## Tags

Y1

## Admissions requirements

None.

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 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.

## Description

The goal of this course is for students to understand how to apply basic mathematics to address complex – real world – problems.

The basic mathematical concepts and procedures that you have learned up to now can be considered as 'mathematical tools'. In high school you were taught how to use these tools by applying them to carefully selected problems, where the required procedure is made explicitly clear. Because the problems involved in real world applications are far more complex than school textbook examples, it is usually not immediately clear which mathematical procedures are best suited to address complex issues. In this course we consider discrete time dynamical models as a tool to examine such issues. We will study such models in the context of several global challenges.

## Course objectives

Skills

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

Apply mathematical reasoning and basic mathematical procedures to gain insight in (not too complex) practical applications

Discuss results of applied mathematical reasoning in practical contexts.

Apply discrete time models in a practical context

Analyse discrete 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) recurrence relations.

The relevance of these principles in the context of global challenges, such as epidemics and arms races.

## 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) 40%

Final exam: 30% (last session)

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

This course has two compulsory textbooks:

(1) All you need in maths!, by J. van de Craats and R. Bosch, 2014

ISBN13: 9789043032858

Pearson Benelux BV

Please make sure you have this book in your posession by the start of the course.

(2) 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. The latest version of the textbook will also be available in Blackboard.

## 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).