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Studiegids

nl en

Mathematical Modelling Fundamentals

Vak
2011-2012

Admission requirements

Prerequisite courses: Exploring mathematics (8101GEMAT) or Numeracy 1- Mathematical Thinking ( 8102ASMAT).

This course is a required prerequisite to the following courses:
Human Evolutionary Dynamics,
Dynamics and structure of Ecological Systems, and
Dynamics of complex systems

Description

This is a course on how to develop and examine mathematical models. We will consider discrete time (recurrence relations) as well as continuous time (differential equations) systems, deterministic systems as well as effects of randomness, and effects of external input on system dynamics. 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, human interactions (game theory), toxicology, and population genetics.

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.

Timetable

Please see the LUC website: www.lucthehague.nl

Mode of instruction

Sessions will consist of short lectures, student presentations, and working groups. 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. During the last weeks you will work on an individual project.

Assessment method

#Interactive engagement with course material: assessed through In-class assignments (10% of final grade): Ongoing

  1. Modelling tools proficiency: assessed in Online exam (20% of final grade): Week 3
  2. Model design, analysis and predictions: assessed in Presentations (20% of final grade): Weekly, during weeks 3 – 6
  3. Model design, analysis and predictions: assessed through Web-postings (2000-3000 words;20% of final grade): Weekly, during weeks 3 – 6
  4. Model criticism and analysis: assessed in Individual project report (5000 – 10,000 words; 30% of final grade): Week 8

Blackboard

This courses is supported by a Blackboard site.

Reading list

Readings will be made available through links on Blackboard

Registration

This course is only open for LUC The Hague students.

Contact information

e-mail p.haccou@luc.leidenuniv.nl

Weekly Overview

Week 1: Getting started;
Week 2: Modelling tools;
Week 3: Model design and analysis;
Week 4 – 6: Modelling in different global challenges contexts;
Week 7+8: Individual projects.

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.