This problem opens a major sequence of activities on the mathematics of 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.

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

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

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

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

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

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

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

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

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

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.

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

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

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

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.

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

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?

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

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

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

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

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.

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

A brief video explaining the idea of a mathematical knot.

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. . . .

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

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. . . .

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.

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

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

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. . . .

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. . . .

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?

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. . . .

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

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

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

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.

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

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

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

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. . . .

Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?

Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever. . . .

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