This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
How do these modelling assumption affect the solutions?
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.
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
An article demonstrating mathematically how various physical
modelling assumptions affect the solution to the seemingly simple
problem of the projectile.
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 account of how mathematics is used in computer games including
geometry, vectors, transformations, 3D graphics, graph theory and
See how the motion of the simple pendulum is not-so-simple after
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
An advanced mathematical exploration supporting our series of articles 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.
First 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?
Why MUST these statistical statements probably be at least a little
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.
Look at the calculus behind the simple act of a car going over a
Sixth in our series of problems on population dynamics for advanced students.
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?
Fifth in our series of problems on population dynamics for advanced students.
Second in our series of problems on population dynamics for advanced students.
Third in our series of problems on population dynamics for advanced students.
Fourth in our series of problems on population dynamics for advanced students.
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.
This is the section of stemNRICH devoted to the advanced applied
mathematics underlying the study of the sciences at higher levels
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
Simple models which help us to investigate how epidemics grow and die out.
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Explore the transformations and comment on what you find.
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. . . .
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. . . .
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. . . .
How do scores on dice and factors of polynomials relate to each
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. . . .
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.
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. . . .
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.
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. . . .
A player has probability 0.4 of winning a single game. What is his
probability of winning a 'best of 15 games' tournament?
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.
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 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 about a fiendishly difficult jigsaw and how to solve it
using a computer program.