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

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

Second in our series of problems 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.

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. . . .

Fifth in our series of problems 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...

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

First 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.

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

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.

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

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.

Fourth in our series of problems on 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!

A brief video explaining the idea of a mathematical knot.

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?

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

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. . . .

Sixth in our series of problems 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?

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. . . .

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

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?

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

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

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. . . .

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.

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.

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!

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. . . .

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

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

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

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

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. . . .

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

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

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

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

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

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

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

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

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.

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