Look at the calculus behind the simple act of a car going over a
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.
Fourth in our series of problems on population dynamics for advanced students.
Third in our series of problems on population dynamics for advanced students.
Given the graph of a supply network and the maximum capacity for
flow in each section find the maximum flow across the network.
Sixth 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.
How do these modelling assumption affect the solutions?
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
See how differential equations might be used to make a realistic
model of a system containing predators and their prey.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
First in our series of problems on population dynamics for advanced students.
Fifth in our series of problems on population dynamics for advanced students.
This is the section of stemNRICH devoted to the advanced applied
mathematics underlying the study of the sciences at higher levels
Formulate and investigate a simple mathematical model for the design of a table mat.
A brief video explaining the idea of a mathematical knot.
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?
Explain why, when moving heavy objects on rollers, the object moves
twice as fast as the rollers. Try a similar experiment yourself.
Explore the transformations and comment on what you find.
A player has probability 0.4 of winning a single game. What is his
probability of winning a 'best of 15 games' tournament?
Why MUST these statistical statements probably be at least a little
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. . . .
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. . . .
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?
Invent scenarios which would give rise to these probability density functions.
See how the motion of the simple pendulum is not-so-simple after
Work in groups to try to create the best approximations to these
engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering
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 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?
At what positions and speeds can the bomb be dropped to destroy the
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.
An account of how mathematics is used in computer games including
geometry, vectors, transformations, 3D graphics, graph theory and
First of all, pick the number of times a week that you would like
to eat chocolate. Multiply this number by 2...
The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.
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.
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.
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
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. . . .
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
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. . . .