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

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

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

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

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.

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

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. . . .

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

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

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. . . .

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

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

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

Sixth in our series of problems 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.

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

Fifth 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.

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

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

Third 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.

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

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

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. . . .

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?

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.

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

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. . . .

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

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. . . .

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

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?

A brief video explaining the idea of a mathematical knot.

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?

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. . . .

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

An account of how mathematics is used in computer games including geometry, vectors, transformations, 3D graphics, graph theory and simulations.

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?

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.

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.

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.

A car is travelling along a dual carriageway at constant speed. Every 3 minutes a bus passes going in the opposite direction, while every 6 minutes a bus passes the car travelling in the same. . . .

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?