At what positions and speeds can the bomb be dropped to destroy the
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?
Why MUST these statistical statements probably be at least a little
How do these modelling assumption affect the solutions?
Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?
Invent scenarios which would give rise to these probability density functions.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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.
Formulate and investigate a simple mathematical model for the design of a table mat.
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
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.
This is the section of stemNRICH devoted to the advanced applied
mathematics underlying the study of the sciences at higher levels
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.
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 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. . . .
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.
Explore the transformations and comment on what you find.
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.
Fourth in our series of problems on population dynamics for advanced students.
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
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
Third in our series of problems on population dynamics for advanced students.
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.
Work in groups to try to create the best approximations to these
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. . . .
Fifth 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
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 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.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
First of all, pick the number of times a week that you would like
to eat chocolate. Multiply this number by 2...
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. . . .
Simple models which help us to investigate how epidemics grow and die out.
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.
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?
A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum. . . .
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. . . .
Given the graph of a supply network and the maximum capacity for
flow in each section find the maximum flow across the network.
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!
Second in our series of problems on population dynamics for advanced students.