Biologian matemaattiset menetelmät 3

A practical introduction to mathematical concepts and methods applied in the life sciences. Part 3: Vectors and matrices.

24.11.2025 - 1.6.2026

3 op

Paikan päälläVerkossa

Syventävät opinnot

We learn mathematics through solving problems of biological interest, with emphasis on applicable skills and hands-on experience.

The full course consists of four parts (each can be taken separately):

Mathematical methods in biology, Part 1: Fundamentals (construction of simple models and basic calculus)
Mathematical methods in biology, Part 2: Probability (handling stochastic phenomena, groundwork for statistics)
Mathematical methods in biology, Part 3: Vectors and matrices (applied to population dynamics, genetics and statistics)
Mathematical methods in biology, Part 4: Dynamic models (techniques to analyse models of ecological interactions, biochemical reactions, etc.)

In Part 3, we build up indispensable tools for studying models with several variables, such as the dynamics of multiple, interacting populations or biochemical reaction networks. The key to analysing such models is given by vectors and matrices. In this part, we learn what vectors and matrices are, how to perform calculations with them and how to analyse linear models in discrete time. Our leading example will be the dynamics of structured populations (age-, size-, spatial etc. structure), with further examples depending on the participants' background and interest (principal component analysis in statistics, stochastic population models and extinction probabilities, genetic drift, quantitative genetics, or a brief foray into density-dependent models of periodical cicadas and chaotic dynamics).

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3 op

Koodi

EEB-013

For modelling systems with interactions (such as ecological systems or biochemical reaction systems) vectors and matrices are the key to enter. This course will equip students with the necessary tools including

what vectors and matrices are and how to make basic calculations with them;
systems of linear equations and the determinant;
eigenvectors and eigenvalues, diagonalization;
the long-term behaviour of matrix models (Perron-Frobenius theory).

Our leading biological example is the dynamics of structured populations (such as age-, size-, or spatial structure). Depending on the participants' background and interest, we close with examples from statistics (principal component analysis), stochastic population growth (extinction probabilities), population genetics (genetic drift), quantitative genetics (correlated response to selection) or a fast foray into density-dependent models (periodical cicadas, chaotic dynamics). This course prepares the students for advanced modelling in Mathematical methods in biology, Part 4.

Completion methods

Participation in teaching (lectures, exercise classes, exam) or exam. The course can be completed entirely as distance learning.

Assessment practices and criteria

Written exam with problems similar to homework exercises, graded 0-5.

Activities and methods in support of learning

2h lectures and 2h exercise classes per week for one study period

Target groups

Open to all: bachelor's and master's students of biosciences, students of other degree programmes, non-degree students, exchange students.

The course is specifically tailored for biology students and assumes no background in mathematics. Both undergraduates and graduate students are welcome.

Teaching period when the course will be offered

Period 3, even years (spring 2024 and 2026)

Recommended time or stage of studies for completion

Recommended for completion in the 1st or 2nd year of MSc studies

Study module

The course is optional in Ecology and Evolutionary Biology, Advanced studies

Expiry of studies

The course expires in 10 years.

Language of instruction

English

EQF level

Second-cycle degree, EQF level 7

Järjestäjä

Helsingin yliopisto

Yhteystiedot

avoin-student@helsinki.fi