This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
At what positions and speeds can the bomb be dropped to destroy the
Formulate and investigate a simple mathematical model for the design of a table mat.
How do these modelling assumption affect the solutions?
An article demonstrating mathematically how various physical
modelling assumptions affect the solution to the seemingly simple
problem of the projectile.
See how differential equations might be used to make a realistic
model of a system containing predators and their prey.
Second in our series of problems on population dynamics for advanced students.
Fifth in our series of problems on population dynamics for advanced students.
Why MUST these statistical statements probably be at least a little
Look at the calculus behind the simple act of a car going over a
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.
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
Invent scenarios which would give rise to these probability density functions.
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.
Third in our series of problems on population dynamics for advanced students.
engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering
Work in groups to try to create the best approximations to these
See how the motion of the simple pendulum is not-so-simple after
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. . . .
Sixth in our series of problems on population dynamics for advanced students.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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?
An account of how mathematics is used in computer games including
geometry, vectors, transformations, 3D graphics, graph theory and
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
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. . . .
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 article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
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. . . .
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.
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?
A player has probability 0.4 of winning a single game. What is his
probability of winning a 'best of 15 games' tournament?
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. . . .
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.
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.
The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.
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 is about a fiendishly difficult jigsaw and how to solve it
using a computer program.
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!
Given the graph of a supply network and the maximum capacity for
flow in each section find the maximum flow across the network.
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.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.