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2010/11 Undergraduate Module Catalogue
MATH1910 Modelling and Investigations
10 creditsClass Size: 110
Module manager: Professor A Mikhailov
Email: sashamik@maths.leeds.ac.uk
Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2010/11
This module is not approved as an Elective
Objectives
- To introduce project work in Applied Mathematics, Pure Mathematics and Statistics.- To develop problem solving and modelling skills.
- To develop communication skills (report writing, poster preparation, oral presentation).
- To develop group working skills.
At the end of this module, students will have completed 3 short (2 week) projects and one long (4 week) project. They will produce a written individual report, a written group report, a group poster and two group oral presentations.
Students will demonstrate problem solving and modelling skills, communication skills and group-working skills.
Syllabus
The emphasis of this module is not on content but rather on the development of a number of personal transferable skills-problem solving, modelling, communication, team working and report writing. Mathematical modelling plays a central role in applied mathematics and statistics as the process by which real-world problems are investigated and solved. The modelling process will be introduced by means of case studies drawn from mechanics, probability and statistics.
In addition various illustrative examples will be used to introduce problem-solving strategies for tackling problems and investigations of a more abstract nature in pure mathematics. Such problem solving, modelling and other skills will be assessed by means of projects.
Organisation of Module: All three departments in mathematics, Applied, Pure and Statistics are involved in teaching this module and students will be required to complete three short projects in the first half of the module. In the second half students will select and work on one longer project.
Each of the three short projects, in Statistics, Applied and Pure Mathematics, will be introduced via a case study and will last for two weeks. Students will be required to work in groups and report within the two weeks.
Each project will be reported in a different way to provide an opportunity to practice various forms of communication:
(a) an individual written report
(b) a group poster presentation
(c) a group oral presentation.
Students will be introduced to the similarities and the differences in approach to solving problems in Statistics, Pure and Applied Mathematics.
Modelling in Applied Mathematics
Students will be introduced to the three-stage modelling process and learn to:
- specify the problem clearly
- set up a simple model: define variables
- state assumptions
- obtain a solution through the application of familiar mathematical techniques
- interpret the solution
- discuss the validity of the solution by identifying limitations of the model and comparing the solution with experimental or observation
- suggest refinements to the model and obtain an improved solution.
Modelling in Statistics
Students will be introduced to the modelling process and learn to:
- specify the problem, (formulated the hypothesis to be tested)
- set up a simple model: define variables; state assumptions
- design and gather an appropriate sample of data or carry out a suitable simulation if required
- identify and estimate appropriate quantities and decide between hypotheses
- validate the model (assumptions).
Problem Solving/ Investigations in Pure Mathematics
Students will be introduced to the process of pure mathematical enquiry and learn to:
- specify a problem
- define variables and introduce a good notation
- specialise the problem and get solutions in special cases
- make conjectures from special cases
- prove conjectures
- refine conjectures
- apply mathematical techniques.
Teaching methods
| Delivery type | Number | Length hours | Student hours |
| Workshop | 31 | 1.00 | 31.00 |
| Lecture | 1 | 1.00 | 1.00 |
| Private study hours | 68.00 | ||
| Total Contact hours | 32.00 | ||
| Total hours (100hr per 10 credits) | 100.00 | ||
Methods of assessment
Coursework
| Assessment type | Notes | % of formal assessment |
| In-course Assessment | . | 100.00 |
| Total percentage (Assessment Coursework) | 100.00 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
Reading list
The reading list is available from the Library websiteLast updated: 01/04/2011
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