Royal Holloway Mathematics Workshops 2008 | Department Of Mathematics, Royal Holloway, University of London

The Mathematics Department at Royal Holloway University of London will be running three workshops early in 2008. The aim of these workshops is to expose students to interesting mathematical challenges in areas which they are unlikely to encounter in their A level studies.

The workshops are aimed at year 12 and 13 students who are expecting to obtain grade A in A-level mathematics. `High-flying' enthusiastic year 11 students are also very welcome. The workshops are designed to be independent of each other, so students can attend any single workshop or all three.

The mathematics department at Royal Holloway is grateful to the British Mathematical Olympiad for their sponsorship of these events.

The workshops will be held on Saturday mornings, beginning at 11:00am. The format is a 45 minute session, followed by a tea break and then a final 45 minute session. Each event will finish at around 1:00pm. All the workshops will take place in room 219 of the McCrea building (Mathematics Department) on the campus of Royal Holloway in Egham, Surrey.

Programme

Saturday January 26, 2008, 11.00am-1.00pm :

Dr. Steven Galbraith:
Pi in the Mandelbrot Set
In this talk the famous Mandelbrot set is defined. An extraordinary
connection between the Mandelbrot set and the number pi will be
described.

Saturday 2nd February 2008, 11.00am-1.00pm

Dr. Carlos Cid:

Codes & Ciphers: The Mathematical World of Secret Writing

Cryptography is the art of secret writing. Derived from the Greek

kryptos (meaning ``hidden'') and grafo (meaning ``write''), cryptography has

been used for centuries by parties wishing to communicate securely.

Cryptographic algorithms (`ciphers') are often designed based on

mathematical ideas, and thus the security of a cipher usually rests on

our inability to efficiently solve problems in algebra, number theory or

combinatorics.

In this talk we give an overview of some of the mathematical ideas used
in the design of ciphers, from ancient times to WWII cipher machines
(e.g. the Enigma) to modern systems currently used in the Internet.
Breaking ciphers are often more fun than designing! Thus we will also
look at the (often very clever) ideas used to break some of these
ciphers, hopefully including some hands-on activities.

Saturday February 9th 2008, 11.00am-1.00pm :
Dr Jens Bolte:
Chaos made simple: the unexpected fate of points under the iteration
of an interval map

In nature the evolution of a complicated system often is practically
unpredictable, although the motion may in principle be deterministic.
This phenomenon is known as "deterministic chaos". It occurs, e.g.,
in the motion of molecules in a container filled with gas. Chaotic
motion can, however, also be found in very simple dynamical systems.
We will introduce and discuss a few examples of such systems which
involve the iteration of certain maps defined on the unit interval
[0,1].

The workshops are free and it it is not necessary to register in advance.
However, we'd like to have a rough idea of numbers, so if you are planning to attend then we would appreciate if you can send a brief email with subject "saturday" to christian dot elsholtz at rhul dot ac dot uk

Last year's programme can be found at

http://www.ma.rhul.ac.uk/workshops2007