Second in our series of problems on population dynamics for advanced students.
Sixth 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
Fourth in our series of problems on population dynamics for advanced students.
Third in our series of problems on population dynamics for advanced students.
First in our series of problems on population dynamics for advanced students.
Fifth in our series of problems 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.
An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.
How do these modelling assumption affect the solutions?
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 what positions and speeds can the bomb be dropped to destroy the
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 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.
This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.
A brief video explaining the idea of a mathematical knot.
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!
Problem solving is at the heart of the NRICH site. All the problems
give learners opportunities to learn, develop or use mathematical
concepts and skills. Read here for more information.
An article demonstrating mathematically how various physical
modelling assumptions affect the solution to the seemingly simple
problem of the projectile.
Explore the transformations and comment on what you find.
Why MUST these statistical statements probably be at least a little
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. . . .
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
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. . . .
How many eggs should a bird lay to maximise the number of chicks
that will hatch? An introduction to optimisation.
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
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
This is the section of stemNRICH devoted to the advanced applied
mathematics underlying the study of the sciences at higher levels
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!
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?
The third installment in our series on the shape of astronomical systems, this article explores galaxies and the universe beyond our solar system.
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
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. . . .
Formulate and investigate a simple mathematical model for the design of a table mat.
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?
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?
Explain why, when moving heavy objects on rollers, the object moves
twice as fast as the rollers. Try a similar experiment yourself.
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. . . .
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.
Two cyclists, practising on a track, pass each other at the starting line and go at constant speeds... Can you find lap times that are such that the cyclists will meet exactly half way round the. . . .