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

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.

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

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.

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

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

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

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

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?

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

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. . . .

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

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

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. . . .

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

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

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?

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

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 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. . . .

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.

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?

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

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

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

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.

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

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

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

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

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

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

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. . . .

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?

Two cyclists, practising on a track, pass each other at the starting line and go at constant speeds... Can you find lap times that are such that the cyclists will meet exactly half way round the. . . .

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

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.

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?