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

Explore the transformations and comment on what you find.

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.

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

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.

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

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

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

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

This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!

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

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.

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?

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

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

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. . . .

Sixth 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

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

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.

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. . . .

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

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

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

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

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

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

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.

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

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.

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

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

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. . . .

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

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

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.

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?

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.

You have two bags, four red balls and four white balls. You must put all the balls in the bags although you are allowed to have one bag empty. How should you distribute the balls between the two. . . .

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?

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. . . .

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?