Termcard for Michaelmas Term 2003

Tuesday 1^st Week
Robin Wilson (Open University & Keble College)
800 Years of Oxford Mathematics
In this lecture the history of Oxford University will be presented from a
mathematical point of view. It should be a good introduction for those new
to Oxford, and also for those who have been here for some time.

Tuesday 2^nd Week
David Acheson (Jesus College)
Surprise, Surprise!
Mathematics is full of surprises, and examples in this lecture include a
strange ‘number trick’ that always gives the answer 1089, some puzzling
geometry, some unexpected fluid motion and the dynamics of the electric
guitar.

Tuesday 3^rd Week
Shaun Stevens (University of East Anglia)
What’s so great about real numbers?
One way of constructing the real numbers from the rationals is in terms of
Cauchy sequences. The notion of convergence relies on the notion of ‘size’
(or absolute value) of a rational. To get the reals, we take the usual
one, and when we make the same constructions with other absolute values we
obtain other fields which, one might argue, are as natural as the reals and
which have a rather unfamiliar geometry and topology yet behave much more
nicely than the reals. They have many applications, in particular, to
number theory.

Tuesday 4^th Week
Peter Cameron (Queen Mary University of London)
Random Latin squares
A Latin square is an nxn square array with entries from the set {1,…,n}
so that each symbol occurs exactly once in each row or column, So the
Cayley table of a group is a Latin square; but there are many others. One
problem is that we don’t know exactly how many. So we can ask: what
properties does a ‘typical’ Latin square have? There are many unsolved
questions about Latin squares, and by looking at random Latin squares we
might be able to throw light on some of these.

Tuesday 5^th Week
Ian Stewart (Warwick)
The Maths Behind the Puzzles
From ancient times to the present day, mathematical techniques and ideas
have been illustrated using puzzles. The talk will look at a variety of
puzzles, extract their mathematical essence, and develop methods to solve
them. The main theme will be how simple questions can lead to deep
mathematical theories.

Tuesday 6^th Week
Henry Stott (Warwick)
Premiership as Poisson: Developing a statistical model of English league
football
In conjunction with the Times, a statistical model for predicting full-time
football scores has been developed and is currently being published each
Saturday. The model is based on the technique of maximum likelihood
estimation using weighted previous match data. We present details on how
the model was constructed and some of the resulting managerial insight into
the game. For further information see
www.timesonline.co.uk/finktank

Tuesday 7^th Week
Richard Brent (OUCL)
Primality testing
For many years mathematicians have searched for a fast and reliable
primality test. This is especially relevant nowadays, as the RSA public-key
cryptosystem requires very large primes in order to generate secure keys.
Recently Agrawal, Kayal and Saxena found a deterministic polynomial-time
primality test. Their algorithm will be described, some improvements by
Bernstein and Lenstra will be mentioned, and why this is not the end of the
story will be explained.

Tuesday 8^th Week

Christmas party