## Tags

Y1

## Admissions requirements

None.

The Mathematical Reasoning course requires less mathematical proficiency than the Mathematical Modelling course. Students who are more comfortable with basic numerical computations rather than complex symbolic manipulation and do not plan to follow higher-level mathematics and modelling courses are advised to choose the 'Mathematical Reasoning' course.

For both courses it is assumed that students satisfy the LUC mathematics admission requirements. If needed, they may make use of the two-week preparatory remedial course in January.

It is assumed that at the start of this course students have a good working knowledge of the following concepts and techniques: arithmetic and algebraic computation, standard functions (polynomials, power functions, exponentials and logarithms), derivatives and graphical analysis. Students are advised to review these subjects before the onset of the course.

## Description

This is a course on how to develop, examine, and assess continuous time dynamical models. Such 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. They allow 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.

We will study models in the context of several global challenges.

## Course objectives

Skills

After successful completion of this course, students should be able to:

Recognize several types of continuous-time models and give examples of practical applications.

Examine effects of varying parameters on model outcomes

Apply continuous time models in a practical context

Analyse continuous time models and interpret their results in a practical context

Knowledge

After successful completion of this course, students know and understand:

Basic principles of dynamical models, such as equilibria, stability, and different types of dynamics of (systems of) ordinary differential equations.

The relevance of these principles in the context of global challenges, such as bioaccumulation of toxic substances, and climate change.

## Timetable

Once available, timetables will be published in the e-Prospectus.

## Mode of instruction

Lectures, assignments, discussions, and projects.

## Assessment

In-class participation: 5%

Quizzes (weeks 2 to 7) 30%

Final exam: 40%

Individual project report: 25% (Reading week)

## 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

Mathematics for Global Challenges, by P. Haccou. This book can be downloaded for free, from: https://www.universiteitleiden.nl/binaries/content/assets/governance-and-global-affairs/luc/rc-office/mathematics_for_gc.pdf

Optional; highly recommended for students who want extra mathematics background information and exercises:

- All you need in maths!, by J. van de Craats and R. Bosch, 2014, ISBN13: 9789043032858, Pearson Benelux BV

## Registration

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

## Contact

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 required prerequisite for the 200-level methods course Modelling Bio-Economic Dynamics.**