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.
At what positions and speeds can the bomb be dropped to destroy the
How do these modelling assumption affect the solutions?
This is about a fiendishly difficult jigsaw and how to solve it
using a computer program.
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
The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.
Why MUST these statistical statements probably be at least a little
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?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Invent scenarios which would give rise to these probability density functions.
See how the motion of the simple pendulum is not-so-simple after
Look at the calculus behind the simple act of a car going over a
Formulate and investigate a simple mathematical model for the design of a table mat.
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.
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. . . .
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.
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
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.
Work in groups to try to create the best approximations to these
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
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?
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 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.
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!
Simple models which help us to investigate how epidemics grow and die out.
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?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Sixth in our series of problems on population dynamics for advanced students.
Second in our series of problems 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.
Fourth in our series of problems on population dynamics for advanced students.
Fifth in our series of problems on population dynamics for advanced students.
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. . . .
See how differential equations might be used to make a realistic
model of a system containing predators and their prey.
The second in a series of articles on visualising and modelling shapes in the history of astronomy.
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. . . .
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.
Given the graph of a supply network and the maximum capacity for
flow in each section find the maximum flow across the network.
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. . . .
An account of how mathematics is used in computer games including
geometry, vectors, transformations, 3D graphics, graph theory and
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and record your findings in truth tables.