Prospectus

# Mathematical Modeling

Course
2015-2016

## Tags

First-year programme

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’ below 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.

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 process, mathematical modelling, is a very powerful means to gain insight in complex issues, such as climate change and the control of epidemics.

Mathematical modelling concerns the translation from practical problem to mathematical expressions and vice versa, the interpretation of mathematical results to practical implications. This involves simplifying a problem, by identifying its most important features, translating the resulting ‘bare bones’ into mathematics, performing the mathematical analysis, and translating the mathematical results into conclusions that are relevant for the original problem.

This course aims to introduce students to the process of mathematical modelling. We will consider fundamental modelling tools, such as parameter dependence, choosing appropriate functions to describe relationships, and using dimensions and units to check model consistency. Further, we will practice some of the cognitive skills required for mathematical modelling, such as generalization and abstraction, contrasting, and evaluation. Finally, we will study some examples of mathematical modelling in complex real world settings to evaluate their effectiveness.

## 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;

• Use dimensions and units to check model consistency

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

## Timetable

Once available, timetables will be published here.

## Mode of instruction

A limited amount of lecturing. Most class time will be spent on group assignments and discussions. This course uses inquiry-based learning, where students are guided to discoveries, by working on assignments that lead step-by-step from exploration to insight.

## Assessment

In-class participation: 10%
Midterm exam: 30%
In class assignments: 30%
Individual assignment: 30%

## Blackboard

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

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

## 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

## Remarks

It is assumed that students have a good working knowledge of the following concepts and techniques: arithmetic and algebraic computation, standard functions (polynomials, power functions, exponentials and logarithms), trigonometry, and functions and graphs. Students are advised to review these concepts and techniques before the onset of the course. If needed, students may make use of the two-week preparatory remedial course in January and/or quantitative/math student assistants provided by LUC. Additional “self-study” materials are available in the form of online resources (for information consult the course convener).

This course is a prerequisite for the 200 level methods courses Game Theory and Environmental Modelling.