Sixth 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.

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

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

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

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.

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

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

Second in our series of problems 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.

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.

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.

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

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

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.

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

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

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?

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. . . .

A brief video explaining the idea of a mathematical knot.

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

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

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

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.

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

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. . . .

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

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. . . .

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

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. . . .

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

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!

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 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?

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.

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

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?

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?

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

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.

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?