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Mathematical Modelling Fundamentals

Vak 2013-2014

Tag(s)

[BSc], S, PSc, MM

Admission Requirements

Prerequisite courses: Numeracy.
This course is a required prerequisite to: Dynamics and structure of Ecological Systems

Description

This is a course on how to develop, examine, and assess mathematical models. Mathematical models are important tools for studying real-life systems. Models provide insight in which factors have important effects, and which are less influential in determining the outcome of complex interactions. It allows us to examine the consequences of scenarios that we cannot, or do not want to, execute in reality. The process of model building itself often enlarges the insight in a complex system significantly, since it makes prior knowledge and assumptions about the system explicit.

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, such as calculus with free parameters, analysis of systems of 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, quizes, 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 lead or participate in discussion sessions throughout the course. During week 7 you will work on a small modeling project from the textbook.

Assessment

Assessment: 4 quizes
Learning aim: Skill development, practice, and expression
Percentage: 30%
Deadline: Weeks 2-7 Mondays

Assessment: Group project presentation
Learning aim: Active engagement with course content
Percentage: 10%
Deadline: Session 1, week 2

Assessment: Group project report
Learning aim: Active engagement with course content
Percentage: 20%
Deadline: Before the start of session 1, week 3

Assessment: Exam
Learning aim: Understanding of course content
Percentage: 20%
Deadline: Week 8

Assessment: Final research essay on a selected model (3000 words)
Learning aim: Application of modelling
Percentage: 20%
Deadline: Week 8 Friday 12 PM

Literature

Compulsory:
Guide to Mathematical Modelling, Dilwyn Edwards & Michael Hamson 2007 (2nd ed.),
Industrial Press, Inc. New York, ISBN: 978-0-8311-3337-5.

Make sure you have this book before the course starts.
Additional material will be provided in Blackboard.

Contact Information

p.haccou@luc.leidenuniv.nl

Weekly Overview

  • Week 1: Getting started
  • Week 2: Modelling Methodology
  • Week 3: Modelling Skills
  • Week 4: Difference equations
  • Week 5: Differential equations
  • Week 6: Random processes
  • Week 7: Modeling based on data & Modeling project

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.