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.

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

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.

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

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

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

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

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

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

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

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

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?

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.

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

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. . . .

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. . . .

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

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

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

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

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

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?

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

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. . . .

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

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.

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.

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

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

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.

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?

This article explores ths history of theories about the shape of our planet. It is the first in a series of articles looking at the significance of geometric shapes in the history of astronomy.

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?

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 record your findings in truth tables.

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. . . .

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