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

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!

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. . . .

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

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

Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever. . . .

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

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

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

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.

Third in our series of problems 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.

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

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 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

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

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.

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

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

Fifth 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?

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. . . .

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

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

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.

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

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

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

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

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

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 advanced mathematical exploration supporting our series of articles on 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?

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

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

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

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?

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. . . .

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?