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 do these modelling assumption affect the solutions?
Invent scenarios which would give rise to these probability density functions.
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?
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. . . .
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Why MUST these statistical statements probably be at least a little
At what positions and speeds can the bomb be dropped to destroy the
An article demonstrating mathematically how various physical
modelling assumptions affect the solution to the seemingly simple
problem of the projectile.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
Given the graph of a supply network and the maximum capacity for
flow in each section find the maximum flow across the network.
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. . . .
This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.
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!
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
See how the motion of the simple pendulum is not-so-simple after
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.
Look at the calculus behind the simple act of a car going over a
engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering
This is the section of stemNRICH devoted to the advanced applied
mathematics underlying the study of the sciences at higher levels
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.
Work in groups to try to create the best approximations to these
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. . . .
Second 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?
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. . . .
A player has probability 0.4 of winning a single game. What is his
probability of winning a 'best of 15 games' tournament?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!
A brief video explaining the idea of a mathematical knot.
First in our series of problems on population dynamics for advanced students.
The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.
Sixth in our series of problems on population dynamics for advanced students.
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
Third in our series of problems on population dynamics for advanced students.
Fifth in our series of problems on population dynamics for advanced students.
Fourth in our series of problems on population dynamics for advanced students.
Formulate and investigate a simple mathematical model for the design of a table mat.
Simple models which help us to investigate how epidemics grow and die out.
How do scores on dice and factors of polynomials relate to each
Explain why, when moving heavy objects on rollers, the object moves
twice as fast as the rollers. Try a similar experiment yourself.
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 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.