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

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

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

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. . . .

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

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

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

Third 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.

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

First 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.

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

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

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

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

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 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?

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.

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

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. . . .

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

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

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

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

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

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. . . .

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. . . .

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. . . .

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

A brief video explaining the idea of a mathematical knot.

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!

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

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.

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

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

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?

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. . . .

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!

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

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

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?

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. . . .