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

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

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

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

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

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

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!

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.

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

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

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

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

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

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. . . .

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. . . .

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

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

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

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

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

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

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

A brief video explaining the idea of a mathematical knot.

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

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

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. . . .

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. . . .

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

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

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.

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

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

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

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

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. . . .

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

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?

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?

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

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. . . .

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?