An article demonstrating mathematically how various physical
modelling assumptions affect the solution to the seemingly simple
problem of the projectile.
How do these modelling assumption affect the solutions?
This is about a fiendishly difficult jigsaw and how to solve it
using a computer program.
The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.
At what positions and speeds can the bomb be dropped to destroy the
Fourth in our series of problems on 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.
Fifth in our series of problems on population dynamics for advanced students.
Second in our series of problems on population dynamics for advanced students.
Sixth in our series of problems on population dynamics for advanced students.
See how differential equations might be used to make a realistic
model of a system containing predators and their prey.
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.
Look at the calculus behind the simple act of a car going over a
Third 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
This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.
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.
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
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. . . .
engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Explain why, when moving heavy objects on rollers, the object moves
twice as fast as the rollers. Try a similar experiment yourself.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
A player has probability 0.4 of winning a single game. What is his
probability of winning a 'best of 15 games' tournament?
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. . . .
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. . . .
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. . . .
Formulate and investigate a simple mathematical model for the design of a table mat.
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.
Invent scenarios which would give rise to these probability density functions.
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
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. . . .
This is the section of stemNRICH devoted to the advanced applied
mathematics underlying the study of the sciences at higher levels
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?
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?
An account of how mathematics is used in computer games including
geometry, vectors, transformations, 3D graphics, graph theory and
The second in a series of articles on visualising and modelling shapes in the history of astronomy.
Given the graph of a supply network and the maximum capacity for
flow in each section find the maximum flow across the network.
In four years 2001 to 2004 Arsenal have been drawn against Chelsea
in the FA cup and have beaten Chelsea every time. What was the
probability of this? Lots of fractions in the calculations!