*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

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*

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