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Up: Year 1
Previous: MC147 Introductory Linear Algebra
MC148 Pure Mathematics at Work
| Credits: 10 |
Convenor: Dr. J. C. Ault |
Semester: 1 (weeks 7 to 12) |
| Prerequisites: |
|
desirable: MC144, MC145 |
| Assessment: |
Project and course work: 20% |
One and a half hour exam: 80% |
| Lectures: |
18 |
Classes: |
9 |
| Tutorials: |
6 |
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).
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.
You will have learnt and gained practice in how to work in
modular arithmetic, how to look at a problem from different
points of view and so to draw new conclusions and you will have had more time to see how a proof of a new result is constructed.
Finally, it is hoped to show that investigating mathematical problems with a ``real-life'' connection is interesting and fun to do.
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.
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
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).
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.
The coursework mark is based on solutions to regular problem sheets.
The examination is a one and a half hour paper in January with questions
based on the mathematics used in the course and not (directly) on the
applications.
Next: MC149 Geometry of the
Up: Year 1
Previous: MC147 Introductory Linear Algebra
Roy L. Crole
10/22/1998