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.
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?
How do these modelling assumption affect the solutions?
The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.
Invent scenarios which would give rise to these probability density functions.
At what positions and speeds can the bomb be dropped to destroy the
A player has probability 0.4 of winning a single game. What is his
probability of winning a 'best of 15 games' tournament?
This is about a fiendishly difficult jigsaw and how to solve it
using a computer program.
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.
Formulate and investigate a simple mathematical model for the design of a table mat.
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
An article demonstrating mathematically how various physical
modelling assumptions affect the solution to the seemingly simple
problem of the projectile.
This is the section of stemNRICH devoted to the advanced applied
mathematics underlying the study of the sciences at higher levels
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. . . .
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
Look at the calculus behind the simple act of a car going over a
See how differential equations might be used to make a realistic
model of a system containing predators and their prey.
engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering
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.
Sixth in our series of problems on population dynamics for advanced students.
Fifth 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.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Simple models which help us to investigate how epidemics grow and die out.
Fourth in our series of problems on population dynamics for advanced students.
Third in our series of problems on population dynamics for advanced students.
Explore the transformations and comment on what you find.
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
First in our series of problems on population dynamics for advanced students.
Second in our series of problems on population dynamics for advanced students.
How do scores on dice and factors of polynomials relate to each
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.
An account of how mathematics is used in computer games including
geometry, vectors, transformations, 3D graphics, graph theory and
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
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.
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .
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
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. . . .
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. . . .
A brief video explaining the idea of a mathematical knot.
This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!