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

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

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!

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.

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

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

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

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

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

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?

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.

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

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. . . .

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. . . .

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

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.

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. . . .

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

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

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

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. . . .

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

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?

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

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

Third 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.

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

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

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

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

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

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.

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

How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.

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.

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?

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?