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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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. . . .

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. . . .

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

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

Third in our series of problems 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?

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

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?

An advanced mathematical exploration supporting our series of articles 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.

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

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.

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

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. . . .

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

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

Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?

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

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

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. . . .

A brief video explaining the idea of a mathematical knot.

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

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?

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance. . . .

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

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?

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and record your findings in truth tables.

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!

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

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. . . .

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.