As anyone who fought their way through analysis in their first term will know: very little in maths comes easy. The most fundamental and fundamentally obvious properties of spaces can be hidden in a world of axiomatic obfuscation, leaving you wondering whether such an obvious truth should be a fair assumption to make. More often than not the answer is "No!" "...and go sit in the corner 'til you learn to be a proper mathematician!"- these dubious assumptions need to be proved from first principles, and it is not likely to be easy.

Many large scale physical properties such as the "roughness" of a piece of sandpaper or the resilience of a sheet of metal depend upon the small scale properties of the medium e.g. atomic arrangement or the presence of defects in the medium. Intuitively, a piece of sandpaper feels "rough" and presents frictional resistance when an object moves across it because it has an uneven ("wiggly") surface.

Anyone who has gone near GCSE chemistry knows that an atom is made up of a nucleus (built out of protons and neutrons) surrounded by an electron cloud. Early quantum mechanics showed us that the electrons are only allowed to take certain quantized energy states, sharing, swapping and taking from other atoms to minimise the overall energy, forming compounds and ions.

But what are the subtleties of this process? How do we determine the 'shape' of these energy states, the so-called orbitals?

PDEs are strange, often impenetrable things, just proving that a solution exists represents a far from trivial task; and any piece of information, however small, can shed invaluable light on the problems they represent. Many techniques exist to help analyze and decode this information, and all find a place in modern mathematics: one such technique appeals to a property of some of the most fundamental objects in mathematics- graphs.

Of all the techniques used to classify topological spaces, few are so simple, so fruitful and so ubiquitous as homology and its dual, cohomology. By breaking a space into discretized parts we spot patterns, monitoring the closed n-dimensional "loops" to give groups, smaller structures that elucidate the whole; yielding vital theorems that, with a little case analysis, can classify the almost indeterminably abstract.

Location: B0.13
Those amazing people, the WMS are having a meeting (read: lots of interesting discussion) about what's happening and what's hot with The Society. Also, they'll be planning the future of The Society, and you're more than welcome to come along, and help decide that future.

Agendas and more details to follow... (suits and ties optional)

I remember once going to see him when he was lying ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."
-G.H. Hardy on Ramanujan

Just a little note to say that the mathsest cafe in all the world continues this week...

Food.

Help.

Joy.

Undergrad workroom wednesdays 2pm-4pm.

Possibly the greatest unsung triumph in mathematics is the classification of the finite simple groups, put together by literally hundreds of mathematicians over the last century. Simple groups are the "building blocks" of symmetry, and the classification throws up 26 oddities, including the infamous "Monster Group".

The proof - spread over some 10000 pages of journal articles - uses some quite impenetrable specialised techniques. But we can get a flavour of it just by looking at some of the simplest cases, using the work of Lagrange, Sylow, Lie, Poincaré and many others.