Sixth 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.
See how differential equations might be used to make a realistic
model of a system containing predators and their prey.
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.
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.
Second in our series of problems on population dynamics for advanced students.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
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.
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
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
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?
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.
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.
How do scores on dice and factors of polynomials relate to each
Explore the transformations and comment on what you find.
Why MUST these statistical statements probably be at least a little
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. . . .
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. . . .
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
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
An article demonstrating mathematically how various physical
modelling assumptions affect the solution to the seemingly simple
problem of the projectile.
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. . . .
How do these modelling assumption affect the solutions?
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!
A player has probability 0.4 of winning a single game. What is his
probability of winning a 'best of 15 games' tournament?
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. . . .
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. . . .
Explain why, when moving heavy objects on rollers, the object moves
twice as fast as the rollers. Try a similar experiment yourself.
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?
Formulate and investigate a simple mathematical model for the design of a table mat.
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.
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.
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 distance. . . .
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 about a fiendishly difficult jigsaw and how to solve it
using a computer program.
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. . . .