MATHS WEEK:MATHEMATICAL THEORIES developed more than 200 years ago have helped overcome problems in modern computing.
Maths has speeded up web browsing, supports social networking and allows YouTube to deliver video clips in a matter of seconds.
The close associations between maths and these services were detailed in a talk yesterday by Dr Neil Hurley, senior lecturer in University College Dublin’s school of computer science and informatics. It was one of the many events taking place this week during Maths Week Ireland.
Dr Hurley delivered the talk, The Maths of Googling, YouTube and Social Networking, at UCD to a packed audience of secondary students. He described discoveries made centuries ago by the mathematicians Leonhard Euler and Joseph Fourier, work that has application today in advanced computing.
In 1735 Euler proved that the “seven bridges of Königsberg” problem could not be solved. It asked whether it was possible to tour the former Prussian city while crossing its seven bridges only once.
In the process Euler laid the groundwork for an important area of maths known as graph theory. Euler accomplished it by stripping down the problem, removing as much detail as possible. He disregarded details relating to the route taken, looking only at the connections made by the bridges.
“Maths is all about coming up with creative ways of looking at problems,” Dr Hurley said.
The relevance to Google and web searching came in the 1990s when browsers mainly searched for key word content in a site, he said. “Google realised the way to get around the problem was instead of looking at content, you look at how one page is connected to another.
“This is an old mathematical idea that came up 250 years ago that has found application in the computer systems we are using today.” Dr Hurley also uses graph theory to study how networks form when individuals connect over the web.
Joseph Fourier’s contribution almost 200 years ago, known as a “Fourier transform”, today provides a way to compress the video files played over YouTube.
It enables large amounts of video content to be delivered quickly.
Today's puzzle
LEAPING FROGS
This is a popular logistics problem that can be enjoyed as a game.
Seven lily pads aligned in a straight line float on a pond. Six of the lilies have a frog on them, with the centre lily empty, and each frog faces the centre. The three frogs on the left are male and the three frogs on the right are females.
A frog can jump on to the next pad if it is free or jump over one other frog on to a free lily pad. As an added proviso, frogs can only jump forward. How many jumps in total will it take for the male and female frogs to change sides? Try using three €1 and three €2 coins as frogs.
(Answer tomorrow)