Wolfram Mathworld

Wolfram Mathworld a fantastic resource for all you mathematicians out there! I have spent a many hours just searching for some of my favourite topics!

It is extremely easy to use and it offers the user clear definitions. It has a very simple interface where you can search for topics or just look around at your own pace. You really must try it! (I sound like some tedious advert!)

Try it out at:

http://mathworld.wolfram.com/

Maths Fact!

The set of numbers {1,2,...,n} has the property that the sum of its cubes is the square of its sum!

1³ + 2³ + ... + n³ = (1 + 2 + ... + n)²

 

 

Tell your friends and family. They will like you for it!

Hardy: A Mathematician’s Apology

Hardy: A Mathematician’s Apology

You rarely get an insight into the workings of a mathematician mind. However in, A Mathematician’s Apology G.H Hardy gives an excellent account of what mathematics is. Its usefulness (or lack of) and how it is more than just a science it is a creative art!

The apology was written as his powers as a mathematician were on the decline. This detail offers the reader an insight into how Hardy viewed his career as a mathematician and how he viewed some of his contemporaries. He mentions his work with Littlewood, his discovery of Ramanujam and his time at Oxford and Cambridge.

Hardy gives a brilliantly composed account of ‘real’ mathematics and this comes from his background in pure mathematics. He was known as ‘a real mathematician’ and this style of thinking comes across in the well-constructed, eloquent argument he proposes for his subject. His dislike of war and the lack of involvement that mathematics has had upon it is displayed in the book. He acknowledges the use of applied mathematics on ballistics however he hardly ranks them as ‘real’. He further states that the mathematics involved are “indeed repulsively ugly and intolerably dull.” You can’t help but like the language he uses.

This book is a must for anyone (not just mathematicians) as it is not only fantastically written but it offers an insight into one of the finest mathematical minds of the twentieth century.          

Maths LoL

Problem 3

Problem 3: You find a body! (Well that's your story to the police anyway)

A body is found at midnight, on a night when the air temperature is 16 degrees C. Its
temperature is 32 degrees, and after another hour, its temperature has gone down to 30.5
degrees. Estimate the time of death.

All problems are also found on the problem page (maths problems not people problems)

Mathematician of the week August Möbius

August Möbius

1790 – 1868

August Möbius was born in Saxony (now more commonly known as a part of Germany). He was an only child and an interesting fact to mention straight away is that his mother was a decedent of one Martin Luther!

Möbius was home schooled until he went to college. Once he had completed his studies at college he entered Leipzig University in 1809. At university his family wanted him to study law (and here comes the but.......) but Möbius found greater pleasure in mathematics (obvious), astronomy and physics and so he changed courses. Moving to 1813 Möbius studied under Gauss who was working at an observatory in Göttingen. So Gauss was able to coach Möbius in astronomy but being the greatest mathematician of his day Gauss was able to give Möbius an excellent mathematical education as well.

The Prussian army tried to draft Möbius to which Möbius was extremely annoyed. I am sure there’s a quote from him in response to being drafted saying something similar to, “no one will be safe from my dagger if they suggest such a thing”. He managed to avoid being drafted and he was given the chair of mathematics at Leipzig University. Apparently he wasn’t a good lecturer (we can’t be perfect all the time) but he was an excellent researcher which led to a promotion to a full professorship.

Der barycentrische Calcul was a classic piece of work on analytical geometry where he introduced the idea of a Möbius net. His name is also attached to the objects Möbius function and Möbius inverse formula these two terms came in later works.

Möbius was also interested in topological ideas and an illustration of this was a problem he posed about five sons to a king.

The problem is as follows:

A king has 5 sons each of which will be given a part of the kingdom when he dies. Can the kingdom be divided in such a way that each region has a common border with the other four?

I will leave you to work it out!

He is also known for the Möbius strip which is a two dimensional surface with only one side. You can make one taking a strip of paper twisting it by 180 degrees and then joining the two ends together. You can then dazzle your friends with your amazing piece of paper!

Mathematician of the week Alan Turing

Alan Turing: 1912 – 1952

Alan Turing was a highly talented mathematician who was born in London in 1912 and by all accounts he was average when he was at school (all the best people are). He was criticized for his poor handwriting and for following his own ideas and methods rather than that of his teachers. How often do we hear that old chestnut from teachers? However whilst he was at his school he managed to win all the prizes in mathematics. (1926).

Now what the teachers did not know that Turing was partaking in a little outside reading and this is where he gained his knowledge at an early age. I think this is evidence of the power of just taking a chair and having a read every now and again.

Let us move forward to 1931 and the young Turing went to Cambridge to study mathematics. He graduated in 1934 and was elected as a fellow of King’s College for work, which helped to prove results in probability theory (central limit theory). So far Turing had just been working in the area of probability. It was 1936 that Turing moved into what would be he foundations of what we now call computer science and he published On Computable Numbers, with an application to the Entscheidungsproblem. It was this paper that Turing introduced us to the “Turing Machine”, (he obviously didn’t call it this) essentially the machine could write or delete a symbol on a tape. In doing so it would be following an algorithm and so change state (start with one result and end up with a different result).

It is now 1939 and with the outbreak of the war Turing moved to Bletchley Park where he was involved in code breaking of the Germans. In doing so he received the O.B.E for his contributions.

1948 and Turing is now in Manchester where he had been invited by Newman. It was here that Turing produced work into computing and decidability. He was elected to the Royal Society of London in 1951 for his early work with Turing Machines.

We can’t have a Biography of the gentleman without a mention of his arrest in 1952 for a homosexual affair he was having. He actually handed himself into the police as has was threatened with blackmail. He offered no defense as he said he was doing nothing wrong (how times have changed for the good).

He was also at this point working for GCHQ. Who due to the circumstances of his arrest stopped his security clearance. We are now in the cold war and the strange circumstances of his death. Turing was conducting an electrolysis experiment and eating an apple (you can see where this is going). He ate half of his apple and died. Upon inspection potassium cyanide was fond on the apple. It was said he knew it was there.

Well that was Turing the father of modern computer science. Apparently he was also a bit of a runner! Good man.

All the usual apologies for mistakes and things like that.