Robust Timetabling for Railway Systems

COURSE OBJECTIVE

In a world that is becoming increasingly quantitative, mathematics belongs to the core of our cultural heritage more than ever. Experiencing the full cycle of the use of mathematics (from theoretical and fundamental questions to an application, and from the application to new questions triggering the development of new theory) will provide a deep understanding of the mutual influence between the mathematical/quantitative-academic paradigm and the real world.

Attainment targets/learning outcomes

• Ability to work with non-standard concepts (such as "strange" algebras)
• Ability to reflect on and discuss formal mathematical concepts ("abstract can be very real")
• Developing an understanding on how real life problems influence mathematical theory building
• Understanding the process of abstraction in theory building
• Ability to communicate an abstract mathematical idea and to present findings of self-study

COURSE CONTENT

The railways are an essential part of the Dutch public transportation infrastructure. Despite the effort in time and money invested into the railway systems, the system is perceived as not operating at the desired level of reliability. So, why is it so hard to come up with a reliable timetable for the railways? This course will delve into the problem of designing periodic timetables for railways. Surprisingly enough an exotic algebra from mathematics helps tackling the problem. We will enter the realm of this exotic algebra, where, for instance, it is true that 3+7=7 and 3 x7=10, and we see how this can be turned into a natural language for the analysis trains. Though trains will be the main topic of our lectures we will also present surprising applications of the technique for development of rescue robots.

The course is self-contained as the mathematical theory used in this course is based on an exotic algebra, which levels the advantage students with a (strong) mathematical background may have. While having timetable design as guiding problem, we will have ample opportunity to discuss and understand some of the fundamental philosophical and logical problems of the foundation mathematics: This is a course about mathematics rather than a mathematics course.

TEACHING METHODS
Lectures and group sessions

TYPE OF ASSESSMENT
Participation in the preparation, presentation and report on chosen self-study topic (group effort, 50%), and written exam (individual, 50 %).