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Mathematical Modelling Fundamentals




Admission Requirements

Exploring mathematics or Numeracy 1: Mathematical Thinking.

This course is a required prerequisite to the following course: Dynamics and Structure of Ecological Systems


This is a course on how to develop and examine mathematical models. We will focus on continuous time (differential equations) systems, and consider deterministic systems as well as effects of randomness.
Besides mathematical analysis, you will learn to perform numerical analyses of model dynamics by means of the R programming language.
With respect to specific applications, the emphasis will be on global challenges, such as such as natural population dynamics, resource exploitation, and human interactions (game theory).

Course Objectives

The course provides you with background knowledge of different types of models and their use. Furthermore, you will gain proficiency in:

  • The use of modelling tools: calculus with free parameters, ordinary differential equations, R programming;

  • Design, adjustment, and refinement of models;

  • Model analysis, and derivation of predictions based on the results;

  • Critical model evaluation.

Mode of Instruction

Sessions will consist of short lectures, student presentations, and in-class assignments. Class sample assignments will be used to illustrate and practice modelling design, analysis, and evaluation. The work mode will vary, from working individually, in pairs, or in groups, to whole-class collaboration. You will be required to prepare presentations and write short reports throughout the course.


Assessment: Written exam
Percentage: 20%
Deadline: Week 8

Assessment: Presentations and discussions
Percentage: 40%
Deadline: Weekly

Assessment: Portfolio of results of weekly assignments, and journal
Percentage: 40%
Deadline: Week 8 (Monday at 17:00)


Readings will be made available through Blackboard or in hard copy during the course.

Contact Information


Weekly Overview

Week 1: Getting started;
Week 2: Modelling tools;
Week 3: Model design and analysis;
Week 4 – 7: Modelling in different global challenges contexts;
Week 8: exam

Preparation for first session

Go to http://cran.r-project.org/

Install R on your laptop according to the instructions given there

On that same website, go to Documentation and
Download and study ‘R for beginners’ (under: contributed)
Download and glance through the manual ‘An introduction to R’ (under: manuals)

Got to http://www.rstudio.org/
Install Rstudio on your laptop according to the instructions given there and look through the documentation on how to use it.

Go to http://www.khanacademy.org/ and brush up your (pre-)calculus skills by watching at least six videos of your choice (you know what you need best!).

You will be required to summarize your learning experiences from these preparations during the first course session.