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

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.

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.

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.

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

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.

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. . . .

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

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.

This problem opens a major sequence of activities on the mathematics of 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.

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.

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.

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. . . .

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

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

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

Given the graph of a supply network and the maximum capacity for flow in each section find the maximum flow across the network.

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. . . .

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?

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. . . .

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

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.

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

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

A brief video explaining the idea of a mathematical knot.

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

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. . . .

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?

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. . . .

The second in a series of articles on visualising and modelling shapes in the history of astronomy.

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