This article explains the concepts involved in scientific mathematical computing. It will be very useful and interesting to anyone interested in computer programming or mathematics.

To win on a scratch card you have to uncover three numbers that add up to more than fifteen. What is the probability of winning a prize?

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

Why MUST these statistical statements probably be at least a little bit wrong?

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?

You have two bags, four red balls and four white balls. You must put all the balls in the bags although you are allowed to have one bag empty. How should you distribute the balls between the two. . . .

Sixth in our series of problems on population dynamics for advanced students.

Fifth in our series of problems on population dynamics for advanced students.

An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.

Simple models which help us to investigate how epidemics grow and die out.

In four years 2001 to 2004 Arsenal have been drawn against Chelsea in the FA cup and have beaten Chelsea every time. What was the probability of this? Lots of fractions in the calculations!

Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.

This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.

This is about a fiendishly difficult jigsaw and how to solve it using a computer program.

Second in our series of problems on population dynamics for advanced students.

First in our series of problems on population dynamics for advanced students.

Fourth in our series of problems on population dynamics for advanced students.

An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.

Third in our series of problems on population dynamics for advanced students.

How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.

Edward Wallace based his A Level Statistics Project on The Mean Game. Each picks 2 numbers. The winner is the player who picks a number closest to the mean of all the numbers picked.

The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.

Invent scenarios which would give rise to these probability density functions.

The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?

The builders have dug a hole in the ground to be filled with concrete for the foundations of our garage. How many cubic metres of ready-mix concrete should the builders order to fill this hole to. . . .

PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics

In this article for teachers, Alan Parr looks at ways that mathematics teaching and learning can start from the useful and interesting things can we do with the subject, including. . . .

PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics

engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering

Work in groups to try to create the best approximations to these physical quantities.

See how the motion of the simple pendulum is not-so-simple after all.

At Holborn underground station there is a very long escalator. Two people are in a hurry and so climb the escalator as it is moving upwards, thus adding their speed to that of the moving steps. . . .

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?

Formulate and investigate a simple mathematical model for the design of a table mat.

This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.

This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!

Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

A brief video explaining the idea of a mathematical knot.

bioNRICH is the area of the stemNRICH site devoted to the mathematics underlying the study of the biological sciences, designed to help develop the mathematics required to get the most from your. . . .

chemNRICH is the area of the stemNRICH site devoted to the mathematics underlying the study of chemistry, designed to help develop the mathematics required to get the most from your study. . . .

Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant. . . .

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .

Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever. . . .