Great Mathematicians 6: Isaac Newton

Newton is such a giant in the history of Maths and Physics that it isn't really possible to do him justice in a short blog post. King's School Grantham: original building Source: Acabashi, via Wikimedia Commons (CC BY-SA 3.0) The basic facts first. Newton was born in Lincolnshire, in eastern England, in 1642. His early family life was unhappy, but he had the fortune to go to a good school - the King's School in Grantham - which gave him an ...

A Wider World (Part 1)

Assuming that you're on this site because you're interested in the kind of reading and writing that your literature and language courses may or may not involve, these three (or maybe more) blog entries will be looking outside and inside of conventional 'English class' materials to provide new directions and unpack some older ones. Widening our sense of graphic novels  Take a look at these four graphic narratives. A Game for Swallows Born in the midst of the Lebanese war when the city ...

Forced Marriages in Britain

According to the Guardian newspaper, over 3,500 reports of forced marriage were made to the police during a three-year period. Charities believe that there are thousands more victims living in conditions of modern slavery in homes across the UK. Data from the Iranian and Kurdish Women’s Rights Organisation recorded 3,546 reports between 2014 and 2016. However, some experts believe that this is merely the tip of the iceberg. During the same period, a UK helpline run by a different NGO received ...

The Paradox of the Condemned Prisoner

The prison governor goes to visit a condemned prisoner in his cell. He tells him that he is due to be executed at midday one day in the following month, but he won't know in advance which day it is. Actually, condemned prisoners are a bit of a gloomy subject for a maths blog: let's change the scene to a school and start again! The head teacher of a school announces that there will be a fire drill at midday one day ...

The Maths Behind Record Breaking

I came across an interesting article the other day looking at the link between record breaking and the "harmonic series" $1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + ....$. If you went through a list of 100 random numbers, have a guess as to how often would you expect to break the record for the largest number so far? Let's take a simpler example. Here are 10 random numbers: 3, 8, 5, 7, 2, 5, 3, 9, 1, 7 Clearly the first number ...

Patterns in Pascal’s Triangle

One of the great joys in Maths is exploring something seemingly very simple and finding layers upon layers of complexity, and connections with other areas of Maths which at first sight appear to be totally separate. I'm sure you have come across Pascal's triangle; here it is: To create each new row, start and finish with 1, and then each number in between is formed by adding the two numbers immediately above. Pattern 1:   One of the most obvious patterns is the ...

Prepare Your Body and Your Mind for the Exams

This will probably be my last blog before you dive into the exams in May. I hope your revision has gone well: there's still time to go over more past papers to become as familiar as possible with the way the examiners ask questions. And don't forget that, in Maths exams, there's only one mark for the correct answer – all the other marks are for working and intermediate answers. So train yourself to write as much as you can ...

Don’t Lose Marks Unnecessarily in Your Maths Exams

There is statistical evidence that 1 in 7 of you will lose marks which you shouldn't lose: in other words, there could be marks which you could easily gain, even if you can't answer a question, but what you put on paper didn't match the examiner's mark scheme. It's unlikely you're going to get 100%. Some questions you just can't see what to do; some you think you can do, but you get the wrong answer; or you run out of ...

The Wine Glass and the Water Glass Puzzle

This is an old one but is a wonderful example of a puzzle with an unexpected, counter-intuitive solution. 'Two 50ml glasses are filled to the brim, one with wine and the other with water. A teaspoon (5ml) of water is transferred to the wine glass and thoroughly mixed in. Then a teaspoon of the mixture is transferred back to the water glass. Question: is there now more water in the wine, or wine in the water?' The more you think about it, ...

Understanding Keywords in Mathematics Exams

Whether you are approaching your final exams, or you're at the stage of mid-course exams, you're probably beginning to put in some practice of past paper questions. Sometimes it isn't the maths which is hard, but understanding the language of the question; and each question will contain certain keywords which tell you how you should be tackling the question, and what you should be writing down. I can't emphasise enough how important it is to understand what, in the context ...