Sampling Methods

In statistics, a population is the complete set of data which is to be analysed. A population may consist of people (e.g. those living in a particular city), or living things (e.g. the population of all humpback whales), but could be any set of objects with something in common (e.g. all cars travelling on a particular road in a 24 hour period). Usually, it isn't possible to analyse a complete population. Why? It would take too long It would be too ...

Sam Lloyd, Master of Puzzles

Sam Lloyd was born in Philadelphia in 1841, but lived most of his life in New York. He was primarily a chess player and composer of chess problems, but he also delighted in mathematical puzzling. Actually, not just mathematical puzzles, but word puzzles; picture puzzles; tangrams; he composed thousands of them. In fact, it was one of his pictorial puzzles which grabbed my attention at a very early age, and possibly sparked my enjoyment of such puzzles. Have a look ...

Help with your IB Mathematics

Whether you are in the first weeks of your diploma course, or whether you are halfway through, there are always going to be some parts of the maths syllabus that make you scratch your head! Over the past couple of years some of the blogs I have written have concentrated on specific topics which I know can benefit from further explanation. I thought it would be helpful to list those blogs here: a reference for those that are new to ...

Games with Dots

Do people still play pencil and paper games these days? I grew up with them in my family – all sorts from number games, word games, drawing games. A number of the mathematical games involve spots or dots and, believe me, they can be fiendishly difficult to win against a good opponent. The simplest of all is boxes. A square grid of dots is created (the bigger you make it, the longer the game). The first player joins two  adjacent dots with either ...

MacTutor History of Mathematics

In my wanderings around the internet I came across a superb resource for anyone interested in, or needing information about, mathematicians, the history of mathematics, mathematical chronologies – even a 'famous curves' index. This is the MacTutor History of Mathematics site, created by John J. O'Connor and Edmund F. Robertson of the University of St. Andrews in Scotland. Under 'Mathematicians of the Day' there's an index of those who were born or died on every day of the year. I'm amazed ...

What Do You Get Asked in University Interviews?

Some universities interview applicants. In the UK, the Oxford and Cambridge interviews are an important part of the application process, Imperial College and UCL tend to interview the majority of applicants. In the US, many Ivy League colleges also carry out interviews. But what should you expect, and how can you prepare? Interviewers stress that they are not testing knowledge, which would be unfair, given that applicants come from many different backgrounds and educational systems. The purpose, says Oxford, is to ...

Putting the “Wow” into Magic Squares!

I'm sure that at some time in your life you've come across a magic square; usually a 4 x 4 table filled in with numbers where every row and column adds to give the same total. Here's an example where the total is 34 and, as a bonus, the two leading diagonals add to give 34 as well.           Well, that's quite nice, but hasn't really got the wow factor, has it? The next one has, though: same numbers, filled in differently.           It's ...

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 ...

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 ...