In this newsletter:

* Latest news
* Mathematical moments
* Browse with Plus
* Live maths


**********

Latest news

* Catching terrorists with maths
A multi-disciplinary approach to complexity
http://plus.maths.org/latestnews/sep-dec08/complexity/index.html

* Born from broken symmetry
The 2008 Nobel Price for physics awarded for research into why we exist
http://plus.maths.org/latestnews/sep-dec08/nobel08/index.html 

* Is maths to blame?
Who is to blame for the current financial crisis
http://plus.maths.org/latestnews/sep-dec08/financecrisis/index.html

Plus... read more on the Plus blog, including why teaspoons have a habit of 
disappearing: http://plus.maths.org/blog

And for all the Plus podcasts, see:
http://plus.maths.org/podcasts/

**********

Mathematical moments

How to price derivatives: The 1997 Nobel Prize in Economics 

It's hard to believe these days, but bankers do occasionally base their 
decisions on rational and robust bits of mathematics. A central player in 
this context is the Black-Scholes equation, which won its discoverers the 
Nobel Prize in Economics almost exactly 21 years ago, on the 14th of 
October 1997. The Black-Scholes equation is a partial differential equation 
which tells you how to price options. An option is a way of reducing risk: 
it's a forward contract giving you the opportunity (but not necessarily the 
obligation) to buy a certain commodity or stock, for example fuel, at some 
specified time in the future for an agreed strike price. An option is an 
example of a so-called derivative, because it derives its value from the 
underlying variable (the fuel price).

Derivatives and options, as we all now know, can be traded in their own 
right, and have the potential to make people very rich, but also to break 
the bank (as happened literally with the Barings Bank in 1995). One 
important question if you're in the business of trading derivatives, is how 
much they should cost. Since options are all about the future, it may seem 
as if pricing them should involve a certain amount clairvoyancy, but in 
fact the Black-Scholes equation does it all for you (for a type of option 
called a "European call"). All you need to know to use the equation are the 
current price of the stock and the strike price of the option, the expiry 
time of the option, the interest rate and an estimate of the volatility of 
the stock.

In their original 1973 paper Black and Scholes built their model on the 
assumption that the stock price was a function of a Brownian motion. A 
Brownian motion is a random motion, like the one you would expect to see 
when you let a particle float in a liquid or gas. Mathematically, you can 
describe it as a stochastic process: at any given time, the stock price 
(or the particle) moves up or down (or, with a particle, in any of the 
available directions) with equal probability. Using this model for stock 
price behaviour, Black and Scholes found that the problem of pricing an 
option becomes equivalent to that of solving the heat equation from 
physics.

The original Black-Scholes model made some simplifying assumptions, for 
example that shares don't pay divident, but it is possible to work around 
many of these and obtain more sophisticated and comprehensive models. These 
have been at the heart of financial mathematics ever since. Unfortunately, 
Fischer Black died two years before the award of the Nobel Prize, so Myron 
S. Scholes and Robert C. Merton (who's name isn't attached to the equation) 
ended up sharing it between the them.

If all of this makes you wonder who should really be blamed for the current 
financial crisis, read the Plus article Is maths to blame? 
http://plus.maths.org/latestnews/sep-dec08/financecrisis/index.html

For more in-depth information on derivatives, read the Plus article Rogue 
trading: http://plus.maths.org/issue16/features/derivatives/index.html


**********

Browse with Plus

More musical maths

This mathematical acapella classic has already made the rounds amongst 
maths lovers (and takes a little group theory to understand), but it's pure 
genius, so we felt it's worth digging up again.

The Klein 4 Group presents "A finite simple group (of order two)":
http://uk.youtube.com/watch?v=BipvGD-LCjU


**********

Live maths

Particle hunting at CERN

Particle physicist Ben Allanach will introduce the largest and most complex 
dedicated experiment on earth. The Large Hadron Collider at CERN (the 
European centre for particle physics) is just starting up after 30 years of 
planning and construction. From the collisions of protons, striking each 
other at almost the speed of light, weird, hitherto undetected, particles 
can be produced. There are theoretical hopes that the Higgs particle, dark 
matter particles and even (as an outside possibility) extra dimensions, 
could be detected by analysing the spray of particles coming from the 
collisions. This lecture will give a flavour of what these exotic particles 
do, and how they might be detected.

When: November 4th 2008, 5.00pm 
Where: Centre for Mathematical Sciences, Clarkson Road, Cambridge CB3 0WA 
Price: Free, but please book by emailing [log in to unmask], stating 
clearly the name and date of the lecture.
More information: http://mmp.maths.org/mmp-events

Our Island Universe

In this free public lecture Professor Ian Morison will explore how the size 
and spiral structure of our own Milky Way has been determined, how it 
relates to others within our local group of galaxies, and how the 
gravitational pull of groups and clusters has determined the large scale 
structure of the Universe.

When: October 30th 2008, 1pm
Where: Staple Inn Hall, High Holborn, London WC1V 7QJ
Price: Free, no booking required
More info: http://www.gresham.ac.uk/event.asp?PageId=45&EventId=796


A feast of curious perspective art and mathematics in London

There are two events on anamorphic art in London:

Anamorphic art - study day and seminar

The National Gallery will host a study day on anamorphic art, as made 
famous by Holbein's painting "The Ambassadors". The study day 
will explore such distorted images and the methods used by different 
artists to create them.

Where: National Gallery, Trafalgar Square, Holborn When: December 13th, 
10.30am - 4pm Price: £20/£17 concessions Info and booking: 
http://www.nationalgallery.org.uk/what/events/dec/1312_curiousperspective.htm


Special seminar - anamorphic art

This technical and demonstrations seminar complements the study day above.

Where: The London Knowledge Lab, 23-29 Emerald Street, London WC1N 3QS
When: December 12th, 2.30pm - 5pm
Price: Free but please book by emailing [log in to unmask]
More info: http://www.lkl.ac.uk/events/maths-art/  


**********

Happy reading from the Plus team!


**********

 If you received this message you have subscribed yourself to the 
 PLUS-ANNOUNCE mailing list via our website. If you do not wish to remain 
 on the list please visit:

http://www.jiscmail.ac.uk/cgi-bin/wa.exe?SUBED1=plus-announce&A=1

and follow the instructions to leave the list.

If you have any comments on this newsletter, or Plus Magazine, please 
contact us at [log in to unmask] - we are always happy to hear from our 
readers!

Feel free to forward this email to anyone you think might be interested.