How do these modelling assumption affect the solutions?
Why MUST these statistical statements probably be at least a little
Look at the calculus behind the simple act of a car going over a
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering
At what positions and speeds can the bomb be dropped to destroy the
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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
First in our series of problems on population dynamics for advanced students.
Second in our series of problems on population dynamics for advanced students.
Fifth 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.
Fourth in our series of problems on population dynamics for advanced students.
Third 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.
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. . . .
Invent scenarios which would give rise to these probability density functions.
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. . . .
This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.
An article demonstrating mathematically how various physical
modelling assumptions affect the solution to the seemingly simple
problem of the projectile.
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.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Formulate and investigate a simple mathematical model for the design of a table mat.
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.
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?
Explain why, when moving heavy objects on rollers, the object moves
twice as fast as the rollers. Try a similar experiment yourself.
A player has probability 0.4 of winning a single game. What is his
probability of winning a 'best of 15 games' tournament?
Given the graph of a supply network and the maximum capacity for
flow in each section find the maximum flow across the network.
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. . . .
Simple models which help us to investigate how epidemics grow and die out.
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
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?
This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!
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. . . .
A brief video explaining the idea of a mathematical knot.
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. . . .
This is the section of stemNRICH devoted to the advanced applied
mathematics underlying the study of the sciences at higher levels
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. . . .
First of all, pick the number of times a week that you would like
to eat chocolate. Multiply this number by 2...
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?
This is about a fiendishly difficult jigsaw and how to solve it
using a computer program.
Bricks are 20cm long and 10cm high. How high could an arch be built
without mortar on a flat horizontal surface, to overhang by 1
metre? How big an overhang is it possible to make like this?
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
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!