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.

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.

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

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

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

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

Fourth 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.

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

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?

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

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

This is the section of stemNRICH devoted to the advanced applied mathematics underlying the study of the sciences at higher levels

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

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

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

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. . . .

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

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

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

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. . . .

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

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

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. . . .

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

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

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. . . .

How do scores on dice and factors of polynomials relate to each other?

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

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?

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.

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

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. . . .

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!

A brief video explaining the idea of a mathematical knot.

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

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.

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

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

Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?