology, Evolution and the theory of games

Spring of odd years (e.g. spring 2019): Stochastic population models, Spatial models in ecology and evolution

Spring of even years (e.g. spring 2020): Adaptive dynamics

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

### Model study plans

#### Example 1

For students interested mainly in biomathematics, who already have good background in mathematics (matrix algebra, differential equations, integrals, some measure theory, probability) and plan to continue with PhD studies in biomathematics

Core courses (20 op): Mathematical modelling, Functional analysis

Specialization courses (20 op): Introduction to mathematical biology, Adaptive dynamics

Optional courses (45 op): three other specialization courses (25 op), a course in dynamical systems and bifurcation theory (10 op, may be a book exam), computer programming (10 op)

**Time schedule if the student starts in an odd year **(e.g. autumn 2019)

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

Mathematical modelling (10 op)

Mathematics of infectious diseases (10 op)

Functional analysis (10 op)

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

Adaptive dynamics (10 op)

Dynamical systems and bifurcations (book-exam)

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

**Year 2, autumn **(30 op):

Introduction to mathematical biology (10 op)

Evolution and the theory of games (5 op)

Pro gradu work with pro gradu seminar (of 15 op)

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

Stochastic population models OR Spatial models in ecology and evolution (10 op)

Pro gradu work with pro gradu seminar (of 20 op)

**Time schedule if the student starts in an even year** (e.g. autumn 2020)

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

Introduction to mathematical biology (10 op)

Evolution and the theory of games (5 op)

Functional analysis (10 op)

Introduction to programming (5 op, period I)

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

Stochastic population models OR Spatial models in ecology and evolution (10 op)

Dynamical systems and bifurcations (book exam)

Pro gradu work (of 5 op)

Advanced course in programming (5 op, period II)

**Year 2, autumn** (30 op):

Mathematical modelling (10 op)

Mathematics of infectious diseases (10 op)

Pro gradu work and pro gradu seminar (of 10 op)

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

Adaptive dynamics (10 op)

Pro gradu work and pro gradu seminar (of 20 op)

#### Example 2

For students interested in computational life sciences, combining mathematical modelling and statistics, assuming more background in statistics rather than mathematics, and planning to work in an application area such as epidemiology

Core courses (20 op): Mathematical modelling, Probability theory

Bachelor level courses (10 op): Differential equations I-II

Specialization courses (20 op): Mathematics of infectious diseases, Stochastic population models

Optional courses (35 op): one more specialization course, computer programming courses, two statistics courses

**An example for students starting in an odd year **(e.g. autumn 2019):

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

Mathematical modelling (10 op)

Mathematics of infectious diseases (10 op)

Differential equations I-II (5+5 op)

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

Adaptive dynamics (10 op)

Trends in biostatistics and bioinformatics (period III, 5 op)

Advanced course in Bayesian statistics (period IV, 5 op)

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

**Year 2, autumn **(30 op):

Evolution and the theory of games (5 op)

Probability theory I + II (5 + 5 op)

Pro gradu work with pro gradu seminar (of 15 op)

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

Stochastic population models (10 op)

Pro gradu work with pro gradu seminar (of 20 op)

#### Example 3

For students interested in a combination of analysis, modelling, and biological applications.

Core courses (20 op): Mathematical modelling, Functional analysis

Specialization courses (20 op): Mathematics of infectious diseases (10 op), Spatial models in ecology and evolution OR Stochastic population models (10 op)

Optional courses (45 op): one more specialization course (10 op), Partial differential equations (10 op), Fourier analysis (5 op), Real analysis (5 op), Complex analysis (10 op), a short computer programming course (5 op)

**Time schedule for students starting in an odd year** (e.g. autumn 2019):

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

Mathematical modelling (10 op)

Mathematics of infectious diseases (10 op)

Functional analysis (10 op)

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

Partial differential equations (10 op)

Fourier analysis I (5 op)

Complex analysis I (10 op)

Introduction to programming (5 op, period III)

**Year 2, autumn **(30 op):

Introduction to mathematical biology (10 op)

Real analysis I (5 op)

Pro gradu work with pro gradu seminar (of 15 op)

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

Spatial models in ecology and evolution OR Stochastic population models (10 op)

Pro gradu work with pro gradu seminar (of 20 op)