Using and Applying Mathematics

The aims for this module are set into the context of the QAA Framework for Higher Education Qualifications and they relate to the SEEC level descriptors for level 5 study.

This module is concerned with looking at ways mathematics can be used to tackle practical problems that have a 'real world' context.  One focus will be on the process of mathematical modelling, with problems approached via either empirical modelling - involving the collection and organisation of data, or analytic modelling - involving an understanding of the underlying structure of the situation.  Selected algorithms will also be used to make predictions about specific situations.  The second focus will be on considering the part that mathematics has played in the development of other fields of study.

In relation to the QAA Framework for Higher Education Qualifications and the SEEC level descriptors for level 5 study, by the end of the module students should be able to:

1. engage in the modelling cycle;
2. choose an appropriate approach to a problem set in a ‘real world’ context;
3. demonstrate an understanding of the limitations of their solutions;
4. communicate mathematical knowledge clearly and concisely using appropriate mathematics formats and resources including ICT;
5. identify and appreciate the fundamental importance of mathematics in shaping and developing society.

The nature of mathematics within ‘real-life’ problem situations.

The modelling process – recognition, formulation, solution, interpretation and validation.

The data-handling process – measurement, data collection data representation, analysis interpretation and conclusion.

There will be opportunities to engage in problem posing, problem solving and thinking mathematically.

Contact Time: will be used to introduce the various problems, give an overview of the modelling process, demonstrate some approaches and techniques and discuss the ongoing work of students.

Non-contact Time: will be used to consolidate techniques, in further reading, in preparation for sessions, in work on students' projects and in the use of computer facilities.

Books: 

Burkhardt, H.  (1981)  The Real World and Mathematics  Glasgow: Blackie

Edwards, D. & Hansom, M.  (1989)  Guide to Mathematical Modelling  Basingstoke: Macmillan

James, D. & McDonald, J.  (1981)  Case Studies in Mathematical Modelling  Cheltenham: Stanley Thornes

Electronic Sources: all accessed June 2011

Association of Teachers of Mathematics available from: www.atm.org.uk

National Centre for Excellence in the Teaching of Mathematics www.ncetm.org.uk 

Nrich  www.nrich.maths.org.uk

Real Mathematics  www.realmaths.com

Exam Boards:

AQA  www.aqa.org.uk

Edexcel  www.edexcel.org.uk

OCR  www.ocr.org.uk

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