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.
Fourth in our series of problems on population dynamics for advanced students.
Fifth 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.
This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.
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.
Second 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.
Sixth in our series of problems on population dynamics for advanced students.
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 our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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. . . .
See how differential equations might be used to make a realistic
model of a system containing predators and their prey.
Formulate and investigate a simple mathematical model for the design of a table mat.
It is possible to identify a particular card out of a pack of 15
with the use of some mathematical reasoning. What is this reasoning
and can it be applied to other numbers of cards?
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. . . .
How do these modelling assumption affect the solutions?
An article demonstrating mathematically how various physical
modelling assumptions affect the solution to the seemingly simple
problem of the projectile.
Work in groups to try to create the best approximations to these
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. . . .
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
engNRICH is the area of the stemNRICH site devoted to the
mathematics underlying the study of engineering
See how the motion of the simple pendulum is not-so-simple after
How do scores on dice and factors of polynomials relate to each
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. . . .
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. . . .
Explain why, when moving heavy objects on rollers, the object moves
twice as fast as the rollers. Try a similar experiment yourself.
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.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
First of all, pick the number of times a week that you would like
to eat chocolate. Multiply this number by 2...
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 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.
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
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
Invent scenarios which would give rise to these probability density functions.
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. . . .
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 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?
A brief video explaining the idea of a mathematical knot.
Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant. . . .