## Tags

First-year programme

## Admissions requirements

LUC offers two first-year mathematics courses in parallel: Mathematical Modelling and Mathematical Reasoning. Both courses assume that students satisfy the LUC mathematics admission requirements (see ‘remarks’ for further details).

The Mathematical Modelling course is the more advanced course, and requires good analytical reasoning skills. Choose this course if you are comfortable with symbolic manipulation and plan to follow higher-level mathematics and modelling courses (see ‘remarks’).

## Description

The goal of this course is to provide students with an introductory foundation in mathematical modelling and programming.

Mathematics has an important role in dealing with the complexity of global challenges. However, this role does not consist of the straightforward application of given mathematical concepts and procedures, as in textbook examples of mathematical applications. The problems connected to global challenges are far too complex to be dealt with directly and require adjustment and simplification before mathematics can be applied. This course will introduce students to the process of mathematical modelling. We will develop and study dynamical models as a means to study changes in time, and examine parameter dependence. Throughout the course we will work on projects that exemplify the role of models in practical applications.

In addition we will teach programming skills with R in this course. This is a versatile, multi-platform computer language, that is used by a large (and increasing) intenational community of scientists. It is used in several higher-level courses at LUC, such as QRM, advanced QRM and Modelling Bioeconomic Dynamics.

## Course objectives

After the course students should be able to:

Describe the role of mathematical modelling in society and in the context of global challenges;

Examine parameter dependence of mathematical relationships;

Interpret and evaluate results of (a selection of) mathematical models in real world contexts;

Develop a dynamical model for (not too complex) practical applications

Write R code to examine model dynamics and plot results

## Timetable

Once available, timetables will be published here.

## Mode of instruction

Lectures, assignments, discussions, and projects.

## Assessment

In-class participation: 10%

Midterm exam: 30% (1 hour, session 1 of week 5)

Three projects in pairs: total 30% (Friday midnight, weeks 2,4,6)

Individual project report: 30% (Friday midnight, week 8)

## Blackboard

There will be a Blackboard site available for this course. Students will be enrolled at least one week before the start of classes.

## Reading list

Quantitative reasoning and the environment

Greg Langkamp and Joseph Hull, 2006 (1st edition)

Pearson Education Inc. (Note: Pearson copyright is 2007)

ISBN-10: 013148527X • ISBN-13: 9780131485273

**Note: you should order this book well in advance!**

## Registration

This course is open to LUC students and LUC exchange students. Registration is coordinated by the Curriculum Coordinator. Interested non-LUC students should contact course.administration@luc.leidenuniv.nl.

## Contact

Dr. P. Haccou (convener): p.haccou@luc.leidenuniv.nl