Mathematics in the Life Sciences

Faculteit Science and Engineering
Jaar 2021/22
Vakcode WMBY006-05
Vaknaam Mathematics in the Life Sciences
Niveau(s) master
Voertaal Engels
Periode semester I a (06-09-2021 till 26-09-2021)

Uitgebreide vaknaam Mathematics in the Life Sciences
Leerdoelen At the end of the course, the student is able to:

1) apply basic mathematical techniques (including differentiation, integration, multivariate analysis, qualitative analysis of dynamical systems, and bifurcation analysis) to dynamical and optimality models in the life sciences.

2) solve mathematical problems in the life sciences with the help of technical computing software (Mathematica).
Omschrijving The course will:

- train basic mathematical skills, such as differentiation and integration;
- introduce students to important mathematical concepts and methods, such as complex numbers, linear algebra, multivariate analysis, and linearization techniques;
- provide insight into the use and interpretation of dynamical models in the life sciences;
- expose students to important classes of example models in the life sciences;
- teach students how to investigate dynamical models with analytical and numerical methods;
- expose students to more advanced concepts and methods, such as chaotic attractors and bifurcation analysis;
- teach students how to solve mathematical problems with the help of technical computing software (Mathematica).

The first week of the course will focus on mathematical key concepts (such as differentiation, integration, Taylor expansion) and on the analysis of one-dimensional dynamical systems (single ordinary differential equations (ODEs) and single recurrence equations).
Students will learn how to solve these systems either analytically or numerically, both with pencil and paper and with a programme like Mathematica, and to perform an equilibrium and stability analysis. Students will also be exposed to bifurcation analysis, catastrophes, and chaotic attractors.

In the second week, complex numbers and concepts of linear algebra (eigenvalues and eigenvectors) will be introduced. Students will learn the basics of multivariate analysis, including multivariate optimization (Hessian). These techniques will allow them to analyse simple stochastic systems, like Markov processes. Students also learn how to analyse 2nd_ order ODEs and recurrence equations.

The third week is devoted to systems of ODEs and recurrence equations. Students learn how to solve linear systems analytically, how to solve non-linear systems numerically, and how to conduct a qualitative analysis of a multidimensional dynamical system (equilibrium and stability analysis).
Uren per week
Onderwijsvorm Hoorcollege (LC), Practisch werk (PRC)
(Interactive lectures, Paper and computer exercises)
Toetsvorm Opdracht (AST)
(End mark = 0.25xAST1 + 0.25xAST2 + 0.5x AST3; Weighted average of the assignment grades should be higher than 5.5.)
Vaksoort master
Coördinator prof. dr. R.S. Etienne
Docent(en) prof. dr. R.S. Etienne ,prof. dr. F.J. Weissing
Verplichte literatuur
Titel Auteur ISBN Prijs
Syllabus and exercises made available on the Student Portal.
Entreevoorwaarden A bachelor course in Biomathematics
Opmerkingen This course is a mandatory course for the track Modelling in the Life Sciences. Therefore students of this track have priority if the course is overbooked.
Opgenomen in
Opleiding Jaar Periode Type
MSc Biology: Modelling in the Life Sciences  ( Track Modelling in the Life Sciences) - semester I a verplicht
MSc Biology: Research  (Compulsory master courses) - semester I a keuze
MSc Biology: Science, Business and Policy  (Compulsory master courses) - semester I a keuze
MSc Biomolecular Sciences  (Electives/Optional modules) - semester I a keuze
MSc Courses for Exchange Students: Biology - semester I a
MSc Ecology and Evolution: Ecology and Conservation  (Electives/optional modules) - semester I a keuze
MSc Ecology and Evolution: Evolutionary Biology  (Electives/optional modules) - semester I a keuze
MSc Marine Biology: Research  (Compulsory master courses) - semester I a keuze