Fifth in our series of problems on population dynamics for advanced students.
Sixth in our series of problems on population dynamics for advanced students.
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.
Second 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.
An advanced mathematical exploration supporting our series of articles 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?
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.
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
See how differential equations might be used to make a realistic
model of a system containing predators and their prey.
This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.
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. . . .
Look at the calculus behind the simple act of a car going over 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.
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. . . .
engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering
How do these modelling assumption affect the solutions?
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
An article demonstrating mathematically how various physical
modelling assumptions affect the solution to the seemingly simple
problem of the projectile.
How do scores on dice and factors of polynomials relate to each
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?
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. . . .
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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.
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.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
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. . . .
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.
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. . . .
At what positions and speeds can the bomb be dropped to destroy the
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.
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. . . .
First of all, pick the number of times a week that you would like
to eat chocolate. Multiply this number by 2...
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.
Simple models which help us to investigate how epidemics grow and die out.
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.
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