Mathematical Modeling
Year:  20152016 

Catalog number:  8001Y112 
Teacher(s): 

Language:  English 
Blackboard:  Yes 
EC:  5 
Level:  100 
Period:  Semester 2, Block IV 
Hours of study:  35:00 hrs 
 No Elective choice
 No Contractonderwijs
 No Exchange
 No Study Abroad
 No Evening course
 No A la Carte
 No Honours Class
Tags
Firstyear programme
Admissions requirements
LUC offers two firstyear 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 higherlevel 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 inquirybased learning, where students are guided to discoveries, by working on assignments that lead stepbystep from exploration to insight.
Assessment
Inclass 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.
Reading list
Quantitative Reasoning and the Environment, Greg Langkamp and Joseph Hull, 2006 (1st edition), Pearson Education Inc. (Note: Pearson copyright is 2007)
ISBN10: 013148527X; ISBN13: 9780131485273
Registration
This course is open to LUC students and LUC exchange students. Registration is coordinated by the Curriculum Coordinator. Interested nonLUC 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 twoweek preparatory remedial course in January and/or quantitative/math student assistants provided by LUC. Additional “selfstudy” 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.
Is part of  Programme type  Semester  Block 

Liberal Arts and Sciences: Global Challenges  Bachelor  2  IV 