Kurssi

Julkaistu 4.4.2025

(Päivitetty 27.8.2025)

Helsingin yliopisto

Biologian matemaattiset menetelmät 1

A practical introduction to mathematical concepts and methods applied in the life sciences. Part 1: Construction of simple models and basic calculus.

11.8.2025 - 30.12.2025

3 op

Ilmoittautuminen auki

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 1, we start from the basics and get familiar with the most commonly used functions. We review the derivative and use it to solve optimization problems (optimal body size and fecundity, optimal foraging) by finding the trait values or behavioural strategies that maximize fitness; we discuss also evolutionarily stable strategies. Next, we use the derivative to build differential equations to model the dynamics of populations (logistic growth, predator-prey systems) and of molecular systems (enzyme kinetics). We discuss how to find the equilibria and establish their stability and study how equilibria can appear or disappear as we vary the parameters of the models.

Sisältää

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Lisätiedot ja ilmoittautuminen

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Tarkentavat tiedot:

Koulutusalat

Luonnontieteet

Laajuus

3 op

Koodi

EEB-011

Students will be able to

visualize functions and get familiar with commonly used functions;
understand the derivative and use it to find optimal trait values and behavioural strategies;
understand and construct models in the form of differential equations;
analyse models with one equation using the concepts of equilibrium and stability;
understand how the qualitative predictions of a model depend on its parameters (basic bifurcations).

The learning outcomes are achieved via studying relevant problems in biology such as population growth, predator-prey systems, enzyme kinetics, optimal fecundity and body size, optimal foraging, evolutionarily stable strategies.

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 1, odd years (fall 2023 and 2025.)

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