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 article explains the concepts involved in scientific mathematical computing. It will be very useful and interesting to anyone interested in computer programming or mathematics.

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

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?

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.

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

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

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

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.

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.

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

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. . . .

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

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

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

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

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

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

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

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

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

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

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

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

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.

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.

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. . . .

Fifth in our series of problems 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 fill in the blanks in truth tables to record. . . .

Second in our series of problems 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.

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

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

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

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

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?

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

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

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. . . .

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

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

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

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

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