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.

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

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

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

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.

Explore the transformations and comment on what you find.

How do these modelling assumption affect the solutions?

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

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

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

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?

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

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

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

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

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

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

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

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

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

Third in our series of problems 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.

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

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

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

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

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

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

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

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

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. . . .

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. . . .

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

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

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?

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?

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

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. . . .

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...

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 fill in the blanks in truth tables to record. . . .

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. . . .

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. . . .

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

Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?

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.