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

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

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

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

At what positions and speeds can the bomb be dropped to destroy the dam?

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

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

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

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

Look at the calculus behind the simple act of a car going over a step.

See how differential equations might be used to make a realistic model of a system containing predators and their prey.

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.

An article demonstrating mathematically how various physical modelling assumptions affect the solution to the seemingly simple problem of the projectile.

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

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

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

Sixth 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.

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

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

Third 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.

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

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

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

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.

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. . . .

A brief video explaining the idea of a mathematical knot.

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

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.

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

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

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

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. . . .

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

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?

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. . . .

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

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

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?

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.

First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...

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

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. . . .

Bricks are 20cm long and 10cm high. How high could an arch be built without mortar on a flat horizontal surface, to overhang by 1 metre? How big an overhang is it possible to make like this?

This article explores ths history of theories about the shape of our planet. It is the first in a series of articles looking at the significance of geometric shapes in the history of astronomy.