Two major areas of combinatorics are enumeration (counting), and graph theory (drawing): in this presentation, we hope to guide the audience through the art of enumerative graph theory (counting what you have drawn). In particular we will look at enumerating spanning trees of graphs, a problem which can be tackled from numerous directions, showcasing many of the combinatorists favourite weapons. Finally we will see some applications of such enumeration in other areas. The presenter is prefers projects involving (easy) problem solving rather than exposition, so the talk should be followable by all.

So join Owen Daniel, and his graphs of many shapes and sizes on Monday night, before we follow a Hamiltonian path to the pub...

Braid Groups can arise naturally in a number of different ways. Intuitively one may view braid groups as 'strands' between some finite sets of points with some naturally defined composition. More formally, one can define braid groups as the fundamental group of some configuration spaces. In turn, these are isomorphic to the mapping class group of the n-punctured disc.

In tonight's discussion group Paul Mortimer will give an introduction to braid groups along with what he covered in his project. This talk may unfortunately not be for the faint hearted. The material was described to us by Paul as "PhD level". He did go on to clarify, "the most difficult aspect of the project was presenting it in a fashion understandable to fellow fourth years." There is therefore some hope that the talk will be an understandable account of Paul's wonderful achievements over the past two terms. Stay Categorical!

Back in 2008, Simon Willerton and Eugenia Cheng from Sheffield University decided to put together a series of videos (http://www.youtube.com/user/TheCatsters#p/u ) to teach the world about category theory. So impressed were we by their lucid and good humoured explanations that we decided to invite them both to come and give talks. To our great delight they both agreed!

Simon Willerton will be giving the first talk. This will take place in MS.02 this Wednesday, where as usual there will be food and drink available afterwards.

Simon's has told us his talk will be on " measuring the size of metric spaces - sets with a notion of 'distance' - and how that might lead to pure algebra having applications in ecology." The talk should be fun and will be accessible to all undergrads.

See you all on Wednesday!

Our first discussion group special of the term will be by everyone's favourite lecturer, Samir Siksek. In the talk we'll hear about some of the fascinating developments at the forefront of number theory, presented in a fun and accessible manner. Afterwards, there will be food and drinks available in the street along with a chance for some discussion. So come along!

Samir provided us with a short description of the talk:

Abstract: The generalized Fermat conjecture concerns the equation in coprime integers . This conjecture has been called the "new holy grail of number theory". In this fun talk we shall survey what is known and explore some recent directions.

Discussion groups are back. WMS's very own informal excursion to the beautiful, and often unseen, shores of maths awesomeness is giving you not one, but two most laden smorgasboards of mathematical fun.

In the first two sessions of the term, some of our old hands will give you a brief insight into some of their favourite areas of mathematics. In seven informal discussionlets (spread over the two nights- monday and thursday), we take you for a walk on the interesting side of maths. Perfect second year essay fodder.