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

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?

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

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.

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

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

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

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

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

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

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

See how the motion of the simple pendulum is not-so-simple after all.

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

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

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

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

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. . . .

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.

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

Third 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.

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

Sixth in our series of problems on 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.

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

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

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.

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

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

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 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. . . .

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. . . .

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. . . .

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

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. . . .

A brief video explaining the idea of a mathematical knot.

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

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.

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?

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

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. . . .