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Up: Year 1
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MC148 Pure Mathematics at Work
| Credits: 10 |
Convenor: Dr. J. C. Ault |
Semester: 1 (weeks 1 to 6) |
| Prerequisites: |
|
desirable: MC144, MC145 |
| Assessment: |
Project and course work: 20% |
One and a half hour exam: 80% |
| Lectures: |
18 |
Classes: |
9 |
| Tutorials: |
none |
Private Study: |
48 |
| Labs: |
none |
Seminars: |
none |
| Project: |
none |
Other: |
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
The project mark is based on a written report of one of the workshops (10%).
The course work mark is based on solutions to regular problem sheets (10%).
The examination is a one and a half hour paper in January with 4 questions
based on the mathematics used in the course (80%); full marks on the paper
are obtainable from 3 complete answers.
Next: MC149 Geometry of the
Up: Year 1
Previous: MC147 Introductory Linear Algebra
S. J. Ambler
11/20/1999