Mathematics Survey

If anyone ever compiled one of those top twenty lists but of mathematicians – then many would expect Srinivasa Ramanujan to be included in it.  This year is the 125th anniversary of the birth of one of the subjects most talented mathematicians.

He was born to a peasant family in South India, and it was in this poor background that Ramanujan began to teach himself maths.  Some say this was actually a very good start for him as being cut off from most of the modern mathematical work of the time, he developed in a different way.

There is no doubt that much of his work ranks up with the greatest contributors of all time. Unfortunately his talent was cut short and he died aged just 32.  His talent has been recognized internationally though and many talented world class mathematicians have devoted their lives to just studying his notebooks.

He was granted a Bachelor of Science degree by Cambridge University and was elected as a fellow to Royal Society in 1918.  He was the first Indian to be granted this great honour.

There are many prizes and even a journal named after him.  This year the American Mathematical Society is publishing a series of articles discussing his legacy and his impact on current maths thinking.  He has even been included in many programmes on the development of maths including a wonderful series on the BBC and one on ITV (check here).  You can I think still watch it on BBC Iplayer but you may need to use a proxy server to watch it – like these.  These servers allow you to hide your real IP address and present a British one instead which is vital if you want to use the Iplayer in USA for example.

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Have you ever wondered how applications manage the huge amount of junk mail that is sent every day. Well the most common method is to use the binary classification, to help filter the junk mail from the real emails.  This means that any system should decide what to do with any individual email based on a simple decision or classification.  That is if an email is junk it should be either deleted or placed in a junk email, if not junk it shoudl be delivered to the recipient.   It’s difficult to implement though as basically it relies on a confidence level of whether the item is junk or not.

This is where the problems starts because a binary classification has no real idea of confidence – it’s either junk or isn’t.  If the system decides that an email is junk and it isn’t then this is called a False Positive.  However if the application decides something is junk and it isn’t then the mistake is known as a False Negative.

There is another problem with using a simple binary classification method, in that sometimes whether an email is junk is very often a subjective decision. One person might consider the hundreds of loan offers arriving in his inbox the very eptiomy of junk email, however someone else may be looking for one these services.  It could be said that there are certain rules which could define a junk or spam email, but an application should consider the emails as simply data.  It is a similar issue in dealing with classification on patient data in the NHS. 

There can be no place for the subjective decision in our binary system – rules must be defined and ambiguity removed.  Most systems slowly build up these rules often using some user interaction.  For example emails can be marked as junk initially and users allowed to confirm these decisions, hence a set of rules can be built up to create an absolute definition.

This can cater for exceptions to the specific rules.   For example some people use encryption programs like PGP to encrypt very important emails.  These of course are a long way from junk status however to an application the email will look like junk and completely unreadable.  Without the key and a facility to decrypt the email, anything like this would get swallowed up by a binary classification system – if you want to read more on this – here’s a primer on email security.

This also allows the system to operate the binary classification system but based on an individuals subjective preferences. Other systems have other methods of reducing mis-classifications – like a temporary area where emails can be retrieved and reclassified with user intervention.

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Math is getting a better reputation by the day don’t you think?  One thing that I noticed the other day, was the show Numb3rs. The show is pretty simple to explain, two brothers one of which is a math whiz and local University professor, another is a FBI agent.  The math whiz brother helps solve cases and is actually the main character of the show, probably the first math whiz main character who seems like a regular guy in the history of tv.

A friend who owns a gift basket business loves the show and thinks it should be required watching for anyone looking into the math’s or science’s as a career, because it can show exactly how good and intense it can be.

Do you agree?

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It’s not a new concept, instead of posting some bland advert in a newspaper sometimes organisations try and spice up their advertisements particularly when looking for specialist positions.  GCHQ, the UK Intelligence organisation used to advertise some positions in encrypted, with the advertisement and contact details hidden in a cipher that applicants needed to crack to apply.

This is what the Air Force decided to do when looking for some new engineers.  They hid the phone number inside a complicated maths equation, meaning you had to solves the puzzle in order to ring up and get the application form.  Unfortunately the number of applicants was extremely low, in fact nobody applied.

The problem turned out not to be the attractiveness of the Air Force as an employer, rather the numerical application process. Unfortunately the puzzle that was published contained two typos that had been introduced inadvertantly, making the puzzle impossible to solve –

Here’s the puzzle with the errors highighted.  Fortunately for the airforce, some clever Reddit users spotted the mistake and informed them of the errors.  The formula incorrctly showed sin to the power of 2x when it should have read sin(2x).  The second error involved replacing the expression (2k-1)! with (2k+1)!.

The errors have now been fixed so if you fancy a job with the Australian Air Force as an engineer then get online and crack that code. For those who live outside Australia you better chck the entry requirements and remember to change your IP address if you get blocked forrm any of the sites – this web page shows how to  use a VPN on your iPAd – http://www.proxyusa.com/iplayer-ipad-us-vpn. In the example it’s for changing to a UK based address for watching the BBC but it works the same way for accessing Aussie sites too great little .

It may be too late to apply though as apparently all the Reddit users who fixed the mistake where exactly the sort of people who the Australian recruiters where looking for!

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