SATURDAY MORNING MATHS WORKSHOPS

For four Saturdays, one each month in January, February, March, and April Philip and I have been attending maths workshops at Warwick University. We were invited to take part and we took up the offer. The workshops were interesting - and they stretched us - but were not so advanced to go straight over our heads.

The first one was about probability and statistics. It started with a short lecture about probability and we did a few experiments - such as how to win more money on the lottery - and found that if there were more than 23 people in the room at one time, the chances would be that two of them would share the same birthday! We then went out of the lecture theatre to another room which had lots of activities laid out on tables, and we moved in groups around the tables, doing the activity, then trying to work out the probabilities behind it. There were prizes if you “won” some of the games.

The second Saturday was on complex numbers. The whole thing happened in a lecture theatre. It explained about i (v-1). We learned what a complex number was, as well as how to add, subtract, multiply, and divide complex numbers. We also looked at the graphical representation of them: with real numbers, you can plot them on a number line to show where they are, but with complex numbers, there is a real part and a complex part, so it needs a graph; the x-axis is the real axis (like a number line), and the y-axis is the complex axis - the number is plotted on these. This is called an “Argand diagram”. We learned also that by plotting the complex numbers on this diagram and using polar co-ordinates, we could multiply and divide the numbers on the graph. Next, we went on to learn about the Mandelbrot set, which is a pretty pattern. It is drawn by taking 0, squaring it, and then adding the complex number on. Then the answer is squared, and the same number is added on again. If this sequence does not have a term in it further than 2 away from the origin, then it is in the Mandelbrot set and it is coloured black on the graph. For points on the graph which make the sequence go above 2, these sequences will go on to infinity, and how quickly the sequence gets above two determines which colour it is shaded. You can keep on zooming in and zooming in and the detail is endless. He showed us this on a computer program, which can be downloaded from Source Forge.net. The patterns are amazing, and it’s all done through complex numbers!

The third workshop was on maths in cryptography, and was primarily based around ciphering and deciphering texts. We listened to a lecture about RSA – the main cipher used to protect digital data as it flies around the world on the Internet. RSA is one of the world's strongest codes, yet it is relatively simple to use; we could encrypt and decrypt small phrases using only a calculator! It works on the theory of “one-way operations”: mathematical operations that are easy to do but require huge computational power to undo. There are not many ways to find this sort of procedure, but the one used for RSA is “clock maths” (modulo arithmetic). The lecture was very interesting, and we all had an interesting time playing around with RSA encryption afterwards. We also covered other, simpler, types of code. From the Caesar cipher, to the pigpen method, we had a go at them. In the last half an hour, we grouped together in teams, with the objective of deciphering several ciphered messages on a piece of paper. Each message was encrypted using a different method, and we had to work out which one, before we could start the decryption process. Thankfully, there were no messages enciphered using RSA, as we didn't have any computers to hand! Easter eggs were given out as prizes. They tasted nice. During the break we watched part of a DVD called “Look Around You”. It was a comedy video “teaching you maths” but it wasn’t really, because it sounded like a load of rubbish to us, as normal maths might sound to somebody who knows nothing about it. It told us things like “we have discovered that the biggest number in the world is in fact 45,000,000. But what about 45,000,001?” However, it was amusing; as it was intended to.

The fourth and final Saturday was called “Logic and Reasoning”. We proved why a 3x3 magic square with the numbers 0-9 in it had to have a 5 in the middle, and also did a Su Doku (which are in the newspapers’ puzzle sections). At least half of the time was spent doing “Lady or Tiger” puzzles however. This was where - for example - there were two rooms with notices on the doors. One of the rooms had a tiger in it, and the other had a lady. If there was a tiger in the room, the notice on the door was false, and if there was a lady in there, the notice was true. From just the notice texts, we had to work out which one was in which room, and so which room to enter (assuming you preferred the lady over the tiger). There were about 12 of these puzzles.

Overall, we enjoyed attending the sessions and learned quite a bit from some of them. I (Ben) enjoyed the complex numbers session the most because it was interesting and I didn’t really know anything about complex numbers before; and the logic and reasoning one the least because it was a bit too repetitive. I (Philip), preferred the codes lecture, as it catered more to my interest in algorithmic programming, and online/digital communications.

If anybody else is invited on them, we recommend you go: you’ll learn lots in an interesting way!

Ben Windsor and Philip Withnall Y9