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

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

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?

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

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

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!

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

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

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

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

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. . . .

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

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

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. . . .

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?

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

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

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.

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

Sixth 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?

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

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. . . .

Second in our series of problems 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.

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

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.

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

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

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. . . .

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

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

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

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

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

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

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

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. . . .

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

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