TRAN5300M Concepts and Mathematics for Modelling Transport Systems

30 creditsClass Size: 30

Module manager: David Watling
Email: d.p.watling@its.leeds.ac.uk

Taught: Semester 1 View Timetable

Year running 2018/19

Pre-requisite qualifications

As for entry onto the MSc Mathematical Modelling for Transport programme

This module is not approved as an Elective

Module summary

Mathematical modelling plays a central role in the analysis, understanding, control and planning of transport systems. This module teaches mathematically-skilled students to be creative in the use of their mathematics to solve such real-world problems, to be able to conceptualise new problems, and to communicate the implications of their work to non-mathematicians.

Objectives

The purpose of the module is as a first course in training a mathematically-skilled person to be a transport modeller in practice or research. It is comprehensive in the sense that we go through all the stages of transport modelling: i) conceptualisation of the real-world system and the philosophical underpinnings of the theories adopted, ii) representation of such systems with a variety of kinds of mathematics iii) developing mathematical methods for a wide variety of transport problems; and iv) communicating the limitations, outcomes and implications.

Learning outcomes
By the end of the module, it is intended that students will have the ability to independently address challenging real-world problems inside the transportation field, many of which they may be unfamiliar with, by a systematic process of conceptualisation, representation, mathematical implementation, and communication of outcomes. Many of the skills learned will also be applicable beyond the transportation field.

Skills outcomes
It is intended that by the end of the module students will be able to:

- conceptualise and mathematically formulate real-world problems of the kinds that arise in the transportation field;
- decide on an appropriate mathematical representation of such a problem;
- implement solutions to simple instances of the problems, analytically or computationally; and
- communicate their work effectively, in terms of assumptions, outcomes and implications.

Syllabus

Transport Systems and the Big Picture. Real-world transport systems and sub-systems. Conceptual representations of real-world sub-systems. History of transport modelling and contexts. Philosophies of transport modelling.
Mathematical Representations of Transport Systems. Discrete, continuous and functional representation of model elements. Dynamical systems, stochastic processes. Fixed points. Optimization. Statistical inference, likelihood. Monte Carlo simulation. Decision theories of choice. Graph theory, networks.

Analysing Transport Systems for:

(a) understanding (e.g. regression, choice models, estimating valuations)
(b) forecasting (e.g. four-stage model, traffic networks, activity timing)
(c) design (e.g. freight/logistics, signal timings, public transport routes)

Teaching methods

 Delivery type Number Length hours Student hours presentation 2 2.50 5.00 Group learning 1 3.00 3.00 Lecture 18 2.00 36.00 Tutorial 8 2.00 16.00 Private study hours 240.00 Total Contact hours 60.00 Total hours (100hr per 10 credits) 300.00

Private study

The whole module is based on the premise of developing students to be independent and able to address new challenges, and so private study will be especially important and emphasised. This will particularly include:

Preparing reports and surveys of information found.
Developing their own computer code to implement methods, and checking using their own mathematical calculations.

Opportunities for Formative Feedback

Informal formative feedback will be given after seminar, presentations and classes.

Formative feedback will also be provided as an output of the group learning sessions.

Methods of assessment

Coursework
 Assessment type Notes % of formal assessment Essay Essay - 2000 words 20.00 Presentation Presentation of Essay 10.00 Literature Review Written - 3000 words 25.00 Presentation Presentation of Literature Review 5.00 Report A report plus computer code 40.00 Total percentage (Assessment Coursework) 100.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated