50 Mathematical Ideas You Really Need to Know

This is the case with the compound limosene which in one form tastes like lemons and in the other like oranges. The drug thalido ...

Caley table for the symmetry group of the tripod Like the triskelion, the tripod without feet has rotational symmetry. But it al ...

symmetry group of the tripod is the smallest group which is not abelian. Abstract groups The trend in algebra in the 20th centur ...

For each element a in G there is an element ā in G with ā ° a = a ° ā = 1 (the element ā is called the inverse element of a). F ...

39 Matrices This is the story of ‘extraordinary algebra’ – a revolution in mathematics which took place in the middle of the 19t ...

A practical example Suppose the matrix A represents the output of the AJAX company in one week. The AJAX company has three facto ...

Look carefully and you’ll see the row by column multiplication, an essential feature of matrix multiplication. If in addition to ...

which does not arise in ordinary algebra where the order of multiplying two numbers together makes no difference to the answer. ...

Another example of using matrices is in the analysis of a flight network for airlines. This will involve both airport hubs and s ...

When a small group of mathematicians created the theory of matrices in the 1850s they did so to solve problems in pure mathemati ...

40 Codes What does Julius Caesar have in common with the transmission of modern digital signals? The short answer is codes and c ...

‘do not invade’. The ‘invade’ instruction is coded by ‘1’ and the ‘do not invade’ instruction by ‘0’. If a 1 or a 0 was incorrec ...

Making messages secret Julius Caesar kept his messages secret by changing around the letters of his message according to a key t ...

745 = 74 × 74 × 74 × 74 × 74 = 2,219,006,624 and 2,219,006,624 = 8,983,832 × 247 + 120 so dividing his huge number by 247 he get ...

Keeping messages secret ...

41 Advanced counting The branch of mathematics called combinatorics is sometimes known as advanced counting. It is not about add ...

In 1858 Alexander Rhind a Scottish antiquarian visiting Luxor came across a 5 metre long papyrus filled with Egyptian mathematic ...

quite ‘small’ configurations give rise to ‘large’ factorial numbers. The number n may be small but n! can be huge. If we’re stil ...

This number, using C for combination, is written^8 C 5 and is In the UK National Lottery the rules require a selection of 6 numb ...

of the schoolgirls comes into its own. It is called cyclic since on each subsequent day the walking schedule is changed from a t ...