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MC148 Pure Mathematics at Work

MC148 Pure Mathematics at Work

Credits: 10 Convenor: Dr. J. C. Ault Semester: 1 (weeks 1 to 6)

Prerequisites: desirable: MC144, MC145
Assessment: Projects and course work: 100% Examination: 0%

Lectures: 18 Problem Classes: 9
Tutorials: none Private Study: 48
Labs: none Seminars: none
Project: none Other: none
Surgeries: none Total: 75

Explanation of Pre-requisites

Use is made of the following concepts from the modules MC144 and MC145: the notion of proof in general; proof by induction; modular arithmetic.

Course Description

The topics to be covered include (in no special order): secret codes (public encryption keys); latin squares (design of experiments); elementary graph theory (travelling salesperson type problems); convex polyhedra (molecular structure).

Aims

To introduce and study various aspects of Pure Mathematics which are used in real life situations, to introduce some novel ways to use the Mathematics learned elsewhere and to enhance the understanding of that Mathematics.

At the end of the module you should be able to see that Pure Mathematics is not just a dry academic exercise, but that it has useful every day applications. There are many more such applications making use of more advanced mathematics much of which will be met in later modules of the Mathematics degree.

It is hoped also to show that investigating mathematical problems with a ``real-life'' connection is interesting and fun to do.

Objectives

To gain practice and facility in working with modular arithmetic. To carry out and write up a simple mathematical investigation. To learn about the principles of public encryption keys.

Transferable Skills

The ability to investigate a problem from different points of view, to draw conclusions and make sensible conjectures with some idea of how to prove them.

Syllabus

Elementary Graph Theory; Convex Polyhedra; Latin Squares; Secret Codes.

Reading list

Background:

N. L. Biggs, Discrete Mathematics, Oxford University Press.

I. Stewart, The Problems of Mathematics, Oxford University Press.

R. J. Wilson and J. J. Watkins, Graphs (an Introductory Approach), Wiley.

Details of Assessment

Details of assessment to be announced. There will be no examination, although there may be class tests.

Next: MC149 Geometry of the Plane Up: Year 1 Previous: MC147 Introductory Linear Algebra

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Last updated: 10/4/2000
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